<html lang="en">

  <head>
    <title>Inter- and intra-animal variation in the integrative properties of stellate cells in the
      medial entorhinal cortex</title>
    <meta charset="utf-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <meta http-equiv="X-UA-Compatible" content="ie=edge">
    <link href="https://unpkg.com/@stencila/thema@2/dist/themes/elife/styles.css" rel="stylesheet">
    <script src="https://unpkg.com/@stencila/thema@2/dist/themes/elife/index.js"
      type="text/javascript"></script>
    <script
      src="https://unpkg.com/@stencila/components@&lt;=1/dist/stencila-components/stencila-components.esm.js"
      type="module"></script>
    <script
      src="https://unpkg.com/@stencila/components@&lt;=1/dist/stencila-components/stencila-components.js"
      type="text/javascript" nomodule=""></script>
  </head>

  <body>
    <main role="main">
      <article itemscope="" itemtype="http://schema.org/Article" data-itemscope="root">
        <h1 itemprop="headline"
          content="Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal co…">
          Inter- and intra-animal variation in the integrative properties of stellate cells in the
          medial entorhinal cortex</h1>
        <meta itemprop="image"
          content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Inter-%20and%20intra-animal%20variation%20in%20the%20integrative%20properties%20of%20stellate%20cells%20in%20the%20medial%20entorhinal%20co%E2%80%A6">
        <ol data-itemprop="authors">
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Hugh Pastoll"><span data-itemprop="givenNames"><span
                itemprop="givenName">Hugh</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Pastoll</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Derek L Garden"><span data-itemprop="givenNames"><span
                itemprop="givenName">Derek</span><span itemprop="givenName">L</span></span><span
              data-itemprop="familyNames"><span itemprop="familyName">Garden</span></span><span
              data-itemprop="affiliations"><a itemprop="affiliation"
                href="#author-organization-1">1</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Ioannis Papastathopoulos"><span
              data-itemprop="givenNames"><span itemprop="givenName">Ioannis</span></span><span
              data-itemprop="familyNames"><span
                itemprop="familyName">Papastathopoulos</span></span><span
              data-itemprop="affiliations"><a itemprop="affiliation"
                href="#author-organization-2">2</a><a itemprop="affiliation"
                href="#author-organization-3">3</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Gülşen Sürmeli"><span data-itemprop="givenNames"><span
                itemprop="givenName">Gülşen</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Sürmeli</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Matthew F Nolan"><span data-itemprop="givenNames"><span
                itemprop="givenName">Matthew</span><span itemprop="givenName">F</span></span><span
              data-itemprop="familyNames"><span itemprop="familyName">Nolan</span></span><span
              data-itemprop="emails"><a itemprop="email"
                href="mailto:mattnolan@ed.ac.uk">mattnolan@ed.ac.uk</a></span><span
              data-itemprop="affiliations"><a itemprop="affiliation"
                href="#author-organization-1">1</a></span>
          </li>
        </ol>
        <ol data-itemprop="affiliations">
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-1"
            id="author-organization-1"><span itemprop="name">Centre for Discovery Brain Sciences,
              University of Edinburgh</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressLocality">Edinburgh</span><span itemprop="addressCountry">United
                Kingdom</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-2"
            id="author-organization-2"><span itemprop="name">The Alan Turing
              Institute</span><address itemscope="" itemtype="http://schema.org/PostalAddress"
              itemprop="address"><span itemprop="addressLocality">London</span><span
                itemprop="addressCountry">United States</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-3"
            id="author-organization-3"><span itemprop="name">School of Mathematics, Maxwell
              Institute and Centre for Statistics, University of Edinburgh</span><address
              itemscope="" itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressLocality">Edinburgh</span><span itemprop="addressCountry">United
                Kingdom</span></address></li>
        </ol><span itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
          <meta itemprop="name" content="Unknown"><span itemscope=""
            itemtype="http://schema.org/ImageObject" itemprop="logo">
            <meta itemprop="url"
              content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
          </span>
        </span><time itemprop="datePublished" datetime="2020-02-13">2020-02-13</time>
        <ul data-itemprop="genre">
          <li itemprop="genre">Research Article</li>
        </ul>
        <ul data-itemprop="about">
          <li itemscope="" itemtype="http://schema.org/DefinedTerm" itemprop="about"><span
              itemprop="name">Neuroscience</span></li>
        </ul>
        <ul data-itemprop="keywords">
          <li itemprop="keywords">entorhinal cortex</li>
          <li itemprop="keywords">synaptic integration</li>
          <li itemprop="keywords">presynaptic function</li>
          <li itemprop="keywords">multi-vesicular release</li>
          <li itemprop="keywords">synaptic vesicle</li>
          <li itemprop="keywords">Mouse</li>
        </ul>
        <ul data-itemprop="identifiers">
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID"
              content="https://registry.identifiers.org/registry/publisher-id"><span
              itemprop="name">publisher-id</span><span itemprop="value"
              data-itemtype="http://schema.org/Number">52258</span>
          </li>
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID" content="https://registry.identifiers.org/registry/doi">
            <span itemprop="name">doi</span><span itemprop="value">10.7554/eLife.52258</span>
          </li>
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID"
              content="https://registry.identifiers.org/registry/elocation-id"><span
              itemprop="name">elocation-id</span><span itemprop="value">e52258</span>
          </li>
        </ul>
        <section data-itemprop="description">
          <h2 data-itemtype="http://schema.stenci.la/Heading">Abstract</h2>
          <meta itemprop="description"
            content="Distinctions between cell types underpin organizational principles for nervous system function. Functional variation also exists between neurons of the same type. This is exemplified by correspondence between grid cell spatial scales and the synaptic integrative properties of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about how functional variability is structured either within or between individuals. Using ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative properties vary between mice and, in contrast to the modularity of grid cell spatial scales, have a continuous dorsoventral organization. Our results constrain mechanisms for modular grid firing and provide evidence for inter-animal phenotypic variability among neurons of the same type. We suggest that neuron type properties are tuned to circuit-level set points that vary within and between animals.">
          <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Distinctions between cell
            types underpin organizational principles for nervous system function. Functional
            variation also exists between neurons of the same type. This is exemplified by
            correspondence between grid cell spatial scales and the synaptic integrative properties
            of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about
            how functional variability is structured either within or between individuals. Using
            ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative
            properties vary between mice and, in contrast to the modularity of grid cell spatial
            scales, have a continuous dorsoventral organization. Our results constrain mechanisms
            for modular grid firing and provide evidence for inter-animal phenotypic variability
            among neurons of the same type. We suggest that neuron type properties are tuned to
            circuit-level set points that vary within and between animals.</p>
        </section>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="introduction">Introduction
        </h2>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The concept of cell types
          provides a general organizing principle for understanding biological structures including
          the brain (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib65">Regev et al., 2017</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib84">Zeng and Sanes,
              2017</a></cite>). The simplest conceptualization of a neuronal cell type, as a
          population of phenotypically similar neurons with features that cluster around a single
          set point (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib79">Wang et al., 2011</a></cite>), is extended by observations of
          variability in cell type features, suggesting that some neuronal cell types may be
          conceived as clustering along a line rather than around a point in a feature space (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib19">Cembrowski and
              Menon, 2018</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib55">O'Donnell and Nolan, 2011</a></cite><a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1A</a>). Correlations between the
          functional organization of sensory, motor and cognitive circuits and the
          electrophysiological properties of individual neuronal cell types suggest that this
          feature variability underlies key neural computations (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib1">Adamson et al., 2002</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib3">Angelo et al.,
              2012</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib24">Fletcher and Williams, 2019</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib28">Garden et al., 2008</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib30">Giocomo et
              al., 2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib46">Kuba et al., 2005</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib55">O'Donnell and Nolan,
              2011</a></cite>). However, within-cell type variability has typically been deduced by
          combining data obtained from multiple animals. By contrast, the structure of variation
          within individual animals or between different animals has received little attention. For
          example, apparent clustering of properties along lines in feature space could reflect a
          continuum of set points, or could result from a small number of discrete set points that
          are obscured by inter-animal variation (<a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1B</a>). Moreover, although
          investigations of invertebrate nervous systems show that set points may differ between
          animals (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36">Goaillard et al., 2009</a></cite>), it is not clear whether mammalian
          neurons exhibit similar phenotypic diversity (<a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1B</a>). Distinguishing these
          possibilities requires many more electrophysiological observations for each animal than
          are obtained in typical studies.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" title="General setup"><label
            data-itemprop="label">General setup</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-warning="FALSE" data-message="FALSE" data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>print(&quot;Load data and general setup&quot;)

# The packages broomExtra, corpcor must also be installed.
library(tidyverse)
library(cowplot)
library(lme4)
library(GGally)
library(MuMIn)
source(&quot;Functions.R&quot;)

# Use standard cowplot theme throughout
theme_set(theme_cowplot())

# Load stellate cell data
fname.sc &lt;- &quot;Data/datatable_sc.txt&quot;
data.import.sc &lt;- read_tsv(fname.sc)

# Strip out rows from data where locations are unknown (are NaN)
data.sc &lt;- data.import.sc %&gt;% drop_na(dvloc)

# Convert dvloc from microns to millimetres - prevents errors in model fitting large dv values
data.sc &lt;- mutate(data.sc, dvlocmm = dvloc/1000)

# Add the number of observations for each mouse as a column
counts &lt;- count(data.sc, id)
data.sc$counts &lt;- counts$n[match(data.sc$id, counts$id)]

# Make sure id, hemi, housing, mlpos, expr, patchdir are factors
col_facs &lt;- c(&quot;id&quot;, &quot;hemi&quot;, &quot;housing&quot;, &quot;mlpos&quot;, &quot;expr&quot;, &quot;patchdir&quot;)
data.sc[col_facs] &lt;- lapply(data.sc[col_facs], factor)

# Load data from Wfs1+ve cells
fname.wfs &lt;- &quot;Data/datatable_cal.txt&quot;
data.import.wfs &lt;- read_tsv(fname.wfs)
data.wfs &lt;- data.import.wfs %&gt;% drop_na(dvloc)
data.wfs &lt;- mutate(data.wfs, dvlocmm = dvloc/1000)

# Convert SC data to nested tidy format. This is required for use of purrr::map, etc.
data.sc_r &lt;- data.sc %&gt;%
  dplyr::select(vm:fi, dvlocmm, id, housing, id, mlpos, hemi, age, housing, expr, patchdir, rectime, counts) %&gt;%
  gather(&quot;property&quot;, &quot;value&quot;, vm:fi) %&gt;%
  group_by(property) %&gt;%
  nest %&gt;%
  ungroup

# Convert Wfs1+ve cell data to tidy format.
data.wfs_r &lt;- filter(data.wfs, classification == &quot;Pyr&quot;) %&gt;%
  select(-classification) %&gt;%
  gather(&quot;property&quot;, &quot;value&quot;, vm:fi) %&gt;%
  group_by(property) %&gt;%
  nest()

# This is required for Figure 4D, E, 7B and Table 1.
# Code is here as it only needs to be run once.

# Model for uncorrelated random intercept and slope
model_vsris &lt;- function(df) {
  lme4::lmer(value ~ dvlocmm +(dvlocmm||id), data = df, REML = FALSE, na.action = na.exclude)
}

# Null model for uncorrelated random intercept and slope
model_vsris_null &lt;- function(df) {
  lme4::lmer(value ~ dvlocmm||id, data = df, REML = FALSE, na.action = na.exclude)
}

# Fit models to the data
data.sc_r &lt;- data.sc_r %&gt;%
  mutate(mm_vsris = map(data, model_vsris))%&gt;%
  mutate(mm_vsris_null = map(data, model_vsris_null))

# General clustering parameters.
k.max &lt;- 8 # Maximum number of clusters

# d.power is the  power to raise Euclidian distances to. Default is 1, Tibshirani used 2.
# NB: changing this requires the threshold fit initial parameter guess values to be changed according to the comments in the &#39;fit_thresholds&#39; function.
d.power &lt;- 2

iter.max &lt;-
  100 # Maximum iterations the kmeans algorithm will run. Default is 10
nstart &lt;-
  50 # The number of times the kmeans algorithm initialises. Total stability needs &gt; 200

# Threshold parameters
threshold_criterion = 0.01 # Specify false positive rate for each evaluated k

# Parameters for uniform sampled simulated datasets. For calculating thresholds and calculated
# reference dispersions.
sim_unif_dataset_sizes &lt;-
  seq(from = 20, to = 100, by = 10) # A wide range is useful for stable fits
sim_unif_n_sims &lt;- 20000 # &gt;10000 provides sufficienty good fits

# Parameters for example multimodal simulation illustration of clustering with different k
mm_sims &lt;- list()
mm_sims$n_ex_modes &lt;- 5 # Number of clusters
mm_sims$ex_mode_sep_sd &lt;-
  c(3.5, 4, 4.5, 5, 5.5, 6) # Separations between cluster centers

# Parameters for evaluating cluster detection sensitivity
mm_sims$n &lt;-
  5000 # Simulated datasets per combination of factors. 5000 provides stable results.
mm_sims$sep_sd_max &lt;-
  6 # Range of separations of standard deviations to evaluate
mm_sims$sep_sd_min &lt;- 3
mm_sims$sep_sd_incr &lt;- 0.5

mm_sims$n_data_max &lt;-  70 # Range of multimodal dataset sizes to evaluate.
mm_sims$n_data_min &lt;- 20
mm_sims$n_data_incr &lt;- 10

mm_sims$k_max &lt;- 8 # Range of numbers of clusters (k) to evaluate
mm_sims$k_min &lt;- 2
mm_sims$k_incr &lt;- 1

# Other variables (help with import, categorisation and plotting)
mouse_ind &lt;-  8 # Mouse to visualise clustering for. Takes integer values.

props_subthresh &lt;- c(&quot;vm&quot;, &quot;ir&quot;, &quot;sag&quot;, &quot;tau&quot;, &quot;resf&quot;, &quot;resmag&quot;)
props_suprathresh &lt;-
  c(&quot;spkthr&quot;, &quot;spkmax&quot;, &quot;spkhlf&quot;, &quot;rheo&quot;, &quot;ahp&quot;, &quot;fi&quot;)
property_names &lt;- c(props_subthresh, props_suprathresh)
props_sub_labels &lt;-
  c(
    &quot;vm&quot; = &quot;Vm&quot;,
    &quot;ir&quot; = &quot;IR&quot;,
    &quot;sag&quot; = &quot;Sag&quot;,
    &quot;tau&quot; = &quot;Mem. tau&quot;,
    &quot;resf&quot; = &quot;Res. freq.&quot;,
    &quot;resmag&quot; = &quot;Res. mag.&quot;
  )
props_supra_labels &lt;-
  c(
    &quot;spkthr&quot; = &quot;Spk. thresh.&quot;,
    &quot;spkmax&quot; = &quot;Spk. max.&quot;,
    &quot;spkhlf&quot; = &quot;Spk. halfwidth&quot;,
    &quot;rheo&quot; = &quot;Rheobase&quot;,
    &quot;ahp&quot; = &quot;AHP&quot;,
    &quot;fi&quot; = &quot;FI&quot;
  )
property_labels &lt;- c(props_sub_labels, props_supra_labels)


# Generate simulated delta gap data. If sim_unif_n_sims is high this will take a long time
# to run. Will look for a loaded version of slopes_store, then for a saved version.
# If it finds neither then will build slopes_store (and dispersion_store).
if (exists(&quot;delta_gaps_store&quot;)) {
  print(&quot;delta_gaps_store already generated, remove it if you want to rebuild or reload it&quot;)
  if (NROW(delta_gaps_store) != sim_unif_n_sims) {
    warning(&quot;Number of simulated uniform datasets differs from parameter value&quot;)
  }
} else {
  if (file.exists(&quot;GapData/unif_sims_delta_gaps_and_dispersions.Rda&quot;)) {
    load(&quot;GapData/unif_sims_delta_gaps_and_dispersions.Rda&quot;)
    print(&quot;Loaded simulated delta gaps and dispersions&quot;)
    if (NROW(delta_gaps_store) != sim_unif_n_sims) {
      warning(&quot;Number of simulated uniform datasets differs from parameter value&quot;)
    }
  } else {
    # Create unif_sims_delta_gaps_and_dispersions.Rda
    gen_unif_sims(sim_unif_n_sims,
                  sim_unif_dataset_sizes,
                  k.max = k.max,
                  d.power = d.power)
    # Load &#39;delta_gaps_store&#39; and &#39;dispersion_store&#39; variables
    load(&quot;GapData/unif_sims_delta_gaps_and_dispersions.Rda&quot;)
  }
}

# Fitting the delta gap thresholds and dispersions
# It&#39;s important to check after each regeneration of simulated data that the threshold fits are appropriate. With less than 10000 runs, the thresholds can be quite noisy and it&#39;s possible that the fits won&#39;t converge. The form of the fitted equations is $y = (a/n^{b}) + c$, where $n$ is the number of data points in the evaluated dataset and $a, b, c$ are the parameters to be fitted.
# 
# In addition, to speed up evaluation of the reference dispersion to calculate the modified gap statistic k_est, it&#39;s also possible to fit the dispersions obtained from the simulated data and reuse this information so that multiple bootstrap samples don&#39;t have to be drawn for every evaluated dataset. Dispersion fits use a different fitting equation: $y = a*log(n) + b$, where $a, b$ are the parameters to be fitted. 

# Get the delta gap thresholds (and the delta gaps themselves for plotting)
delta_gaps_thresholds &lt;-
  get_delta_gaps_thresh_vals(delta_gaps_store,
                             threshold_criterion =
                               threshold_criterion)
# Fit delta_slope_thresh_vals
threshold_fit_results &lt;-
  fit_thresholds(wd, delta_gaps_thresholds, sim_unif_dataset_sizes)

# Find the average dispersion for each k across all simulations (prevents having to re-simulate
# several uniform distributions every time the modified gap statistic is evaluated)
mean_dispersions &lt;- get_mean_dispersions(dispersion_store)
# Fit mean_dispersions with log function
dispersion_fit_results &lt;-
  fit_dispersions(wd, mean_dispersions, sim_unif_dataset_sizes)
</code></pre>
          </stencila-code-chunk>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1a" title="Figure 1A">
          <label data-itemprop="label">Figure 1A</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 9
#&#39; @height 9

# Make cell distributions for each &#39;cell type&#39;
numcells &lt;- 100
Cell_A &lt;- tibble(x = rnorm(numcells, 10, 1),
                       y = rnorm(numcells, 12, 1),
                       cell = &quot;A&quot;)
Cell_B &lt;- tibble(x = runif(numcells, min = 20, max = 40) + rnorm(numcells,0,1),
                       y = rnorm(numcells, 25, 2),
                       cell = &quot;B&quot;)
Cell_C &lt;- tibble(x = rnorm(numcells, 10, 2),
                       y = rnorm(numcells, 35, 2),
                       cell = &quot;C&quot;)
Cell_D &lt;- tibble(x = rnorm(numcells, 30, 2),
                       y = rnorm(numcells, 10, 2),
                       cell = &quot;D&quot;)
 
CellFeatures &lt;- bind_rows(Cell_A, Cell_B, Cell_C, Cell_D)

# Plot &#39;cell features&#39; using a colour blind friendly palette (from http://www.cookbook-r.com/Graphs/Colors_(ggplot2)/).
cbPalette &lt;- c(&quot;#E69F00&quot;, &quot;#D55E00&quot;, &quot;#56B4E9&quot;, &quot;#009E73&quot;)

CF_plot &lt;- ggplot(CellFeatures, aes(x, y, colour = cell)) +
  geom_point() +
  xlim(0,45) +
  ylim(0,45) +
  labs(x = &quot;Feature 1&quot;, y = &quot;Feature 2&quot;, colour = &quot;Cell Type&quot;, title = &quot;Cell type separation&quot;) +
  scale_colour_manual(values=cbPalette) +
  theme_classic() +
  theme(legend.position = &quot;bottom&quot;,
        axis.ticks = element_blank(),
        axis.text = element_blank(),
        legend.text = element_blank())
CF_plot</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="classification-and-variability-of-neuronal-cell-types">Classification and
              variability of neuronal cell types</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Neuronal cell types are
              identifiable by features clustering around a distinct point (blue, green and yellow)
              or a line (orange) in feature space. The clustering implies that neuron types are
              defined by either a single set point (blue, green and yellow) or by multiple set
              points spread along a line (orange).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1b" title="Figure 1B">
          <label data-itemprop="label">Figure 1B</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code># Example &#39;modular&#39; data
numcells &lt;- 20
MF_A &lt;- tibble(x = c(rnorm(numcells, 26, 0.5), rnorm(numcells, 31, 0.5), rnorm(numcells, 36, 0.5)),
                   y = rnorm(numcells*3, 25, 2),
                   animal = &quot;1&quot;)
MF_B &lt;- tibble(x = c(rnorm(numcells, 28.5, 0.5), rnorm(numcells, 33.5, 0.5), rnorm(numcells, 38.5, 0.5)),
                    y = rnorm(numcells*3, 25, 2),
                    animal = &quot;2&quot;)
                   
ModularFeatures &lt;- rbind(MF_A, MF_B)

# Example &#39;orthogonal&#39; data
numcells &lt;- 60

OOF_A &lt;- tibble(x = runif(numcells, min = 25, max = 40) + rnorm(numcells,0,1),
                y = rnorm(numcells, 23, 1),
                animal = &quot;1&quot;)
OOF_B &lt;- tibble(x = runif(numcells, min = 25, max = 40) + rnorm(numcells,0,1),
                y = rnorm(numcells, 27, 1),
                animal = &quot;2&quot;)
     
OrthogOffsetFeatures &lt;- rbind(OOF_A, OOF_B)

# Example &#39;offset&#39; data
numcells &lt;- 60

LOF_A &lt;- tibble(x = runif(numcells, min = 25, max = 35) + rnorm(numcells,0,1),
                y = rnorm(numcells, 25, 2),
                animal = &quot;1&quot;)
LOF_B &lt;- tibble(x = runif(numcells, min = 30, max = 40) + rnorm(numcells,0,1),
                y = rnorm(numcells, 25, 2),
                animal = &quot;2&quot;)
LinearOffsetFeatures &lt;- rbind(LOF_A, LOF_B)

# Combine into a plot
ModularFeatures$scheme &lt;- &quot;modular&quot;
OrthogOffsetFeatures$scheme &lt;- &quot;orthog&quot;
LinearOffsetFeatures$scheme &lt;- &quot;offset&quot;
IntraAnimal &lt;- bind_rows(ModularFeatures, OrthogOffsetFeatures, LinearOffsetFeatures)
IntraAnimal$scheme &lt;- as.factor(IntraAnimal$scheme)
IntraAnimal$scheme = factor(IntraAnimal$scheme, c(&quot;modular&quot;, &quot;orthog&quot;,&quot;offset&quot;))
labels_schemes &lt;- c(modular = &quot;Modular&quot;, orthog = &quot;Orthogonal&quot;, offset = &quot;Offset&quot;)

IntraAnimalPlot &lt;- ggplot(IntraAnimal, aes(x, y, alpha = animal)) +
  geom_point(colour = cbPalette[2]) +
  xlim(20,45) +
  ylim(20,30) +
  labs(x = &quot;Feature 1&quot;, y = &quot;Feature 2&quot;, alpha = &quot;Animal&quot;, title = &quot;Within cell type variability&quot;) +
  facet_wrap(~scheme, nrow = 3, labeller = labeller(scheme = labels_schemes)) +
  theme_classic() +
  theme(strip.background = element_blank(),
        axis.ticks = element_blank(),
        axis.text = element_blank()) +
  scale_alpha_discrete(range=c(0.1,1)) +
  theme(legend.position = &quot;bottom&quot;,
        legend.text = element_blank())

print(IntraAnimalPlot)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="classification-and-variability-of-neuronal-cell-types-1">Classification and
              variability of neuronal cell types</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Phenotypic variability of a
              single neuron type could result from distinct set points that subdivide the neuron
              type but appear continuous when data from multiple animals are combined (modular),
              from differences in components of a set point that do not extend along a continuum but
              that in different animals cluster at different locations in feature space
              (orthogonal), or from differences between animals in the range covered by a continuum
              of set points (offset). These distinct forms of variability can only be made apparent
              by measuring the features of many neurons from multiple animals.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 1—figure supplement 1"><label data-itemprop="label">Figure 1—figure
            supplement 1</label><img src="index.html.media/fig1-figsupp1.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="a-quantitative-adaptation-of-the-gap-statistic-clustering-algorithm">A
              quantitative adaptation of the gap statistic clustering algorithm.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A–C</strong>) Logic of the gap
              statistic. (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>)
              Simulated clustered dataset with three modes (k = 3) (open gray circles) (upper) and
              the corresponding simulated reference dataset drawn from a uniform distribution with
              lower and upper limits set by the minimum and maximum values from the corresponding
              clustered dataset (open gray diamonds). Data were allocated to clusters by running a
              K-means algorithm 20 times on each set of data and selecting the partition with the
              lowest average intracluster dispersion. Red, green, blue and yellow dashed ovals show
              a realization of the data subsets allocated to each cluster when k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">Eval</sub> = 1, 2, 3 and 4 modes.
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) The
              average value of the log intracluster dispersion for the clustered (open circles) and
              reference (open diamonds) datasets for each value of k tested in panel (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">C</strong>) Gap values
              resulting from the difference between the clustered and reference values for each k in
              panel (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>).
              Many (≥500 in this paper) reference distributions are generated and their mean
              intracluster dispersion values are subtracted from those arising from the clustered
              distribution to maximize the reliability of the Gap values. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>) A procedure for selecting the
              optimal k depending on the associated gap values. Quantitative procedure for selecting
              optimal k (k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub>).
              ∆Gap values (open circles) are obtained by subtracting from the Gap value of a given k
              the Gap value for the previous k (∆Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub> = Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub> – Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k-1</sub>). For each ∆Gap<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub>, if the ∆Gap value
              is greater than a threshold (filled triangles) associated with that ∆Gap<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub>, that ∆Gap<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub> will be k<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub>, if no ∆Gap
              exceeds, the threshold, k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> = 1. In the figure, for
              ∆Gap<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub> = 2, 3, 4
              (brown, pink and cyan), the ∆Gap value exceeds its threshold only when ∆Gap<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub> = 3. Therefore
              k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> = 3.
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">E–G</strong>)
              Determination of ∆Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub> thresholds. (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">E</strong>) Histograms of
              ∆Gap values calculated from 20,000 simulated datasets drawn from uniform distributions
              for each ∆Gap<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub>
              (brown, pink and cyan, respectively, for ∆Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub> = 2, 3, 4) for a single dataset
              size (n = 40). ∆Gap thresholds (filled triangles) are the values beyond which 1% of
              the ∆Gap values fall and vary with ∆Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub>. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">F</strong>) Histograms of ∆Gap values for
              a range of dataset sizes (n = 20, 40, 100) and their associated thresholds. (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">G</strong>) Plot of the ∆Gap
              thresholds as a function of dataset size and ∆Gap<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">k</sub>. For separate ∆Gap<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">k</sub>, ∆Gap threshold
              values are fitted well by a hyperbolic function of dataset size. These fits provide a
              practical method of finding the appropriate ∆Gap threshold for an arbitrary dataset
              size.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 1—figure supplement 2"><label data-itemprop="label">Figure 1—figure
            supplement 2</label><img src="index.html.media/fig1-figsupp2.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="discrimination-of-continuous-from-modular-organizations-using-the-adapted-gap-statistic-algorithm">
              Discrimination of continuous from modular organizations using the adapted gap
              statistic algorithm.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Simulated datasets (each
              n = 40) drawn from continuous (uniform, k = 1 mode) (upper) and modular (multimodal
              mixture of Gaussians with k = 2 modes) (lower) distributions, and plotted against
              simulated dorsoventral locations. Also shown are the probability density functions
              (pdf) used to generate each dataset (light blue) and the densities estimated post-hoc
              from the generated data as kernel smoothed densities (light gray pdfs). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) Histograms
              showing the distribution of k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> from 1000 simulated datasets
              drawn from each pdf in panel (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>). k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> is determined for each
              dataset by a modified gap statistic algorithm (see <a href="#fig1s1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 1</a> above).
              When k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> = 1,
              the dataset is considered to be continuous (unclustered), when k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> ≥2, the dataset is considered
              to be modular (clustered). The algorithm operates only on the feature values and does
              not use location information. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) Illustration of a set of
              clustered (k = 2) pdfs with the distance (in standard deviations) between clusters
              ranging from 2 to 6 (upper). Systematic evaluation of the ability of the modified gap
              statistic algorithm to detect clustered organization (k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> ≥2) in simulated datasets of
              different size (n = 20 to 100) drawn from the clustered (filled blue) and continuous
              (open blue) pdfs (lower). The proportion of datasets drawn from the continuous
              distribution that have k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub> ≥2 is the false positive (FP)
              rate (pFP = <sub itemscope="" itemtype="http://schema.stenci.la/Subscript">0.07). The
                light gray filled circle shows the smallest dataset size (n = 40) with SD = 5, where
                the proportion of datasets detected as clustered (p</sub>detect<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">) is </sub>0.8. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>). Plot showing how p<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> at n = 40,
              SD = 5 changes when datasets are drawn from pdfs with different numbers of clusters (n
              modes from 2 to 8). Further evaluation of the analysis of additional clusters is
              represented in the following figure.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 1—figure supplement 3"><label data-itemprop="label">Figure 1—figure
            supplement 3</label><img src="index.html.media/fig1-figsupp3.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="additional-evaluation-of-the-adapted-gap-statistic-algorithm">Additional
              evaluation of the adapted gap statistic algorithm.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A–C</strong>) Plots showing how p<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> (the ability
              of the modified gap statistic algorithm to detect clustered organization) depends on
              dataset size and separation between cluster modes in simulated datasets drawn from
              clustered pdfs with different numbers of modes. The gray markers indicate n = 40,
              SD = 5 (as shown in <a href="#fig1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Figure 1E</a>). In each plot, p<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> is shown as a
              function of simulated dataset size and separation between modes when k = 3 (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>), k = 5 (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) and k = 8
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">C</strong>), which was
              the maximum number of clusters evaluated. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D–F</strong>) Histograms showing the
              counts of k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub>
              from the 1000 simulated n = 40, SD = 5 datasets (gray filled circles) illustrated in
              panels (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">A–C</strong>),
              respectively. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">G</strong>) p<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">detect</sub> as a function of dataset
              size and mode separation with k = 5 when cluster modes are unevenly sampled. Sample
              sizes from clusters vary randomly with each dataset. A single mode can contribute from
              all to none of the points in any simulated dataset. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">H</strong>) p<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">detect</sub> as a function of dataset
              size and mode separation with k = 5 when the distance between mode centers increases
              by a factor of sqrt(2) between sequential cluster pairs. Data are shown for different
              initial separations (the distance between the first two cluster centers) ranging from
              1 to 4 (with corresponding separations between the final cluster pair ranging from 4
              to 16).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 1—figure supplement 4"><label data-itemprop="label">Figure 1—figure
            supplement 4</label><img src="index.html.media/fig1-figsupp4.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="comparing-the-adapted-gap-statistic-algorithm-with-discontinuity-measures-for-discreteness">
              Comparing the adapted gap statistic algorithm with discontinuity measures for
              discreteness.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Counts of log discontinuity
              ratio scores generated from a simulated uniform data distribution. The data
              distribution was ordered and then sampled either at positions drawn at random from a
              uniform distribution (dark blue) or at positions with a fixed increment (light blue).
              For the data sampled at random positions, approximately half of the scores are &gt;0
              and for even sampling all scores are &gt;0. Therefore, a threshold score &gt;0 does
              not distinguish discrete from continuous distributions. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Comparison of p<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> as a function
              of dataset size for the adapted gap statistic algorithm, the discontinuity (upper) and
              the discreteness algorithm (lower). Each algorithm is adjusted to yield a 7% false
              positive rate. Each column shows simulations of data with different numbers of modes
              (k).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 1—figure supplement 5"><label data-itemprop="label">Figure 1—figure
            supplement 5</label><img src="index.html.media/fig1-figsupp5.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="evaluation-of-modularity-of-grid-firing-using-an-adapted-gap-statistic-algorithm">
              Evaluation of modularity of grid firing using an adapted gap statistic algorithm.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Examples of grid spacing
              for individual neurons (crosses) from different mice. Kernel smoothed densities (KSDs)
              were generated with either a wide (solid gray) or a narrow (dashed lines) kernel. The
              number of modes estimated using the modified gap statistic algorithm is ≥ 2 for all
              but one animal (animal 4) with n ≥ 20 (animals 3 and 7 have &lt; 20 recorded cells).
              We did not have location information for animal 2.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Stellate cells in layer 2 (SCs)
          of the medial entorhinal cortex (MEC) provide a striking example of correspondence between
          functional organization of neural circuits and variability of electrophysiological
          features within a single cell type. The MEC contains neurons that encode an animal’s
          location through grid-like firing fields (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib27">Fyhn et al., 2004</a></cite>).
          The spatial scale of grid fields follows a dorsoventral organization (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib42">Hafting et al.,
              2005</a></cite>), which is mirrored by a dorsoventral organization in key
          electrophysiological features of SCs (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib10">Boehlen et al.,
              2010</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib21">Dodson et al., 2011</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib28">Garden et al., 2008</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib30">Giocomo et
              al., 2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib33">Giocomo and Hasselmo, 2008</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib58">Pastoll et al.,
              2012</a></cite>). Grid cells are further organized into discrete modules (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>), with the cells within a module having a similar grid scale and
          orientation (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib6">Barry et al., 2007</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib40">Gu et al., 2018</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et
              al., 2012</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib82">Yoon et al., 2013</a></cite>); progressively more ventral modules are
          composed of cells with wider grid spacing (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>). Studies that demonstrate dorsoventral organization of integrative
          properties of SCs have so far relied on the pooling of relatively few measurements per
          animal. Hence, it is unclear whether the organization of these cellular properties is
          modular, as one might expect if they directly set the scale of grid firing fields in
          individual grid cells (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib30">Giocomo et al., 2007</a></cite>). The possibility that set points for
          electrophysiological properties of SCs differ between animals has also not been
          considered previously.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Evaluation of variability
          between and within animals requires statistical approaches that are not typically used in
          single-cell electrophysiological investigations. Given appropriate assumptions,
          inter-animal differences can be assessed using mixed effect models that are well
          established in other fields (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib4">Baayen et al., 2008</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib29">Geiler-Samerotte et al.,
              2013</a></cite>). Because tests of whether data arise from modular as opposed to
          continuous distributions have received less general attention, to facilitate detection of
          modularity using relatively few observations, we introduce a modification of the gap
          statistic algorithm (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib75">Tibshirani et al., 2001</a></cite>) that estimates the number of modes
          in a dataset while controlling for observations expected by chance (see
          &#39;Materials and methods&#39; and <a href="#fig1s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplements 1</a><a
            href="#fig1s5" itemscope="" itemtype="http://schema.stenci.la/Link">5</a>). This
          algorithm performs well compared with discreteness metrics that are based on the standard
          deviation of binned data (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib32">Giocomo et al., 2014</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>), which we find are prone to high false-positive rates (<a
            href="#fig1s4" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—figure
            supplement 4A</a>). We find that recordings from approximately 30 SCs per animal should
          be sufficient to detect modularity using the modified gap statistic algorithm and given
          the experimentally observed separation between grid modules (see
          &#39;Materials and methods&#39; and <a href="#fig1s2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplements 2</a><a
            href="#fig1s3" itemscope="" itemtype="http://schema.stenci.la/Link">3</a>). Although
          methods for high-quality recording from SCs in ex-vivo brain slices are well established
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib59">Pastoll et
              al., 2012</a></cite>), typically fewer than five recordings per animal were made in
          previous studies, which is many fewer than our estimate of the minimum number of
          observations required to test for modularity.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We set out to establish the
          nature of the set points that establish the integrative properties of SCs by measuring
          intra- and inter-animal variation in key electrophysiological features using experiments
          that maximize the number of SCs recorded per animal. Our results suggest that set points
          for individual features of a neuronal cell type are established at the level of neuronal
          cell populations, differ between animals and follow a continuous organization.</p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="results">Results</h2>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="sampling-integrative-properties-from-many-neurons-per-animal">Sampling integrative
          properties from many neurons per animal</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Before addressing intra- and
          inter-animal variability, we first describe the data set used for the analyses that
          follow. We established procedures to facilitate the recording of integrative properties of
          many SCs from a single animal (see &#39;Materials and methods&#39;). With these
          procedures, we measured and analyzed electrophysiological features of 836 SCs (n/mouse:
          range 11–55; median = 35) from 27 mice (median age = 37 days, age range = 18–57 days). The
          mice were housed either in a standard home cage (dimensions: 0.2 × 0.37 m, N = 18 mice,
          n = 583 neurons) or from postnatal day 16 in a 2.4 × 1.2 m cage, which provided a large
          environment that could be freely explored (N = 9, n = 253, median age = 38 days) (<a
            href="#fig2s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 2—figure
            supplement 1</a>). For each neuron, we measured six sub-threshold integrative properties
          (<a href="#fig2" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 2A–B</a>) and
          six supra-threshold integrative properties (<a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2C</a>). Unless indicated otherwise, we
          report the analysis of datasets that combine the groups of mice housed in standard and
          large home cages and that span the full range of ages.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig2" title="Figure 2">
          <label data-itemprop="label">Figure 2</label><img src="index.html.media/fig2.jpg" alt=""
            itemscope="" itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="dorsoventral-organization-of-intrinsic-properties-of-stellate-cells-from-a-single-animal">
              Dorsoventral organization of intrinsic properties of stellate cells from a single
              animal.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A–C</strong>) Waveforms (gray traces) and
              example responses (black traces) from a single mouse for step (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>), ZAP (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) and ramp (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) stimuli (left). The properties
              derived from each protocol are shown plotted against recording location (each data
              point is a black cross) (right). KSDs with arbitrary bandwidth are displayed to the
              right of each data plot to facilitate visualization of the property’s distribution
              when location information is disregarded (light gray pdfs). (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Injection of a series of
              current steps enables the measurement of the resting membrane potential (V<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">rest</sub>) (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">i</strong>), the input
              resistance (IR) (ii), the sag coefficient (sag) (iii) and the membrane time constant
              (τ<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">m</sub>) (iv).
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) Injection
              of ZAP current waveform enables the calculation of an impedance amplitude profile,
              which was used to estimate the resonance resonant frequency (Res. F) (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">i</strong>) and magnitude
              (Res. mag) (ii). (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) Injection of a slow current
              ramp enabled the measurement of the rheobase (i); the slope of the current-frequency
              relationship (I-F slope) (ii); using only the first five spikes in each response
              (enlarged zoom, lower left), the AHP minimum value (AHP<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">min</sub>) (iii); the spike maximum
              (Spk. max) (iv); the spike threshold (Spk. thr.) (v); and the spike width at half
              height (Spk. HW) (vi).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 2—figure supplement 1"><label data-itemprop="label">Figure 2—figure
            supplement 1</label><img src="index.html.media/fig2-figsupp1.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="large-environment-for-housing">Large environment for housing.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A, B</strong>) The large cage environment
              viewed from above (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) and from inside (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>).</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Because SCs are found
          intermingled with pyramidal cells in layer 2 (L2PCs), and as misclassification of L2PCs as
          SCs would probably confound investigation of intra-SC variation, we validated our criteria
          for distinguishing each cell type. To establish characteristic electrophysiological
          properties of L2PCs, we recorded from neurons in layer 2 that were identified by
          Cre-dependent marker expression in a <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Wfs1</em><sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">Cre</sup> mouse line (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib72">Sürmeli et al.,
              2015</a></cite>). Expression of Cre in this line, and in a similar line (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib44">Kitamura et al.,
              2014</a></cite>), labels L2PCs that project to the CA1 region of the hippocampus, but
          does not label SCs (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib44">Kitamura et al., 2014</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib72">Sürmeli et al.,
              2015</a></cite>). We identified two populations of neurons in layer 2 of MEC that were
          labelled in <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Wfs1</em><sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">Cre</sup> mice (<a
            href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 3A–C</a>). The
          more numerous population had properties consistent with L2PCs (<a href="#fig3"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 3A,G</a>) and could be
          separated from the unidentified population on the basis of a lower rheobase (<a
            href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 3C</a>). The
          unidentified population had firing properties that were typical of layer 2 interneurons
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib37">Gonzalez-Sulser et al., 2014</a></cite>). A principal component analysis
          (PCA) (<a href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            3D–F</a>) clearly separated the L2PC population from the SC population, but did not
          identify subpopulations of SCs. The properties of the less numerous population were also
          clearly distinct from those of SCs (<a href="#fig3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 3A,C</a>). These data demonstrate that
          the SC population used for our analyses is distinct from other cell types also found in
          layer 2 of the MEC.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig3" title="Figure 3">
          <label data-itemprop="label">Figure 3</label><img src="index.html.media/fig3.jpg" alt=""
            itemscope="" itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="distinct-and-dorsoventrally-organized-properties-of-layer-2-stellate-cells">
              Distinct and dorsoventrally organized properties of layer 2 stellate cells.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Representative action
              potential after hyperpolarization waveforms from a SC (left), a pyramidal cell
              (middle) and an unidentified cell (right). The pyramidal and unidentified cells were
              both positively labelled in <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">Wfs1<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">C</sup></em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript">re</sup> mice. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Plot of the first versus the
              second principal component from PCA of the properties of labelled neurons in <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">Wfs1</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript">Cre</sup> mice reveals two
              populations of neurons. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) Histogram showing the
              distribution of rheobase values of cells positively labelled in <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">Wfs1</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript">Cre</sup> mice. The two groups
              identified in panel (B) can be distinguished by their rheobase. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>) Plot of the first two
              principal components from PCA of the properties of the L2PC (n = 44, green) and SC
              populations (n = 836, black). Putative pyramidal cells (x) and SCs (+) are colored
              according to their dorsoventral location (inset shows the scale). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">E</strong>) Proportion of
              total variance explained by the first five principal components for the analysis in
              panel (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">D</strong>).
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">F</strong>) Histograms
              of the locations of recorded SCs (upper) and L2PCs (lower). (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">G</strong>) All values of measured
              features from all mice are plotted as a function of the dorsoventral location of the
              recorded cells. Lines indicate fits of a linear model to the complete datasets for SCs
              (black) and L2PCs (green). Putative pyramidal cells (x, green) and SCs (+, black).
              Adjusted R<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>
              values use the same color scheme.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 3G—executable version"><label data-itemprop="label">Figure 3G—executable
            version</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 30
#&#39; @height 20
plot_sc_wfs &lt;- data.sc %&gt;%
  select(vm:fi, dvlocmm) %&gt;%
  mutate(classification = &quot;SC&quot;)
plot_wfs &lt;- data.wfs %&gt;%
  select(vm:fi, dvlocmm, classification)
plot_sc_wfs &lt;- bind_rows(plot_sc_wfs, plot_wfs) %&gt;%
  gather(&quot;property&quot;, &quot;value&quot;, vm:fi)

labels_intercepts &lt;-
  c(
    ahp = &quot;AHP min. (mV)&quot;,
    fi = &quot;F-I (Hz / pA)&quot;,
    ir = &quot;IR (MΩ)&quot;,
    resf = &quot;Res F (Hz)&quot;,
    resmag = &quot;Res. mag.&quot;,
    rheo = &quot;Rheobase (pA)&quot;,
    sag = &quot;Sag&quot;,
    spkhlf = &quot;Spike h-w (ms)&quot;,
    spkmax = &quot;Spike max. (mV)&quot;,
    spkthr = &quot;Spike thres. (mV)&quot;,
    tau = &quot;Tm (ms)&quot;,
    vm = &quot;Vrest (mV)&quot;
    )

figure_3 &lt;- ggplot(plot_sc_wfs, aes(dvlocmm,value)) +
  geom_point(aes(colour = classification)) +
  scale_x_continuous(name = &quot;Location (mm)&quot;,
                     breaks = c(0, 1, 2)) +
  scale_colour_discrete(name = &quot;Neuron type&quot;) +
  facet_wrap(~property,
             scales = &quot;free_y&quot;,
             labeller = labeller(property = labels_intercepts)) +
  theme_classic() +
  theme(axis.title.y = element_blank(),
        strip.background = element_blank())
print(figure_3)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="distinct-and-dorsoventrally-organized-properties-of-layer-2-stellate-cells-1">
              Distinct and dorsoventrally organized properties of layer 2 stellate cells.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">G</strong>) All values of measured
              features from all mice are plotted as a function of the dorsoventral location of the
              recorded cells. Lines indicate fits of a linear model to the complete datasets for SCs
              (black) and L2PCs (green). Putative pyramidal cells (x, green) and SCs (+, black).
              Adjusted R<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>
              values use the same color scheme.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To further validate the large
          SC dataset, we assessed the location-dependence of individual electrophysiological
          features, several of which have previously been found to depend on the dorso-ventral
          location of the recorded neuron (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib10">Boehlen et al.,
              2010</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib11">Booth et al., 2016</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib28">Garden et al., 2008</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib30">Giocomo et
              al., 2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib58">Pastoll et al., 2012</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib83">Yoshida et al.,
              2013</a></cite>). We initially fit the dependence of each feature on dorsoventral
          position using a standard linear regression model. We found substantial (adjusted R<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup> &gt;0.1)
          dorsoventral gradients in input resistance, sag, membrane time constant, resonant
          frequency, rheobase and the current-frequency (I-F) relationship (<a href="#fig3"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 3G</a>). In contrast to the
          situation in SCs, we did not find evidence for dorsoventral organization of these features
          in L2PCs (<a href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            3G</a>). Thus, our large dataset replicates the previously observed dependence of
          integrative properties of SCs on their dorsoventral position, and shows that this location
          dependence further distinguishes SCs from L2PCs.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="inter-animal-differences-in-the-intrinsic-properties-of-stellate-cells">Inter-animal
          differences in the intrinsic properties of stellate cells</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To what extent does variability
          between the integrative properties of SCs at a given dorsoventral location arise from
          differences between animals? Comparing specific features between individual animals
          suggested that their distributions could be almost completely non-overlapping, despite
          consistent and strong dorsoventral tuning (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4A</a>). If this apparent inter-animal
          variability results from the random sampling of a distribution determined by a common
          underlying set point, then fitting the complete data set with a mixed model in which
          animal identity is included as a random effect should reconcile the apparent differences
          between animals (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4B</a>). In this scenario, the
          conditional R<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>
          estimated from the mixed model, in other words, the estimate of variance explained by
          animal identity and location, should be similar to the marginal R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> value, which indicates the
          variance explained by location only. By contrast, if differences between animals
          contribute to experimental variability, the mixed model should predict different fitting
          parameters for each animal, and the estimated conditional R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> should be greater than the
          corresponding marginal R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4C</a>).</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure"
          title="Figure 4A—executable version"><label data-itemprop="label">Figure 4A—executable
            version</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 12
#&#39; @height 6

(rheo_example &lt;- ggplot(filter(data.sc, id == &quot;mouse_20131106&quot; | id == &quot;mouse_20140113&quot;), aes(dvloc, rheo)) +
  geom_point(aes(colour = id), shape = 3) +
  labs(x = &quot;Location (µm)&quot;, y = &quot;Rheobase (pA)&quot;, colour = &quot;Mouse&quot;)) +
  theme(axis.title = element_text(size = 7),
          axis.text = element_text(size = 7),
          axis.title.x = element_text(vjust = 2.5),
          legend.text = element_text(size = 5),
          legend.title=element_text(size=5),
          legend.key.size = unit(0.2, &quot;cm&quot;),
          legend.position = &quot;right&quot;,
          legend.key = element_rect(fill = &quot;white&quot;, colour = &quot;black&quot;)) +
  scale_colour_manual(labels = c(&quot;&quot;, &quot;&quot;), values = c(&quot;red&quot;, &quot;blue&quot;))
</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="inter-animal-variability-and-dependence-on-environment-of-intrinsic-properties-of-stellate-cells">
              Inter-animal variability and dependence on environment of intrinsic properties of
              stellate cells.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Examples of rheobase as a
              function of dorsoventral position for two mice.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig4bcd"
          title="Figure 4B,C,D"><label data-itemprop="label">Figure 4B,C,D</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 12
#&#39; @height 4

# Generate simulated data

# Makes properties for each subject
make_real_vals &lt;-
  function(n_subjects,
           intersd_int = 1,
           intersd_slope = 1) {
    tb &lt;-
      tibble(
        id = 1:n_subjects,
        int = rnorm(n_subjects, 1, intersd_int),
        slope = rnorm(n_subjects, 1, intersd_slope)
      )
  }

# Make data for each subject
make_data &lt;-
  function(subject_params,
           loc_n = 20,
           loc_max = 1,
           intrasd = 1) {
    total_points &lt;- c(loc_n * count(subject_params))[[1]]
    tb &lt;- tibble(
      id = rep(subject_params$id, loc_n),
      loc = rep(runif(total_points, 0, loc_max)),
      param = loc * subject_params$slope +
        subject_params$int + rnorm(total_points, 0, intrasd)
    )
  }

# Formats figures
var_gp_format &lt;- function(gg) {
  gg &lt;- gg +
    ylim(0, 3) +
    ylab(&quot;Feature&quot;) +
    xlab(&quot;Location&quot;) +
    theme(axis.text = element_blank())
}

# Generate data simulating dorsoventral organisation without inter-animal variability
without_var_gp &lt;- make_real_vals(20, 0, 0)
without_var_gp_data &lt;- make_data(without_var_gp, 20, 1, 0.5)

# Plot fits to each animal separately
without_var_gp_gg &lt;-
  ggplot(without_var_gp_data, aes(loc, param, group = id)) +
  stat_smooth(geom = &quot;line&quot;, method = lm, se = FALSE) +
  ylim(0, 3)


without_var_gp_gg &lt;- var_gp_format(without_var_gp_gg) +
  theme(axis.title = element_text(size = 9),
        axis.title.x = element_text(vjust = 2)) +
  labs(x = &quot;&quot;) +
  scale_x_continuous(
    labels = function(breaks) {
      rep_along(breaks, &quot;&quot;)
    }
  )

# Predictions for fitting with a mixed effect model
without_var_gp_mm &lt;-
  lmer(param ~ loc + (loc ||
                        id), data = without_var_gp_data, REML = FALSE)
mm_without_predictplot &lt;-
  predict_plot_2(
    without_var_gp_data,
    without_var_gp_mm,
    without_var_gp_data$loc,
    without_var_gp_data$param
  )

mm_without_predictplot &lt;- var_gp_format(mm_without_predictplot) +
  annotate(
    &quot;text&quot;,
    x = 0.6,
    y = 0.6,
    label = &quot;paste(italic(R) ^ 2, \&quot;marginal = .31\&quot;)&quot;,
    parse = TRUE,
    size = 2
  ) +
  annotate(
    &quot;text&quot;,
    x = 0.6,
    y = 0.2,
    label = &quot;paste(italic(R) ^ 2, \&quot;conditional = .31\&quot;)&quot;,
    parse = TRUE,
    size = 2
  )  +
  theme(axis.title = element_text(size = 9),
        axis.title.x = element_text(vjust = 2))


mm_without_predictplot &lt;- mm_without_predictplot +
  labs(x = &quot;&quot;, y = &quot;&quot;)

plot_grid(without_var_gp_gg, mm_without_predictplot)


# Generate data simulating dorsoventral organisation with inter-animal variability
with_var_gp &lt;- make_real_vals(20, 0.2, 0.2)
with_var_gp_data &lt;- make_data(with_var_gp, 20, 1, 0.2)

# Plot fits to each animal separately
with_var_gp_gg &lt;-
  ggplot(with_var_gp_data, aes(loc, param, group = id)) +
  stat_smooth(geom = &quot;line&quot;, method = lm, se = FALSE)

with_var_gp_gg &lt;- var_gp_format(with_var_gp_gg) +
  theme(axis.title = element_text(size = 9),
        axis.title.x = element_text(vjust = 2))

# Predictions for fitting with a mixed effect model
with_var_gp_mm &lt;-
  lmer(param ~ loc + (loc ||
                        id), data = with_var_gp_data, REML = FALSE)

mm_with_predictplot &lt;-
  predict_plot_2(with_var_gp_data,
                 with_var_gp_mm,
                 with_var_gp_data$loc,
                 with_var_gp_data$param)

mm_with_predictplot &lt;- var_gp_format(mm_with_predictplot) +
  annotate(
    &quot;text&quot;,
    x = 0.6,
    y = 0.6,
    label = &quot;paste(italic(R) ^ 2, \&quot;marginal = .49\&quot;)&quot;,
    parse = TRUE,
    size = 2
  ) +
  annotate(
    &quot;text&quot;,
    x = 0.6,
    y = 0.2,
    label = &quot;paste(italic(R) ^ 2, \&quot;conditional = .73\&quot;)&quot;,
    parse = TRUE,
    size = 2
  ) +
  theme(axis.title = element_text(size = 9),
        axis.title.x = element_text(vjust = 2))

mm_with_predictplot &lt;- mm_with_predictplot +
  labs(y = &quot;&quot;)

plot_grid(with_var_gp_gg, mm_with_predictplot)


# The code below requires mixed effect models to have been fit to data in data.sc_r

# Rheobase predictions from fits with a standard linear model
rheo_predictplot &lt;-  ggplot(filter(data.sc_r, property == &quot;rheo&quot;)$data[[1]], aes(x = dvlocmm, y = value, group = id)) +
    stat_smooth(geom = &quot;line&quot;, method = lm, se = FALSE)
rheo_predictplot &lt;- gg_rheo_format(rheo_predictplot, 0, 600)

rheo_predictplot_mod &lt;- rheo_predictplot +
    theme(axis.title = element_text(size = 9), axis.text = element_text(size = 7), axis.title.x = element_text(vjust = 2.5))


# Rheobase predictions from mixed model fits
mm_rheo_predictplot &lt;- predict_plot(filter(data.sc_r, property == &quot;rheo&quot;)$data[[1]],
                               filter(data.sc_r, property == &quot;rheo&quot;)$mm_vsris[[1]])
mm_rheo_predictplot  &lt;- gg_rheo_format(mm_rheo_predictplot, 0, 600)

mm_rheo_predictplot_mod &lt;- mm_rheo_predictplot +
    annotate(&quot;text&quot;, x = 1, y = 130, label = &quot;paste(italic(R) ^ 2, \&quot;marginal = .38\&quot;)&quot;, parse = TRUE, size = 2) +
    annotate(&quot;text&quot;, x = 1, y = 50, label = &quot;paste(italic(R) ^ 2, \&quot;conditional = .65\&quot;)&quot;, parse = TRUE, size = 2) +
    theme(axis.title = element_text(size = 9), axis.text = element_text(size = 7), axis.title.x = element_text(vjust = 2.5))

mm_rheo_predictplot_mod &lt;- mm_rheo_predictplot_mod +
  labs(y = &quot;&quot;)

plot_grid(rheo_predictplot_mod, mm_rheo_predictplot_mod)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="inter-animal-variability-and-dependence-on-environment-of-intrinsic-properties-of-stellate-cells-1">
              Inter-animal variability and dependence on environment of intrinsic properties of
              stellate cells.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B, C</strong>) Each line is the fit of
              simulated data from a different subject for datasets in which there is no
              inter-subject variability (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) or in which intersubject
              variability is present (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>). Fitting data from each
              subject independently with linear regression models suggests intersubject variation in
              both datasets (left). By contrast, after fitting mixed effect models (right)
              intersubject variation is no longer suggested for the dataset in which it is absent
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) but
              remains for the dataset in which it is present (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>). (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>) Each line is the fit of
              rheobase as a function of dorsoventral location for a single mouse. The fits were
              carried out independently for each mouse (left) or using a mixed effect model with
              mouse identity as a random effect (right).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig4e" title="Figure 4E">
          <label data-itemprop="label">Figure 4E</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 25
#&#39; @height 25

combined_intercepts_slopes &lt;-
  prep_int_slopes(data.sc_r, &quot;property&quot;, &quot;mm_vsris&quot;)

id_housing &lt;-  distinct(data.sc, id, housing, age, sex)
combined_intercepts_slopes &lt;-
  left_join(combined_intercepts_slopes, id_housing, by = &quot;id&quot;)

combined_intercepts_slopes$property_factors &lt;-
  as.factor(combined_intercepts_slopes$property)

combined_intercepts_slopes$property_factors = factor(
  combined_intercepts_slopes$property_factors,
  c(
    &quot;vm&quot;,
    &quot;ir&quot;,
    &quot;sag&quot;,
    &quot;tau&quot;,
    &quot;resf&quot;,
    &quot;resmag&quot;,
    &quot;rheo&quot;,
    &quot;fi&quot;,
    &quot;ahp&quot;,
    &quot;spkmax&quot;,
    &quot;spkthr&quot;,
    &quot;spkhlf&quot;
  )
)


labels_intercepts &lt;-
  c(
    ahp = &quot;AHP min. (mV)&quot;,
    fi = &quot;F-I (Hz / pA)&quot;,
    ir = &quot;IR (MΩ)&quot;,
    resf = &quot;Res F (Hz)&quot;,
    resmag = &quot;Res. mag.&quot;,
    rheo = &quot;Rheobase (pA)&quot;,
    sag = &quot;Sag&quot;,
    spkhlf = &quot;Spike h-w (ms)&quot;,
    spkmax = &quot;Spike max. (mV)&quot;,
    spkthr = &quot;Spike thres. (mV)&quot;,
    tau = &quot;Tm (ms)&quot;,
    vm = &quot;Vrest (mV)&quot;
  )

print(
    ggplot(
      combined_intercepts_slopes,
      aes(x = measure, y = value_1, colour = housing)
    ) +
    geom_line(aes(group = id)) +
    geom_jitter(aes(y = value_2), width = 0.2, alpha = 0.5) +
    #geom_boxplot(aes(y = value_2), alpha = 0.1) +
    stat_summary(
      aes(y = value_2),
      fun.y = &quot;mean&quot;,
      fun.ymin = &quot;mean&quot;,
      fun.ymax = &quot;mean&quot;,
      size = 0.2,
      geom = &quot;crossbar&quot;
    ) +
    scale_x_discrete(
      limits = c(
        &quot;ind_intercept&quot;,
        &quot;ind_intercept_slope&quot;,
        &quot;global_intercept&quot;,
        &quot;global_intercept_slope&quot;
      ),
      label = c(&quot;I&quot;, &quot;I + S&quot;, &quot;&quot;, &quot;&quot;)
    ) +
    facet_wrap(
      ~ property_factors,
      scales = &quot;free&quot;,
      labeller = labeller(property_factors = labels_intercepts)
    ) +
    theme_classic() +
    hist_theme +
    theme(
      axis.line.x = element_blank(),
      axis.ticks.x = element_blank(),
      legend.position = &quot;bottom&quot;
    )
)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="inter-animal-variability-and-dependence-on-environment-of-intrinsic-properties-of-stellate-cells-2">
              Inter-animal variability and dependence on environment of intrinsic properties of
              stellate cells.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">E</strong>) The intercept (I), sum of the
              intercept and slope (I + S), and slopes realigned to a common intercept (right) for
              each mouse obtained by fitting mixed effect models for each property as a function of
              dorsoventral position.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig4"
          title="Figure 4—figure supplement 1"><label data-itemprop="label">Figure 4—figure
            supplement 1</label><img src="index.html.media/fig4-figsupp1.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="properties-of-scs-in-medial-and-lateral-slices">Properties of SCs in medial and
              lateral slices.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Membrane properties of SCs
              from slices containing more medial (blue) and more lateral (red) parts of the MEC
              plotted as a function of dorsal ventral position. Neurons from more medial slices had
              a higher spike threshold, a lower spike maximum and a less-negative spike
              after-hyperpolarization (see <a href="#supp6" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 6</a>). Properties are
              labelled as in <a href="#fig2" itemscope=""
                itemtype="http://schema.stenci.la/Link">Figure 2</a>.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Fitting the experimental
          measures for each feature with mixed models suggests that differences between animals
          contribute substantially to the variability in properties of SCs. In contrast to simulated
          data in which inter-animal differences are absent (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4B</a>), differences in fits between
          animals remained after fitting with the mixed model (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4D</a>). This corresponds with
          expectations from fits to simulated data containing inter-animal variability (<a
            href="#fig4" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4C</a>). To
          visualize inter-animal variability for all measured features, we plot for each animal the
          intercept of the model fit (I), the predicted value at a location 1 mm ventral from the
          intercept (I+S), and the slope (lines) (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4E</a>). Strikingly, even for features
          such as rheobase and input resistance (IR) that are highly tuned to a neurons’
          dorsoventral position, the extent of variability between animals is similar to the
          extent to which the property changes between dorsal and mid-levels of the MEC.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">If set points that determine
          integrative properties of SCs do indeed differ between animals, then mixed models should
          provide a better account of the data than linear models that are generated by pooling data
          across all animals. Consistent with this, we found that mixed models for all
          electrophysiological features gave a substantially better fit to the data than linear
          models that considered all neurons as independent (adjusted p&lt;2×10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−17</sup> for all models, χ<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup> test, <a
            href="#table1" itemscope="" itemtype="http://schema.stenci.la/Link">Table 1</a>).
          Furthermore, even for properties with substantial (R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> value &gt;0.1) dorsoventral
          tuning, the conditional R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> value for the mixed effect model
          was substantially larger than the marginal R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> value (<a href="#fig4"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4D</a> and <a href="#table1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Table 1</a>). Together, these
          analyses demonstrate inter-animal variability in key electrophysiological features of SCs,
          suggesting that the set points that establish the underlying integrative properties differ
          between animals.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph"><strong itemscope=""
            itemtype="http://schema.stenci.la/Strong">Table 1. Dependence of the
            electrophysiological features of SCs on dorsoventral position.</strong></p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Key statistical parameters from
          analyses of the relationship between each measured electrophysiological feature and
          dorsoventral location. The data are ordered according to the marginal R2 for each
          property’s relationship with dorsoventral position. Slope is the population slope from
          fitting a mixed effect model for each feature with location as a fixed effect (mm−1), with
          p(slope) obtained by comparing this model to a model without location as a fixed effect
          (χ2 test). For all properties except the spike thereshold, the slope was unlikely to have
          arisen by chance (p&lt;0.05). The marginal and conditional R2 values, and the minimum and
          maximum slopes across all mice, are obtained from the fits of mixed effect models that
          contain location as a fixed effect. The estimate p(vs linear) is obtained by comparing the
          mixed effect model containing location as a fixed effect with a corresponding linear model
          without random effects (χ2 test). The values of p(slope) and p(vs linear) were adjusted
          for multiple comparisons using the method of Benjamini and Hochberg (1995). Units for the
          slope measurements are units for the property mm−1. The data are from 27 mice.</p>
        <table itemscope="" itemtype="http://schema.org/Table">
          <thead>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Feature</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Slope</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">P (slope)</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Marginal R<sup
                  itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup></th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Conditional R<sup
                  itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup></th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Slope (min)</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Slope (max)</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">P (vs linear)</th>
            </tr>
          </thead>
          <tbody>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">IR (MΩ)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">11.794</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">8.39e-17</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.383</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.532</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">9.630</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">14.262</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">4.33e-40</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Rheobase (pA)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−119.887</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">9.07e-15</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.382</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.652</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−153.873</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−76.130</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.55e-43</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">I-F slope (Hz/pA)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.036</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.06e-10</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.228</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.561</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.019</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.087</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.82e-34</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Tm (ms)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">2.646</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">3.70e-12</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.192</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.343</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.809</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">3.979</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.20e-29</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Res. frequency (Hz)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−1.334</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">4.13e-09</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.122</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.553</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−2.299</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.342</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.37e-65</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Sag</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.033</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.06e-10</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.121</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.347</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.016</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.043</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.91e-38</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Spike maximum (mV)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.900</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.85e-05</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.064</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.436</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−1.288</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">3.297</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.14e-50</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Res. magnitude</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.114</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">6.34e-08</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.064</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.198</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.138</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.087</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">9.13e-20</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Vm (mV)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.884</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">3.67e-05</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.046</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.348</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−1.965</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.150</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">8.73e-35</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Spike AHP (mV)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.645</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.93e-02</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.011</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.257</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−1.828</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.408</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.82e-17</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Spike width (ms)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.017</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">1.93e-02</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.010</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.643</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−0.021</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.055</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">7.04e-139</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Spike threshold (mV)
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.082</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">8.20e-01</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.000</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">0.510</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">−2.468</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">2.380</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">2.03e-17</td>
            </tr>
          </tbody>
        </table>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="experience-dependence-of-intrinsic-properties-of-stellate-cells">Experience-dependence
          of intrinsic properties of stellate cells</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Because neuronal integrative
          properties may be modified by changes in neural activity (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib85">Zhang and Linden,
              2003</a></cite>), we asked whether experience influences the measured
          electrophysiological features of SCs. We reasoned that modifying the space through which
          animals can navigate may drive experience-dependent plasticity in the MEC. As standard
          mouse housing has dimensions less than the distance between the firing fields of more
          ventrally located grid cells (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib12">Brun et al., 2008</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib42">Hafting et
              al., 2005</a></cite>), in a standard home cage, only a relatively small fraction of
          ventral grid cells is likely to be activated, whereas larger housing should lead to
          the activation of a greater proportion of ventral grid cells. We therefore tested whether
          the electrophysiological features of SCs differ between mice housed in larger environments
          (28,800 cm<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>)
          and those with standard home cages (740 cm<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We compared the mixed models
          described above to models in which housing was also included as a fixed effect. To
          minimize the effects of age on SCs (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib10">Boehlen et al.,
              2010</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib16">Burton et al., 2008</a></cite><a href="#supp2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 2</a>), we focused these and
          subsequent analyses on mice between P33 and P44 (N = 25, n = 779). We found that larger
          housing was associated with a smaller sag coefficient, indicating an increased sag
          response, a lower resonant frequency and a larger spike half-width (adjusted p&lt;0.05; <a
            href="#fig4" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4E</a>, <a
            href="#supp3" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            3</a>). These differences were primarily from changes to the magnitude rather than the
          location-dependence of each feature. Other electrophysiological features appeared
          to be unaffected by housing.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To determine whether
          inter-animal differences remain after accounting for housing, we compared mixed models
          that include dorsoventral location and housing as fixed effects with equivalent linear
          regression models in which individual animals were not accounted for. Mixed models
          incorporating animal identity continued to provide a better account of the data, both for
          features that were dependent on housing (adjusted p&lt;2.8×10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−21</sup>) and for features that were not
          (adjusted p&lt;1.4×10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−7</sup>) (<a href="#supp4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 4</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Together, these data suggest
          that specific electrophysiological features of SCs may be modified by experience of large
          environments. After accounting for housing, significant inter-animal variation remains,
          suggesting that additional mechanisms acting at the level of animals rather than
          individual neurons also determine differences between SCs.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="inter-animal-differences-remain-after-accounting-for-additional-experimental-parameters">
          Inter-animal differences remain after accounting for additional experimental parameters
        </h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To address the possibility that
          other experimental or biological variables could contribute to inter-animal differences,
          we evaluated the effects of home cage size (<a href="#supp3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary files 3</a><a href="#supp4"
            itemscope="" itemtype="http://schema.stenci.la/Link">4</a>), brain hemisphere (<a
            href="#supp5" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            5</a>), mediolateral position (<a href="#fig4s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4—figure supplement 1</a> and <a
            href="#supp6" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            6</a>), the identity of the experimenter (<a href="#supp7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 7</a>) and time since slice
          preparation (<a href="#supp8" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary files 8</a> and <a href="#supp9"
            itemscope="" itemtype="http://schema.stenci.la/Link">9</a>). Several of the variables
          influenced some measured electrophysiological features, for example properties primarily
          related to the action potential waveform depended on the mediolateral position of the
          recorded neuron (<a href="#supp6" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 6</a><cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib18">Canto and Witter,
              2012</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib83">Yoshida et al., 2013</a></cite>), but significant inter-animal
          differences remained after accounting for each variable. We carried out further analyses
          using models that included housing, mediolateral position, experimenter identity and the
          direction in which sequential recordings were obtained as fixed effects (<a href="#supp10"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 10</a>),
          and using models fit to minimal datasets in which housing, mediolateral position and the
          recording direction were identical (<a href="#supp11" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 11</a>). These analyses again
          found evidence for significant inter-animal differences.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Inter-animal differences could
          arise if the health of the recorded neurons differed between brain slices. To minimize
          this possibility, we standardized our procedures for tissue preparation (see
          &#39;Materials and methods&#39;), such that slices were of consistent high quality as
          assessed by low numbers of unhealthy cells and by visualization of soma and dendrites of
          neurons in the slice. Several further observations are consistent with comparable quality
          of slices between experiments. First, if the condition of the slices had differed
          substantially between animals, then in better quality slices, it should be easier to
          record from more neurons, in which case features that depend on tissue quality would
          correlate with the number of recorded neurons. However, the majority (10/12) of
          the electrophysiological features were not significantly (p&gt;0.2) associated with the
          number of recorded neurons (<a href="#supp12" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 12</a>). Second, analyses of
          inter-animal differences that focus only on data from animals for which &gt;35 recordings
          were made, which should only be feasible with uniformly high-quality brain slices, are
          consistent with conclusions from analysis of the larger dataset (<a href="#supp13"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 13</a>). Third,
          the conditional R<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>
          values of electrophysiological features of L2PCs are much lower than those for SCs
          recorded under the same experimental conditions (<a href="#table1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Table 1</a> and <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>), suggesting that
          inter-animal variation may be specific to SCs and cannot be explained by slice conditions.
          Together, these analyses indicate that differences between animals remain after accounting
          for experimental and technical factors that might contribute to variation in the measured
          features of SCs.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="the-distribution-of-intrinsic-properties-is-consistent-with-a-continuous-rather-than-a-modular-organization">
          The distribution of intrinsic properties is consistent with a continuous rather than a
          modular organization</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The dorsoventral organization
          of SC integrative properties is well established, but whether this results from within
          animal variation consistent with a small number of discrete set points that underlie a
          modular organization (<a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1B</a>) is unclear. To evaluate
          modularity, we used datasets with n ≥ 34 SCs (N = 15 mice, median age = 37 days, age
          range = 18–43 days). We focus initially on rheobase, which is the property with the
          strongest correlation to dorsoventral location, and resonant frequency, which is related
          to the oscillatory dynamics underlying dorsoventral tuning in some models of grid firing
          (e.g. <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib14">Burgess
              et al., 2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib30">Giocomo et al., 2007</a></cite>). For n ≥ 34 SCs, we expect that if
          properties are modular, then this would be detected by the modified gap statistic in at
          least 50% of animals (<a href="#fig1s2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplements 2C</a> and <a
            href="#fig1s3" itemscope="" itemtype="http://schema.stenci.la/Link">3</a>). By contrast,
          we find that for datasets from the majority of animals, the modified gap statistic
          identifies only a single mode in the distribution of rheobase values (<a href="#fig5"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 5A</a> and <a href="#fig6"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 6</a>) (N = 13/15) and of
          resonant frequencies (<a href="#fig5" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 5B</a> and <a href="#fig6" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 6</a>) (N = 14/15), indicating that these
          properties have a continuous rather than a modular distribution. Consistent with this,
          smoothed distributions did not show clearly separated peaks for either property (<a
            href="#fig5" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 5</a>). The
          mean and 95% confidence interval for the probability of evaluating a dataset as clustered
          (p<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub>) was 0.133
          and 0.02–0.4 for rheobase and 0.067 and 0.002–0.32 for resonant frequency. These values of
          p<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> were not
          significantly different from the proportions expected given the false positive rate of 0.1
          in the complete absence of clustering (p=0.28 and 0.66, binomial test). Thus, the rheobase
          and resonant frequency of SCs, although depending strongly on a neuron’s dorsoventral
          position, do not have a detectable modular organization.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig5" title="Figure 5">
          <label data-itemprop="label">Figure 5</label><img src="index.html.media/fig5.jpg" alt=""
            itemscope="" itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="rheobase-and-resonant-frequency-do-not-have-a-detectable-modular-organization">
              Rheobase and resonant frequency do not have a detectable modular organization.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A, B</strong>) Rheobase (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>) and resonant
              frequency (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>)
              are plotted as a function of dorsoventral position separately for each animal. Marker
              color and type indicate the age and housing conditions of the animal (‘+’ standard
              housing, ‘x’ large housing). KSDs (arbitrary bandwidth, same for all animals) are also
              shown. The number of clusters in the data (k<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">est</sub>) is indicated for each
              animal (<span itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
                  class="mjx-chtml"><span class="mjx-math"
                    aria-label="{\displaystyle \hat{\mathrm{k}}}"><span class="mjx-mrow"
                      aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span
                            class="mjx-mstyle"><span class="mjx-mrow"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-munderover"><span class="mjx-stack"><span
                                        class="mjx-over"
                                        style="height: 0.213em; padding-bottom: 0.06em; padding-left: 0.014em;"><span
                                          class="mjx-mo" style="vertical-align: top;"><span
                                            class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.298em;">^</span></span></span><span
                                        class="mjx-op"><span class="mjx-texatom"><span
                                            class="mjx-mrow"><span class="mjx-mi"><span
                                                class="mjx-char MJXc-TeX-main-R"
                                                style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>).
            </p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig6" title="Figure 6">
          <label data-itemprop="label">Figure 6</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 25
#&#39; @height 10

# Note that reference data in GapData is generated through simulation. It was re-generated for the executable manuscript and so plots may look slightly different to the original manuscript. The conclusions are robust to the seeds for data generation. The reference data is loaded/generated with the setup code above (see block: &quot;Clustering Gap Data Setup&quot;).

# Evaluate the stellate cell (sc) data for k_est
fname &lt;- &quot;Data/datatable_sc.txt&quot;
sc_data &lt;-
  read_tsv(
    fname,
    col_types = cols(
      .default = &quot;d&quot;,
      mlpos = &quot;c&quot;,
      hemi = &quot;c&quot;,
      id = &quot;c&quot;,
      housing = &quot;c&quot;,
      expr = &quot;c&quot;,
      patchdir = &quot;c&quot;
    )
  )

sc_data_long &lt;-
  sc_data %&gt;% filter(totalcells &gt;= 30) %&gt;% select(property_names, id, dvloc) %&gt;% gather(key =
                                                                                          &quot;property&quot;,
                                                                                        value = &quot;measurement&quot;,
                                                                                        property_names,
                                                                                        na.rm = TRUE)

# Initialise list to store tibbles for cluster evaluation of each combination of animal
# and measured property
sc_cluster_data_list &lt;- list()
list_ind &lt;- 0L # To track the list index inside the double loop

for (m in unique(sc_data_long$id)) {
  for (p in property_names) {
    # The data for one measured property for a single animal
    data &lt;- sc_data_long %&gt;% filter(id == m, property == p)
    
    # Use the fitted parameters to obtain thresholds and dispersions. Note that where there
    # are measurement NAs in the original data, they will have already been removed, so the
    # fits are for the right dataset size.
    thresholds &lt;- get_thresh_from_params(data, k.max,
                                         threshold_fit_results$thresh_params[[1]])
    dispersions &lt;- get_dispersions_from_params(data, k.max,
                                               dispersion_fit_results$dispersion_params[[1]])
    
    # The clustering evaluation outputs
    cluster_out &lt;-
      get_k_est(
        data$measurement,
        kmeans,
        iter.max = iter.max,
        nstart = nstart,
        K.max = k.max,
        B = NULL,
        d.power = d.power,
        thresholds = thresholds,
        dispersions = dispersions
      )
    
    # Construct tibble that combines cluster evaluation output with other data in long format
    list_ind &lt;- list_ind + 1 # Increment list index counter
    dimnames(cluster_out$cluster)[[2]] &lt;-
      as.integer(1:k.max) # to set &#39;as.tibble()&#39; behaviour
    sc_cluster_data_list[[list_ind]] &lt;-
      as.tibble(cluster_out$cluster) %&gt;% bind_cols(data) %&gt;%
      mutate(k_est = rep(cluster_out$k_est, nrow(cluster_out$cluster))) %&gt;%
      gather(key = &quot;k_eval&quot;,
             value = &quot;cluster&quot;,
             dimnames(cluster_out$cluster)[[2]])
  }
}
# Aggregated data in long format. Most granular level is single measurement cluster membership
# for a specified k. This is the main input to further SC data analyses.
sc_cluster_data_long &lt;- bind_rows(sc_cluster_data_list) %&gt;%
  mutate(k_eval = as.integer(k_eval), cluster = as.factor(cluster)) %&gt;% # Change class for plotting
  mutate(prop_type = case_when(property %in% props_subthresh ~ &quot;subthr&quot;, TRUE ~ &quot;suprathr&quot;))

# Plot k_est counts for subthreshold and suprathreshold properties
(
  clusters_a &lt;-
    sc_cluster_data_long %&gt;% filter(prop_type == &quot;subthr&quot;) %&gt;% distinct(id, property, k_est) %&gt;%
    ggplot() + geom_bar(aes(x = k_est)) +
    facet_wrap(
      vars(property),
      ncol = 6,
      labeller = as_labeller(props_sub_labels)
    ) +
    labs(y = &quot;Count&quot;, x = &quot; &quot;) +
    scale_x_continuous(
      labels = c(rep(&quot; &quot;, k.max)),
      breaks = 1:k.max,
      limits = c(0.5, k.max + 0.5)
    )
)

# Required Figure 6A to gave been generated first
(
  clusters_b &lt;-
    sc_cluster_data_long %&gt;% filter(prop_type == &quot;suprathr&quot;) %&gt;%
    distinct(id, property, k_est) %&gt;%
    ggplot() + geom_bar(aes(x = k_est)) +
    facet_wrap(
      vars(property),
      ncol = 6,
      labeller = as_labeller(props_supra_labels)
    ) +
    labs(
      x = bquote( ~ &quot;Estimated number of clusters, &quot; ~ k[est]),
      y = &quot;Count&quot;
    ) +
    scale_x_continuous(
      labels = c(&quot;1&quot;, rep(&quot;&quot;, k.max - 2), toString(k.max)),
      breaks = 1:k.max,
      limits = c(0.5, k.max + 0.5)
    )
)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="significant-modularity-is-not-detectable-for-any-measured-property">Significant
              modularity is not detectable for any measured property.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A, B</strong>) Histograms showing the
              k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est </sub>(<span
                itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
                  class="mjx-chtml"><span class="mjx-math"
                    aria-label="{\displaystyle \hat{\mathrm{k}}}"><span class="mjx-mrow"
                      aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span
                            class="mjx-mstyle"><span class="mjx-mrow"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-munderover"><span class="mjx-stack"><span
                                        class="mjx-over"
                                        style="height: 0.213em; padding-bottom: 0.06em; padding-left: 0.014em;"><span
                                          class="mjx-mo" style="vertical-align: top;"><span
                                            class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.298em;">^</span></span></span><span
                                        class="mjx-op"><span class="mjx-texatom"><span
                                            class="mjx-mrow"><span class="mjx-mi"><span
                                                class="mjx-char MJXc-TeX-main-R"
                                                style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) counts
              across all mice for each different measured sub-threshold (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) and supra-threshold (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) intrinsic
              property. The maximum k evaluated was 8. The proportion of each measured property with
              k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub>&gt;1 was
              compared using binomial tests (with N = 15) to the proportion expected if the
              underlying distribution of that property is always clustered with all separation
              between modes ≥5 standard deviations (pink text), or if the underlying distribution of
              the property is uniform (purple text). For all measured properties, the values of
              k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> (<span
                itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
                  class="mjx-chtml"><span class="mjx-math"
                    aria-label="{\displaystyle \hat{\mathrm{k}}}"><span class="mjx-mrow"
                      aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span
                            class="mjx-mstyle"><span class="mjx-mrow"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-munderover"><span class="mjx-stack"><span
                                        class="mjx-over"
                                        style="height: 0.213em; padding-bottom: 0.06em; padding-left: 0.014em;"><span
                                          class="mjx-mo" style="vertical-align: top;"><span
                                            class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.298em;">^</span></span></span><span
                                        class="mjx-op"><span class="mjx-texatom"><span
                                            class="mjx-mrow"><span class="mjx-mi"><span
                                                class="mjx-char MJXc-TeX-main-R"
                                                style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) were
              indistinguishable (p&gt;0.05) from the data generated from a uniform distribution and
              differed from the data generated from a multi-modal distribution (p&lt;1×10<sup
                itemscope="" itemtype="http://schema.stenci.la/Superscript">−6</sup>).</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">When we investigated the other
          measured integrative properties, we also failed to find evidence for modularity. Across
          all properties, for any given property, at most 3 out of 15 mice were evaluated as having
          a clustered organization using the modified gap statistic (<a href="#fig6" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 6</a>). This does not differ
          significantly from the proportion expected by chance when no modularity is present
          (p&gt;0.05, binomial test). Consistent with this, the average proportion of datasets
          evaluated as modular across all measured features was 0.072 ± 0.02 (± SEM), which is
          similar to the expected false-positive rate. By contrast, the properties of grid firing
          fields previously recorded with tetrodes in behaving animals (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>) were detected as having a modular organization using the modified gap
          statistic (<a href="#fig1s5" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            1—figure supplement 5</a>). For seven grid-cell datasets with n ≥ 20, the mean for p<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">detect</sub> is 0.86, with 95%
          confidence intervals of 0.42 to 0.996. We note here that discontinuity algorithms that
          were previously used to assess the modularity of grid field properties (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib32">Giocomo et al.,
              2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib71">Stensola et al., 2012</a></cite>) did indicate significant modularity in
          the majority of the intrinsic properties measured in our dataset (N = 13/15 and N = 12/15,
          respectively), but this was attributable to false positives resulting from the relatively
          even sampling of recording locations (see <a href="#fig1s4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 4A</a>). Therefore,
          we conclude that it is unlikely that any of the intrinsic integrative properties of SCs
          that we examined have organization within individual animals resembling the modular
          organization of grid cells in behaving animals.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="multiple-sources-of-variance-contribute-to-diversity-in-stellate-cell-intrinsic-properties">
          Multiple sources of variance contribute to diversity in stellate cell intrinsic properties
        </h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Finally, because many of the
          measured electrophysiological features of SCs emerge from shared ionic mechanisms (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib21">Dodson et al.,
              2011</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib28">Garden et al., 2008</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib58">Pastoll et al.,
              2012</a></cite>), we asked whether dorsoventral tuning reflects a single core
          mechanism and whether inter-animal differences are specific to this mechanism or manifest
          more generally.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Estimation of conditional
          independence for measurements at the level of individual neurons (<a href="#fig7"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 7A</a>) or individual
          animals (<a href="#fig7" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            7B</a>) was consistent with the expectation that particular classes of membrane ion
          channels influence multiple electrophysiologically measured features. The first five
          dimensions of a principal components analysis (PCA) of all measured electrophysiological
          features accounted for almost 80% of the variance (<a href="#fig7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 7C</a>). Examination of the rotations
          used to generate the principal components suggested relationships between individual
          features that are consistent with our evaluation of the conditional independence structure
          of the measured features (<a href="#fig7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 7D and A</a>). When we fit the principal
          components using mixed models with location as a fixed effect and animal identity as a
          random effect, we found that the first two components depended significantly on
          dorsoventral location (<a href="#fig7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 7E</a> and <a href="#supp14" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 14</a>) (marginal R<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup> = 0.50 and 0.09 and
          adjusted p=1.09×10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−15</sup> and 1.05 × 10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−4</sup>, respectively). Thus, the
          dependence of multiple electrophysiological features on dorsoventral position may be
          reducible to two core mechanisms that together account for much of the variability between
          SCs in their intrinsic electrophysiology.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7a" title="Figure 7A">
          <label data-itemprop="label">Figure 7A</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 8
#&#39; @height 8

data.sc_neurons &lt;- data.sc %&gt;% dplyr::select(vm:fi) %&gt;%
  na.omit
Q_neurons &lt;- calcQ(data.sc_neurons)

Q_neurons &lt;- as.matrix(Q_neurons)
colnames(Q_neurons) &lt;- colnames(data.sc_neurons)
rownames(Q_neurons) &lt;- colnames(data.sc_neurons)

order_names &lt;-
  c(
    &quot;vm&quot;,
    &quot;ir&quot;,
    &quot;sag&quot;,
    &quot;tau&quot;,
    &quot;resf&quot;,
    &quot;resmag&quot;,
    &quot;rheo&quot;,
    &quot;fi&quot;,
    &quot;ahp&quot;,
    &quot;spkmax&quot;,
    &quot;spkthr&quot;,
    &quot;spkhlf&quot;
  )

Q_neurons &lt;-
  Q_neurons[match(order_names, rownames(Q_neurons)), match(order_names, colnames(Q_neurons))]

new_names &lt;-
  c(&quot;Vm&quot;,
    &quot;IR&quot;,
    &quot;Sag&quot;,
    &quot;Tm&quot;,
    &quot;ResF&quot;,
    &quot;ResM&quot;,
    &quot;Rheo&quot;,
    &quot;F-I&quot;,
    &quot;AHP&quot;,
    &quot;Smax&quot;,
    &quot;Sthr&quot;,
    &quot;SHW&quot;)

colnames(Q_neurons) &lt;- new_names
rownames(Q_neurons) &lt;- new_names

(
  Q_neurons_plot &lt;-
    ggcorr(
      data = NULL,
      cor_matrix = Q_neurons,
      geom = &quot;circle&quot;,
      min_size = 0,
      max_size = 5,
      legend.size = 7,
      size = 2
    )
)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Partial correlations between
              the electrophysiological features investigated at the level of individual
              neurons. Partial correlations outside of the 95% basic bootstrap confidence intervals
              are color coded. Non-significant correlations are colored white. Properties shown are
              the resting membrane potential (Vm), input resistance (IR), membrane potential sag
              response (sag), membrane time constant (Tm), resonance frequency (Rm), resonance
              magnitude (Rm), rheobase (Rheo), slope of the current frequency relationship (FI),
              peak of the action potential after hyperpolarization (AHP), peak of the action
              potential (Smax) voltage threshold for the action potential (Sthr) and half-width of
              the action potential (SHW).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7b" title="Figure 7B">
          <label data-itemprop="label">Figure 7B</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 8
#&#39; @height 8

data_summary.mm_vsris &lt;- prep_int_slopes_PCA(data.sc_r, &quot;property&quot;, &quot;mm_vsris&quot;)

data_intercepts &lt;-  spread(data_summary.mm_vsris[,1:3], property, ind_intercept)
data_slopes &lt;-  spread(data_summary.mm_vsris[,c(1:2, 4)], property, ind_slope)


data.sc_fits &lt;- data_intercepts %&gt;% dplyr::select(ahp:vm) %&gt;%
  na.omit

Q_intercepts &lt;- calcQ(data.sc_fits)

Q_intercepts &lt;- as.matrix(Q_intercepts)
colnames(Q_intercepts) &lt;- colnames(data.sc_fits)
rownames(Q_intercepts) &lt;- colnames(data.sc_fits)

Q_intercepts &lt;- Q_intercepts[match(order_names, rownames(Q_intercepts)), match(order_names, colnames(Q_intercepts))]

colnames(Q_intercepts) &lt;- new_names
rownames(Q_intercepts) &lt;- new_names

(Q_intercepts_plot &lt;- ggcorr(data = NULL, cor_matrix = Q_intercepts, geom = &quot;circle&quot;, min_size = 0, max_size = 5, legend.size = 7, size = 2))
</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data-1">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Partial correlations between
              the electrophysiological features investigated at the level of animals. Partial
              correlations outside of the 95% basic bootstrap confidence intervals are color coded.
              Non-significant correlations are colored white. Properties shown are the resting
              membrane potential (Vm), input resistance (IR), membrane potential sag response (sag),
              membrane time constant (Tm), resonance frequency (Rm), resonance magnitude (Rm),
              rheobase (Rheo), slope of the current frequency relationship (FI), peak of the action
              potential after hyperpolarization (AHP), peak of the action potential (Smax) voltage
              threshold for the action potential (Sthr) and half-width of the action potential
              (SHW).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7c" title="Figure 7C">
          <label data-itemprop="label">Figure 7C</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 8
#&#39; @height 8

data.pca &lt;- dplyr::select(data.sc, vm:fi, dvlocmm, id, housing, id, mlpos, hemi, sex, age, housing, expr, patchdir, rectime) %&gt;%
  filter(age &gt; 32 &amp; age &lt;45 &amp; expr == &quot;HP&quot;)

all.pca &lt;- prcomp(drop_na(data.pca[1:12], fi),
                  retx = TRUE,
                  scale = TRUE)

prop.var.df &lt;- as.data.frame(summary(all.pca)$importance[2,])
colnames(prop.var.df) &lt;- c(&quot;PropVar&quot;)
prop.var.df$components &lt;- 1:12
(all.pca.prop.var.plot &lt;- ggplot(prop.var.df, aes(components, PropVar)) +
  geom_bar(stat = &quot;identity&quot;) +
  scale_x_discrete(&quot;Component&quot;) +
  ylab(&quot;Proportion of variance&quot;) +
    theme(title = element_text(size = 9), axis.text = element_text(size = 9)))</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data-2">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) Proportion of variance
              explained by each principal component. To remove variance caused by animal age and the
              experimenter identity, the principal component analysis used a reduced dataset
              obtained by one experimenter and restricted to animals between 32 and 45 days old
              (N = 25, n = 572).</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7d" title="Figure 7D">
          <label data-itemprop="label">Figure 7D</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 8
#&#39; @height 8

# Requires Figure 7C to have been generated.
(all.pca.biplot &lt;- pca_biplot(as.data.frame(all.pca$rotation), fontsize = 2, order_names = order_names, new_names = c(&quot;Vm&quot;, &quot;IR&quot;, &quot;Sag&quot;, &quot;Tm&quot;, &quot;Res. F&quot;, &quot;Res. Mag.&quot;, &quot;Rheo&quot;, &quot;FI&quot;, &quot;AHPmax&quot;, &quot;Spk. max&quot;, &quot;Spk. thr&quot;, &quot;Spk. HW&quot;)) +
    theme(text = element_text(size = 9)) +
    xlim(-0.5, 0.55))</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data-3">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>) Loading plot for the first two
              principal components.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7e" title="Figure 7E">
          <label data-itemprop="label">Figure 7E</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 13
#&#39; @height 7

all.pca.x &lt;- bind_cols(as_tibble(all.pca$x), drop_na(data.pca, fi))

out.pca.x_g1_5 &lt;- all.pca.x %&gt;%
  gather(&quot;component&quot;, &quot;value&quot;, 1:5)
(
  pc1to5_plot &lt;-
    ggplot(data = out.pca.x_g1_5, aes(
      x = dvlocmm, y = value, colour = housing
    )) +
    geom_point(alpha = 0.5) +
    facet_wrap(~ component, ncol = 5) +
    scale_x_continuous(&quot;DV location (mm)&quot;, c(0, 1, 2)) +
    theme_classic() +
    PCA_theme +
    theme(legend.position = &quot;bottom&quot;)
)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data-4">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">E</strong>) The first five principal
              components plotted as a function of position. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">F</strong>) Intercept (I), intercept plus
              the slope (I + S) and slopes aligned to the same intercept, for fits for each animal
              of the first five principal components to a mixed model with location as a fixed
              effect and animal as a random effect.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7f" title="Figure 7F">
          <label data-itemprop="label">Figure 7F</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 13
#&#39; @height 6

# Reform data for use with dplyr.
out.pca.x_g &lt;- all.pca.x %&gt;%
  gather(&quot;component&quot;, &quot;value&quot;, 1:12) %&gt;%
  group_by(component) %&gt;%
  nest() %&gt;%
  ungroup()

# Fit models
out.pca.x_g &lt;- out.pca.x_g %&gt;%
  mutate(mixedmodel_vsris = map(data, model_vsris)) %&gt;%
  mutate(mixedmodel_vsris_null = map(data, model_vsris_null))

# Extract summary data from the fit
out.pca.x_g &lt;- out.pca.x_g %&gt;%
  mutate(vsris_glance = map(mixedmodel_vsris, broom::glance)) %&gt;%
  mutate(vsris_null_glance = map(mixedmodel_vsris_null, broom::glance))

# Preparation for making the figure
combined_intercepts_slopes_PCA &lt;-
  prep_int_slopes(out.pca.x_g, &quot;component&quot;, &quot;mixedmodel_vsris&quot;)

id_housing_PCA &lt;-  distinct(all.pca.x, id, housing)

combined_intercepts_slopes_PCA &lt;-
  left_join(combined_intercepts_slopes_PCA, id_housing_PCA, by = &quot;id&quot;)

combined_intercepts_slopes_PCA$component_factors &lt;-
  as.factor(combined_intercepts_slopes_PCA$component)

combined_intercepts_slopes_PCA$component_factors = factor(
  combined_intercepts_slopes_PCA$component_factors,
  c(
    &quot;PC1&quot;,
    &quot;PC2&quot;,
    &quot;PC3&quot;,
    &quot;PC4&quot;,
    &quot;PC5&quot;,
    &quot;PC6&quot;,
    &quot;PC7&quot;,
    &quot;PC8&quot;,
    &quot;PC9&quot;,
    &quot;PC10&quot;,
    &quot;PC11&quot;
  )
)

# Plot the figure
print(
  ggplot(
    subset(
      combined_intercepts_slopes_PCA,
      component %in% c(&quot;PC1&quot;, &quot;PC2&quot;, &quot;PC3&quot;, &quot;PC4&quot;, &quot;PC5&quot;)
    ),
    aes(x = measure, y = value_1, colour = housing)
  ) +
  geom_line(aes(group = id)) +
  geom_jitter(aes(y = value_2), width = 0.2) +
  scale_x_discrete(
    limits = c(
      &quot;ind_intercept&quot;,
      &quot;ind_intercept_slope&quot;,
      &quot;global_intercept&quot;,
      &quot;global_intercept_slope&quot;
    ),
    label = c(&quot;I&quot;, &quot;I + S&quot;, &quot;&quot;, &quot;&quot;)
  ) +
  facet_wrap( ~ component_factors, ncol = 5) +
  theme_classic() +
  hist_theme +
  theme(
    axis.line.x = element_blank(),
    axis.ticks.x = element_blank(),
    axis.text.x = element_text(angle = 90)
  ) +
  theme(legend.position = &quot;none&quot;)
)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="feature-relationships-and-inter-animal-variability-after-reducing-dimensionality-of-the-data-5">
              Feature relationships and inter-animal variability after reducing dimensionality of
              the data.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">F</strong>) Intercept (I), intercept plus
              the slope (I + S) and slopes aligned to the same intercept, for fits for each animal
              of the first five principal components to a mixed model with location as a fixed
              effect and animal as a random effect.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Is inter-animal variation
          present in PCA dimensions that account for dorsoventral variation? The intercept, but not
          the slope of the dependence of the first two principal components on dorsoventral position
          depended on housing (adjusted p=0.039 and 0.027) (<a href="#fig7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 7E,F</a> and <a href="#supp15"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 15</a>). After
          accounting for housing, the first two principal components were still better fit by models
          that include animal identity as a random effect (adjusted p=3.3×10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−9</sup> and 4.1 × 10<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−86</sup>), indicating remaining
          inter-animal differences in these components (<a href="#supp16" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 16</a>). A further nine of
          the next ten higher-order principal components did not depend on housing (adjusted
          p&gt;0.1) (<a href="#supp15" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 15</a>), while eight differed
          significantly between animals (adjusted p&lt;0.05) (<a href="#supp16" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 16</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Together, these analyses
          indicate that the dorsoventral organization of multiple electrophysiological features of
          SCs is captured by two principal components, suggesting two main sources of variance, both
          of which are dependent on experience. Significant inter-animal variation in the major
          sources of variance remains after accounting for experience and experimental parameters.
        </p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="discussion">Discussion</h2>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Phenotypic variation is found
          across many areas of biology (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib29">Geiler-Samerotte et al.,
              2013</a></cite>), but has received little attention in investigations of mammalian
          nervous systems. We find unexpected inter-animal variability in SC properties, suggesting
          that the integrative properties of neurons are determined by set points that differ
          between animals and are controlled at a circuit level (<a href="#fig8" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 8</a>). Continuous, location-dependent
          organization of set points for SC integrative properties provides new constraints on
          models for grid cell firing. More generally, the existence of inter-animal differences in
          set points has implications for experimental design and raises new questions about how
          the integrative properties of neurons are specified.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig8" title="Figure 8">
          <label data-itemprop="label">Figure 8</label><img src="index.html.media/fig8.jpg" alt=""
            itemscope="" itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="models-for-intra--and-inter-animal-variation">Models for intra- and inter-animal
              variation.</h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) The configuration of a cell
              type can be conceived of as a trough (arrow head) in a developmental landscape (solid
              line). In this scheme, the trough can be considered as a set point. Differences
              between cells (filled circles) reflect variation away from the set point. (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) Neurons from
              different animals or located at different dorsoventral positions can be conceptualized
              as arising from different troughs in the developmental landscape. (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">C</strong>) Variation may
              reflect inter-animal differences in factors that establish gradients (upper left) and
              in factors that are uniformly distributed (lower left), combining to generate set
              points that depend on animal identity and location (right). Each line corresponds to
              schematized properties of a single animal.</p>
          </figcaption>
        </figure>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="a-conceptual-framework-for-within-cell-type-variability">A conceptual framework for
          within cell type variability</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Theoretical models suggest how
          different cell types can be generated by varying target concentrations of intracellular
          Ca<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2+</sup> or rates of
          ion channel expression (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib56">O'Leary et al., 2014</a></cite>). The within cell type variability
          predicted by these models arises from different initial conditions and may explain
          the variability in our data between neurons from the same animal at the same dorsoventral
          location (<a href="#fig8" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            8A</a>). By contrast, the dependence of integrative properties on position and their
          variation between animals implies additional mechanisms that operate at the circuit level
          (<a href="#fig8" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 8B</a>). In
          principle, this variation could be accounted for by inter-animal differences in
          dorsoventrally tuned or spatially uniform factors that influence ion channel expression or
          target points for intracellular Ca<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2+</sup> (<a href="#fig8" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 8C</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The mechanisms for within cell
          type variability that are suggested by our results may differ from inter-animal variation
          described in invertebrate nervous systems. In invertebrates, inter-animal variability is
          between properties of individual identified neurons (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib36">Goaillard et al.,
              2009</a></cite>), whereas in mammalian nervous systems, neurons are not individually
          identifiable and the variation that we describe here is at the level of cell populations.
          From a developmental perspective in which cell identity is considered as a trough in a
          state-landscape through which each cell moves (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib79">Wang et al., 2011</a></cite>),
          variation in the population of neurons of the same type could be conceived as cell
          autonomous deviations from set points corresponding to the trough (<a href="#fig8"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 8A</a>). Our finding that
          variability among neurons of the same type manifests between as well as within animals,
          could be explained by differences between animals in the position of the trough or set
          point in the developmental landscape (<a href="#fig8" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 8B</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Our comparison of neurons from
          animals in standard and large cages provides evidence for the idea that within cell-type
          excitable properties are modified by experience (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib85">Zhang and Linden,
              2003</a></cite>). For example, granule cells in the dentate gyrus that receive input
          from SCs increase their excitability when animals are housed in enriched environments
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib38">Green and
              Greenough, 1986</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib57">Ohline and Abraham,
              2019</a></cite>). Our experiments differ in that we increased the size of the
          environment with the goal of activating more ventral grid cells, whereas previous
          enrichment experiments have focused on increasing the environmental complexity and
          availability of objects for exploration. Further investigation will be required to
          dissociate the influence of each factor on excitability.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="implications-of-continuous-dorsoventral-organization-of-stellate-cell-integrative-properties-for-grid-cell-firing">
          Implications of continuous dorsoventral organization of stellate cell integrative
          properties for grid cell firing</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Dorsoventral gradients
          in the electrophysiological features of SCs have stimulated cellular models for the
          organization of grid firing (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib15">Burgess, 2008</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib34">Giocomo and Hasselmo,
              2008</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib39">Grossberg and Pilly, 2012</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib55">O'Donnell and Nolan,
              2011</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib81">Widloski and Fiete, 2014</a></cite>). Increases in spatial scale
          following deletion of HCN1 channels (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib31">Giocomo et al.,
              2011</a></cite>), which in part determine the dorsoventral organization of SC
          integrative properties (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib28">Garden et al., 2008</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib35">Giocomo and Hasselmo,
              2009</a></cite>), support a relationship between the electrophysiological properties
          of SCs and grid cell spatial scales. Our data argue against models that explain this
          relationship through single cell computations (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib15">Burgess, 2008</a></cite>; <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib14">Burgess et al.,
              2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib30">Giocomo et al., 2007</a></cite>), as in this case, the modularity of
          integrative properties of SCs is required to generate modularity of grid firing. A
          continuous dorsoventral organization of the electrophysiological properties of SCs could
          support the modular grid firing generated by self-organizing maps (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib39">Grossberg and Pilly,
              2012</a></cite>) or by synaptic learning mechanisms (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib45">Kropff and Treves,
              2008</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib76">Urdapilleta et al., 2017</a></cite>). It is less clear how a continuous
          gradient would affect the organization of grid firing predicted by continuous attractor
          network models, which can instead account for modularity by limiting synaptic interactions
          between modules (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib13">Burak and Fiete, 2009</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib17">Bush and Burgess,
              2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib26">Fuhs and Touretzky, 2006</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib41">Guanella et al.,
              2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib70">Shipston-Sharman et al., 2016</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib81">Widloski and Fiete,
              2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib82">Yoon et al., 2013</a></cite>). Modularity of grid cell firing could also
          arise through the anatomical clustering of calbindin-positive L2PCs (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib63">Ray et al., 2014</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib64">Ray and
              Brecht, 2016</a></cite>). Because many SCs do not appear to generate grid codes and as
          the most abundant functional cell type in the MEC appears to be non-grid spatial neurons
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib20">Diehl et al.,
              2017</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib43">Hardcastle et al., 2017</a></cite>), the continuous dorsoventral
          organization of SC integrative properties may also impact grid firing indirectly through
          modulation of these codes.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Our results add to previous
          comparisons of medially and laterally located SCs (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib18">Canto and Witter,
              2012</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib83">Yoshida et al., 2013</a></cite>). The similar dorsoventral organization
          of subthreshold integrative properties of SCs from medial and lateral parts of the MEC
          appears consistent with the organization of grid cell modules recorded in behaving animals
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et
              al., 2012</a></cite>). How mediolateral differences in firing properties (<a
            href="#fig4s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4—figure
            supplement 1</a>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib18">Canto and Witter, 2012</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib83">Yoshida et al.,
              2013</a></cite>) might contribute to spatial computations within the MEC is unclear.
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The continuous dorsoventral
          variation of the electrophysiological features of SCs suggested by our analysis is
          consistent with continuous dorsoventral gradients in gene expression along layer 2 of the
          MEC (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib62">Ramsden
              et al., 2015</a></cite>). For example, labelling of the mRNA and protein for the HCN1
          ion channel suggests a continuous dorsoventral gradient in its expression (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib53">Nolan et al.,
              2007</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib62">Ramsden et al., 2015</a></cite>). It is also consistent with single-cell
          RNA sequencing analysis of other brain areas, which indicates that although the expression
          profiles for some cell types cluster around a point in feature space, others lie along a
          continuum (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib19">Cembrowski and Menon, 2018</a></cite>). It will be interesting in future
          to determine whether gene expression continua establish corresponding continua of
          electrophysiological features (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib47">Liss et al., 2001</a></cite>).
        </p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="functional-consequences-of-within-cell-type-inter-animal-variability">Functional
          consequences of within cell type inter-animal variability</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">What are the functional roles
          of inter-animal variability? In the crab stomatogastric ganglion, inter-animal variation
          correlates with circuit performance (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib36">Goaillard et al.,
              2009</a></cite>). Accordingly, variation in intrinsic properties of SCs might
          correlate with differences in grid firing (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib22">Domnisoru et al.,
              2013</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib40">Gu et al., 2018</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib66">Rowland et al.,
              2018</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib68">Schmidt-Hieber and Häusser, 2013</a></cite>) or behaviors that rely on
          SCs (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib44">Kitamura
              et al., 2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib61">Qin et al., 2018</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib74">Tennant et al.,
              2018</a></cite>). It is interesting in this respect that there appear to be
          inter-animal differences in the spatial scale of grid modules (Figure 5 of <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>). Modification of grid field scaling following deletion of HCN1
          channels is also consistent with this possibility (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib31">Giocomo et al.,
              2011</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib48">Mallory et al., 2018</a></cite>). Alternatively, inter-animal
          differences may reflect multiple ways to achieve a common higher-order phenotype.
          According to this view, coding of spatial location by SCs would not differ between animals
          despite lower level variation in their intrinsic electrophysiological features. This is
          related to the idea of degeneracy at the level of single-cell electrophysiological
          properties (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib49">Marder and Goaillard, 2006</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib51">Mittal and Narayanan,
              2018</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib56">O'Leary et al., 2014</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib73">Swensen and Bean,
              2005</a></cite>), except that here the electrophysiological features differ between
          animals whereas the higher-order circuit computations may nevertheless be similar.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In conclusion, our results
          identify substantial within cell type variation in neuronal integrative properties that
          manifests between as well as within animals. This has implications for experimental design
          and model building as the distribution of replicates from the same animal will differ from
          those obtained from different animals (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib50">Marder and Taylor,
              2011</a></cite>). An important future goal will be to distinguish causes of
          inter-animal variation. Many behaviors are characterized by substantial inter-animal
          variation (e.g. <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib77">Villette et al., 2017</a></cite>), which could result from variation in
          neuronal integrative properties, or could drive this variation. For example, it is
          possible that external factors such as social interactions may affect brain circuitry
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib78">Wang et al.,
              2011</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib80">Wang et al., 2014</a></cite>), although these effects appear to be
          focused on frontal cortical structures rather than circuits for spatial computations
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib80">Wang et al.,
              2014</a></cite>). Alternatively, stochastic mechanisms operating at the population
          level may drive the emergence of inter-animal differences during the development of SCs
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib23">Donato et
              al., 2017</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64">Ray and Brecht, 2016</a></cite>). Addressing these questions may turn
          out to be critical to understanding the relationship between cellular biophysics and
          circuit-level computations in cognitive circuits (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib69">Schmidt-Hieber and Nolan,
              2017</a></cite>).</p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="materials-and-methods">
          Materials and methods</h2>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading" id="mouse-strains">Mouse strains
        </h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">All experimental procedures
          were performed under a United Kingdom Home Office license and with approval of the
          University of Edinburgh’s animal welfare committee. Recordings of many SCs per animal used
          C57Bl/6J mice (Charles River). Recordings targeting calbindin cells used a <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Wfs1</em><sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">Cre</sup> line (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Wfs1</em>-Tg3-CreERT2) obtained from Jackson
          Labs (Strain name: B6;C3-Tg(<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Wfs1</em>-cre/ERT2)3Aibs/J; stock
          number:009103) crossed to RCE:loxP (R26R CAG-boosted EGFP) reporter mice (described in
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib52">Miyoshi et
              al., 2010</a></cite>). To promote expression of Cre in the mice, tamoxifen (Sigma, 20
          mg/ml in corn oil) was administered on three consecutive days by intraperitoneal
          injections, approximately 1 week before experiments. Mice were group housed in a 12 hr
          light/dark cycle with unrestricted access to food and water (light on 07.30–19.30 hr).
          Mice were usually housed in standard 0.2 × 0.37 m cages that contained a cardboard roll
          for enrichment. A subset of the mice was instead housed from pre-weaning ages in a larger
          2.4 × 1.2 m cage that was enriched with up to 15 bright plastic objects and
          eight cardboard rolls (<a href="#fig2s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2—figure supplement 1</a>). Thus, the
          large cages had more items but at a slightly lower density (large cages — up to 1 item per
          0.125 m<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>; standard
          cages — 1 item per 0.074 m<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup>). All experiments in the standard
          cage used male mice. For experiments in the large cage, two mice were female, six mice
          were male and one was not identified. Because we did not find significant effects of sex
          on individual electrophysiologically properties, all mice were included in the analyses
          reported in the text. When only male mice were included, the effects of housing on the
          first principal component remained significant, whereas the effects of housing on
          individual electrophysiologically properties no longer reach statistical significance
          after correcting for multiple comparisons. Additional analyses that consider only male
          mice are provided in the code associated with the manuscript.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading" id="slice-preparation">Slice
          preparation</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Methods for preparation of
          parasagittal brain slices containing medial entorhinal cortex were based on procedures
          described previously (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib59">Pastoll et al., 2012</a></cite>). Briefly, mice were sacrificed by
          cervical dislocation and their brains carefully removed and placed in cold (2–4°C)
          modified ACSF, with composition (in mM): NaCl 86, NaH<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">2</sub>PO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">4</sub> 1.2, KCl 2.5, NaHCO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">3</sub> 25, glucose 25,
          sucrose 75, CaCl<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">2</sub>
          0.5, and MgCl<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">2</sub> 7.
          Brains were then hemisected and sectioned, also in modified ACSF at 4–8°C, using a
          vibratome (Leica VT1200S). To minimize variation in the slicing angle, the hemi-section
          was cut along the midline of the brain and the cut surface of the brain was glued to the
          cutting block. After cutting, brains were placed at 36°C for 30 min in standard ACSF, with
          composition (in mM): NaCl 124, NaH<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">2</sub>PO4 1.2, KCl 2.5, NaHCO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">3</sub> 25, glucose 20,
          CaCl<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">2</sub> 2, and MgCl<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">2</sub> 1. They were then
          allowed to cool passively to room temperature. All slices were prepared by the same
          experimenter (HP), who followed the same procedure on each day.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading" id="recording-methods">Recording
          methods</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Whole-cell patch-clamp
          recordings were made between 1 to 10 hr after slice preparation using procedures described
          previously (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib60">Pastoll et al., 2013</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib58">Pastoll et al.,
              2012</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib59">Pastoll et al., 2012</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib72">Sürmeli et al.,
              2015</a></cite>). Recordings were made from slice perfused in standard ACSF maintained
          at 34–36°C. In these conditions, we observe spontaneous fast inhibitory and excitatory
          postsynaptic potentials, but do not find evidence for tonic GABAergic or glutamatergic
          currents. Patch electrodes were filled with the following intracellular solution (in mM):
          K gluconate 130; KCl 10, HEPES 10, MgCl<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">2</sub> 2, EGTA 0.1, Na<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">2</sub>ATP 2, Na<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">2</sub>GTP 0.3 and NaPhosphocreatine 10.
          The open tip resistance was 4–5 MΩ, all seal resistances were &gt;2 GΩ and series
          resistances were &lt;30 MΩ. Recordings were made in current clamp mode using Multiclamp
          700B amplifiers (Molecular Devices, Sunnyvale, CA, USA) connected to PCs via Instrutech
          ITC-18 interfaces (HEKA Elektronik, Lambrecht, Germany) and using Axograph X acquisition
          software (<a href="http://axographx.com/" itemscope=""
            itemtype="http://schema.stenci.la/Link">http://axographx.com/</a>). Pipette capacitance
          and series resistances were compensated using the capacitance neutralization and
          bridge-balance amplifier controls. An experimentally measured liquid junction potential of
          12.9 mV was not corrected for. Stellate cells were identified by their large sag response
          and the characteristic waveform of their action potential after hyperpolarization
          (see <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib2">Alonso and
              Klink, 1993</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib37">Gonzalez-Sulser et al., 2014</a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib53">Nolan et al., 2007</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib58">Pastoll et
              al., 2012</a></cite>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To maximize the number of cells
          recorded per animal, we adopted two strategies. First, to minimize the time required to
          obtain data from each recorded cell, we measured electrophysiological features using a
          series of three short protocols following initiation of stable whole-cell recordings. We
          used responses to sub-threshold current steps to estimate passive membrane properties (<a
            href="#fig2" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 2A</a>), a
          frequency modulated sinusoidal current waveform (ZAP waveform) to estimate impedance
          amplitude profiles (<a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2B</a>), and a linear current ramp to
          estimate the action potential threshold and firing properties (<a href="#fig2"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 2C</a>). From analysis of
          data obtained with these protocols, we obtained 12 quantitative measures that describe the
          sub- and supra-threshold integrative properties of each recorded cell (<a href="#fig2"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 2A–C</a>). Second, for the
          majority of mice, two experimenters made recordings in parallel from neurons in two
          sagittal brain sections from the same hemisphere. The median dorsal-ventral extent of the
          recorded SCs was 1644 µm (range 0–2464 µm). Each experimenter aimed to sample recording
          locations evenly across the dorsoventral extent of the MEC, and for most animals, each
          experimenter recorded sequentially from opposite extremes of the dorsoventral axis. Each
          experimenter varied the starting location for recording between animals. For several
          features, the direction of recording affected their measured dependence on dorsoventral
          location, but the overall dependence of these features on dorsoventral location was robust
          to this effect (<a href="#supp9" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 9</a>).</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="measurement-of-electrophysiological-features-and-neuronal-location">Measurement of
          electrophysiological features and neuronal location</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Electrophysiological recordings
          were analyzed in Matlab (Mathworks) using a custom-written semi-automated pipeline. We
          defined each feature as follows (see also <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib53">Nolan et al., 2007</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib58">Pastoll et
              al., 2012</a></cite>): resting membrane potential was the mean of the membrane
          potential during the 1 s prior to injection of the current steps used to assess
          subthreshold properties; input resistance was the steady-state voltage response to the
          negative current steps divided by their amplitude; membrane time constant was the time
          constant of an exponential function fit to the initial phase of membrane potential
          responses to the negative current steps; the sag coefficient was the steady-state divided
          by the peak membrane potential response to the negative current steps; resonance frequency
          was the frequency at which the peak membrane potential impedance was found to occur;
          resonance magnitude was the ratio between the peak impedance and the impedance at a
          frequency of 1 Hz; action potential threshold was calculated from responses to positive
          current ramps as the membrane potential at which the first derivative of the membrane
          potential crossed 20 mv ms<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">−1</sup> averaged across the first five
          spikes, or fewer if fewer spikes were triggered; rheobase was the ramp current at the
          point when the threshold was crossed on the first spike; spike maximum was the mean peak
          amplitude of the action potentials triggered by the positive current ramp; spike width was
          the duration of the action potentials measured at the voltage corresponding to the
          midpoint between the spike threshold and spike maximum; the AHP minimum was the negative
          peak membrane potential of the after hyperpolarization following the first action
          potential when a second action potential also occurred; and the F-I slope was the linear
          slope of the relationship between the spike rate and the injected ramp current over a 500
          ms window.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The location of each recorded
          neuron was estimated as described previously (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib28">Garden et al., 2008</a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib59">Pastoll et
              al., 2012</a></cite>). Following each recording, a low magnification image was taken
          of the slice with the patch-clamp electrode at the recording location. The image was
          calibrated and then the distance measured from the dorsal border of the MEC along the
          border of layers 1 and 2 to the location of the recorded cell.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="analysis-of-location-dependence-experience-dependence-and-inter-animal-differences">
          Analysis of location-dependence, experience-dependence and inter-animal differences</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Analyses of location-dependence
          and inter-animal differences used R 3.4.3 (R Core Team, Vienna, Austria) and R Studio
          1.1.383 (R Studio Inc, Boston, MA).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To fit linear mixed effect
          models, we used the lme4 package (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib8">Bates et al., 2014</a></cite>).
          Features of interest were included as fixed effects and animal identity was included as a
          random effect. All reported analyses are for models with the minimal a priori random
          effect structure, in other words the random effect was specified with uncorrelated slope
          and intercept. We also evaluated models in which only the intercept, or correlated
          intercept and slope were specified as the random effect. Model assessment was performed
          using Akaike Information Criterion (AIC) scores. In general, models with either random
          slope and intercept, or correlated random slope and intercept, had lower AIC scores than
          random intercept only models, indicating a better fit to the data. We used the former set
          of models for all analyses of all properties for consistency and because a maximal effect
          structure may be preferable on theoretical grounds (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib5">Barr et al., 2013</a></cite>).
          We evaluated assumptions including linearity, normality, homoscedasticity and influential
          data points. For some features, we found modest deviations from these assumptions that
          could be remedied by handling non-linearity in the data using a copula transformation.
          Model fits were similar following transformation of the data. However, we focus here on
          analyses of the untransformed data because the physical interpretation of
          the resulting values for data points is clearer.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To evaluate
          the location-dependence of a given feature, p-values were calculated using a χ<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup> test comparing
          models to null models with no location information but identical random effect
          specification. To calculate marginal and conditional R<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">2</sup> of mixed effect models, we used
          the MuMin package (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib7">Bartoń, 2014</a></cite>). To evaluate additional fixed effects, we used
          Type II Wald χ<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup>
          test tests provided by the car package (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib25">Fox and Weisberg,
              2018</a></cite>). To compare mixed effect with equivalent linear models, we used a
          χ<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">2</sup> test to compare
          the calculated deviance for each model. For clarity, we have reported key statistics in
          the main text and provide full test statistics in the Supplemental Tables. In addition,
          the code from which the analyses can be fully reproduced is available at <a
            href="https://github.com/MattNolanLab/Inter_Intra_Variation" itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/MattNolanLab/Inter_Intra_Variation</a> (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib54">Nolan,
              2020</a></cite>; copy archived at <a
            href="https://github.com/elifesciences-publications/Inter_Intra_Variation" itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/elifesciences-publications/Inter_Intra_Variation</a>).
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To evaluate partial
          correlations between features, we used the function cor2pcor from the R package corpcor
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib67">Schafer et
              al., 2017</a></cite>). Principal components analysis used core R functions.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="implementation-of-tests-for-modularity">Implementation of tests for modularity</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To establish statistical tests
          to distinguish ‘modular’ from ‘continuous’ distributions given relatively few
          observations, we classified datasets as continuous or modular by modifying the gap
          statistic algorithm (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib75">Tibshirani et al., 2001</a></cite>). The gap statistic estimates the
          number of clusters (k<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">est</sub>) that best account for the data
          in any given dataset (<a href="#fig1s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 1A-C</a>). However,
          this estimate may be prone to false positives, particularly where the numbers of
          observations are low. We therefore introduced a thresholding mechanism for tuning the
          sensitivity of the algorithm so that the false-positive rate, which is the rate of
          misclassifying datasets drawn from continuous (uniform) distributions as ‘modular’, is
          low, constant across different numbers of cluster modes and insensitive to dataset size
          (<a href="#fig1s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—figure
            supplement 1D-G</a>). With this approach, we are able to estimate whether a dataset is
          best described as lacking modularity (k<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">est</sub> = 1), or having a given number of
          modes (k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> &gt; 1).
          Below, we describe tests carried out to validate the approach.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To illustrate the sensitivity
          and specificity of the modified gap statistic algorithm, we applied it to simulated
          datasets drawn either from a uniform distribution (k = 1, n = 40) or from a bimodal
          distribution with separation between the modes of five standard deviations (k = 2, n = 40,
          sigma = 5) (<a href="#fig1s2" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            1—figure supplement 2A</a>). We set the thresholding mechanism so that k<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> for each distinct k
          (where k<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">est</sub> ≥2) has a
          false-positive rate of 0.01. In line with this, testing for 2 ≤ k<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">est</sub> ≤ 8 (the maximum k expected to
          occur in grid spacing in the MEC), across multiple (N = 1000) simulated datasets drawn
          from the uniform distribution, produced a low false-positive rate (P(k<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">est</sub>)≥2 = <sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">0.07), whereas when the data were drawn
            from the bimodal distribution, the ability to detect modular organization
            (p</sub>detect<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">) was good
            (P[k</sub>est<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">]≥2 = </sub>0.8) (<a href="#fig1s2"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 2B</a>).
          The performance of the statistic improved with larger separation between clusters and with
          greater numbers of data points per dataset (<a href="#fig1s2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 2C</a>) and is
          relatively insensitive to the numbers of clusters (<a href="#fig1s2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 2D</a>). The
          algorithm maintains high rates of p<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">detect</sub> when modes have varying
          densities and when sigma between modes varies in a manner similar to grid spacing data (<a
            href="#fig1s3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—figure
            supplement 3</a>).</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="analysis-of-extracellular-recording-data-from-other-laboratories">Analysis of
          extracellular recording data from other laboratories</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Recently described algorithms
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib32">Giocomo et
              al., 2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib71">Stensola et al., 2012</a></cite>) address the problem of identifying
          modularity when data are sampled from multiple locations and data values vary as a
          function of location, as is the case for the mean spacing of grid fields for cells at
          different dorsoventral locations recorded in behaving animals using tetrodes (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib42">Hafting et al.,
              2005</a></cite>). They generate log-normalized discontinuity (which we refer to here
          as lnDS) or discreteness scores, which are the log of the ratio of discontinuity or
          discreteness scores for the data points of interest and for the sampling locations, with
          positive values interpreted as evidence for clustering (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib32">Giocomo et al.,
              2014</a></cite>; <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib71">Stensola et al., 2012</a></cite>). However, in simulations of datasets
          generated from a uniform distribution with evenly spaced recording locations, we find that
          the lnDS is always greater than zero (<a href="#fig1s4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 4A</a>). This is
          because evenly spaced locations result in a discontinuity score that approaches zero, and
          therefore the log ratio of the discontinuity of the data to this score will be positive.
          Thus, for evenly spaced data, the lnDS is guaranteed to produce false-positive results.
          When locations are instead sampled from a uniform distribution, approximately half of
          the simulated datasets have a log discontinuity ratio greater than 0 (<a href="#fig1s4"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 4A</a>),
          which in previous studies would be interpreted as evidence of modularity (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib32">Giocomo et al.,
              2014</a></cite>). Similar discrepancies arise for the discreteness measure (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et al.,
              2012</a></cite>). To address these issues, we introduced a log discontinuity ratio
          threshold, so that the discontinuity method could be matched to produce a similar
          false-positive rate to the adapted gap statistic algorithm used in the example above.
          After including this modification, we found that for a given false-positive rate, the
          adapted gap statistic is more sensitive at detecting modularity in the simulated datasets
          (<a href="#fig4s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4—figure
            supplement 1B</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To establish whether the
          modified gap statistic detects clustering in experimental data, we applied it to
          previously published grid cell data recorded with tetrodes from awake behaving animals
          (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a href="#bib71">Stensola et
              al., 2012</a></cite>). We find that the modified gap statistic identified clustered
          grid spacing for 6 of 7 animals previously identified as having grid modules and with
          n ≥ 20. For these animals, the number of modules was similar (but not always identical) to
          the number of previously identified modules (<a href="#fig1s5" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—figure supplement 5</a>). By contrast,
          the modified gap statistic does not identify clustering in five of six sets of recording
          locations, confirming that the grid clustering is likely not a result of uneven sampling
          of locations (we could not test the seventh as location data were not available). The
          thresholded discontinuity score also detects clustering in the same five of the six tested
          sets of grid data. From the six grid datasets detected as clustered with the modified gap
          statistic, we estimated the separation between clusters by fitting the data with a mixture
          of Gaussians, with the number of modes set by the value of k obtained with the modified
          gap statistic. This analysis suggested that the largest spacing between contiguous modules
          in each mouse is always &gt;5.6 standard deviations (mean = 20.5 ± 5.0 standard
          deviations). Thus, the modified gap statistic detects modularity within the grid system
          and indicates that previous descriptions of grid modularity are, in general, robust to the
          possibility of false positives associated with the discreteness and discontinuity methods.
        </p>
        <section data-itemprop="references">
          <h2 data-itemtype="http://schema.stenci.la/Heading">References</h2>
          <ol>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib1">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="CL Adamson"><span data-itemprop="givenNames"><span
                      itemprop="givenName">CL</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Adamson</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MA Reid"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Reid</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ZL Mo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ZL</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Mo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="J Bowne-English"><span
                    data-itemprop="givenNames"><span itemprop="givenName">J</span></span><span
                    data-itemprop="familyNames"><span
                      itemprop="familyName">Bowne-English</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="RL Davis"><span data-itemprop="givenNames"><span
                      itemprop="givenName">RL</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Davis</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2002">2002</time><span
                itemprop="headline">Firing features and potassium channel content of murine spiral
                ganglion neurons vary with cochlear location</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">447</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">The Journal of Comparative Neurology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">331</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">350</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Firing%20features%20and%20potassium%20channel%20content%20of%20murine%20spiral%20ganglion%20neurons%20vary%20with%20cochlear%20location">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib2">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="A Alonso"><span data-itemprop="givenNames"><span
                      itemprop="givenName">A</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Alonso</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="R Klink"><span data-itemprop="givenNames"><span
                      itemprop="givenName">R</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Klink</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="1993">1993</time><span
                itemprop="headline">Differential electroresponsiveness of stellate and
                pyramidal-like cells of medial entorhinal cortex layer II</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">70</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neurophysiology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">128</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">143</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Differential%20electroresponsiveness%20of%20stellate%20and%20pyramidal-like%20cells%20of%20medial%20entorhinal%20cortex%20layer%20II">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib3">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="K Angelo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">K</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Angelo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EA Rancz"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Rancz</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Pimentel"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Pimentel</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C Hundahl"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hundahl</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="J Hannibal"><span data-itemprop="givenNames"><span
                      itemprop="givenName">J</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hannibal</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="A Fleischmann"><span
                    data-itemprop="givenNames"><span itemprop="givenName">A</span></span><span
                    data-itemprop="familyNames"><span
                      itemprop="familyName">Fleischmann</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="B Pichler"><span data-itemprop="givenNames"><span
                      itemprop="givenName">B</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Pichler</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="TW Margrie"><span data-itemprop="givenNames"><span
                      itemprop="givenName">TW</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Margrie</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2012">2012</time><span
                itemprop="headline">A biophysical signature of network affiliation and sensory
                processing in mitral cells</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">488</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Nature</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">375</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">378</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=A%20biophysical%20signature%20of%20network%20affiliation%20and%20sensory%20processing%20in%20mitral%20cells">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib4">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="RH Baayen"><span data-itemprop="givenNames"><span
                      itemprop="givenName">RH</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Baayen</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DJ Davidson"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Davidson</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DM Bates"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bates</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Mixed-effects modeling with crossed random effects for subjects
                and items</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">59</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Memory and Language</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">390</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">412</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Mixed-effects%20modeling%20with%20crossed%20random%20effects%20for%20subjects%20and%20items">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib5">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DJ Barr"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Barr</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="R Levy"><span data-itemprop="givenNames"><span
                      itemprop="givenName">R</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Levy</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C Scheepers"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Scheepers</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="HJ Tily"><span data-itemprop="givenNames"><span
                      itemprop="givenName">HJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Tily</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2013">2013</time><span
                itemprop="headline">Random effects structure for confirmatory hypothesis testing:
                keep it maximal</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">68</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Memory and Language</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">255</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">278</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Random%20effects%20structure%20for%20confirmatory%20hypothesis%20testing:%20keep%20it%20maximal">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib6">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C Barry"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Barry</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="R Hayman"><span data-itemprop="givenNames"><span
                      itemprop="givenName">R</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hayman</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="N Burgess"><span data-itemprop="givenNames"><span
                      itemprop="givenName">N</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burgess</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="KJ Jeffery"><span data-itemprop="givenNames"><span
                      itemprop="givenName">KJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Jeffery</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2007">2007</time><span
                itemprop="headline">Experience-dependent rescaling of entorhinal grids</span><span
                itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">10</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Nature Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">682</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">684</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Experience-dependent%20rescaling%20of%20entorhinal%20grids">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib7">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="K Bartoń"><span data-itemprop="givenNames"><span
                      itemprop="givenName">K</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bartoń</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2014">2014</time><a itemprop="url"
                href="https://CRAN.R-project.org/package=MuMIn"><span itemprop="headline">MuMIn:
                  Multi-Model Inference</span></a><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher"><span
                  itemprop="name">R package version 1.10. 0</span><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=R%20package%20version%201.10.%200">
                </span></span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=MuMIn:%20Multi-Model%20Inference">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib8">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Bates"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bates</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="M Mächler"><span data-itemprop="givenNames"><span
                      itemprop="givenName">M</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Mächler</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="B Bolker"><span data-itemprop="givenNames"><span
                      itemprop="givenName">B</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bolker</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Walker"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Walker</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2014">2014</time><a itemprop="url"
                href="https://arxiv.org/abs/1406.5823"><span itemprop="headline">Fitting linear
                  Mixed-Effects models using lme4</span></a><span itemscope=""
                itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                  itemprop="name">arXiv</span></span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Fitting%20linear%20Mixed-Effects%20models%20using%20lme4">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib9">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="Y Benjamini"><span data-itemprop="givenNames"><span
                      itemprop="givenName">Y</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Benjamini</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="Y Hochberg"><span data-itemprop="givenNames"><span
                      itemprop="givenName">Y</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hochberg</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="1995">1995</time><span
                itemprop="headline">Controlling the false discovery rate: a practical and powerful
                approach to multiple testing</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">57</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of the Royal Statistical Society: Series
                    B</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">289</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">300</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Controlling%20the%20false%20discovery%20rate:%20a%20practical%20and%20powerful%20approach%20to%20multiple%20testing">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib10">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="A Boehlen"><span data-itemprop="givenNames"><span
                      itemprop="givenName">A</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Boehlen</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="U Heinemann"><span data-itemprop="givenNames"><span
                      itemprop="givenName">U</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Heinemann</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="I Erchova"><span data-itemprop="givenNames"><span
                      itemprop="givenName">I</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Erchova</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2010">2010</time><span
                itemprop="headline">The range of intrinsic frequencies represented by medial
                entorhinal cortex stellate cells extends with age</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">30</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">4585</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">4589</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=The%20range%20of%20intrinsic%20frequencies%20represented%20by%20medial%20entorhinal%20cortex%20stellate%20cells%20extends%20with%20age">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib11">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="CA Booth"><span data-itemprop="givenNames"><span
                      itemprop="givenName">CA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Booth</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="T Ridler"><span data-itemprop="givenNames"><span
                      itemprop="givenName">T</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Ridler</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="TK Murray"><span data-itemprop="givenNames"><span
                      itemprop="givenName">TK</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Murray</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MA Ward"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Ward</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="E Groot"><span data-itemprop="givenNames"><span
                      itemprop="givenName">E</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Groot</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="M Goodfellow"><span
                    data-itemprop="givenNames"><span itemprop="givenName">M</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Goodfellow</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="KG Phillips"><span data-itemprop="givenNames"><span
                      itemprop="givenName">KG</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Phillips</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="AD Randall"><span data-itemprop="givenNames"><span
                      itemprop="givenName">AD</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Randall</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="JT Brown"><span data-itemprop="givenNames"><span
                      itemprop="givenName">JT</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Brown</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2016">2016</time><span
                itemprop="headline"
                content="Electrical and network neuronal properties are preferentially disrupted in Dorsal, but not ventral, medial en…">Electrical
                and network neuronal properties are preferentially disrupted in Dorsal, but not
                ventral, medial entorhinal cortex in a mouse model of tauopathy</span><span
                itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">36</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">312</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">324</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Electrical%20and%20network%20neuronal%20properties%20are%20preferentially%20disrupted%20in%20Dorsal,%20but%20not%20ventral,%20medial%20en%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib12">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="VH Brun"><span data-itemprop="givenNames"><span
                      itemprop="givenName">VH</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Brun</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="T Solstad"><span data-itemprop="givenNames"><span
                      itemprop="givenName">T</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Solstad</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="KB Kjelstrup"><span
                    data-itemprop="givenNames"><span itemprop="givenName">KB</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Kjelstrup</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="M Fyhn"><span data-itemprop="givenNames"><span
                      itemprop="givenName">M</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fyhn</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MP Witter"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MP</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Witter</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EI Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MB Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Progressive increase in grid scale from dorsal to ventral medial
                entorhinal cortex</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">18</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Hippocampus</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1200</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1212</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Progressive%20increase%20in%20grid%20scale%20from%20dorsal%20to%20ventral%20medial%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib13">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="Y Burak"><span data-itemprop="givenNames"><span
                      itemprop="givenName">Y</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burak</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="IR Fiete"><span data-itemprop="givenNames"><span
                      itemprop="givenName">IR</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fiete</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2009">2009</time><span
                itemprop="headline">Accurate path integration in continuous attractor network models
                of grid cells</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">5</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">PLOS Computational Biology</span></span></span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Accurate%20path%20integration%20in%20continuous%20attractor%20network%20models%20of%20grid%20cells">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib14">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="N Burgess"><span data-itemprop="givenNames"><span
                      itemprop="givenName">N</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burgess</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C Barry"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Barry</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="J O'Keefe"><span data-itemprop="givenNames"><span
                      itemprop="givenName">J</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">O'Keefe</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2007">2007</time><span
                itemprop="headline">An oscillatory interference model of grid cell
                firing</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">17</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Hippocampus</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">801</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">812</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=An%20oscillatory%20interference%20model%20of%20grid%20cell%20firing">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib15">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="N Burgess"><span data-itemprop="givenNames"><span
                      itemprop="givenName">N</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burgess</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Grid cells and theta as oscillatory interference: theory and
                predictions</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">18</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Hippocampus</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1157</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1174</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Grid%20cells%20and%20theta%20as%20oscillatory%20interference:%20theory%20and%20predictions">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib16">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="BG Burton"><span data-itemprop="givenNames"><span
                      itemprop="givenName">BG</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burton</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MN Economo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MN</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Economo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="GJ Lee"><span data-itemprop="givenNames"><span
                      itemprop="givenName">GJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Lee</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="JA White"><span data-itemprop="givenNames"><span
                      itemprop="givenName">JA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">White</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Development of theta rhythmicity in entorhinal stellate cells of
                the juvenile rat</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">100</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neurophysiology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">3144</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">3157</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Development%20of%20theta%20rhythmicity%20in%20entorhinal%20stellate%20cells%20of%20the%20juvenile%20rat">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib17">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Bush"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bush</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="N Burgess"><span data-itemprop="givenNames"><span
                      itemprop="givenName">N</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Burgess</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2014">2014</time><span
                itemprop="headline">A hybrid oscillatory interference/continuous attractor network
                model of grid cell firing</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">34</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">The Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">5065</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">5079</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=A%20hybrid%20oscillatory%20interference/continuous%20attractor%20network%20model%20of%20grid%20cell%20firing">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib18">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="CB Canto"><span data-itemprop="givenNames"><span
                      itemprop="givenName">CB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Canto</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MP Witter"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MP</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Witter</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2012">2012</time><span
                itemprop="headline">Cellular properties of principal neurons in the rat entorhinal
                cortex II the medial entorhinal cortex</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">22</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Hippocampus</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1277</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1299</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Cellular%20properties%20of%20principal%20neurons%20in%20the%20rat%20entorhinal%20cortex%20II%20the%20medial%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib19">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MS Cembrowski"><span
                    data-itemprop="givenNames"><span itemprop="givenName">MS</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Cembrowski</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="V Menon"><span data-itemprop="givenNames"><span
                      itemprop="givenName">V</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Menon</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2018">2018</time><span
                itemprop="headline">Continuous variation within cell types of the nervous
                system</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">41</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Trends in Neurosciences</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">337</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">348</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Continuous%20variation%20within%20cell%20types%20of%20the%20nervous%20system">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib20">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="GW Diehl"><span data-itemprop="givenNames"><span
                      itemprop="givenName">GW</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Diehl</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="OJ Hon"><span data-itemprop="givenNames"><span
                      itemprop="givenName">OJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hon</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Leutgeb"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Leutgeb</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="JK Leutgeb"><span data-itemprop="givenNames"><span
                      itemprop="givenName">JK</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Leutgeb</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2017">2017</time><span
                itemprop="headline"
                content="Grid and nongrid cells in medial entorhinal cortex represent spatial location and environmental features with…">Grid
                and nongrid cells in medial entorhinal cortex represent spatial location and
                environmental features with complementary coding schemes</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">94</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Neuron</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">83</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">92</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Grid%20and%20nongrid%20cells%20in%20medial%20entorhinal%20cortex%20represent%20spatial%20location%20and%20environmental%20features%20with%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib21">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="PD Dodson"><span data-itemprop="givenNames"><span
                      itemprop="givenName">PD</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Dodson</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="H Pastoll"><span data-itemprop="givenNames"><span
                      itemprop="givenName">H</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Pastoll</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MF Nolan"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MF</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Nolan</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2011">2011</time><span
                itemprop="headline"
                content="Dorsal-ventral organization of theta-like activity intrinsic to entorhinal stellate neurons is mediated by di…">Dorsal-ventral
                organization of theta-like activity intrinsic to entorhinal stellate neurons is
                mediated by differences in stochastic current fluctuations</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">589</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">The Journal of Physiology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">2993</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">3008</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Dorsal-ventral%20organization%20of%20theta-like%20activity%20intrinsic%20to%20entorhinal%20stellate%20neurons%20is%20mediated%20by%20di%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib22">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C Domnisoru"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Domnisoru</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="AA Kinkhabwala"><span
                    data-itemprop="givenNames"><span itemprop="givenName">AA</span></span><span
                    data-itemprop="familyNames"><span
                      itemprop="familyName">Kinkhabwala</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DW Tank"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DW</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Tank</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2013">2013</time><span
                itemprop="headline">Membrane potential dynamics of grid cells</span><span
                itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">495</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Nature</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">199</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">204</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Membrane%20potential%20dynamics%20of%20grid%20cells">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib23">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="F Donato"><span data-itemprop="givenNames"><span
                      itemprop="givenName">F</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Donato</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="RI Jacobsen"><span data-itemprop="givenNames"><span
                      itemprop="givenName">RI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Jacobsen</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MB Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EI Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2017">2017</time><span
                itemprop="headline">Stellate cells drive maturation of the entorhinal-hippocampal
                circuit</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">355</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Science</span></span></span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Stellate%20cells%20drive%20maturation%20of%20the%20entorhinal-hippocampal%20circuit">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib24">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LN Fletcher"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LN</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fletcher</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="SR Williams"><span data-itemprop="givenNames"><span
                      itemprop="givenName">SR</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Williams</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2019">2019</time><span
                itemprop="headline">Neocortical topology governs the dendritic integrative capacity
                of layer 5 pyramidal neurons</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">101</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Neuron</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">76</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">90</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Neocortical%20topology%20governs%20the%20dendritic%20integrative%20capacity%20of%20layer%205%20pyramidal%20neurons">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib25">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="J Fox"><span data-itemprop="givenNames"><span
                      itemprop="givenName">J</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fox</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Weisberg"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Weisberg</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2018">2018</time><span
                itemprop="headline">An R Companion to Applied Regression</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher"><span
                  itemprop="name">SAGE Publications</span><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=SAGE%20Publications">
                </span></span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=An%20R%20Companion%20to%20Applied%20Regression">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib26">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MC Fuhs"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MC</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fuhs</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DS Touretzky"><span
                    data-itemprop="givenNames"><span itemprop="givenName">DS</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Touretzky</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2006">2006</time><span
                itemprop="headline">A spin glass model of path integration in rat medial entorhinal
                cortex</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">26</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">4266</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">4276</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=A%20spin%20glass%20model%20of%20path%20integration%20in%20rat%20medial%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib27">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="M Fyhn"><span data-itemprop="givenNames"><span
                      itemprop="givenName">M</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fyhn</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Molden"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Molden</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MP Witter"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MP</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Witter</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EI Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MB Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2004">2004</time><span
                itemprop="headline">Spatial representation in the entorhinal cortex</span><span
                itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">305</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Science</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1258</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1264</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Spatial%20representation%20in%20the%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib28">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DL Garden"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DL</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Garden</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="PD Dodson"><span data-itemprop="givenNames"><span
                      itemprop="givenName">PD</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Dodson</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C O'Donnell"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">O'Donnell</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MD White"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MD</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">White</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MF Nolan"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MF</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Nolan</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Tuning of synaptic integration in the medial entorhinal cortex
                to the organization of grid cell firing fields</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">60</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Neuron</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">875</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">889</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Tuning%20of%20synaptic%20integration%20in%20the%20medial%20entorhinal%20cortex%20to%20the%20organization%20of%20grid%20cell%20firing%20fields">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib29">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="KA Geiler-Samerotte"><span
                    data-itemprop="givenNames"><span itemprop="givenName">KA</span></span><span
                    data-itemprop="familyNames"><span
                      itemprop="familyName">Geiler-Samerotte</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="CR Bauer"><span data-itemprop="givenNames"><span
                      itemprop="givenName">CR</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bauer</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Li"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Li</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="N Ziv"><span data-itemprop="givenNames"><span
                      itemprop="givenName">N</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Ziv</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Gresham"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Gresham</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ML Siegal"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ML</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Siegal</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2013">2013</time><span
                itemprop="headline">The details in the distributions: why and how to study
                phenotypic variability</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">24</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Current Opinion in Biotechnology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">752</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">759</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=The%20details%20in%20the%20distributions:%20why%20and%20how%20to%20study%20phenotypic%20variability">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib30">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EA Zilli"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Zilli</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="E Fransén"><span data-itemprop="givenNames"><span
                      itemprop="givenName">E</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Fransén</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ME Hasselmo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ME</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hasselmo</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2007">2007</time><span
                itemprop="headline">Temporal frequency of subthreshold oscillations scales with
                entorhinal grid cell field spacing</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">315</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Science</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1719</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1722</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Temporal%20frequency%20of%20subthreshold%20oscillations%20scales%20with%20entorhinal%20grid%20cell%20field%20spacing">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib31">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="SA Hussaini"><span data-itemprop="givenNames"><span
                      itemprop="givenName">SA</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hussaini</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="F Zheng"><span data-itemprop="givenNames"><span
                      itemprop="givenName">F</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Zheng</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ER Kandel"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ER</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Kandel</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MB Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EI Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2011">2011</time><span
                itemprop="headline">Grid cells use HCN1 channels for spatial scaling</span><span
                itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">147</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Cell</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1159</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1170</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Grid%20cells%20use%20HCN1%20channels%20for%20spatial%20scaling">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib32">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="T Stensola"><span data-itemprop="givenNames"><span
                      itemprop="givenName">T</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Stensola</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="T Bonnevie"><span data-itemprop="givenNames"><span
                      itemprop="givenName">T</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Bonnevie</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="T Van Cauter"><span
                    data-itemprop="givenNames"><span itemprop="givenName">T</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Van Cauter</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MB Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MB</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EI Moser"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EI</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Moser</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2014">2014</time><span
                itemprop="headline">Topography of head direction cells in medial entorhinal
                cortex</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">24</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Current Biology</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">252</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">262</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Topography%20of%20head%20direction%20cells%20in%20medial%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib33">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ME Hasselmo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ME</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hasselmo</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline"
                content="Time constants of h current in layer ii stellate cells differ along the dorsal to ventral Axis of medial ento…">Time
                constants of h current in layer ii stellate cells differ along the dorsal to ventral
                Axis of medial entorhinal cortex</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">28</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">9414</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">9425</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Time%20constants%20of%20h%20current%20in%20layer%20ii%20stellate%20cells%20differ%20along%20the%20dorsal%20to%20ventral%20Axis%20of%20medial%20ento%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib34">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ME Hasselmo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ME</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hasselmo</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2008">2008</time><span
                itemprop="headline">Computation by oscillations: implications of experimental data
                for theoretical models of grid cells</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">18</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Hippocampus</span></span></span><span itemprop="pageStart"
                data-itemtype="http://schema.org/Number">1186</span><span itemprop="pageEnd"
                data-itemtype="http://schema.org/Number">1199</span><span itemscope=""
                itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Computation%20by%20oscillations:%20implications%20of%20experimental%20data%20for%20theoretical%20models%20of%20grid%20cells">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib35">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="LM Giocomo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">LM</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Giocomo</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="ME Hasselmo"><span data-itemprop="givenNames"><span
                      itemprop="givenName">ME</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Hasselmo</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2009">2009</time><span
                itemprop="headline"
                content="Knock-out of HCN1 subunit flattens dorsal-ventral frequency gradient of medial entorhinal neurons in adult mi…">Knock-out
                of HCN1 subunit flattens dorsal-ventral frequency gradient of medial entorhinal
                neurons in adult mice</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">29</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">7625</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">7630</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Knock-out%20of%20HCN1%20subunit%20flattens%20dorsal-ventral%20frequency%20gradient%20of%20medial%20entorhinal%20neurons%20in%20adult%20mi%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib36">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="JM Goaillard"><span
                    data-itemprop="givenNames"><span itemprop="givenName">JM</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Goaillard</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="AL Taylor"><span data-itemprop="givenNames"><span
                      itemprop="givenName">AL</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Taylor</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="DJ Schulz"><span data-itemprop="givenNames"><span
                      itemprop="givenName">DJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Schulz</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="E Marder"><span data-itemprop="givenNames"><span
                      itemprop="givenName">E</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Marder</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2009">2009</time><span
                itemprop="headline">Functional consequences of animal-to-animal variation in circuit
                parameters</span><span itemscope="" itemtype="http://schema.org/PublicationVolume"
                itemprop="isPartOf"><span itemprop="volumeNumber"
                  data-itemtype="http://schema.org/Number">12</span><span itemscope=""
                  itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Nature Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">1424</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">1430</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Functional%20consequences%20of%20animal-to-animal%20variation%20in%20circuit%20parameters">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib37">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="A Gonzalez-Sulser"><span
                    data-itemprop="givenNames"><span itemprop="givenName">A</span></span><span
                    data-itemprop="familyNames"><span
                      itemprop="familyName">Gonzalez-Sulser</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Parthier"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Parthier</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="A Candela"><span data-itemprop="givenNames"><span
                      itemprop="givenName">A</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Candela</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="C McClure"><span data-itemprop="givenNames"><span
                      itemprop="givenName">C</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">McClure</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="H Pastoll"><span data-itemprop="givenNames"><span
                      itemprop="givenName">H</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Pastoll</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="D Garden"><span data-itemprop="givenNames"><span
                      itemprop="givenName">D</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Garden</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="G Sürmeli"><span data-itemprop="givenNames"><span
                      itemprop="givenName">G</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Sürmeli</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="MF Nolan"><span data-itemprop="givenNames"><span
                      itemprop="givenName">MF</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Nolan</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2014">2014</time><span
                itemprop="headline">GABAergic projections from the medial septum selectively inhibit
                interneurons in the medial entorhinal cortex</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">34</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neuroscience</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">16739</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">16743</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=GABAergic%20projections%20from%20the%20medial%20septum%20selectively%20inhibit%20interneurons%20in%20the%20medial%20entorhinal%20cortex">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib38">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="EJ Green"><span data-itemprop="givenNames"><span
                      itemprop="givenName">EJ</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Green</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="WT Greenough"><span
                    data-itemprop="givenNames"><span itemprop="givenName">WT</span></span><span
                    data-itemprop="familyNames"><span itemprop="familyName">Greenough</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="1986">1986</time><span
                itemprop="headline"
                content="Altered synaptic transmission in Dentate Gyrus of rats reared in complex environments: evidence from hippocam…">Altered
                synaptic transmission in Dentate Gyrus of rats reared in complex environments:
                evidence from hippocampal slices maintained in vitro</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">55</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">Journal of Neurophysiology</span></span></span><span
                itemprop="pageStart" data-itemtype="http://schema.org/Number">739</span><span
                itemprop="pageEnd" data-itemtype="http://schema.org/Number">750</span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>
              </span>
              <meta itemprop="image"
                content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Altered%20synaptic%20transmission%20in%20Dentate%20Gyrus%20of%20rats%20reared%20in%20complex%20environments:%20evidence%20from%20hippocam%E2%80%A6">
            </li>
            <li itemscope="" itemtype="http://schema.org/Article" itemprop="citation" id="bib39">
              <ol data-itemprop="authors">
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="S Grossberg"><span data-itemprop="givenNames"><span
                      itemprop="givenName">S</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Grossberg</span></span>
                </li>
                <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
                  <meta itemprop="name" content="PK Pilly"><span data-itemprop="givenNames"><span
                      itemprop="givenName">PK</span></span><span data-itemprop="familyNames"><span
                      itemprop="familyName">Pilly</span></span>
                </li>
              </ol><time itemprop="datePublished" datetime="2012">2012</time><span
                itemprop="headline"
                content="How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rat…">How
                entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient
                of cell response rates in a self-organizing map</span><span itemscope=""
                itemtype="http://schema.org/PublicationVolume" itemprop="isPartOf"><span
                  itemprop="volumeNumber" data-itemtype="http://schema.org/Number">8</span><span
                  itemscope="" itemtype="http://schema.org/Periodical" itemprop="isPartOf"><span
                    itemprop="name">PLOS Computational Biology</span></span></span><span
                itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
                <meta itemprop="name" content="Unknown"><span itemscope=""
                  itemtype="http://schema.org/ImageObject" itemprop="logo">
                  <meta itemprop="url"
                    content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
                </span>