{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Identifying specific evolutionary trajectories and modelling the outcome of adaptive strategies at the molecular levels is a major challenge in evolutionary systems biology @bib55. The evolution of novel metabolic pathways from existing parts may be predicted using constraint-based modelling (CBM) @bib52. In CBM, selective pressures are coded via the objective functions for which the model is optimised. The factors which constrain evolution are integrated into the models via changes in model inputs or outputs and via flux constraints. We hypothesised that the evolution of the agriculturally important trait of C4 photosynthesis is accessible to CBM.\n", "\n", "C4 photosynthesis evolved independently in at least 67 independent origins in the plant kingdom @bib65 and it allows colonisation of marginal habitats @bib63 and high biomass production in annuals such as crops \\[@bib62; @bib23]. The C4 cycle acts as a biochemical pump which enriches the CO~2~ concentration at the site of Rubisco to overcome a major limitation of carbon fixation @bib62. Enrichment is beneficial because Rubisco, the carbon fixation enzyme, can react productively with CO~2~ and form two molecules of 3-PGA, but it also reacts with O~2~ and produces 2-phosphoglycolate which requires detoxification by photorespiration @bib51. The ratio between both reactions is determined by the enzyme specificity towards CO~2~, by the temperature, and the concentrations of both reactants, which in turn is modulated by stresses such as drought and pathogen load. Evolution of Rubisco itself is constrained since any increase in specificity is paid for by a reduction in speed @bib73. Lower speeds most likely cause maladaptivity since Rubisco is a comparatively slow enzyme and can comprise up to 50% of the total leaf protein @bib24. In the C4 cycle, phosphoenolpyruvate carboxylase affixes CO~2~ to a C3 acid, phosphoenolpyruvate (PEP), forming a C4 acid, oxaloacetate (OAA). After stabilisation of the resulting C4 acid by reduction to malate or transamination to aspartate, it is transferred to the site of Rubisco and decarboxylated by one of three possible decarboxylation enzymes, NADP-dependent malic enzyme (NADP-ME), NAD-dependent malic enzyme (NAD-ME), or PEP carboxykinase (PEP-CK) \\[@bib30; @bib67]. Species such as corn (_Zea mays_) @bib57 and great millet (_Sorghum bicolor_) @bib20 use NADP-ME, species like common millet (_Panicum miliaceum_) @bib30 and African spinach (_Gynandropsis gynandra_) \\[@bib25; @bib82] use NAD-ME and species such as guinea grass (_Panicum maximum_) @bib12 use mainly PEP-CK with the evolutionary constraints leading to one or the other enzyme unknown. Mixed forms are only known to occur between a malic enzyme and PEP-CK but not between both malic enzymes @bib83. After decarboxylation, the C3 acid diffuses back to the site of phosphoenolpyruvate carboxylase (PEPC) and is recycled for another C4 cycle by pyruvate phosphate dikinase (PPDK) \\[@bib30; @bib67]. All the enzymes involved in the C4 cycle are also present in C3 plants @bib4. In its most typical form, this C4 cycle is distributed between different cell types in a leaf in an arrangement called Kranz anatomy @bib29. Initial carbon fixation by PEPC occurs in the mesophyll cell, the outer layer of photosynthetic tissue. The secondary fixation by Rubisco after decarboxylation occurs in an inner layer of photosynthetic tissue, the bundle sheath which in turn surrounds the veins. Both cells are connected by plasmodesmata which are pores with limited transfer specificity between cells. A model which may test possible carbon fixation pathways at the molecular level thus requires two cell architectures connected by transport processes @bib15.\n", "\n", "CBM of genome-scale or close to it are well suited to study evolution (summarised in @bib55). Evolution of different metabolic modes from a ground state, the metabolism of _Escherichia coli_, such as glycerol usage @bib39 or endosymbiotic metabolism @bib54 have been successfully predicted. Metabolic maps of eukaryotic metabolism are of higher complexity compared to bacteria since they require information about intracellular compartmentation and intracellular transport @bib21 and may require multicellular approaches. In plants, aspects of complex metabolic pathways, such as the energetics of CAM photosynthesis @bib17, and fluxes in C3 and C4 metabolism \\[@bib11; @bib28; @bib19; @bib2; @bib64] have been elucidated with genome scale models. The C4 cycle is not predicted by these current C4 models unless the C4 cycle is forced by constraints \\[@bib28; @bib47]. In the C4GEM model, the fluxes representing the C4 cycle are a priori constrained to the cell types @bib28, and in the Mallmann model, the C4 fluxes are induced by activating flux through PEPC @bib47. Models in which specific a priori constraints activated C4 were successfully used to study metabolism under conditions of photosynthesis, photorespiration, and respiration @bib64 and to study N-assimilation under varying conditions @bib71. However, they are incapable of testing under which conditions the pathway may evolve.\n", "\n", "Schematic models suggest that the C4 cycle evolves from its ancestral metabolic state C3 photosynthesis along a sequence of stages (summarised in @bib62; @bib14). In the presence of tight vein spacing and of photosynthetically active bundle sheath cells (i.e. Kranz anatomy), a key intermediate in which the process of photorespiration is divided between cell types is thought to evolve \\[@bib48; @bib63; @bib31; @bib6]. The metabolic fluxes in this intermediate suggest an immediate path towards C4 photosynthesis \\[@bib47; @bib14]. @bib31 built a kinetic model in which the complex C4 cycle was represented by a single enzyme, PEPC. Assuming carbon assimilation as a proxy for fitness, the model showed that the evolution from a C3 progenitor species with Kranz-type anatomy towards C4 photosynthesis occurs in modular, individually adaptive steps on a Mount Fuji fitness landscape. It is frequently assumed that evolution of C4 photosynthesis requires water limitation \\[@bib14; @bib31; @bib47]. However, ecophysiological research showed that C4 can likely evolve in wet habitats \\[@bib53; @bib44]. CBM presents a possible avenue to study the evolution of C4 photosynthesis including its metabolic complexity _in silico_.\n", "\n", "In this study, we establish a generic two-celled, constraint-based model starting from the _Arabidopsis_ core model @bib2. We test under which conditions and constraints C4 photosynthesis is predicted as the optimal solution. Finally, we test which constraints result in the prediction of the particular C4 modes with their different decarboxylation enzymes. In the process, we demonstrate that evolution is predictable at the molecular level in an eukaryotic system and define the selective pressures and limitations guiding the 'choice' of metabolic flux." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Materials and methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Flux Balance Analysis" ] }, { "cell_type": "markdown", "metadata": { "variables": { "}_{FBA": "
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\n", " | Count | \n", "
---|---|
total metabolites | \n", "413 | \n", "
total reactions | \n", "572 | \n", "
transport reactions | \n", "139 | \n", "
export reactions | \n", "90 | \n", "
import reactions | \n", "8 | \n", "
Lower bound [μmol/(m^2^s)] | Upper bound [μmol/(m^2^s)] | |
---|---|---|
Reaction ID | ||
Im_hnu | \n", "0.000000 | \n", "1000.000000 | \n", "
Im_CO2 | \n", "0.000000 | \n", "20.000000 | \n", "
Im_H2O | \n", "-1000000.000000 | \n", "1000000.000000 | \n", "
Im_Pi | \n", "0.000000 | \n", "1000000.000000 | \n", "
Im_NO3 | \n", "0.000000 | \n", "1000000.000000 | \n", "
Im_NH4 | \n", "0.000000 | \n", "0.000000 | \n", "
Im_SO4 | \n", "0.000000 | \n", "1000000.000000 | \n", "
Im_H2S | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_O2 | \n", "-1000000.000000 | \n", "1000000.000000 | \n", "
Ex_Ala_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ala_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ala_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ala_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Arg_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Arg_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Arg_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Arg_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asn_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asn_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asn_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asn_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asp_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asp_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asp_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Asp_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Cys_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Cys_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Cys_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Cys_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gln_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gln_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gln_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gln_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Glu_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Glu_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Glu_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Glu_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gly_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gly_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gly_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Gly_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_His_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_His_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_His_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_His_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ile_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ile_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ile_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ile_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Leu_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Leu_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Leu_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Leu_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Lys_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Lys_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Lys_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Lys_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Met_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Met_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Met_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Met_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Phe_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Phe_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Phe_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Phe_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Pro_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Pro_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Pro_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Pro_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ser_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ser_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ser_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Ser_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Thr_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Thr_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Thr_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Thr_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Trp_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Trp_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Trp_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Trp_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Tyr_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Tyr_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Tyr_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Tyr_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Val_c | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Val_h | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Val_m | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Val_p | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_starch | \n", "0.000000 | \n", "1000000.000000 | \n", "
Ex_Glc | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Frc | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Suc | \n", "0.000000 | \n", "1000000.000000 | \n", "
Ex_cellulose | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Mas | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_MACP | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_Tre | \n", "0.000000 | \n", "0.000000 | \n", "
Ex_AA | \n", "0.000000 | \n", "1000000.000000 | \n", "
\n", " | Flux [μmol/(m^2^s)] | \n", "
---|---|
Compartment | \n", "\n", " |
cytosol | \n", "0.042683 | \n", "
chloroplast | \n", "0.152707 | \n", "
mitochondria | \n", "0.009111 | \n", "
peroxisome | \n", "0.007667 | \n", "
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\n", " | Count | \n", "
---|---|
Number of metabolites | \n", "826 | \n", "
Number of reactions | \n", "1144 | \n", "
\n", " | Count | \n", "
---|---|
Number of metabolites | \n", "826 | \n", "
Number of reactions | \n", "1188 | \n", "
\n", " | Count | \n", "
---|---|
Number of metabolites | \n", "828 | \n", "
Number of reactions | \n", "1191 | \n", "
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