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    <title>Evolution of C4 photosynthesis predicted by constraint-based modelling</title>
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      <article itemscope="" itemtype="http://schema.org/Article" data-itemscope="root">
        <h1 itemprop="headline">Evolution of C4 photosynthesis predicted by constraint-based
          modelling</h1>
        <meta itemprop="image"
          content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Evolution%20of%20C4%20photosynthesis%20predicted%20by%20constraint-based%20modelling">
        <ol data-itemprop="authors">
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Mary-Ann Blätke"><span data-itemprop="givenNames"><span
                itemprop="givenName">Mary-Ann</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Blätke</span></span><span data-itemprop="emails"><a
                itemprop="email"
                href="mailto:blaetke@ipk-gatersleben.de">blaetke@ipk-gatersleben.de</a></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="Andrea Bräutigam"><span data-itemprop="givenNames"><span
                itemprop="givenName">Andrea</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Bräutigam</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a><a itemprop="affiliation"
                href="#author-organization-2">2</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">Leibniz Institute of Plant Genetics and
              Crop Plant Research (IPK)</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressLocality">Tübingen</span><span
                itemprop="addressCountry">Germany</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-2"
            id="author-organization-2"><span itemprop="name">Computational Biology, Faculty of
              Biology, Bielefeld University, Universitätsstraße</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressLocality">Bielefeld</span><span
                itemprop="addressCountry">Germany</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="2019-12-04">2019-12-04</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">Computational and Systems Biology</span></li>
          <li itemscope="" itemtype="http://schema.org/DefinedTerm" itemprop="about"><span
              itemprop="name">Plant Biology</span></li>
        </ul>
        <ul data-itemprop="keywords">
          <li itemprop="keywords">metabolic networks</li>
          <li itemprop="keywords">constraint-based model</li>
          <li itemprop="keywords">C4 photosynthesis</li>
          <li itemprop="keywords">model evolution</li>
          <li itemprop="keywords">flux balance analysis</li>
          <li itemprop="keywords">None</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">49305</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.49305</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">e49305</span>
          </li>
        </ul>
        <section data-itemprop="description">
          <h2 data-itemtype="http://schema.stenci.la/Heading">Abstract</h2>
          <meta itemprop="description"
            content="Constraint-based modelling (CBM) is a powerful tool for the analysis of evolutionary trajectories. Evolution, especially evolution in the distant past, is not easily accessible to laboratory experimentation. Modelling can provide a window into evolutionary processes by allowing the examination of selective pressures which lead to particular optimal solutions in the model. To study the evolution of C4 photosynthesis from a ground state of C3 photosynthesis, we initially construct a C3 model. After duplication into two cells to reflect typical C4 leaf architecture, we allow the model to predict the optimal metabolic solution under various conditions. The model thus identifies resource limitation in conjunction with high photorespiratory flux as a selective pressure relevant to the evolution of C4. It also predicts that light availability and distribution play a role in guiding the evolutionary choice of possible decarboxylation enzymes. The data shows evolutionary CBM in eukaryotes predicts molecular evolution with precision.">
          <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Constraint-based modelling
            (CBM) is a powerful tool for the analysis of evolutionary trajectories. Evolution,
            especially evolution in the distant past, is not easily accessible to laboratory
            experimentation. Modelling can provide a window into evolutionary processes by allowing
            the examination of selective pressures which lead to particular optimal solutions in the
            model. To study the evolution of C4 photosynthesis from a ground state of C3
            photosynthesis, we initially construct a C3 model. After duplication into two cells to
            reflect typical C4 leaf architecture, we allow the model to predict the optimal
            metabolic solution under various conditions. The model thus identifies resource
            limitation in conjunction with high photorespiratory flux as a selective pressure
            relevant to the evolution of C4. It also predicts that light availability and
            distribution play a role in guiding the evolutionary choice of possible decarboxylation
            enzymes. The data shows evolutionary CBM in eukaryotes predicts molecular evolution with
            precision.</p>
        </section>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="introduction">Introduction
        </h2>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Identifying specific
          evolutionary trajectories and modelling the outcome of adaptive strategies at the
          molecular levels is a major challenge in evolutionary systems biology <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib55"><span>55</span><span>Papp et al.</span><span>2011</span></a></cite>. The
          evolution of novel metabolic pathways from existing parts may be predicted using
          constraint-based modelling (CBM) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib52"><span>52</span><span>Orth et al.</span><span>2010</span></a></cite>. 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.
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">C4 photosynthesis evolved
          independently in at least 67 independent origins in the plant kingdom <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib65"><span>65</span><span>Scheben et al.</span><span>2017</span></a></cite>
          and it allows colonisation of marginal habitats <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib63"><span>63</span><span>Sage et al.</span><span>2012</span></a></cite> and
          high biomass production in annuals such as crops <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib62"><span>62</span><span>Sage</span><span>2004</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib23"><span>23</span><span>Edwards et
                  al.</span><span>2010</span></a></cite></span>. The C4 cycle acts as a biochemical
          pump which enriches the CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> concentration at the site of
          Rubisco to overcome a major limitation of carbon fixation <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib62"><span>62</span><span>Sage</span><span>2004</span></a></cite>. Enrichment
          is beneficial because Rubisco, the carbon fixation enzyme, can react productively with
          CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and form two molecules of
          3-PGA, but it also reacts with O<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and produces
          2-phosphoglycolate which requires detoxification by photorespiration <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib51"><span>51</span><span>Ogren and Bowes</span><span>1971</span></a></cite>.
          The ratio between both reactions is determined by the enzyme specificity towards CO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>, 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 <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib73"><span>73</span><span>Spreitzer and
                Salvucci</span><span>2002</span></a></cite>. Lower speeds most likely cause
          maladaptivity since Rubisco is a comparatively slow enzyme and can comprise up to 50% of
          the total leaf protein <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a
              href="#bib24"><span>24</span><span>Ellis</span><span>1979</span></a></cite>. In the C4
          cycle, phosphoenolpyruvate carboxylase affixes CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> 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) <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib30"><span>30</span><span>Hatch</span><span>1987</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib67"><span>67</span><span>Schlüter et
                  al.</span><span>2016</span></a></cite></span>. Species such as corn (<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Zea mays</em>) <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib57"><span>57</span><span>Pick et al.</span><span>2011</span></a></cite> and
          great millet (<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Sorghum
            bicolor</em>) <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib20"><span>20</span><span>Döring et
                al.</span><span>2016</span></a></cite> use NADP-ME, species like common millet (<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Panicum miliaceum</em>) <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib30"><span>30</span><span>Hatch</span><span>1987</span></a></cite> and
          African spinach (<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Gynandropsis
            gynandra</em>) <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib25"><span>25</span><span>Feodorova et
                  al.</span><span>2010</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib82"><span>82</span><span>Voznesenskaya et
                  al.</span><span>2007</span></a></cite></span> use NAD-ME and species such as
          guinea grass (<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Panicum
            maximum</em>) <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib12"><span>12</span><span>Bräutigam et
                al.</span><span>2014</span></a></cite> 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 <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib83"><span>83</span><span>Wang et al.</span><span>2014</span></a></cite>.
          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) <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib30"><span>30</span><span>Hatch</span><span>1987</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib67"><span>67</span><span>Schlüter et
                  al.</span><span>2016</span></a></cite></span>. All the enzymes involved in the C4
          cycle are also present in C3 plants <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib4"><span>4</span><span>Aubry et al.</span><span>2011</span></a></cite>. In
          its most typical form, this C4 cycle is distributed between different cell types in a leaf
          in an arrangement called Kranz anatomy <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib29"><span>29</span><span>Haberlandt and
                Engelmann</span><span>1904</span></a></cite>. 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 <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib15"><span>15</span><span>Bräutigam and
                Weber</span><span>2010</span></a></cite>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">CBM of genome-scale or close to
          it are well suited to study evolution (summarised in <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib55"><span>55</span><span>Papp et al.</span><span>2011</span></a></cite>).
          Evolution of different metabolic modes from a ground state, the metabolism of <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Escherichia coli</em>, such as
          glycerol usage <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib39"><span>39</span><span>Lewis et
                al.</span><span>2010</span></a></cite> or endosymbiotic metabolism <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib54"><span>54</span><span>Pál et al.</span><span>2006</span></a></cite> 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 <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib21"><span>21</span><span>Duarte</span><span>2004</span></a></cite> and may
          require multicellular approaches. In plants, aspects of complex metabolic pathways, such
          as the energetics of CAM photosynthesis <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib17"><span>17</span><span>Cheung et al.</span><span>2014</span></a></cite>,
          and fluxes in C3 and C4 metabolism <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib11"><span>11</span><span>Boyle
                  and Morgan</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib28"><span>28</span><span>Gomes de
                  Oliveira Dal’Molin et al.</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib19"><span>19</span><span>de
                  Oliveira Dal'Molin et al.</span><span>2010</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib2"><span>2</span><span>Arnold and
                  Nikoloski</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib64"><span>64</span><span>Saha et
                  al.</span><span>2011</span></a></cite></span> 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 <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib28"><span>28</span><span>Gomes de
                  Oliveira Dal’Molin et al.</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mallmann
                  et al.</span><span>2014</span></a></cite></span>. In the C4GEM model, the fluxes
          representing the C4 cycle are a priori constrained to the cell types <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib28"><span>28</span><span>Gomes de Oliveira Dal’Molin et
                al.</span><span>2011</span></a></cite>, and in the Mallmann model, the C4 fluxes are
          induced by activating flux through PEPC <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib47"><span>47</span><span>Mallmann et al.</span><span>2014</span></a></cite>.
          Models in which specific a priori constraints activated C4 were successfully used to study
          metabolism under conditions of photosynthesis, photorespiration, and respiration <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib64"><span>64</span><span>Saha et al.</span><span>2011</span></a></cite> and
          to study N-assimilation under varying conditions <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib71"><span>71</span><span>Simons et al.</span><span>2013</span></a></cite>.
          However, they are incapable of testing under which conditions the pathway may evolve.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Schematic models suggest that
          the C4 cycle evolves from its ancestral metabolic state C3 photosynthesis along a sequence
          of stages (summarised in <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a
              href="#bib62"><span>62</span><span>Sage</span><span>2004</span></a></cite>; <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib14"><span>14</span><span>Bräutigam and
                Gowik</span><span>2016</span></a></cite>). 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 <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib48"><span>48</span><span>Monson</span><span>1999</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib63"><span>63</span><span>Sage et
                  al.</span><span>2012</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib31"><span>31</span><span>Heckmann
                  et al.</span><span>2013</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib6"><span>6</span><span>Bauwe</span><span>2010</span></a></cite></span>.
          The metabolic fluxes in this intermediate suggest an immediate path towards C4
          photosynthesis <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib47"><span>47</span><span>Mallmann et
                  al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib14"><span>14</span><span>Bräutigam and
                  Gowik</span><span>2016</span></a></cite></span>. <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib31"><span>31</span><span>Heckmann et al.</span><span>2013</span></a></cite>
          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 <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib14"><span>14</span><span>Bräutigam and
                  Gowik</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib31"><span>31</span><span>Heckmann
                  et al.</span><span>2013</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mallmann
                  et al.</span><span>2014</span></a></cite></span>. However, ecophysiological
          research showed that C4 can likely evolve in wet habitats <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib53"><span>53</span><span>Osborne
                  and Freckleton</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib44"><span>44</span><span>Lundgren
                  and Christin</span><span>2017</span></a></cite></span>. CBM presents a possible
          avenue to study the evolution of C4 photosynthesis including its metabolic complexity <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">in silico</em>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In this study, we establish a
          generic two-celled, constraint-based model starting from the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>. 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 &#39;choice&#39; of metabolic flux.</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="flux-balance-analysis">Flux
          Balance Analysis</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Flux balance analysis (FBA) is
          a CBM approach <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib52"><span>52</span><span>Orth et
                al.</span><span>2010</span></a></cite> to investigate the steady-state behaviour of
          a metabolic network defined by its stoichiometric matrix <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="S"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span></span></span>.
          By employing linear programming, FBA allows computing an optimised flux distribution that
          minimises and/or maximises the synthesis and/or consumption rate of one specific
          metabolite or a combination of various metabolites. Next to the steady-state assumption
          and stoichiometric matrix <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="S"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span></span></span>,
          FBA relies on the definition of the reaction directionality and reversibility, denoted by
          the lower bound <span itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math" aria-label="{v}_{min}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span
                        class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></span></span>
          and upper bound <span itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math" aria-label="{v}_{max}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span
                        class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span>
          , as well as the definition of an objective function <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="z"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span>.
          The objective function <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="z"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span>
          defines a flux distribution <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="v"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span></span>,
          with respect to an objective <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="c"><span class="mjx-mrow" aria-hidden="true"><span
                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span></span></span>.
        </p><span itemscope="" itemtype="http://schema.stenci.la/MathBlock"><span
            class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math"
              aria-label="{\displaystyle \begin{array}{ll}\text{min/max}&amp; {z}_{{}_{FBA}}={c}^{T}v\\ \text{s.t.}\\ &amp; S\cdot v=0\\ &amp; {v}_{min}\le v\le {v}_{max}\end{array}}"><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-mtable"
                          style="vertical-align: -2.455em; padding: 0px 0.167em;"><span
                            class="mjx-table"><span class="mjx-mtr" style="height: 1.411em;"><span
                                class="mjx-mtd"
                                style="padding: 0px 0.5em 0px 0px; text-align: left; width: 4.028em;"><span
                                  class="mjx-mrow" style="margin-top: -0.141em;"><span
                                    class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.446em; padding-bottom: 0.593em;">min/max</span></span><span
                                    class="mjx-strut"></span></span></span><span class="mjx-mtd"
                                style="padding: 0px 0px 0px 0.5em; text-align: left; width: 6.881em;"><span
                                  class="mjx-mrow" style="margin-top: -0.141em;"><span
                                    class="mjx-msubsup"><span class="mjx-base"
                                      style="margin-right: -0.003em;"><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span><span
                                      class="mjx-sub"
                                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-msubsup"><span class="mjx-base"><span
                                                class="mjx-texatom"><span
                                                  class="mjx-mrow"></span></span></span><span
                                              class="mjx-sub"
                                              style="font-size: 83.3%; vertical-align: -0.317em; padding-right: 0.06em;"><span
                                                class="mjx-texatom" style=""><span
                                                  class="mjx-mrow"><span class="mjx-mi"><span
                                                      class="mjx-char MJXc-TeX-math-I"
                                                      style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span
                                                    class="mjx-mi"><span
                                                      class="mjx-char MJXc-TeX-math-I"
                                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                                                    class="mjx-mi"><span
                                                      class="mjx-char MJXc-TeX-math-I"
                                                      style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span
                                    class="mjx-mo MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                                    class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span></span><span
                                      class="mjx-sup"
                                      style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span></span></span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                                    class="mjx-strut"></span></span></span></span><span
                              class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd"
                                style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span
                                  class="mjx-mrow" style="margin-top: -0.2em;"><span
                                    class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.298em; padding-bottom: 0.372em;">s.t.</span></span><span
                                    class="mjx-strut"></span></span></span><span class="mjx-mtd"
                                style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                                  style="margin-top: -0.2em;"></span></span></span><span
                              class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd"
                                style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span
                                  class="mjx-mrow" style="margin-top: -0.2em;"><span
                                    class="mjx-strut"></span></span></span><span class="mjx-mtd"
                                style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                                  class="mjx-mrow" style="margin-top: -0.2em;"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span><span
                                    class="mjx-mo MJXc-space2"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.004em; padding-bottom: 0.298em;"></span></span><span
                                    class="mjx-mi MJXc-space2"><span
                                      class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                                    class="mjx-mo MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                                    class="mjx-mn MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span
                                    class="mjx-strut"></span></span></span></span><span
                              class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd"
                                style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span
                                  class="mjx-mrow" style="margin-top: -0.2em;"><span
                                    class="mjx-strut"></span></span></span><span class="mjx-mtd"
                                style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                                  class="mjx-mrow" style="margin-top: -0.2em;"><span
                                    class="mjx-msubsup"><span class="mjx-base"><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                                      class="mjx-sub"
                                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span><span
                                    class="mjx-mo MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span
                                    class="mjx-mi MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                                    class="mjx-mo MJXc-space3"><span
                                      class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span
                                    class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                                      class="mjx-sub"
                                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span><span
                                    class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The degeneracy problem, the
          possible existence of alternate optimal solutions, is one of the major issues of
          constraint-based optimisation, such as FBA <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib46"><span>46</span><span>Mahadevan and
                Schilling</span><span>2003</span></a></cite>. To avoid this problem, we use the
          parsimonious version of FBA (pFBA) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib39"><span>39</span><span>Lewis et al.</span><span>2010</span></a></cite>.
          This approach incorporates the flux parsimony as a constraint to find the solution with
          the minimum absolute flux value among the alternative optima, which is in agreement with
          the assumption that the cell is evolutionary optimised to allocate a minimum amount of
          resources to achieve its objective.</p><span itemscope=""
          itemtype="http://schema.stenci.la/MathBlock"><span class="mjx-chtml MJXc-display"
            style="text-align: center;"><span class="mjx-math"
              aria-label="\begin{array}{cc}\text{min/max}\hfill &amp; {z}_{{}_{pFBA}}=\sum \left|{v}_{i}\right|\hfill \\ \text{s.t.}\hfill &amp; \\ &amp; S\cdot v=0\hfill \\ &amp; {v}_{min}\le v\le {v}_{max}\hfill \\ &amp; {c}^{T}v={z}_{{}_{FBA}}\hfill \end{array}"><span
                class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable"
                  style="vertical-align: -3.288em; padding: 0px 0.167em;"><span
                    class="mjx-table"><span class="mjx-mtr" style="height: 1.466em;"><span
                        class="mjx-mtd"
                        style="padding: 0px 0.5em 0px 0px; text-align: left; width: 4.028em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">min/max</span></span><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0px 0px 0px 0.5em; text-align: left; width: 6.881em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span
                            class="mjx-msubsup"><span class="mjx-base"
                              style="margin-right: -0.003em;"><span class="mjx-texatom"><span
                                  class="mjx-mrow"><span class="mjx-mi"><span
                                      class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-msubsup"><span class="mjx-base"><span
                                        class="mjx-texatom"><span
                                          class="mjx-mrow"></span></span></span><span
                                      class="mjx-sub"
                                      style="font-size: 83.3%; vertical-align: -0.317em; padding-right: 0.06em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-size1-R"
                              style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span><span
                            class="mjx-mrow MJXc-space1"><span class="mjx-mo"><span
                                class="mjx-char MJXc-TeX-main-R"
                                style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span
                              class="mjx-msubsup"><span class="mjx-base"><span
                                  class="mjx-texatom"><span class="mjx-mrow"><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                                class="mjx-sub"
                                style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                  class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span></span><span
                              class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span><span
                            class="mjx-strut"></span></span></span></span><span class="mjx-mtr"
                      style="height: 1.4em;"><span class="mjx-mtd"
                        style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.372em;">s.t.</span></span><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow"
                          style="margin-top: -0.2em;"><span
                            class="mjx-strut"></span></span></span></span><span class="mjx-mtr"
                      style="height: 1.4em;"><span class="mjx-mtd"
                        style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow"
                          style="margin-top: -0.2em;"><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span><span
                            class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.004em; padding-bottom: 0.298em;"></span></span><span
                            class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                            class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span
                            class="mjx-strut"></span></span></span></span><span class="mjx-mtr"
                      style="height: 1.4em;"><span class="mjx-mtd"
                        style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow"
                          style="margin-top: -0.2em;"><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span
                            class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span
                            class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span><span
                            class="mjx-strut"></span></span></span></span><span class="mjx-mtr"
                      style="height: 1.411em;"><span class="mjx-mtd"
                        style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow"
                          style="margin-top: -0.141em;"><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span
                          class="mjx-mrow" style="margin-top: -0.141em;"><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span></span><span
                              class="mjx-sup"
                              style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span></span></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                            class="mjx-msubsup MJXc-space3"><span class="mjx-base"
                              style="margin-right: -0.003em;"><span class="mjx-texatom"><span
                                  class="mjx-mrow"><span class="mjx-mi"><span
                                      class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-msubsup"><span class="mjx-base"><span
                                        class="mjx-texatom"><span
                                          class="mjx-mrow"></span></span></span><span
                                      class="mjx-sub"
                                      style="font-size: 83.3%; vertical-align: -0.317em; padding-right: 0.06em;"><span
                                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                              style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span
                            class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">All FBA experiments in this
          study employ pFBA and are performed using the cobrapy module in a python 2.7 environment
          run on a personal computer (macOS Sierra, 4 GHz Intel Core i7, 32 GB 1867 MHz DDR3). All
          FBA experiments are available as jupyter notebooks in the supplementary material and can
          also be accessed and executed from the GitHub repository <a
            href="https://github.com/ma-blaetke/CBM_C3_C4_Metabolism" itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/ma-blaetke/CBM_C3_C4_Metabolism</a> (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib10"><span>10</span><span>Blätke</span><span>2019</span></a></cite>; copy
          archived at <a href="https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism"
            itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism</a>).
        </p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="1" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>##### Import Modules #####

## numpy
import numpy as np

## pandas
import pandas as pd
pd.set_option(&#39;display.max_rows&#39;, None)
pd.set_option(&#39;display.max_columns&#39;, None)
pd.set_option(&#39;display.width&#39;, None)
pd.set_option(&#39;display.max_colwidth&#39;, None)

## plotly
import plotly
import plotly.graph_objects as go
from plotly.subplots import make_subplots

## cobra
import cobra

## escher
from escher import Builder

## ipython HTML display
from IPython.display import HTML

## goatools
from goatools import obo_parser

## tqdm
from tqdm.notebook import trange, tqdm

## string
import string

print(f&quot;Code Cell 1: Import Python Modules&quot;)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 1: Import Python Modules
</code></pre>
          </figure>
        </stencila-code-chunk>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="2" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 2: Set Parameters&quot;)

##### Set Parameters #####

inf = float(1e6) </code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 2: Set Parameters
</code></pre>
          </figure>
        </stencila-code-chunk>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="3" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 3: Define Functions&quot;)

##### Define Functions - SBML Model and FBA #####

## Load SBML model
def load_sbml_model():
    
    &#39;&#39;&#39;
    Return cobra model

            Parameters:

            Returns:
                    cobra_model (cobra.model): cobra model of specified sbm file
    &#39;&#39;&#39;
        
    sbml_file = &#39;elife-49305.ipython.src/2018-23-05-mb-genC3.sbml&#39;
    cobra_model = cobra.io.sbml.read_sbml_model(sbml_file)
    
    return cobra_model

## Add reactions to model
def add_rxn(name, D_mets, model, rev=True):
    
    &#39;&#39;&#39;
    Add new reaction to cobra model

            Parameters:
                    name (str): short name/id of reaction
                    D_mets (dict): dictionary of metabolites and their stoichimetric coeffcients attending at reaction
                    model (cobra.model): cobra model to add the reaction
                    rev (bool): reversiblity of reaction (default: True)

            Returns:
                    
    &#39;&#39;&#39;
    
    r_name = name
    r_obj = cobra.Reaction(rname)
    r_obj.name = r_name
    r_obj.id = r_name
    model.add_reaction(r_obj)
    r_obj.add_metabolites(D_mets)
    r_obj.objective_coefficient = 0
    r_obj.bounds = (-inf,inf) if rev else (0,inf)

## Set flux of a reaction to a fixed value
def set_fixed_flux(r_id, val, model):
    
    &#39;&#39;&#39;
    Set flux of reaction to a fixed value

            Parameters:
                    r_id (str): reaction id
                    val (float): flux value
                    model (cobra.model): cobra model to add the reaction

            Returns:
    &#39;&#39;&#39;
    
    r_obj = model.reactions.get_by_id(r_id)
    r_obj.bounds = (val,val)
    
## Set lower and upper flux bound of a reaction
def set_bounds(r_id, val_tuple, model):
    
    &#39;&#39;&#39;
    Set flux bounds of reaction

            Parameters:
                    r_id (str): reaction id
                    val_tuple (tuple): (lower_bound, upper_bound)
                    model (cobra.model): cobra model to add the reaction

            Returns:
    &#39;&#39;&#39;
    
    r_obj = model.reactions.get_by_id(r_id)
    r_obj.bounds = val_tuple

## Set flux ratio for two reactions
def set_fixed_flux_ratio(r_dict, name, model):
    
    &#39;&#39;&#39;
    Set flux ratio of two reactions

            Parameters:
                    r_dict (dict): rdictionary with two keys (reaction ids) and their proportion in the ratio {r_id1: prop1, r_ids2: prop2}
                    name (str): name of constraint
                    model (cobra.model): cobra model to add the reaction

            Returns:
    &#39;&#39;&#39;
        
    if len(r_dict) == 2:
        r_id1 = list(r_dict.keys())[0]
        r_obj1 = model.reactions.get_by_id(r_id1)
        r_v1 = list(r_dict.values())[0]
        r_id2 = list(r_dict.keys())[1]
        r_obj2 = model.reactions.get_by_id(r_id2)
        r_v2 = list(r_dict.values())[1]
        const = model.problem.Constraint(
            float(r_v1) * r_obj2.flux_expression - float(r_v2) * r_obj1.flux_expression, 
            lb = 0.0, 
            ub = 0.0, 
            name = name)
        model.add_cons_vars(const)
        return const</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 3: Define Functions
</code></pre>
          </figure>
        </stencila-code-chunk>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="generic-model-for-c3-metabolism">Generic model for C3 metabolism</h3>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="metabolic-model">Metabolic
          model</h4>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The generic model representing
          the metabolism of a mesophyll cell of a mature photosynthetically active C3 leaf, further
          on called <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">one-cell</em>
          model, is based on the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>. The model is compartmentalised into
          cytosol (c), chloroplast (h), mitochondria (m), and peroxisome (p). Each reaction in the
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite> was compared with the corresponding
          entry in AraCyc <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib49"><span>49</span><span>Mueller et
                al.</span><span>2003</span></a></cite>. Based on the given information, we corrected
          co-factors, gene associations, enzyme commission numbers and reversibility (information
          from BRENDA <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib68"><span>68</span><span>Schomburg et al.</span><span>2002</span></a></cite>
          were included). The gene associations and their GO terms <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib3"><span>3</span><span>Ashburner et al.</span><span>2000</span></a></cite>
          of the cellular components were used to correct the location of reactions. Major additions
          to the model are the cyclic electron flow <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib70"><span>70</span><span>Shikanai</span><span>2016</span></a></cite>,
          alternative oxidases in mitochondria and chloroplast <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib81"><span>81</span><span>Vishwakarma et
                al.</span><span>2015</span></a></cite>, as well as several transport processes
          between the compartments and the cytosol <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib42"><span>42</span><span>Linka and Weber</span><span>2010</span></a></cite>.
          NAD-dependent dehydrogenase to oxidise malate is present in all compartments <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib27"><span>27</span><span>Gietl</span><span>1992</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib9"><span>9</span><span>Berkemeyer et
                  al.</span><span>1998</span></a></cite></span>, which excludes the interconversion
          of NAD and NADP by cycles through the nitrate reductase present in the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model. Correctly
          defining the protonation state of the metabolites in the various cellular compartments is
          a general drawback of metabolic models due to the lack of knowledge in that area. This
          issue mainly affects biochemical reactions and transport reactions involving protons. We
          added a sink/source reaction for protons in the form:</p><span itemscope=""
          itemtype="http://schema.stenci.la/MathBlock"><span class="mjx-chtml MJXc-display"
            style="text-align: center;"><span class="mjx-math"
              aria-label="\begin{array}{cc}\leftrightarrow H\mathrm{\_}\{x\}\hfill &amp; x=c,h,m,p\hfill \end{array}"><span
                class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable"
                  style="vertical-align: -0.288em; padding: 0px 0.167em;"><span
                    class="mjx-table"><span class="mjx-mtr" style="height: 1.075em;"><span
                        class="mjx-mtd"
                        style="padding: 0px 0.5em 0px 0px; text-align: left; width: 4.238em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span
                            class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0px 0px 0px 0.5em; text-align: left; width: 5.63em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                            class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span
                            class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span
                            class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span
                            class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span
                            class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">to all compartments to prevent
          futile fluxes of protons and other metabolites coupled through the proton transport. The
          curated <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model
          is provided in <a href="#fig1sdata1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—source data 1</a>.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="4" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 4: Load Metabolic Model of C3 Photosynthesis in Arabidposis thaliana&quot;)

##### Load model #####
c3_model = load_sbml_model()

# Model summary
c3_num_mets = len(c3_model.metabolites)
c3_num_rxn = len(c3_model.reactions)
c3_num_transport_rxn = len(c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Tr_&#39;))))
c3_num_export_rxn = len(c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Ex_&#39;))))
c3_num_import_rxn = len(c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Im_&#39;))))

df_c3_model_summary = pd.DataFrame([c3_num_mets, c3_num_rxn, c3_num_transport_rxn, c3_num_export_rxn, c3_num_import_rxn],
                                   index=[&#39;total metabolites&#39;,&#39;total reactions&#39;,&#39;transport reactions&#39;, &#39;export reactions&#39; ,&#39;import reactions&#39;], columns=[&#39;Count&#39;])
df_c3_model_summary</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 4: Load Metabolic Model of C3 Photosynthesis in Arabidposis thaliana
</code></pre>
            <table itemscope="" itemtype="http://schema.org/Table">
              <thead>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Count</th>
                </tr>
              </thead>
              <tbody>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">total metabolites
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">413</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">total reactions</td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">572</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">transport reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">139</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">export reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">90</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">import reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">8</span></td>
                </tr>
              </tbody>
            </table>
          </figure>
        </stencila-code-chunk>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="import">Import</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="5" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 5: Add Constraints on Metabolite Input&quot;)

##### Add constraints on metabolite uptake #####

## CONSTRAINT: CO2 uptake rate in C3 plants is about 20 μmol/(m2*s)
f_c3_CO2 = 20 #[μmol/(m2*s)] 
set_bounds(&#39;Im_CO2&#39;, (0, f_c3_CO2), c3_model)

## CONSTRAINT: max. photon consumption 1000 μE
f_c3_hnu = 1000 #[μE] 
set_bounds(&#39;Im_hnu&#39;, (0, f_c3_hnu), c3_model)

## CONSTRAINT:  Fluxes of other import reactions
set_bounds(&#39;Im_H2O&#39;, (-inf, inf), c3_model)
set_bounds(&#39;Im_H2S&#39;, (0.,0.), c3_model)
set_bounds(&#39;Im_NH4&#39;, (0., 0.), c3_model)
set_bounds(&#39;Im_NO3&#39;, (0., inf), c3_model)
set_bounds(&#39;Im_Pi&#39;, (0., inf), c3_model)
set_bounds(&#39;Im_SO4&#39;, (0., inf), c3_model)
set_bounds(&#39;Ex_O2&#39;, (-inf, inf), c3_model)
set_bounds(&#39;Ex_Suc&#39;, (0., inf), c3_model)
set_bounds(&#39;Ex_starch&#39;, (0., inf), c3_model)
set_bounds(&#39;Ex_AA&#39;, (0., inf), c3_model)

</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 5: Add Constraints on Metabolite Input
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">As in <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>, we assume photoautotrophic growth
          conditions. Only the import of light, water, CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>, inorganic phosphate (<span
            itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{Pi}"><span
                  class="mjx-mrow" aria-hidden="true"><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;">P</span></span><span
                        class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                          style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span></span></span></span></span></span></span>),
          nitrate/ammonium, and sulphates/hydrogen sulphide is allowed, compare <a href="#table3"
            itemscope="" itemtype="http://schema.stenci.la/Link">Table 3</a>. More specifically, we
          do only allow for nitrate uptake, since it is the main source (80%) of nitrogen in leaves
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib45"><span>45</span><span>Macduff and
                Bakken</span><span>2003</span></a></cite>. The CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> uptake is limited to
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_c3_CO2</code><output slot="output"></output></stencila-code-expression>
          μmol/(m<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib37"><span>37</span><span>Lacher</span><span>2003</span></a></cite>.
          Therefore, the carbon input constrains the model.</p>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="export">Export</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="6" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 6: Add Constraints on Metabolite Output&quot;)
##### Add constraints on metabolite secretion #####

## CONSTRAINT:  Fluxes of other import reactions
set_bounds(&#39;Ex_O2&#39;, (-inf, inf), c3_model)
set_bounds(&#39;Ex_Suc&#39;, (0., inf), c3_model)
set_bounds(&#39;Ex_starch&#39;, (0., inf), c3_model)
set_bounds(&#39;Ex_AA&#39;, (0., inf), c3_model)

## CONSTRAINT: Output of sucrose : total amino acid 
r_suc_aa = (2.2, 1.0)
const_c3_suc_aa = set_fixed_flux_ratio({&#39;Ex_Suc&#39;:r_suc_aa[0],&#39;Ex_AA&#39;:r_suc_aa[1]}, &#39;const_c3_suc_aa&#39;, c3_model)

## CONSTRAINT: Output of sucrose : starch
r_suc_starch = (1.0, 1.0)
const_c3_suc_starch = set_fixed_flux_ratio({&#39;Ex_Suc&#39;:r_suc_starch[0],&#39;Ex_starch&#39;:r_suc_starch[1]}, &#39;const_c3_suc_starch&#39;, c3_model)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 6: Add Constraints on Metabolite Output
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In contrast to <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>, we focus on mature, fully
          differentiated and photosynthetic active leaves supporting the growth of the plant through
          the export of nutrients in the phloem sap, mainly sucrose and amino acids. An output
          reaction for sucrose <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Ex_Suc</em> is already included in the
          model. An additional export reaction <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Ex_AA</em> represents the relative
          proportion of 18 amino acids in the phloem sap of <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> as stoichiometric
          coefficients in accordance to experimentally measured data from <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib85"><span>85</span><span>Wilkinson and
                Douglas</span><span>2003</span></a></cite>. The ratio of exported sucrose : total
          amino acid is estimated to be <stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_suc_aa[0]</code><output slot="output"></output>
          </stencila-code-expression> : <stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_suc_aa[1]</code><output slot="output"></output>
          </stencila-code-expression><span data-itemtype="http://schema.org/Number">0</span><cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib85"><span>85</span><span>Wilkinson and
                Douglas</span><span>2003</span></a></cite>. This ratio is included as a flux ratio
          constraint of the reactions <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Ex_Suc</em> and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Ex_AA</em>. Furthermore, it is known that
          the export of sucrose and the formation of starch is approximately the same <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib74"><span>74</span><span>Stitt and
                Zeeman</span><span>2012</span></a></cite>, which is reflected by the flux ratio
          constraint <span itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math"
                aria-label="{v}_{Ex\mathrm{\_}Suc}:{v}_{Ex\mathrm{\_}starch}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span
                        class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.23em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span></span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.151em; padding-bottom: 0.372em;">:</span></span><span
                    class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span
                        class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.219em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span></span></span></span></span></span></span></span></span>
          = <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_suc_starch[0]</code><output slot="output"></output>
          </stencila-code-expression>:<stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_suc_starch[1]</code><output slot="output"></output>
          </stencila-code-expression>. The model allows for the export of water and oxygen. The flux
          of all other export reactions is set to 0, see <a href="#table3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Table 3</a> for a summary.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="table3" title="Table 3.">
          <label data-itemprop="label">Table 3.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-execution_count="7" data-programminglanguage="python">
            <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>print(f&quot;Code Cell 7: Create Table on Flux Boundary Constraints of Input and Output Reactions&quot;)
#### Table 3 ####

#{
#  &quot;caption&quot;: &quot;#### Flux boundary constraints of Im-/export reactions&quot;,
# &quot;id&quot;: &quot;table3&quot;,
#  &quot;label&quot;: &quot;Table 3.&quot;,
#  &quot;trusted&quot;: true
#}

index = c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Ex_&#39;) or rxn.id.startswith(&#39;Im_&#39;))).list_attr(&#39;id&#39;)
lower_bounds = c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Ex_&#39;) or rxn.id.startswith(&#39;Im_&#39;))).list_attr(&#39;lower_bound&#39;)
upper_bounds = c3_model.reactions.query(lambda rxn: (rxn.id.startswith(&#39;Ex_&#39;) or rxn.id.startswith(&#39;Im_&#39;))).list_attr(&#39;upper_bound&#39;)
cols = [&#39;Lower bound [μmol/(m^2^s)]&#39;, &#39;Upper bound [μmol/(m^2^s)]&#39; ]

df_ex_im_rxn_bounds = pd.DataFrame(np.array([lower_bounds, upper_bounds]).T,index=index, columns=cols)
df_ex_im_rxn_bounds.index.name = &#39;Reaction ID&#39;

df_ex_im_rxn_bounds.style.applymap(lambda val: &#39;color: red&#39; if val != 0 else &#39;color: black&#39;)</code></pre>
            <figure slot="outputs">
              <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 7: Create Table on Flux Boundary Constraints of Input and Output Reactions
</code></pre>
              <table id="T_b217f_" itemscope="" itemtype="http://schema.org/Table">
                <thead>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Lower bound
                      [μmol/(m^2^s)]</th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Upper bound
                      [μmol/(m^2^s)]</th>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Reaction ID</th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  </tr>
                </thead>
                <tbody>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_hnu</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_CO2</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">20</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_H2O</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">-1000000</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_Pi</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_NO3</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_NH4</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_SO4</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Im_H2S</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_O2</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">-1000000</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ala_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ala_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ala_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ala_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Arg_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Arg_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Arg_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Arg_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asn_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asn_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asn_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asn_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asp_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asp_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asp_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Asp_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Cys_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Cys_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Cys_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Cys_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gln_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gln_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gln_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gln_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Glu_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Glu_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Glu_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Glu_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gly_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gly_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gly_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Gly_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_His_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_His_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_His_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_His_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ile_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ile_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ile_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ile_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Leu_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Leu_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Leu_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Leu_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Lys_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Lys_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Lys_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Lys_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Met_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Met_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Met_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Met_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Phe_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Phe_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Phe_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Phe_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Pro_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Pro_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Pro_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Pro_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ser_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ser_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ser_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Ser_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Thr_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Thr_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Thr_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Thr_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Trp_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Trp_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Trp_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Trp_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Tyr_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Tyr_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Tyr_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Tyr_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Val_c</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Val_h</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Val_m</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Val_p</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_starch</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Glc</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Frc</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Suc</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_cellulose</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Mas</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_MACP</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_Tre</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Ex_AA</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0</span></td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">1000000</span></td>
                  </tr>
                </tbody>
              </table>
            </figure>
          </stencila-code-chunk>
          <figcaption>
            <h5 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="flux-boundary-constraints-of-im-export-reactions">Flux boundary constraints of
              Im-/export reactions</h5>
          </figcaption>
        </figure>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="additional-constraints">
          Additional Constraints</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="8" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 8: Add Constraints on ATP maintenance costs&quot;)

## CONSTRAINT: Maintenance cost
atp_cost_L3_m = 0.009111187245501572 #Mitochondria-L3-ATP Cost [µmol*s-1*m-2]
atp_cost_L3_h = 0.15270708327974447 #Chloroplast-L3-ATP Cost [µmol*s-1*m-2]
atp_cost_L3_p = 0.0076669066992201855 #Peroxisome-L3-ATP Cost [µmol*s-1*m-2]
atp_cost_L3_c = 0.042683072918274702 #Cytosl/Other-L3-ATP Cost [µmol*s-1*m-2]

set_fixed_flux(&#39;NGAM_c&#39;,atp_cost_L3_c + atp_cost_L3_p, c3_model)
set_fixed_flux(&#39;NGAM_m&#39;,atp_cost_L3_m, c3_model)
set_fixed_flux(&#39;NGAM_h&#39;,atp_cost_L3_h, c3_model)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 8: Add Constraints on ATP maintenance costs
</code></pre>
          </figure>
        </stencila-code-chunk>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="table4" title="Table 4.">
          <label data-itemprop="label">Table 4.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-execution_count="9" data-programminglanguage="python">
            <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#### Table 4 ####

#{
#  &quot;caption&quot;: &quot;#### Maintenance costs by compartment&quot;,
#  &quot;id&quot;: &quot;table4&quot;,
#  &quot;label&quot;: &quot;Table 4.&quot;,
#  &quot;trusted&quot;: true
#}

df_maintenance = pd.DataFrame([atp_cost_L3_c,atp_cost_L3_h, atp_cost_L3_m, atp_cost_L3_p], index=[&#39;cytosol&#39;,&#39;chloroplast&#39;,&#39;mitochondria&#39;,&#39;peroxisome&#39;], columns=[&#39;Flux [μmol/(m^2^s)]&#39;])
df_maintenance.index.name = &#39;Compartment&#39;
df_maintenance</code></pre>
            <figure slot="outputs">
              <table itemscope="" itemtype="http://schema.org/Table">
                <thead>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Flux
                      [μmol/(m^2^s)]</th>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Compartment</th>
                    <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  </tr>
                </thead>
                <tbody>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">cytosol</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0.042683</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">chloroplast</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0.152707</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">mitochondria</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0.009111</span></td>
                  </tr>
                  <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell">peroxisome</td>
                    <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                        data-itemtype="http://schema.org/Number">0.007667</span></td>
                  </tr>
                </tbody>
              </table>
            </figure>
          </stencila-code-chunk>
          <figcaption>
            <h5 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="maintenance-costs-by-compartment">Maintenance costs by compartment</h5>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We explicitly include the
          maintenance costs in our model to cover the amounts of ATP that is used to degradation and
          re-synthesis proteins for each compartment. <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib40"><span>40</span><span>Li et al.</span><span>2017</span></a></cite>
          specifies the ATP costs for protein degradation and synthesis of each compartment of a
          mature <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> leaf.
          Based on the given data, we were able to calculate the flux rates to constrain the
          maintenance reactions in each compartment (<a href="#table4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Table 4</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model contains maintenance
          reactions only for the cytsol (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">NGAM_c</em>), chloroplast (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">NGAM_h</em>) and mitochondria (<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">NGAM_m</em>) in the form:</p>
        <span itemscope="" itemtype="http://schema.stenci.la/MathBlock"><span
            class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math"
              aria-label="\begin{array}{cc}ATP\mathrm{\_}\{x\}+H2O\mathrm{\_}\{x\}\to ADP\mathrm{\_}\{x\}+H\mathrm{\_}\{x\}+Pi\mathrm{\_}\{x\}\hfill &amp; x=c,h,m\hfill \end{array}"><span
                class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable"
                  style="vertical-align: -0.288em; padding: 0px 0.167em;"><span
                    class="mjx-table"><span class="mjx-mtr" style="height: 1.075em;"><span
                        class="mjx-mtd"
                        style="padding: 0px 0.5em 0px 0px; text-align: left; width: 24.252em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.109em;">P</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span
                            class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span
                            class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span
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                              style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span
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                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.109em;">P</span></span><span
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                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.109em;">P</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span
                            class="mjx-strut"></span></span></span><span class="mjx-mtd"
                        style="padding: 0px 0px 0px 0.5em; text-align: left; width: 4.682em;"><span
                          class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                            class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                            class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span
                            class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span
                            class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span
                            class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">An equivalent maintenance
          reaction cannot be formulated for the peroxisome since in the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model ATP/ADP are not included
          as peroxisomal metabolites. The flux through the maintenance reactions is fixed to the
          determined maintenance costs given in <a href="#table4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Table 4</a>. The peroxisomal maintenance costs
          are added to the cytosolic maintenance costs.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="10" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 10: Add Constraint on Rubisco Oxygenation : Decarboxylation Ratio&quot;)

## CONSTRAINT: oxygenation : decarboxylation = 1 : 10
r_c3_rbc_rbo = (10.0, 1.0)
const_c3_rbc_rbo = set_fixed_flux_ratio({&#39;RBC_h&#39;:r_c3_rbc_rbo[0],&#39;RBO_h&#39;:r_c3_rbc_rbo[1]}, &#39;const_c3_rbc_rbo&#39;, c3_model)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 10: Add Constraint on Rubisco Oxygenation : Decarboxylation Ratio
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and O<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> partial pressures determine
          the ratio of the oxygenation : carboxylation rate of Rubisco (given by reactions <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">RBO_h</em> and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">RBC_h</em>) and can be described by the
          mathematical expression:</p><span itemscope=""
          itemtype="http://schema.stenci.la/MathBlock"><span class="mjx-chtml MJXc-display"
            style="text-align: center;"><span class="mjx-math"
              aria-label="{\displaystyle \frac{{v}_{RBO\mathrm{\_}h}}{{v}_{RBC\mathrm{\_}h}}=\frac{1}{{S}_{R}}\cdot \frac{{p}_{{O}_{2}}}{{p}_{C{O}_{2}}},}"><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-mfrac"><span class="mjx-box MJXc-stacked"
                            style="width: 3.094em; padding: 0px 0.12em;"><span class="mjx-numerator"
                              style="width: 3.094em; top: -1.232em;"><span class="mjx-msubsup"><span
                                  class="mjx-base"><span class="mjx-texatom"><span
                                      class="mjx-mrow"><span class="mjx-mi"><span
                                          class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                                  class="mjx-sub"
                                  style="font-size: 70.7%; vertical-align: -0.229em; padding-right: 0.071em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span></span></span></span></span></span><span
                              class="mjx-denominator" style="width: 3.094em; bottom: -0.91em;"><span
                                class="mjx-msubsup"><span class="mjx-base"><span
                                    class="mjx-texatom"><span class="mjx-mrow"><span
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                                          style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                                  class="mjx-sub"
                                  style="font-size: 70.7%; vertical-align: -0.23em; padding-right: 0.071em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
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                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
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                                          style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span></span></span></span></span></span><span
                              style="border-bottom: 1.3px solid; top: -0.296em; width: 3.094em;"
                              class="mjx-line"></span></span><span
                            style="height: 2.142em; vertical-align: -0.91em;"
                            class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span
                            class="mjx-char MJXc-TeX-main-R"
                            style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                          class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked"
                            style="width: 1.385em; padding: 0px 0.12em;"><span class="mjx-numerator"
                              style="width: 1.385em; top: -1.368em;"><span class="mjx-mn"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span
                              class="mjx-denominator"
                              style="width: 1.385em; bottom: -0.953em;"><span
                                class="mjx-msubsup"><span class="mjx-base"
                                  style="margin-right: -0.032em;"><span class="mjx-texatom"><span
                                      class="mjx-mrow"><span class="mjx-mi"><span
                                          class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span></span><span
                                  class="mjx-sub"
                                  style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span></span></span></span><span
                              style="border-bottom: 1.3px solid; top: -0.296em; width: 1.385em;"
                              class="mjx-line"></span></span><span
                            style="height: 2.32em; vertical-align: -0.953em;"
                            class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space2"><span
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                            style="padding-top: 0.004em; padding-bottom: 0.298em;"></span></span><span
                          class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked"
                            style="width: 2.139em; padding: 0px 0.12em;"><span class="mjx-numerator"
                              style="width: 2.139em; top: -1.433em;"><span class="mjx-msubsup"><span
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                                          style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span></span></span><span
                                  class="mjx-sub"
                                  style="font-size: 70.7%; vertical-align: -0.36em; padding-right: 0.071em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                        class="mjx-msubsup"><span class="mjx-base"><span
                                            class="mjx-texatom"><span class="mjx-mrow"><span
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                                                  class="mjx-char MJXc-TeX-math-I"
                                                  style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span></span></span></span><span
                                          class="mjx-sub"
                                          style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span
                                            class="mjx-texatom" style=""><span
                                              class="mjx-mrow"><span class="mjx-mn"><span
                                                  class="mjx-char MJXc-TeX-main-R"
                                                  style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span><span
                              class="mjx-denominator"
                              style="width: 2.139em; bottom: -1.112em;"><span
                                class="mjx-msubsup"><span class="mjx-base"><span
                                    class="mjx-texatom"><span class="mjx-mrow"><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span></span></span><span
                                  class="mjx-sub"
                                  style="font-size: 70.7%; vertical-align: -0.36em; padding-right: 0.071em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                        class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                          style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span
                                        class="mjx-msubsup"><span class="mjx-base"><span
                                            class="mjx-texatom"><span class="mjx-mrow"><span
                                                class="mjx-mi"><span
                                                  class="mjx-char MJXc-TeX-math-I"
                                                  style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span></span></span></span><span
                                          class="mjx-sub"
                                          style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span
                                            class="mjx-texatom" style=""><span
                                              class="mjx-mrow"><span class="mjx-mn"><span
                                                  class="mjx-char MJXc-TeX-main-R"
                                                  style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span><span
                              style="border-bottom: 1.3px solid; top: -0.296em; width: 2.139em;"
                              class="mjx-line"></span></span><span
                            style="height: 2.546em; vertical-align: -1.112em;"
                            class="mjx-vsize"></span></span><span class="mjx-mo"><span
                            class="mjx-char MJXc-TeX-main-R"
                            style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span></span></span></span></span></span></span></span></span>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">where <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="{S}_{R}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"
                      style="margin-right: -0.032em;"><span class="mjx-texatom"><span
                          class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span></span></span></span></span></span></span>
          specifies the ability of Rubisco to bind CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> over O<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>. In the case of a mature leave
          and ambient CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and O<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> partial pressures in temperate
          regions with adequate water supply, the ratio <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="{v}_{RB{O}_{h}}/{v}_{RB{C}_{h}}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span
                        class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.229em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 83.3%; vertical-align: -0.295em; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span></span></span></span></span></span></span></span></span><span
                    class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span
                          class="mjx-char MJXc-TeX-main-R"
                          style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span
                    class="mjx-msubsup"><span class="mjx-base"><span class="mjx-texatom"><span
                          class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span></span></span><span
                      class="mjx-sub"
                      style="font-size: 70.7%; vertical-align: -0.23em; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span
                            class="mjx-msubsup"><span class="mjx-base"
                              style="margin-right: -0.045em;"><span class="mjx-texatom"><span
                                  class="mjx-mrow"><span class="mjx-mi"><span
                                      class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span></span></span><span
                              class="mjx-sub"
                              style="font-size: 83.3%; vertical-align: -0.295em; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span></span></span></span></span></span></span></span></span></span></span></span></span>
          is fixed and is predicted to be <stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">int(r_c3_rbc_rbo[0])</code><output slot="output"></output>
          </stencila-code-expression>:<stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">int(r_c3_rbc_rbo[1])</code><output slot="output"></output>
          </stencila-code-expression>, which is encoded by an additional flux ratio constraint.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="11" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 11: Add Constraint on NADPH dehydrogenase and plastoquinol oxidase&quot;)

## CONSTRAINT: fluxes through the chloroplastic NADPH dehydrogenase and plastoquinol oxidase were set to zero 
#because the contributions of NADPH dehydrogenase (Yamamoto et al., 2011) and plastoquinol oxidase 
#(Josse et al., 2000) to photosynthesis are thought to be minor.
set_bounds(&#39;AOX4_h&#39;,(0,0), c3_model)
set_bounds(&#39;iCitDHNADP_h&#39;,(0,0), c3_model)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 11: Add Constraint on NADPH dehydrogenase and plastoquinol oxidase
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We assume no flux for the
          chloroplastic NADPH dehydrogenase (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">iCitDHNADP_h</em>) and plastoquinol oxidase
          (<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">AOX4_h</em>) because <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib33"><span>33</span><span>Josse et al.</span><span>2000</span></a></cite> and
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib88"><span>88</span><span>Yamamoto et
                al.</span><span>2011</span></a></cite> have shown that their effect on the
          photosynthesis is minor.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="12" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 12: Add additional Transport Constraints&quot;)

## CONSTRAINT: NTT is only active at night
set_fixed_flux(&#39;Tr_NTT&#39;,0, c3_model)

## CONSTRAINT: No uncoupled pyruvate transport
set_bounds(&#39;Tr_Pyr1&#39;,(0,0), c3_model)
set_bounds(&#39;Tr_Pyr2&#39;,(0,0), c3_model)

## CONSTRAINT: 
set_bounds(&#39;G6PDH_h&#39;, (0.,0.), c3_model)
set_bounds(&#39;PPIF6PK_c&#39;, (0,0.), c3_model)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 12: Add additional Transport Constraints
</code></pre>
          </figure>
        </stencila-code-chunk>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="objective">Objective</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="13" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 13: Add Objective - Optimize Sucrose Output&quot;)

## Optimize/Maximize sucrose output
r_c3_opt_id = &quot;Ex_Suc&quot;
r_c3_opt_obj = c3_model.reactions.get_by_id(r_c3_opt_id)
r_c3_opt_obj.objective_coefficient = 1.</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 13: Add Objective - Optimize Sucrose Output
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In accordance with the
          assumption of mature, fully differentiated and photosynthetic active leaf, the model’s
          objective is to maximise the phloem sap output defined by reactions
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_c3_opt_id</code><output slot="output"></output>
          </stencila-code-expression>. Additionally, we assume that the involved plant cells put
          only a minimal metabolic effort, in the form of energy and resources, into the production
          of phloem sap as possible. This assumption is in correspondence with minimising the
          nitrogen investment by reducing the number of enzymes that are active in a metabolic
          network. Therefore, we perform a parsimonious FBA to minimise the total flux.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For enhanced compliance with
          the recent standards of the systems biology community, the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model is encoded in SBML level
          3. Meta-information on subsystems, publications, cross-references are provided as evidence
          code in the form of MIRIAM URI’s. FBA related information, gene association rules, charge
          and formula of a species element are encoded using the Flux Balance Constraints package
          developed for SBML level 3. All fluxes in the model are consistently defined
          as μmol/(m<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s).</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="generic-model-for-c4-metabolism">Generic model for C4 metabolism</h3>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="metabolic-model-1">Metabolic
          model</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="14" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 14: Initiate  Metabolic Model of C4 Photosynthesis&quot;)

## Intitialize C4 model
c4_model = cobra.Model(&#39;c4_model&#39;)

## Define cell types
cell_types = [&#39;M&#39;, &#39;B&#39;]

## Duplicate metabolites
for m in c3_model.metabolites:
    for cell in cell_types:
        m_dt = cobra.Metabolite(&#39;[&#39;+cell+&#39;]_&#39;+m.id, name = m.formula, compartment = m.compartment)
        c4_model.add_metabolites([m_dt])

## Duplicate reactions
for r_c3_obj in c3_model.reactions:
    for cell in cell_types:
        r_c4_obj = cobra.Reaction(&#39;[&#39;+cell+&#39;]_&#39;+r_c3_obj.id)
        r_c4_obj.name = r_c3_obj.name
        r_c4_obj.subsystem = r_c3_obj.subsystem
        r_c4_obj.bounds = r_c3_obj.bounds
        c4_model.add_reaction(r_c4_obj)
        r_c4_obj.add_metabolites({&#39;[&#39;+cell+&#39;]_&#39;+m_c3_obj.id: r_c3_obj.get_coefficient(m_c3_obj) for m_c3_obj in r_c3_obj.metabolites})
        
## Model Summary
c4_num_mets = len(c4_model.metabolites)
c4_num_rxn = len(c4_model.reactions)

df_c4_model_summary = pd.DataFrame([c4_num_mets, c4_num_rxn], index=[&#39;Number of metabolites&#39;,&#39;Number of reactions&#39;], columns=[&#39;Count&#39;])
df_c4_model_summary</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 14: Initiate  Metabolic Model of C4 Photosynthesis
</code></pre>
            <table itemscope="" itemtype="http://schema.org/Table">
              <thead>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Count</th>
                </tr>
              </thead>
              <tbody>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of
                    metabolites</td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">826</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">1144</span></td>
                </tr>
              </tbody>
            </table>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The generic model of C4
          metabolism, short <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">two-cell</em> model, comprises two copies of
          the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model to
          represent one mesophyll and one bundle sheath cell. Reactions and metabolites belonging to
          the metabolic network of the mesophyll are indicated with the prefix <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">[M]</em>, whereas the prefix for the bundle
          sheath is <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">[B]</em>. The
          separate mesophyll and bundle sheath networks are connected via reversible transport
          reactions of the cytosolic metabolites indicated with the prefix <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">[MB]</em>, <a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2</a>. The C4 evolution not only confined
          Rubisco to the bundle sheath cells, the CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> concentrating mechanism
          steadily supplies Rubisco with CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> in such a way that the
          oxygenation rate is negligible. Therefore, the bundle sheath network is equipped with two
          Rubisco populations. The native Rubisco population binds external CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and adheres to forced
          oxygenation : carboxylation ratios, where the optimised evolutionary population binds only
          internal CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and the carboxylation occurs
          independently of the oxygenation. External CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> is defined as _[B]_CO2_ex_<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">{_c,h</em>} supplied by the
          mesophyll network. Internal CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> given by _[B]_CO2_<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">{_c,h,m</em>} originates from
          reactions in the bundle sheath network producing CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>. External CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> in the bundle sheath network
          is only allowed to move to the chloroplast <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">[B]_Tr_CO2h_Ex</em> and to react with
          Rubisco <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">[B]_RBC_h_Ex</em>.
          The differentiation of two Rubisco populations binding either external or internal CO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> approximates the
          concentration-dependent shift of the oxygenation : carboxylation ratio.</p>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="imports">Imports</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="15" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 15: Adapt CO2 Input Constraint&quot;)


## CONSTRAINT: CO2 uptake rate uin C4 plants is higher, about 40 μmol/(m2*s)
f_C4_CO2_M = 40 #[μmol/(m2*s)] 
set_bounds(&#39;[M]_Im_CO2&#39;, (0, f_C4_CO2_M), c4_model)

## CONSTRAINT: No CO2 uptake in bundle sheat cells due to suberin layer in cell membranes
f_C4_CO2_B = 0 #[μmol/(m2*s)] 
set_fixed_flux(&#39;[B]_Im_CO2&#39;, f_C4_CO2_B, c4_model)

## Other constraints on inputs are directly transfered from the c3 model</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 15: Adapt CO2 Input Constraint
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">As for the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model, we assume
          photoautotrophic growth conditions, see <a href="#table3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Table 3</a>. During C4 evolution the CO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> assimilation became more
          efficient allowing higher CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> assimilation rates. <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Zea mays</em> achieves up to
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_C4_CO2_M</code><output slot="output"></output>
          </stencila-code-expression> μmol/(m<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s) ([M]_Im_CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib60"><span>60</span><span>Rozema</span><span>1993</span></a></cite>. We
          assume that the CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> uptake from the environment by
          the bundle sheath has to be bridged by the mesophyll. Therefore, the input flux of
          [B]_Im_CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> is set to
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_C4_CO2_B</code><output slot="output"></output>
          </stencila-code-expression>.</p>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="exports">Exports</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="16" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 16: Adapt Output Constraints&quot;)

## CONSTRAINT: Output of sucrose : total amino acid and sucrose : starch
r_suc_aa = (2.2, 1.0)
const_c4_suc_aa_b = set_fixed_flux_ratio({&#39;[B]_Ex_Suc&#39;:r_suc_aa[0],&#39;[B]_Ex_AA&#39;:r_suc_aa[1]}, &#39;const_c4_suc_aa_b&#39;, c4_model)
const_c4_suc_aa_m = set_fixed_flux_ratio({&#39;[M]_Ex_Suc&#39;:r_suc_aa[0],&#39;[M]_Ex_AA&#39;:r_suc_aa[1]}, &#39;const_c4_suc_aa_m&#39;, c4_model)

r_suc_starch = (1.0, 1.0)
const_c4_suc_starch_b = set_fixed_flux_ratio({&#39;[B]_Ex_Suc&#39;:r_suc_starch[0],&#39;[B]_Ex_starch&#39;:r_suc_starch[1]}, &#39;const_c4_suc_starch_b&#39;, c4_model)
const_c4_suc_starch_m = set_fixed_flux_ratio({&#39;[M]_Ex_Suc&#39;:r_suc_starch[0],&#39;[M]_Ex_starch&#39;:r_suc_starch[1]}, &#39;const_c4_suc_starch_m&#39;, c4_model)


## Other constraints on outputs are directly transfered from the c4 model</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 16: Adapt Output Constraints
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The outputs of the <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model are
          transferred to the mesophyll and bundle sheath network, as well as the corresponding flux
          ratios, see <a href="#table3" itemscope="" itemtype="http://schema.stenci.la/Link">Table
            3</a>.</p>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="additional-constraints-1">
          Additional Constraints</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="17" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 17: Add Metabolite Exchange Reactions&quot;)


## Metabolites excluded from M/BS exchange
no_transport = [&#39;NO3&#39;,&#39;NO2&#39;, &#39;O2&#39;,&#39;Na&#39;, &#39;H2S&#39;, &#39;SO4&#39;,
                &#39;H2O&#39;,&#39;FBP&#39;,&#39;F26BP&#39;,&#39;DPGA&#39;,&#39;H&#39;,&#39;ACD&#39;,&#39;AC&#39;,&#39;M_DASH_THF&#39;, &#39;5M_DASH_THF&#39;, &#39;H_DASH_Cys&#39;, &#39;aH_DASH_Cys&#39;, &#39;ORO&#39;, &#39;DHO&#39;,
                &#39;GABA&#39;,&#39;A_DASH_Ser&#39;,&#39;PRPP&#39;,&#39;AD&#39;,&#39;THF&#39;,&#39;DHF&#39;,&#39;ADN&#39;,&#39;Mas&#39;,&#39;CoA&#39;,&#39;GluP&#39;,
                &#39;A_DASH_CoA&#39;,&#39;cellulose1&#39;,&#39;cellulose2&#39;,&#39;cellulose3&#39;,&#39;starch1&#39;,
                &#39;starch2&#39;,&#39;starch3&#39;,&#39;TRXox&#39;,&#39;TRXrd&#39;,&#39;Glu_DASH_SeA&#39;,&#39;T6P&#39;,&#39;aMet&#39;,
                &#39;PPi&#39;, &#39;P5C&#39;, &#39;NH4&#39;, &#39;Pi&#39;, &#39;CO2&#39;, &#39;OAA&#39;,&#39;HCO3&#39;, 
                &#39;UTP&#39;, &#39;UDP&#39;, &#39;UDPG&#39;, &#39;ATP&#39;, &#39;ADP&#39;, &#39;AMP&#39;, &#39;IMP&#39;, &#39;XMP&#39;, 
                &#39;GTP&#39;, &#39;GDP&#39;, &#39;GMP&#39;, &#39;OMP&#39;, &#39;UMP&#39;, &#39;CTP&#39;, &#39;GDP&#39;, &#39;CDP&#39;, &#39;dADP&#39;, 
                &#39;dCDP&#39;, &#39;dGDP&#39;, &#39;dUDP&#39;, &#39;dUTP&#39;, &#39;dUMP&#39;, &#39;dTMP&#39;, &#39;dTDP&#39;, &#39;GTP&#39;, 
                &#39;dATP&#39;, &#39;dCTP&#39;, &#39;dGTP&#39;, &#39;dTTP&#39;, &#39;NAD&#39;, &#39;NADH&#39;, &#39;NADP&#39;, &#39;NADPH&#39;]

## dd M/BS exchange reactions
L_r_transport = []
for m_c3_obj in c3_model.metabolites:
    if m_c3_obj.id[-1:] == &#39;c&#39; and m_c3_obj.id[:-2] not in no_transport:
        r_c4_obj = cobra.Reaction(&#39;[MB]_&#39;+m_c3_obj.id)
        r_c4_obj.name = &#39;[MB]_&#39;+m_c3_obj.id
        r_c4_obj.subsystem = &#39;Exchange&#39;
        r_c4_obj.bounds = (-inf, inf)
        c4_model.add_reaction(r_c4_obj)
        r_c4_obj.add_metabolites({&#39;[M]_&#39;+m_c3_obj.id: -1,&#39;[B]_&#39;+m_c3_obj.id: 1 })
        L_r_transport.append(&#39;[MB]_&#39;+m_c3_obj.id)
        
## Model Summary
c4_num_mets = len(c4_model.metabolites)
c4_num_rxn = len(c4_model.reactions)

df_c4_model_summary = pd.DataFrame([c4_num_mets, c4_num_rxn], index=[&#39;Number of metabolites&#39;,&#39;Number of reactions&#39;], columns=[&#39;Count&#39;])
df_c4_model_summary</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 17: Add Metabolite Exchange Reactions
</code></pre>
            <table itemscope="" itemtype="http://schema.org/Table">
              <thead>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Count</th>
                </tr>
              </thead>
              <tbody>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of
                    metabolites</td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">826</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">1188</span></td>
                </tr>
              </tbody>
            </table>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The mesophyll and bundle sheath
          networks are connected by a range of cytosolic transport metabolites including amino
          acids, sugars (glucose, fructose, sucrose, trehalose, ribose), single phosphorylated sugar
          (glucose-6-phosphate, glucose-1-phosphate, fructose-6-phosphate, sucrose-6-phosphate),
          mono-/di-/tri-carboxylic acids (phosphoenolpyruvate, pyruvate, citrate, cis-aconitate,
          isocitrate, <span itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math" aria-label="\alpha"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">α</span></span></span></span></span></span>-ketoglutarate,
          succinate, fumarate, malate), glyceric acids (2-Phosphoglycerate, 3-Phosphoglycerate),
          glycolate, glycerate, glyceraldehyde-3-phosphate, di-hydroxyacetone-phosphate and CO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub>. Nucleotides, NAD/NADH,
          NADP/NADPH, pyrophosphate, inorganic phosphate are not considered as transport
          metabolites. Oxaloacetate has been excluded as transport metabolite since concentrations
          of oxaloacetate are very low <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">in vivo</em> and it is reasonably unstable
          in aqueous solutions. Other small molecules that can be imported by the bundle sheath from
          the environment, as well as protons and HCO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">3</span></sub><sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">-</sup>, are not exchanged between the
          two cell types.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="18" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 18: Add Constraints for CO2 Uptake in BS Cells and Rubisco Carboxylation : Oxygenation Ratio&quot;)


## CONSTRAINT: Add external CO2 species to bundle sheath
#(the original CO2 species is treated as internal CO2)
m_list_CO_Ex= [&#39;[B]_CO2_ex_c&#39;,&#39;[B]_CO2_ex_h&#39;]

for m_id in m_list_CO_Ex:
    m_obj = cobra.Metabolite(m_id)
    c4_model.add_metabolites(m_obj)

## CONSTRAINT: Copy reactions &#39;Tr_CO2h&#39;, &#39;RBC_h&#39; and replace internal CO2 with external CO2 in the copied reactions 
r_list_CO_Ex = [&#39;Tr_CO2h&#39;, &#39;RBC_h&#39;]

for r_id in r_list_CO_Ex:
    r_obj = c4_model.reactions.get_by_id(&#39;[B]_&#39;+r_id)
    r_obj_Ex = cobra.Reaction(r_obj.id+&#39;_Ex&#39;)
    r_obj_Ex.name = r_obj.id+&#39;_Ex&#39;
    r_obj_Ex.subsystem = r_obj.subsystem
    r_obj_Ex.bounds = r_obj.bounds
    c4_model.add_reaction(r_obj_Ex)
    r_obj_Ex.add_metabolites({m_obj.id if not m_obj.id[:-2] == &#39;[B]_CO2&#39; else &#39;[B]_CO2_ex&#39;+m_obj.id[-2:]: r_obj.get_coefficient(m_obj) 
                                  for m_obj in r_obj.metabolites})

## CONSTRAINT: CO2 exchange between mesophyll and bundle sheat
r_c4_obj = cobra.Reaction(&#39;[MB]_CO2_c&#39;)
r_c4_obj.name = &#39;[MB]_CO2_c&#39;
r_c4_obj.subsystem = &#39;Exchange&#39;
r_c4_obj.bounds = (-inf, inf)
c4_model.add_reaction(r_c4_obj)
r_c4_obj.add_metabolites({&#39;[M]_CO2_c&#39;: -1,&#39;[B]_CO2_ex_c&#39;: 1 })
L_r_transport.append(&#39;[MB]_CO2_c&#39;)

## CONSTRAINT: oxygenation : carboxylation = 1 : 3
r_c4_rbc_rbo = (3.0, 1.0)
const_c4_rbc_rbo_b = set_fixed_flux_ratio({&#39;[B]_RBC_h_Ex&#39;:r_c4_rbc_rbo[0],&#39;[B]_RBO_h&#39;:r_c4_rbc_rbo[1]}, &#39;const_c4_rbc_rbo_b&#39;, c4_model)
const_c4_rbc_rbo_m = set_fixed_flux_ratio({&#39;[M]_RBC_h&#39;:r_c4_rbc_rbo[0],&#39;[M]_RBO_h&#39;:r_c4_rbc_rbo[1]}, &#39;const_c4_rbc_rbo_m&#39;, c4_model)

#Model Summary
c4_num_mets = len(c4_model.metabolites)
c4_num_rxn = len(c4_model.reactions)

df_c4_model_summary = pd.DataFrame([c4_num_mets, c4_num_rxn], index=[&#39;Number of metabolites&#39;,&#39;Number of reactions&#39;], columns=[&#39;Count&#39;])
df_c4_model_summary</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 18: Add Constraints for CO2 Uptake in BS Cells and Rubisco Carboxylation : Oxygenation Ratio
</code></pre>
            <table itemscope="" itemtype="http://schema.org/Table">
              <thead>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell"></th>
                  <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Count</th>
                </tr>
              </thead>
              <tbody>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of
                    metabolites</td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">828</span></td>
                </tr>
                <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Number of reactions
                  </td>
                  <td itemscope="" itemtype="http://schema.stenci.la/TableCell"><span
                      data-itemtype="http://schema.org/Number">1191</span></td>
                </tr>
              </tbody>
            </table>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The ATP costs for cell
          maintenance in the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">genC3</em>
          model are assigned to both cell types in the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">two-cell</em> model. Due to declining CO<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> concentrations over
          evolutionary time and/or adverse conditions which close the stromata, the oxygenation :
          carboxylation ratio of the native Rubisco population in the bundle sheath and the
          mesophyll is increased and can be predicted as <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_c4_rbc_rbo[0]</code><output slot="output"></output>
          </stencila-code-expression> : <stencila-code-expression programming-language="py"
            itemscope="" itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">r_c4_rbc_rbo[1]</code><output slot="output"></output>
          </stencila-code-expression>, the corresponding flux ratios are adapted accordingly.</p>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="19" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 19: Add Constraint on Photon Uptake&quot;)

## Reaction variables for light uptake
B_Im_hnu = c4_model.reactions.get_by_id(&quot;[B]_Im_hnu&quot;)
M_Im_hnu = c4_model.reactions.get_by_id(&quot;[M]_Im_hnu&quot;)

## CONSTRAINT: Total Photon uptake limited to 1000 µE
f_c4_hnu_ub = 1000 #[μE] 
f_c4_hnu_lb = 0 #[μE] 

const_hnu_sum = c4_model.problem.Constraint(
    B_Im_hnu.flux_expression + M_Im_hnu.flux_expression,
    lb = f_c4_hnu_lb,
    ub = f_c4_hnu_ub,
    name = &#39;const_hnu_sum&#39;,
)

c4_model.add_cons_vars(const_hnu_sum)

## CONSTRAINT: Total Photon uptake by bundle sheath must be less equal than in mesophyll
const_hnu_ratio = c4_model.problem.Constraint( 
    M_Im_hnu.flux_expression - B_Im_hnu.flux_expression, 
    lb = f_c4_hnu_lb, 
    ub = f_c4_hnu_ub, 
    name = &#39;const_hnu_ratio&#39;)

c4_model.add_cons_vars(const_hnu_ratio)</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 19: Add Constraint on Photon Uptake
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Furthermore, we assume that the
          total photon uptake in the mesophyll and bundle sheath is in the range of 
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_c4_hnu_lb</code><output slot="output"></output>
          </stencila-code-expression> μmol/(m<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s) to <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_c4_hnu_lb</code><output slot="output"></output>
          </stencila-code-expression> μmol/(m<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s). Since they are more central
          in the leaf, the photon uptake by the bundle sheath must be equal or less compared to the
          mesophyll.</p>
        <h4 itemscope="" itemtype="http://schema.stenci.la/Heading" id="objective-1">Objective</h4>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="20" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>print(f&quot;Code Cell 20: Add Objective to Optimize Sucrose Output&quot;)

## Optimize/Maximize sucrose output
r_opt_id = &quot;[B]_Ex_Suc&quot;
r_opt_obj = c4_model.reactions.get_by_id(r_opt_id)
r_opt_obj.objective_coefficient = 1.</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 20: Add Objective to Optimize Sucrose Output
</code></pre>
          </figure>
        </stencila-code-chunk>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The maximisation of the phloem
          sap output through the bundle sheath and the minimisation of the metabolic effort are kept
          as objectives in the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">two-cell</em> model.</p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="results">Results</h2>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="the-curated-arabidopsis-core-model-predicts-physiological-results">The curated <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model
          predicts physiological results</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Flux balance analysis requires
          five types of information, the metabolic map of the organism, the input, the output, a set
          of constraints (i.e. limitations on input, directionality of reactions, forced flux
          through reactions), and optimisation criteria for the algorithm which approximate the
          selective pressures the metabolism evolved under. In this context, inputs define the
          resources that need to be taken up by the metabolic network to fulfil a particular
          metabolic function, which is related to the outputs, for example the synthesis of
          metabolites part of the biomass or other specific products. In CBM, the objective is most
          likely related to the in- and/or outputs.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For reconstruction of the C3
          metabolic map we curated the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite> manually (<a href="#table1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Table 1</a>) to represent the
          metabolism of a mesophyll cell in a mature photosynthetically active leaf of a C3 plant ,
          further on called <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model (provided in <a
            href="#fig1sdata1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1—source
            data 1</a>). The <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model is a
          bottom-up-assembled, large-scale model relying solely on <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em>-specific annotations and
          the inclusion of only manually curated reactions of the primary metabolism. The <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core model is
          accurate with respect to mass and energy conservation, allowing optimal nutrient
          utilisation and biochemically sound predictions <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>.</p>
        <table id="table1" itemscope="" itemtype="http://schema.org/Table">
          <caption><label data-itemprop="label">Table 1.</label>
            <div itemprop="caption">
              <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
                id="curation-of-the-arabidopsis-core-model-from-narrative-bib2">Curation of the <em
                  itemscope="" itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> core
                model from <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
                  data-citationmode="Narrative"><a href="#bib2"><span>2</span><span>Arnold and
                      Nikoloski</span><span>2014</span></a></cite>.</h4>
            </div>
          </caption>
          <thead>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell"><em itemscope=""
                  itemtype="http://schema.stenci.la/Emphasis">Arabidopsis core model</em></th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Observation</th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell"><em itemscope=""
                  itemtype="http://schema.stenci.la/Emphasis">one-cell model</em></th>
              <th itemscope="" itemtype="http://schema.stenci.la/TableCell">Reference</th>
            </tr>
          </thead>
          <tbody>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">NADP-dependent malate
                dehydrogenases in all compartments</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">cycles through nitrate
                reductase to interconvert NAD and NADP</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">NAD-dependent malate
                dehydrogenases in all compartments, NADP-dependent malate dehydrogenase only in
                chloroplast</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib76"><span>76</span><span>Swarbreck et
                      al.</span><span>2008</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Cyclic electron flow
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">absence of cyclic
                electron flow</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib70"><span>70</span><span>Shikanai</span><span>2016</span></a></cite>)
              </td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Alternative oxidase</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">missing alternative
                routes for electrons to pass the electron transport chain to reduce oxygen</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added alternative
                oxidase reactions to the chloroplast and mitochondria</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib81"><span>81</span><span>Vishwakarma et
                      al.</span><span>2015</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Alanine transferase</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">No alanine transferase
                in cytosol Alanine transferase</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib41"><span>41</span><span>Liepman and
                      Olsen</span><span>2003</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Transport chloroplast
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no maltose transporter
                by MEX1</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib42"><span>42</span><span>Linka and
                      Weber</span><span>2010</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no glucose transporter
                by MEX1 and pGlcT MEX1</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no unidirectional
                transport of ATP, ADP, AMP by BT-like</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no Mal/OAA, Mal/Pyr, and
                Mal/Glu exchange by DiTs</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no folate transporter by
                FBT and FOLT1</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Transport Mitochondria
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no Mal/OAA, Cit/iCit,
                Mal/KG exchange by DTC</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib42"><span>42</span><span>Linka and
                      Weber</span><span>2010</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no H+ importer by UCPs
                import</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no OAA/Pi exchange by
                DIC1-3</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no ATP/Pi exchange by
                APCs</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no NAD/ADP and NAD/AMP
                exchange by NDT2</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no ThPP/ATP exchange by
                TPCs</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no Asp/Glu by AGCs</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no uncoupled Ala
                exchange</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Transport peroxisome
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">missing NAD/NADH,
                NAD/ADP, NAD/AMP exchange by PXN</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib42"><span>42</span><span>Linka and
                      Weber</span><span>2010</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no ATP/ADP and ATP/AMP
                exchange by PNCs</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup> sinks/sources</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup> sinks/source reaction for
                the cytosol and futile transport cycles introduced by H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup> -coupled transport
                reactions</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup> sinks/source reaction added
                for each compartment</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell"></td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">ATPase stoichiometry
              </td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">False H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup>/ATP ratios for the
                plastidal and mitochondrial ATP synthase</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">H<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">+</sup>/ATP ratio set to 3 : 1
                (chloroplast) and 4:1 (mitochondria)</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib56"><span>56</span><span>Petersen et
                      al.</span><span>2012</span></a></cite>; <cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib79"><span>79</span><span>Turina et
                      al.</span><span>2016</span></a></cite>)</td>
            </tr>
            <tr itemscope="" itemtype="http://schema.stenci.la/TableRow">
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">Alanine/aspartate
                transferase</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">no direct conversion of
                alanine and aspartate</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">added to cytosol,
                chloroplast and mitochondria</td>
              <td itemscope="" itemtype="http://schema.stenci.la/TableCell">(<cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib69"><span>69</span><span>Schultz and
                      Coruzzi</span><span>1995</span></a></cite>; <cite itemscope=""
                  itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                    href="#bib22"><span>22</span><span>Duff et
                      al.</span><span>2012</span></a></cite>)</td>
            </tr>
          </tbody>
        </table>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For the inputs, we considered a
          photoautotrophic growth scenario with a fixed CO<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> uptake of about
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">f_c3_CO2</code><output slot="output"></output></stencila-code-expression>
           μmol/(m<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>s) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib37"><span>37</span><span>Lacher</span><span>2003</span></a></cite>. Light,
          sulphates, and phosphate are freely available. Due to the observation that nitrate is the
          main source (80%) of nitrogen in leaves in many species <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib45"><span>45</span><span>Macduff and
                Bakken</span><span>2003</span></a></cite>, we set nitrate as the sole nitrogen
          source. If both ammonia and nitrate are allowed, the model will inevitably predict the
          physiologically incorrect sole use of ammonia since fewer reactions and less energy are
          required to convert it into glutamate, the universal amino group currency in plants. Water
          and oxygen can be freely exchanged with the environment in both directions.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To compute the output, we
          assume a mature fully differentiated and photosynthetically active leaf, which is
          optimised for the synthesis and export of sucrose and amino acids to the phloem under
          minimal metabolic effort. Following the examples of models in bacteria, many plant models
          use a biomass function which assumes that the leaf is required to build itself <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib19"><span>19</span><span>de
                  Oliveira Dal'Molin et al.</span><span>2010</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib2"><span>2</span><span>Arnold and
                  Nikoloski</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib64"><span>64</span><span>Saha et
                  al.</span><span>2011</span></a></cite></span> using photoautotrophic that is <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite> or heterotrophic that is <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib17"><span>17</span><span>Cheung et al.</span><span>2014</span></a></cite>
          energy and molecule supply. In plants, however, leaves transition from a sink phase in
          which they build themselves from metabolites delivered by the phloem to a source phase in
          which they produce metabolites for other organs including sink leaves <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib78"><span>78</span><span>Turgeon</span><span>1989</span></a></cite>. The
          composition of <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> phloem exudate <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib85"><span>85</span><span>Wilkinson and
                Douglas</span><span>2003</span></a></cite> was used to constrain the relative
          proportions of the 18 amino acids and the ratio of sucrose : total amino acids (r<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">suc_aa<a href="" itemscope=""
              itemtype="http://schema.stenci.la/Link"><span
                data-itemtype="http://schema.org/Number">0</span></a> : r_suc_aa<a href=""
              itemscope="" itemtype="http://schema.stenci.la/Link"><span
                data-itemtype="http://schema.org/Number">1</span></a>). To account for daily carbon
            storage as starch for export during the night, we assume that half of the assimilated
            carbon is stored in the _one-cell</em> model. We explicitly account for maintenance
          costs by the use of a generic ATPase and use the measured ATP costs for protein
          degradation and synthesis of a mature <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Arabidopsis</em> leaf <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib40"><span>40</span><span>Li et al.</span><span>2017</span></a></cite> as a
          constraint. We initially assume a low photorespiratory flux according to the ambient
          CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> and O<sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript"><span
              data-itemtype="http://schema.org/Number">2</span></sub> partial pressures considering
          no heat, drought, salt or osmotic stress which may alter the ratio towards higher flux
          towards the oxygenation reaction.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To develop a largely
          unconstrained model and detect possible errors in the metabolic map, we initially kept the
          model unconstrained with regard to fixed fluxes, flux ratios, and reaction directions.
          Different model iterations were run in (re-)design, simulate, validate cycles against
          known physiology with errors sequentially eliminated and a minimal set of constraints
          required for a C3 model recapitulating extant plant metabolism determined. After each
          change, the CBM predicted all fluxes which were output as a table and manually examined
          (for example see <a href="#fig1sdata2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1—source data 2</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The initial FBA resulted in
          carbon fixation by enzymes such as the malic enzymes which, in reality, are constrained by
          the kinetics of the enzymes towards decarboxylation. All decarboxylation reactions were
          made unidirectional towards decarboxylation to prevent erroneous carbon fixation in the
          flux distribution. The next iteration of FBA predicted loops through nitrate reductases
          which ultimately converted NADH to NADPH. We traced this loop to an error in the initial
          model, in which malate dehydrogenases in the cytosol and mitochondrion were NADP-dependent
          instead of NAD-dependent. After correction of the co-factor in the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model, the loops through
          nitrate reductases were no longer observed. Another iteration predicted excessive flux
          through the mitochondrial membrane where multiple metabolites were exchanged and
          identified missing transport processes as the likely reason. Based on <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib42"><span>42</span><span>Linka and Weber</span><span>2010</span></a></cite>,
          we added known fluxes across the mitochondrial and plastidic envelope membranes which
          remedied the excessive fluxes in the solution. The chloroplastic ADP/ATP carrier protein
          is constrained to zero flux since its mutant is only affected during the night but not if
          light is available <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib59"><span>59</span><span>Reiser et
                al.</span><span>2004</span></a></cite>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The obtained flux distribution
          still contained excessive fluxes through multiple transport proteins across internal
          membranes which ultimately transferred protons between the organelles and the cytosol.
          Since for most if not all transport proteins the precise protonation state of metabolites
          during transport is unknown and hence cannot be correctly integrated into the model, we
          allowed protons to appear and disappear as needed in all compartments. This provision
          precludes conclusions about the energetics of membrane transport. ATP generation occurred
          in a distorted way distributed across different organelles which were traced to the H<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">+</sup> consumption of the
          ATPases in mitochondria and chloroplasts. The stoichiometry was altered to to 3:1
          (chloroplast) and 4:1 (mitochondria) <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib56"><span>56</span><span>Petersen
                  et al.</span><span>2012</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib79"><span>79</span><span>Turina
                  et al.</span><span>2016</span></a></cite></span>. We assume no flux for the
          chloroplastic NADPH dehydrogenase and plastoquinol oxidase because <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib33"><span>33</span><span>Josse et
                  al.</span><span>2000</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib88"><span>88</span><span>Yamamoto
                  et al.</span><span>2011</span></a></cite></span> have shown that their effect on
          photosynthesis is minor.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In preparation for modelling
          the C4 cycle, we ensured that all reactions known to occur in C4 (i.e. malate/pyruvate
          exchange, likely via DiT2 in maize <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib84"><span>84</span><span>Weissmann
                et al.</span><span>2016</span></a></cite>, possibly promiscuous amino transferases
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib22"><span>22</span><span>Duff et al.</span><span>2012</span></a></cite>) are
          present in the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">one-cell</em>
          model, since <cite itemscope="" itemtype="http://schema.stenci.la/Cite"
            data-citationmode="Narrative"><a href="#bib4"><span>4</span><span>Aubry et
                al.</span><span>2011</span></a></cite> showed that all genes encoding enzymes and
          transporters underlying the C4 metabolism are already present in the genome of C3 plants.
          We integrated cyclic electron flow <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib70"><span>70</span><span>Shikanai</span><span>2016</span></a></cite> and
          alternative oxidases in the mitochondria <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib81"><span>81</span><span>Vishwakarma et
                al.</span><span>2015</span></a></cite>, since both have been hypothesised to be
          important during the evolution and/or execution of the C4 cycle. Models and analysis
          workflows provided as jupyter notebooks <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib77"><span>77</span><span>Thomas et al.</span><span>2016</span></a></cite>
          are available as supplementary material or can be accessed on GitHub <a
            href="https://github.com/ma-blaetke/CBM_C3_C4_Metabolism" itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/ma-blaetke/CBM_C3_C4_Metabolism</a> (<cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib10"><span>10</span><span>Blätke</span><span>2019</span></a></cite>; copy
          archived at <a href="https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism"
            itemscope=""
            itemtype="http://schema.stenci.la/Link">https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism</a>).
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model comprises in total
          <stencila-code-expression programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">c3_num_mets</code><output slot="output"></output>
          </stencila-code-expression> metabolites and <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">c3_num_rxn</code><output slot="output"></output>
          </stencila-code-expression> reactions, whereof <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">c3_num_transport_rxn</code><output slot="output"></output>
          </stencila-code-expression> are internal transporters, <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">c3_num_export_rxn</code><output slot="output"></output>
          </stencila-code-expression> are export and <stencila-code-expression
            programming-language="py" itemscope=""
            itemtype="http://schema.stenci.la/CodeExpression"><code class="py"
              slot="text">c3_num_import_rxn</code><output slot="output"></output>
          </stencila-code-expression> import reactions (see also below), which are involved in 59
          subsystems. <a href="#fig1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            1</a> provides an overview of the primary subsystems according to <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
              href="#bib2"><span>2</span><span>Arnold and
                Nikoloski</span><span>2014</span></a></cite>.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1" title="Figure 1.">
          <label data-itemprop="label">Figure 1.</label><img src="index.html.media/fig1.jpg" alt=""
            itemscope="" itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="schematic-representation-of-the-primary-subsystems-in-the-one-cell-model-and-the-used-inputoutput-constraints-adapted-from-narrative-bib2">
              Schematic representation of the primary subsystems in the <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">one-cell</em> model and the used
              input/output constraints; adapted from <cite itemscope=""
                itemtype="http://schema.stenci.la/Cite" data-citationmode="Narrative"><a
                  href="#bib2"><span>2</span><span>Arnold and
                    Nikoloski</span><span>2014</span></a></cite>.</h4>
          </figcaption>
        </figure>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="21" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>######################################################################################################################################
######################################################################################################################################
##############                                        EXPERIMENT 1: Effect of CO2 Uptake                                ##############
######################################################################################################################################
######################################################################################################################################
print(f&quot;Code Cell 21: Experiment 1 -- Effect of CO2 Uptake&quot;)

#Create copy of c3 model
c3_model_exp1 = c3_model.copy()

#Optimize/Maximize sucrose output
result_exp1_1_fba = c3_model_exp1.optimize(&#39;maximize&#39;) #perform FBA

#Optimize/Minimize total flux
if result_exp1_1_fba.status == &#39;optimal&#39;: 
    result_exp1_1_pfba = cobra.flux_analysis.parsimonious.pfba(c3_model_exp1)
    
#Fetch flux for CO2 uptake
v_co2_exp1 = result_exp1_1_pfba.fluxes[&#39;Im_CO2&#39;]

#Array defining proprtion of CO2 uptake 
co2_ratios_exp1 = np.linspace(0,1,21)

df_result_exp1 = pd.DataFrame()
#Iterate over proportions of CO2 uptake
for co2_ratio in tqdm(co2_ratios_exp1):
    
    #Fix upper flux bound for photon uptake
    set_bounds(&#39;Im_CO2&#39;, (0, v_co2_exp1 * co2_ratio), c3_model_exp1)
    
    #Optimize/Maximize sucrose output
    result_exp1_2_fba = c3_model_exp1.optimize(&#39;maximize&#39;) #perform FBA
    
    #Optimize/Minimize total flux
    if result_exp1_2_fba.status == &#39;optimal&#39;: # check if feasible
        result_exp1_2_pfba  = cobra.flux_analysis.parsimonious.pfba(c3_model_exp1) #perform pFBA
        if result_exp1_2_pfba.status == &#39;optimal&#39;:
            df_result_exp1[v_co2_exp1 * co2_ratio] = result_exp1_2_pfba.fluxes</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 21: Experiment 1 -- Effect of CO2 Uptake
</code></pre>
            <pre class="language-text" itemscope=""
              itemtype="http://schema.stenci.la/CodeBlock"><code>  0%|          | 0/21 [00:00&lt;?, ?it/s]</code></pre>
          </figure>
        </stencila-code-chunk>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1s1"
          title="Figure 1—figure supplement 1"><label data-itemprop="label">Figure 1—figure
            supplement 1</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-execution_count="22" data-programminglanguage="python">
            <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>######################################################################
##############        Figure 1—figure supplement 1      ##############
######################################################################

#{
#  &quot;caption&quot;: &quot;#### Effect of CO~2. Dependence of the phloem output on CO~2~ input flux in the range 0 μmol/(m^2^s)–20 μmol/(m^2^s). Sucrose and starch are produced in the same amounts, each of them consists of 12 C-atoms.&quot;,
#  &quot;id&quot;: &quot;fig1s1&quot;,
#  &quot;label&quot;: &quot;Figure 1—figure supplement 1&quot;,
#  &quot;trusted&quot;: true
#}

#Define reactions of interest by id
r_ids_exp1 = [&#39;Ex_Suc&#39;,&#39;Ex_AA&#39;]

#Create figure
fig_exp1 = go.Figure()

#Add traces for reactions of interest
for r_id in r_ids_exp1:
    
    #Create trace
    trace = go.Scatter(
        y = df_result_exp1.loc[r_id,:],
        x = df_result_exp1.columns,
        name = r_id,
        mode = &#39;lines+markers&#39;,
        )
    
    #Add trace
    fig_exp1.add_trace(trace)

#Update xaxes
fig_exp1.update_xaxes(
    title = dict(
        text = &#39;CO\u2082 Uptake [µmol/(m\u00B2s)]&#39;,
        font = dict(size=18)
    ),
    tickfont = dict(size=16)
)

#Update yaxes
fig_exp1.update_yaxes(
    title = dict(
        text = &#39;Flux [µmol/(m\u00B2s)]&#39;,
        font = dict(size=18)
    ),
    tickfont = dict(size=16)
)

#Update layout
fig_exp1.update_layout(
    width=1000, 
    height=500,
    title = dict(
        text=&#39;&lt;b&gt;Phloem Export&lt;/b&gt;&#39;,
        x=0.5,
        font=dict(size=20)
    ),
    legend=dict(
        font=dict(size=18),
    )
)

#Show figure
fig_exp1.show()</code></pre>
            <figure slot="outputs"><span data-itemtype="http://schema.stenci.la/Null">null</span>
              <stencila-image-plotly>
                <picture>
                  <script type="application/vnd.plotly.v1+json">
                    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          <figcaption>
            <h5 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="effect-of-co2-dependence-of-the-phloem-output-on-co2-input-flux-in-the-range-0-μmolm2s20-μmolm2s-sucrose-and-starch-are-produced-in-the-same-amounts-each-of-them-consists-of-12-c-atoms">
              Effect of CO<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">2.
                Dependence of the phloem output on CO</sub>2~ input flux in the range 0 μmol/(m<sup
                itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>s)–20 μmol/(m<sup
                itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>s). Sucrose and starch are
              produced in the same amounts, each of them consists of 12 C-atoms.</h5>
          </figcaption>
        </figure>
        <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
          data-execution_count="23" data-programminglanguage="python">
          <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
            slot="text"><code>######################################################################################################################################
######################################################################################################################################
##############                                           EXPERIMENT 2: Effect of PPFD                                   ##############
######################################################################################################################################
######################################################################################################################################
print(f&quot;Code Cell 23: Experiment 2 -- Effect of PPFD&quot;)

#Create copy of c3 model
c3_model_exp2 = c3_model.copy()

#Optimize/Maximize sucrose output
result_exp2_1_fba = c3_model_exp2.optimize(&#39;maximize&#39;) #perform FBA

#Optimize/Minimize total flux
if result_exp2_1_fba.status == &#39;optimal&#39;: 
    result_exp2_1_pfba = cobra.flux_analysis.parsimonious.pfba(c3_model_exp2)
    
#Fetch flux for photon uptake
v_hnu_exp2 = result_exp2_1_pfba.fluxes[&#39;Im_hnu&#39;]

#Array defining proprtion of photon uptake 
hnu_ratios_exp2 = np.linspace(0,2,21)

df_result_exp2 = pd.DataFrame()

#Iterate over proportions of photon uptake
for hnu_ratio in tqdm(hnu_ratios_exp2):
    
    #Fix upper flux bound for photon uptake
    set_bounds(&#39;Im_hnu&#39;, (v_hnu_exp2 * hnu_ratio, v_hnu_exp2 * hnu_ratio), c3_model_exp2)
    
    #Optimize/Maximize sucrose output
    result_exp2_2_fba = c3_model_exp2.optimize(&#39;maximize&#39;) #perform FBA
    
    #Optimize/Minimize total flux
    if result_exp2_2_fba.status == &#39;optimal&#39;: # check if feasible
        result_exp2_2_pfba  = cobra.flux_analysis.parsimonious.pfba(c3_model_exp2) #perform pFBA
        if result_exp2_2_pfba.status == &#39;optimal&#39;:
            df_result_exp2[v_hnu_exp2 * hnu_ratio] = result_exp2_2_pfba.fluxes</code></pre>
          <figure slot="outputs">
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>Code Cell 23: Experiment 2 -- Effect of PPFD
</code></pre>
            <pre class="language-text" itemscope=""
              itemtype="http://schema.stenci.la/CodeBlock"><code>  0%|          | 0/21 [00:00&lt;?, ?it/s]</code></pre>
            <pre class="language-text" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"><code>/Users/blaetke/opt/anaconda3/envs/elife-49305-era/lib/python3.9/site-packages/cobra/util/solver.py:508: UserWarning:

Solver status is &#39;infeasible&#39;.

</code></pre>
          </figure>
        </stencila-code-chunk>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1s2"
          title="Figure 1—figure supplement 2"><label data-itemprop="label">Figure 1—figure
            supplement 2</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-execution_count="24" data-programminglanguage="python">
            <pre class="language-python" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>######################################################################
##############         Figure 1—figure supplement 2     ##############
######################################################################

#{
#  &quot;caption&quot;: &quot;#### PPFD variation. Dependence of phloem output on the PPFD in the range 0 μmol/(m^2^s)–400 μmol/(m^2^s). Sucrose and starch are produced in the same amounts, each of them consists of 12 C-atoms.&quot;,
#  &quot;id&quot;: &quot;fig1s2,
#  &quot;label&quot;: &quot;Figure 1—figure supplement 2&quot;,
#  &quot;trusted&quot;: true
#}

#Define reactions of interest by id
r_ids_exp2 = [&#39;Ex_Suc&#39;,&#39;Ex_AA&#39;]

#Create figure
fig_exp2 = go.Figure()

#Add traces for reactions of interest
for r_id in r_ids_exp2:
    
    #Create trace
    trace = go.Scatter(
        y = df_result_exp2.loc[r_id,:],
        x = df_result_exp2.columns,
        name = r_id,
        mode = &#39;lines+markers&#39;,
        )
    
    #Add trace
    fig_exp2.add_trace(trace)

#Update xaxes
fig_exp2.update_xaxes(
    title = dict(
        text = &#39;&lt;b&gt;PPFD [µE]&lt;/b&gt;&#39;,
        font = dict(size=18)
    ),
    tickfont = dict(size=16)
)

#Update yaxes
fig_exp2.update_yaxes(
    title = dict(
        text = &#39;Flux [µmol/(m\u00B2s)]&#39;,
        font = dict(size=18)
    ),
    tickfont = dict(size=16)
)

#Update layout
fig_exp2.update_layout(
    width=1000, 
    height=500,
    title = dict(
        text=&#39;Phloem Export&#39;,
        x=0.5,
        font=dict(size=20)
    ),
    legend=dict(
        font=dict(size=18),
    )
)

#Show figure
fig_exp2.show()</code></pre>
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