Saadat 2021 model

\begin{align*}
  \frac{d 3PGA}{dt} &= 2 \cdot \frac{CO2 (dissolved) \cdot RUBP \cdot vmax\_rubisco\_carboxylase}{(CO2 (dissolved) + km\_rubisco\_carboxylase\_CO2 (dissolved)) \cdot (RUBP + km\_rubisco\_carboxylase\_RUBP \cdot (1 + \frac{FBP}{ki\_rubisco\_carboxylase\_FBP} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA} + \frac{nadph}{ki\_rubisco\_carboxylase\_nadph} + \frac{pi}{ki\_rubisco\_carboxylase\_pi}))} \\
  & - kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{3PGA \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_pga} \\ 
  \frac{d BPGA}{dt} &= kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - kre\_gadph \cdot (BPGA \cdot nadph \cdot protons - \frac{GAP \cdot nadp \cdot pi}{keq\_gadph}) \\ 
  \frac{d GAP}{dt} &= kre\_gadph \cdot (BPGA \cdot nadph \cdot protons - \frac{GAP \cdot nadp \cdot pi}{keq\_gadph}) \\
  & - kre\_triose\_phosphate\_isomerase \cdot (GAP - \frac{DHAP}{keq\_triose\_phosphate\_isomerase}) \\
  & - kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & - kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - \frac{GAP \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_gap} \\ 
  \frac{d DHAP}{dt} &= kre\_triose\_phosphate\_isomerase \cdot (GAP - \frac{DHAP}{keq\_triose\_phosphate\_isomerase}) \\
  & - kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & - \frac{DHAP \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_dhap} \\ 
  \frac{d FBP}{dt} &= kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - \frac{FBP \cdot vmax\_fbpase}{FBP + km\_fbpase\_s \cdot (1 + \frac{F6P}{ki\_fbpase\_F6P} + \frac{pi}{ki\_fbpase\_pi})} \\ 
  \frac{d F6P}{dt} &= \frac{FBP \cdot vmax\_fbpase}{FBP + km\_fbpase\_s \cdot (1 + \frac{F6P}{ki\_fbpase\_F6P} + \frac{pi}{ki\_fbpase\_pi})} \\
  & - kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & - kre\_g6pi \cdot (F6P - \frac{G6P}{keq\_g6pi}) \\ 
  \frac{d G6P}{dt} &= kre\_g6pi \cdot (F6P - \frac{G6P}{keq\_g6pi}) \\
  & - kre\_phosphoglucomutase \cdot (G6P - \frac{G1P}{keq\_phosphoglucomutase}) \\ 
  \frac{d G1P}{dt} &= kre\_phosphoglucomutase \cdot (G6P - \frac{G1P}{keq\_phosphoglucomutase}) \\
  & - \frac{G1P \cdot atp \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{adp}{ki\_ex\_g1p}) \cdot (atp + km\_ex\_g1p\_atp) + \frac{km\_ex\_g1p\_atp \cdot pi}{F6P \cdot ki\_ex\_g1p\_F6P + FBP \cdot ki\_ex\_g1p\_FBP + 3PGA \cdot ki\_ex\_g1p\_3PGA})} \\ 
  \frac{d SBP}{dt} &= kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & - \frac{SBP \cdot vmax\_SBPase}{SBP + km\_SBPase\_s \cdot (1 + \frac{pi}{ki\_SBPase\_pi})} \\ 
  \frac{d S7P}{dt} &= - kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & + \frac{SBP \cdot vmax\_SBPase}{SBP + km\_SBPase\_s \cdot (1 + \frac{pi}{ki\_SBPase\_pi})} \\ 
  \frac{d E4P}{dt} &= - kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & + kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\ 
  \frac{d X5P}{dt} &= kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & + kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - kre\_ribulose\_phosphate\_epimerase \cdot (X5P - \frac{RU5P}{keq\_ribulose\_phosphate\_epimerase}) \\ 
  \frac{d R5P}{dt} &= kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - kre\_ribose\_phosphate\_isomerase \cdot (R5P - \frac{RU5P}{keq\_ribose\_phosphate\_isomerase}) \\ 
  \frac{d RUBP}{dt} &= - \frac{CO2 (dissolved) \cdot RUBP \cdot vmax\_rubisco\_carboxylase}{(CO2 (dissolved) + km\_rubisco\_carboxylase\_CO2 (dissolved)) \cdot (RUBP + km\_rubisco\_carboxylase\_RUBP \cdot (1 + \frac{FBP}{ki\_rubisco\_carboxylase\_FBP} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA} + \frac{nadph}{ki\_rubisco\_carboxylase\_nadph} + \frac{pi}{ki\_rubisco\_carboxylase\_pi}))} \\
  & + \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))} \\ 
  \frac{d RU5P}{dt} &= kre\_ribose\_phosphate\_isomerase \cdot (R5P - \frac{RU5P}{keq\_ribose\_phosphate\_isomerase}) \\
  & + kre\_ribulose\_phosphate\_epimerase \cdot (X5P - \frac{RU5P}{keq\_ribulose\_phosphate\_epimerase}) \\
  & - \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))} \\ 
  \frac{d atp}{dt} &= convf \cdot kf\_atp\_synthase \cdot (\frac{adp}{convf} - \frac{atp}{convf \cdot keq\_atp\_synthase}) \\
  & - kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))} \\
  & - \frac{G1P \cdot atp \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{adp}{ki\_ex\_g1p}) \cdot (atp + km\_ex\_g1p\_atp) + \frac{km\_ex\_g1p\_atp \cdot pi}{F6P \cdot ki\_ex\_g1p\_F6P + FBP \cdot ki\_ex\_g1p\_FBP + 3PGA \cdot ki\_ex\_g1p\_3PGA})} \\
  & - atp \cdot kf\_ex\_atp \\ 
  \frac{d fd\_ox}{dt} &= fd\_red \cdot kf\_ferredoxin\_thioredoxin\_reductase \cdot tr\_ox \\
  & + 2 \cdot kf\_cyclic\_electron\_flow \cdot pq\_ox \cdot {fd\_red}^{2} \\
  & + 2 \cdot \frac{vmax\_fnr \cdot (\frac{nadp \cdot {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2}}{convf \cdot km\_fnr\_nadp} - \frac{nadph \cdot {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2}}{convf \cdot keq\_fnr \cdot km\_fnr\_nadp})}{-1 + (1 + \frac{nadp}{convf \cdot km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_red}{km\_fnr\_fd\_red}) + (1 + \frac{nadph}{convf \cdot km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_ox}{km\_fnr\_fd\_red})} \\
  & - ps1states \cdot fd\_ox \cdot vmax\_ferredoxin\_reductase - \frac{ps1states \cdot fd\_red \cdot vmax\_ferredoxin\_reductase}{keq\_ferredoxin\_reductase} \\ 
  \frac{d protons\_lumen}{dt} &= - \frac{HPR}{bH} \cdot kf\_atp\_synthase \cdot (\frac{adp}{convf} - \frac{atp}{convf \cdot keq\_atp\_synthase}) \\
  & + \frac{4}{bH} \cdot \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & + \frac{2}{bH} \cdot 0.5 \cdot ps2states \cdot k2 \\
  & - \frac{1}{bH} \cdot kf\_proton\_leak \cdot (protons\_lumen - 4000 \cdot {10}^{- pH}) \\ 
  \frac{d lhc}{dt} &= - \frac{1 \cdot kStt7 \cdot lhc}{1 + {\frac{pq\_ox}{PQ\_tot \cdot km\_lhc\_state\_transition\_12}}^{n\_ST}} \\
  & + kPph1 \cdot lhc\_prot \\ 
  \frac{d nadph}{dt} &= convf \cdot \frac{vmax\_fnr \cdot (\frac{nadp \cdot {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2}}{convf \cdot km\_fnr\_nadp} - \frac{nadph \cdot {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2}}{convf \cdot keq\_fnr \cdot km\_fnr\_nadp})}{-1 + (1 + \frac{nadp}{convf \cdot km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_red}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_red}{km\_fnr\_fd\_red}) + (1 + \frac{nadph}{convf \cdot km\_fnr\_nadp}) \cdot (1 + {\frac{fd\_ox}{km\_fnr\_fd\_red}}^{2} + \frac{fd\_ox}{km\_fnr\_fd\_red})} \\
  & - kre\_gadph \cdot (BPGA \cdot nadph \cdot protons - \frac{GAP \cdot nadp \cdot pi}{keq\_gadph}) \\
  & - \frac{MDA \cdot nadph \cdot vmax\_mda\_reductase\_2}{MDA \cdot km\_mda\_reductase\_2\_nadph + MDA \cdot nadph + km\_mda\_reductase\_2\_MDA \cdot km\_mda\_reductase\_2\_nadph + km\_mda\_reductase\_2\_MDA \cdot nadph} \\
  & - \frac{GSSG \cdot nadph \cdot vmax\_glutathion\_reductase}{GSSG \cdot km\_glutathion\_reductase\_nadph + GSSG \cdot nadph + km\_glutathion\_reductase\_GSSG \cdot km\_glutathion\_reductase\_nadph + km\_glutathion\_reductase\_GSSG \cdot nadph} \\
  & - kf\_ex\_nadph \cdot nadph \\ 
  \frac{d pc\_ox}{dt} &= - 2 \cdot \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & + ps1states \cdot PPFD \cdot (1 - PSII\_cross\_section) \\ 
  \frac{d pq\_ox}{dt} &= \max(- kcat\_b6f, kcat\_b6f \cdot (pq\_red \cdot {pc\_ox}^{2} - \frac{pq\_ox \cdot {pc\_red}^{2}}{keq\_b6f})) \\
  & - kf\_cyclic\_electron\_flow \cdot pq\_ox \cdot {fd\_red}^{2} \\
  & - kf\_ndh \cdot pq\_ox - 0.5 \cdot ps2states \cdot k2 \\
  & + O2\_lumen \cdot kPTOX \cdot pq\_red \\ 
  \frac{d psbs\_de}{dt} &= - \frac{kf\_lhc\_protonation \cdot psbs\_de \cdot {protons\_lumen}^{kh\_lhc\_protonation}}{{protons\_lumen}^{kh\_lhc\_protonation} + {4000 \cdot {10}^{- ksat\_lhc\_protonation}}^{kh\_lhc\_protonation}} \\
  & + kf\_lhc\_deprotonation \cdot psbs\_pr \\ 
  \frac{d vx}{dt} &= - \frac{kf\_violaxanthin\_deepoxidase \cdot vx \cdot {protons\_lumen}^{kh\_violaxanthin\_deepoxidase}}{{protons\_lumen}^{kh\_violaxanthin\_deepoxidase} + {4000 \cdot {10}^{- ksat\_violaxanthin\_deepoxidase}}^{kh\_violaxanthin\_deepoxidase}} \\
  & + kf\_zeaxanthin\_epoxidase \cdot zx \\ 
  \frac{d MDA}{dt} &= - 2 \cdot kf\_mda\_reductase\_1 \cdot {MDA}^{2} \\
  & - 2 \cdot \frac{MDA \cdot nadph \cdot vmax\_mda\_reductase\_2}{MDA \cdot km\_mda\_reductase\_2\_nadph + MDA \cdot nadph + km\_mda\_reductase\_2\_MDA \cdot km\_mda\_reductase\_2\_nadph + km\_mda\_reductase\_2\_MDA \cdot nadph} \\
  & + 2 \cdot \frac{H2O2 \cdot XT \cdot ascorbate}{\frac{H2O2}{kf2} + \frac{H2O2}{kf4} + \frac{ascorbate}{kf1} + H2O2 \cdot ascorbate \cdot (\frac{1}{kf3} + \frac{1}{kf5}) + \frac{kr1}{kf1 \cdot kf2} + \frac{H2O2 \cdot kr2}{kf2 \cdot kf3} + \frac{H2O2 \cdot kr4}{kf4 \cdot kf5} + \frac{kr1 \cdot kr2}{kf1 \cdot kf2 \cdot kf3}} \\ 
  \frac{d H2O2}{dt} &= convf \cdot ps1states \cdot O2\_lumen \cdot kMehler \\
  & - \frac{H2O2 \cdot XT \cdot ascorbate}{\frac{H2O2}{kf2} + \frac{H2O2}{kf4} + \frac{ascorbate}{kf1} + H2O2 \cdot ascorbate \cdot (\frac{1}{kf3} + \frac{1}{kf5}) + \frac{kr1}{kf1 \cdot kf2} + \frac{H2O2 \cdot kr2}{kf2 \cdot kf3} + \frac{H2O2 \cdot kr4}{kf4 \cdot kf5} + \frac{kr1 \cdot kr2}{kf1 \cdot kf2 \cdot kf3}} \\ 
  \frac{d DHA}{dt} &= kf\_mda\_reductase\_1 \cdot {MDA}^{2} \\
  & - \frac{DHA \cdot GSH \cdot vmax\_dehydroascorbate\_reductase}{K + DHA \cdot GSH + DHA \cdot km\_dehydroascorbate\_reductase\_GSH + GSH \cdot km\_dehydroascorbate\_reductase\_DHA} \\ 
  \frac{d GSSG}{dt} &= - \frac{GSSG \cdot nadph \cdot vmax\_glutathion\_reductase}{GSSG \cdot km\_glutathion\_reductase\_nadph + GSSG \cdot nadph + km\_glutathion\_reductase\_GSSG \cdot km\_glutathion\_reductase\_nadph + km\_glutathion\_reductase\_GSSG \cdot nadph} \\
  & + \frac{DHA \cdot GSH \cdot vmax\_dehydroascorbate\_reductase}{K + DHA \cdot GSH + DHA \cdot km\_dehydroascorbate\_reductase\_GSH + GSH \cdot km\_dehydroascorbate\_reductase\_DHA} \\ 
  \frac{d tr\_ox}{dt} &= - fd\_red \cdot kf\_ferredoxin\_thioredoxin\_reductase \cdot tr\_ox \\
  & + 5 \cdot E\_inactive \cdot kf\_tr\_activation \cdot tr\_red \\ 
  \frac{d E\_inactive}{dt} &= - 5 \cdot E\_inactive \cdot kf\_tr\_activation \cdot tr\_red \\
  & + 5 \cdot E\_active \cdot kf\_tr\_inactivation
\end{align*}