Matuszyńska 2019 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{NADPH}{ki\_rubisco\_carboxylase\_NADPH} + \frac{Orthophosphate}{ki\_rubisco\_carboxylase\_Orthophosphate} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA}))} \\
  & - kre\_phosphoglycerate\_kinase \cdot (ATP \cdot 3PGA - \frac{ADP \cdot BPGA}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{3PGA \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_pga} \\ 
  \frac{d BPGA}{dt} &= kre\_phosphoglycerate\_kinase \cdot (ATP \cdot 3PGA - \frac{ADP \cdot BPGA}{keq\_phosphoglycerate\_kinase}) \\
  & - kre\_gadph \cdot (BPGA \cdot NADPH \cdot protons - \frac{GAP \cdot NADP \cdot Orthophosphate}{keq\_gadph}) \\ 
  \frac{d GAP}{dt} &= kre\_gadph \cdot (BPGA \cdot NADPH \cdot protons - \frac{GAP \cdot NADP \cdot Orthophosphate}{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{Orthophosphate}{ki\_fbpase\_Orthophosphate})} \\ 
  \frac{d F6P}{dt} &= \frac{FBP \cdot vmax\_fbpase}{FBP + km\_fbpase\_s \cdot (1 + \frac{F6P}{ki\_fbpase\_F6P} + \frac{Orthophosphate}{ki\_fbpase\_Orthophosphate})} \\
  & - 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{ATP \cdot G1P \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{ADP}{ki\_ex\_g1p}) \cdot (ATP + km\_ex\_g1p\_ATP) + \frac{Orthophosphate \cdot km\_ex\_g1p\_ATP}{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{Orthophosphate}{ki\_SBPase\_Orthophosphate})} \\ 
  \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{Orthophosphate}{ki\_SBPase\_Orthophosphate})} \\ 
  \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{NADPH}{ki\_rubisco\_carboxylase\_NADPH} + \frac{Orthophosphate}{ki\_rubisco\_carboxylase\_Orthophosphate} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA}))} \\
  & + \frac{ATP \cdot RU5P \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{Orthophosphate}{ki\_phosphoribulokinase\_Orthophosphate} + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA})) \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{ATP \cdot RU5P \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{Orthophosphate}{ki\_phosphoribulokinase\_Orthophosphate} + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA})) \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 (ATP \cdot 3PGA - \frac{ADP \cdot BPGA}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{ATP \cdot RU5P \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{Orthophosphate}{ki\_phosphoribulokinase\_Orthophosphate} + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA})) \cdot (ATP \cdot (1 + \frac{ADP}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_ATP \cdot (1 + \frac{ADP}{ki\_phosphoribulokinase\_5}))} \\
  & - \frac{ATP \cdot G1P \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{ADP}{ki\_ex\_g1p}) \cdot (ATP + km\_ex\_g1p\_ATP) + \frac{Orthophosphate \cdot km\_ex\_g1p\_ATP}{F6P \cdot ki\_ex\_g1p\_F6P + FBP \cdot ki\_ex\_g1p\_FBP + 3PGA \cdot ki\_ex\_g1p\_3PGA})} \\ 
  \frac{d Ferredoxine (oxidised)}{dt} &= 2 \cdot Plastoquinone (oxidised) \cdot kf\_cyclic\_electron\_flow \cdot {Ferredoxine (reduced)}^{2} \\
  & + 2 \cdot \frac{vmax\_fnr \cdot (\frac{NADP \cdot {\frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}}^{2}}{convf \cdot km\_fnr\_NADP} - \frac{NADPH \cdot {\frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)}}^{2}}{convf \cdot keq\_fnr \cdot km\_fnr\_NADP})}{-1 + (1 + \frac{NADP}{convf \cdot km\_fnr\_NADP}) \cdot (1 + {\frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}}^{2} + \frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}) + (1 + \frac{NADPH}{convf \cdot km\_fnr\_NADP}) \cdot (1 + {\frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)}}^{2} + \frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)})} \\
  & - A1 \cdot PPFD \cdot (1 - PSII\_cross\_section) \\ 
  \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 (Plastoquinone (reduced) \cdot {Plastocyanine (oxidised)}^{2} - \frac{Plastoquinone (oxidised) \cdot {Plastocyanine (reduced)}^{2}}{keq\_b6f})) \\
  & + \frac{2}{bH} \cdot 0.5 \cdot B1 \cdot k2 \\
  & - \frac{1}{bH} \cdot kf\_proton\_leak \cdot (protons\_lumen - 4000 \cdot {10}^{- pH}) \\ 
  \frac{d Light-harvesting complex}{dt} &= - \frac{1 \cdot Light-harvesting complex \cdot kStt7}{1 + {\frac{Plastoquinone (oxidised)}{PQ\_tot \cdot km\_lhc\_state\_transition\_12}}^{n\_ST}} \\
  & + Light-harvesting complex (protonated) \cdot kPph1 \\ 
  \frac{d NADPH}{dt} &= convf \cdot \frac{vmax\_fnr \cdot (\frac{NADP \cdot {\frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}}^{2}}{convf \cdot km\_fnr\_NADP} - \frac{NADPH \cdot {\frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)}}^{2}}{convf \cdot keq\_fnr \cdot km\_fnr\_NADP})}{-1 + (1 + \frac{NADP}{convf \cdot km\_fnr\_NADP}) \cdot (1 + {\frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}}^{2} + \frac{Ferredoxine (reduced)}{km\_fnr\_Ferredoxine (reduced)}) + (1 + \frac{NADPH}{convf \cdot km\_fnr\_NADP}) \cdot (1 + {\frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)}}^{2} + \frac{Ferredoxine (oxidised)}{km\_fnr\_Ferredoxine (reduced)})} \\
  & - kre\_gadph \cdot (BPGA \cdot NADPH \cdot protons - \frac{GAP \cdot NADP \cdot Orthophosphate}{keq\_gadph}) \\ 
  \frac{d Plastocyanine (oxidised)}{dt} &= - 2 \cdot \max(- kcat\_b6f, kcat\_b6f \cdot (Plastoquinone (reduced) \cdot {Plastocyanine (oxidised)}^{2} - \frac{Plastoquinone (oxidised) \cdot {Plastocyanine (reduced)}^{2}}{keq\_b6f})) \\
  & + A1 \cdot PPFD \cdot (1 - PSII\_cross\_section) \\ 
  \frac{d Plastoquinone (oxidised)}{dt} &= \max(- kcat\_b6f, kcat\_b6f \cdot (Plastoquinone (reduced) \cdot {Plastocyanine (oxidised)}^{2} - \frac{Plastoquinone (oxidised) \cdot {Plastocyanine (reduced)}^{2}}{keq\_b6f})) \\
  & - Plastoquinone (oxidised) \cdot kf\_cyclic\_electron\_flow \cdot {Ferredoxine (reduced)}^{2} \\
  & - Plastoquinone (oxidised) \cdot kf\_ndh \\
  & - 0.5 \cdot B1 \cdot k2 \\
  & + O2 (dissolved)\_lumen \cdot Plastoquinone (reduced) \cdot kPTOX \\ 
  \frac{d PsbS (de-protonated)}{dt} &= - \frac{PsbS (de-protonated) \cdot kf\_lhc\_protonation \cdot {protons\_lumen}^{kh\_lhc\_protonation}}{{protons\_lumen}^{kh\_lhc\_protonation} + {4000 \cdot {10}^{- ksat\_lhc\_protonation}}^{kh\_lhc\_protonation}} \\
  & + PsbS (protonated) \cdot kf\_lhc\_deprotonation \\ 
  \frac{d Violaxanthin}{dt} &= - \frac{Violaxanthin \cdot kf\_violaxanthin\_deepoxidase \cdot {protons\_lumen}^{kh\_violaxanthin\_deepoxidase}}{{protons\_lumen}^{kh\_violaxanthin\_deepoxidase} + {4000 \cdot {10}^{- ksat\_violaxanthin\_deepoxidase}}^{kh\_violaxanthin\_deepoxidase}} \\
  & + Zeaxanthin \cdot kf\_zeaxanthin\_epoxidase
\end{align*}