Poolman 2000 CBB model
The Poolman 2000 model is a kinetic model of the Calvin–Benson cycle, the carbon-fixation pathway of C3 plant chloroplasts. Rubisco carboxylase and oxygenase compete for ribulose-1,5-bisphosphate, while downstream enzymes such as FBPase and SBPase regenerate it, with the whole cycle driven by dissolved CO₂, NADPH and ATP.
Enzyme activities scale with their maximal turnover and are subject to product inhibition, letting the model reproduce the steady-state behaviour and regulation of carbon assimilation.
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Review and edit model structure, biological variables, and kinetic parameters.
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\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} &= - 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})} \\
& + \frac{adp \cdot pi \cdot vmax\_atp\_synthase}{(adp + km\_atp\_synthase\_adp) \cdot (km\_atp\_synthase\_pi + pi)}
\end{align*}Edit analysis
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