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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Model Details
Review and edit model structure, biological variables, and kinetic parameters.
| Name | Tex name | Initial value | Actions |
|---|---|---|---|
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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*}Fit to data
Fit settings
| Setting | Value |
|---|---|
| Fit backend | |
| Function evaluations per progress update | |
| Maximum total function evaluations | |
| Stop once residual norm reaches |
Curriculum learning (advanced)
Every bar shares one fixed step budget. Drag a divider to move a cutoff, drag a bar's top edge (or focus it and use the arrow keys) to change its share — the final stage isn't draggable, it always gets whatever's left. Double-click a bar or use its + to split it, use a divider's × (or Delete/Backspace while it's focused) to remove it.
Split into equal stages:
min viable
t=0 t=100
| Stage | Data cutoff | Iteration budget |
|---|---|---|
| 1 (final) | full data | 1000 iterations (runs to convergence within this) |
Data
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| Parameter | Fit | Log-space | Initial guess / fixed value | Fitted value |
|---|---|---|---|---|
| CO2__dissolved_ | — | |||
| nadph | — | |||
| protons | — | |||
| A_P | — | |||
| NADP_ | — | |||
| Pi_tot | — | |||
| E0_rubisco_carboxylase | — | |||
| kcat_rubisco_carboxylase | — | |||
| km_rubisco_carboxylase_RUBP | — | |||
| km_rubisco_carboxylase_CO2__dissolved_ | — | |||
| ki_rubisco_carboxylase_3PGA | — | |||
| ki_rubisco_carboxylase_FBP | — | |||
| ki_rubisco_carboxylase_SBP | — | |||
| ki_rubisco_carboxylase_pi | — | |||
| ki_rubisco_carboxylase_nadph | — | |||
| kre_phosphoglycerate_kinase | — | |||
| keq_phosphoglycerate_kinase | — | |||
| kre_gadph | — | |||
| keq_gadph | — | |||
| kre_triose_phosphate_isomerase | — | |||
| keq_triose_phosphate_isomerase | — | |||
| kre_aldolase_dhap_gap | — | |||
| keq_aldolase_dhap_gap | — | |||
| kre_aldolase_dhap_e4p | — | |||
| keq_aldolase_dhap_e4p | — | |||
| E0_fbpase | — | |||
| kcat_fbpase | — | |||
| km_fbpase_s | — | |||
| ki_fbpase_F6P | — | |||
| ki_fbpase_pi | — | |||
| kre_transketolase_gap_f6p | — | |||
| keq_transketolase_gap_f6p | — | |||
| kre_transketolase_gap_s7p | — | |||
| keq_transketolase_gap_s7p | — | |||
| E0_SBPase | — | |||
| kcat_SBPase | — | |||
| km_SBPase_s | — | |||
| ki_SBPase_pi | — | |||
| kre_ribose_phosphate_isomerase | — | |||
| keq_ribose_phosphate_isomerase | — | |||
| kre_ribulose_phosphate_epimerase | — | |||
| keq_ribulose_phosphate_epimerase | — | |||
| E0_phosphoribulokinase | — | |||
| kcat_phosphoribulokinase | — | |||
| km_phosphoribulokinase_RU5P | — | |||
| km_phosphoribulokinase_atp | — | |||
| ki_phosphoribulokinase_3PGA | — | |||
| ki_phosphoribulokinase_RUBP | — | |||
| ki_phosphoribulokinase_pi | — | |||
| ki_phosphoribulokinase_4 | — | |||
| ki_phosphoribulokinase_5 | — | |||
| kre_g6pi | — | |||
| keq_g6pi | — | |||
| kre_phosphoglucomutase | — | |||
| keq_phosphoglucomutase | — | |||
| pi_ext | — | |||
| km_ex_pga | — | |||
| km_ex_gap | — | |||
| km_ex_dhap | — | |||
| km_N_translocator_pi_ext | — | |||
| km_N_translocator_pi | — | |||
| kcat_N_translocator | — | |||
| E0_N_translocator | — | |||
| km_ex_g1p_G1P | — | |||
| km_ex_g1p_atp | — | |||
| ki_ex_g1p | — | |||
| ki_ex_g1p_3PGA | — | |||
| ki_ex_g1p_F6P | — | |||
| ki_ex_g1p_FBP | — | |||
| E0_ex_g1p | — | |||
| kcat_ex_g1p | — | |||
| km_atp_synthase_adp | — | |||
| km_atp_synthase_pi | — | |||
| kcat_atp_synthase | — | |||
| E0_atp_synthase | — |
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