Zhu et al. (2009) Calvin Cycle model
The Zhu 2009 model is a deliberately simplified kinetic model of the Calvin-Benson-Bassham (CBB) cycle, the carbon-fixing dark reactions of photosynthesis. It tracks only five metabolites — ribulose-1,5-bisphosphate (RuBP), 3-phosphoglycerate (PGA), 1,3-bisphosphoglycerate (DPGA), glyceraldehyde-3-phosphate (GAP), and ribulose-5-phosphate (Ru5P) — and lumps the many intermediate steps of the cycle into a handful of Michaelis-Menten reactions, with ATP supplied as a fixed external parameter rather than a dynamic variable. This reduction keeps the system small enough to be analysed mathematically while still capturing the essential autocatalytic structure of carbon fixation, where RuBP is both consumed by RuBisCO and regenerated downstream.
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Model Details
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| Name | Tex name | Initial value | Actions |
|---|---|---|---|
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Generated LaTeX Code
\begin{align*}
\frac{d RuBP}{dt} &= - \frac{RuBP \cdot V1\_max}{K\_m1 + RuBP} \\
& + \frac{ATP \cdot Ru5P \cdot V13\_max}{(ATP + K\_m132) \cdot (K\_m131 + Ru5P)} \\
\frac{d PGA}{dt} &= 2 \cdot \frac{RuBP \cdot V1\_max}{K\_m1 + RuBP} \\
& - \frac{ATP \cdot PGA \cdot V2\_max}{(ATP + K\_m22) \cdot (K\_m21 + PGA)} \\
& - \frac{ATP \cdot PGA \cdot V5\_max}{(ATP + K\_m52) \cdot (K\_m51 + PGA)} \\
\frac{d DPGA}{dt} &= \frac{ATP \cdot PGA \cdot V2\_max}{(ATP + K\_m22) \cdot (K\_m21 + PGA)} \\
& - \frac{DPGA \cdot V3\_max}{DPGA + K\_m3} \\
\frac{d Ru5P}{dt} &= 0.6 \cdot \frac{GAP \cdot V4\_max}{GAP + K\_m4} \\
& - \frac{ATP \cdot Ru5P \cdot V13\_max}{(ATP + K\_m132) \cdot (K\_m131 + Ru5P)} \\
\frac{d GAP}{dt} &= \frac{DPGA \cdot V3\_max}{DPGA + K\_m3} \\
& - \frac{GAP \cdot V4\_max}{GAP + K\_m4} \\
& - \frac{GAP \cdot V6\_max}{GAP + K\_m6}
\end{align*}