Zhu 2009, Nonlinear Anal.

The Zhu 2009 model is a deliberately simplified kinetic model of the Calvin-Benson-Bassham (CBB) cycle, the carbon-fixing 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). The many intermediate steps of the cycle are lumped into a handful of Michaelis-Menten reactions, and ATP, NADPH, CO2 and inorganic phosphate are all treated as fixed external parameters rather than dynamic variables. This reduction keeps the system small enough to be analyzed mathematically while still capturing the essential autocatalytic structure of carbon fixation, in which RuBP is both consumed by RuBisCO and regenerated downstream.

The model was constructed to enumerate all of the cycle's possible steady states, and Zhu et al. showed that, although the system admits more than one mathematical steady state, only a single one is physiologically feasible. It is therefore included in GreenSloth less as a predictive tool and more as an example of how the multistationarity and stability of the CBB cycle can be studied, a question that has since motivated a substantial body of follow-up mathematical work on CBB cycle dynamics.

Model definition