A Calvin bestiary

TL;DR

This paper analyzes various mathematical models of the Calvin cycle, establishing existence and stability of steady states, and clarifies the nature of larger models, including differential-algebraic systems with multiple steady states.

Contribution

It compares existing models, proves multiple steady states in a complex model, and clarifies the differential-algebraic nature of the Pettersson-Ryde-Pettersson model.

Findings

Multiple positive steady states exist under certain parameters.

The Pettersson-Ryde-Pettersson model is a differential-algebraic system.

Survey of stability results for five-variable models.

Abstract

This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are surveyed. Next a number of larger models related to one introduced by Pettersson and Ryde-Pettersson are discussed. The mathematical nature of this model is clarified, showing that it is naturally defined as a system of differential-algebraic equations. It is proved that there are choices of parameters for which this model admits more than one positive steady state. This is done by analysing the limit where the storage of sugars from the cycle as starch is shut down. There is also a discussion of the minimal models for the cycle due to Hahn.