Dynamical properties of models for the Calvin cycle

TL;DR

This paper analyzes the long-term behavior of mathematical models for the Calvin cycle, revealing conditions for multiple stationary solutions, substrate depletion, runaway growth, and the effects of including ATP explicitly.

Contribution

It provides a detailed analysis of the asymptotic behavior of various Calvin cycle models, highlighting the impact of model choices on solution dynamics.

Findings

Existence of two positive stationary solutions in some models

Presence of substrate depletion and runaway solutions under certain conditions

Including ATP explicitly prevents runaway solutions

Abstract

Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric coefficients and chemical kinetics and whether or not diffusion is taken into account. This paper studies the long-time behaviour of solutions of several of these systems, concentrating on the ODE case. In some examples it is shown that there exist two positive stationary solutions. In several cases it is shown that there exist solutions where the concentrations of all substrates tend to zero at late times and others (runaway solutions) where the concentrations of all substrates increase without limit. In another case, where the concentration of ATP is explicitly included, runaway solutions are ruled out.