A parameter condition for ruling out multiple equilibria of the photosynthetic carbon metabolism

Abstract

In this paper, we propose a reduced molecular network for the photosynthetic carbon metabolism, which can describe the following key characteristics: Calvin cycle, utilization of photosynthate, and photorespiration. Taking the concentrations of the nine major metabolites as variables, we represent the reduced network by deriving a nonlinear differential‐algebraic system with 48 parameters, and theoretically study the multi‐equilibrium property in the photosynthetic carbon metabolism. Specifically, we equivalently transform the original 9‐dimensional system into an independent 2‐dimensional subsystem with ten parameters, and show that the original system has no more than one physiologically feasible equilibrium when the ten parameters of the subsystem stay in a certain field around the nominal value of each parameter, no matter what values the other 38 parameters in the original model are taken. Such a theoretical result not only provides profound insights for qualitatively understanding of the dynamic features of the photosynthetic carbon metabolism, but also can be used to make an accurate judgement on a correct strategy for improving the photosynthesis in plants. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Dynamical Properties of Models for the Calvin Cycle

“…This led to the question of whether the relevant mathematical models admit more than one stable positive stationary solution. For related work see also [21], [4], [13] and [14]. It was already shown in [9] that a simple model using mass action kinetics (the model called MA) never admits even one solution of this type.…”

Multi‐equilibrium property of metabolic networks: MMN module

“…Multi‐equilibrium of metabolic networks is a fundamental and significant property in systems biology , including the capacity for admitting multiple equilibria and the dynamic behaviors of the equilibria. The former considers the existence of multiple equilibria and the latter focuses mainly on their stabilities.…”