Analysis on steady states of photosynthetic carbon metabolic system

In this paper, we propose a reduced molecular network of the photosynthetic carbon metabolism, which includes the nine major metabolites with 48 parameters. The reduced molecular network can represent the key ingredients of photosynthetic carbon metabolism, i.e. the autocatalytic cycle, the utilization of photosynthate, and the effect of photorespiration. Based on the model, we theoretically study steady states or stable equilibria of photosynthetic carbon metabolism, and prove that such a system actually has at most one feasible steady state in the domain of a parameter set defined around nominal values for that parameter set. Specifically, we first equivalently transform the original system into an independent 2-dimensional subsystem which contains just 10 parameters, and then show that steady states of the original system can be determined by the 2-dimensional subsystem uniquely. Finally, we show that when the 10 parameters for the 2-dimensional subsystem all stay in an appropriate domain around the nominal value of each parameter, the reduced model has at most one physiologically feasible steady state no matter how the other 38 parameters in the original model are taken. In addition, we also derive parameter domain to ensure such an asymptotical behavior.