Sufficient Conditions for Coordination of Coupled Nonlinear Biochemical Systems: Analysis of a Simple, Representative Example

Abstract

Under conditions of stress and environmental fluctuations, how do coupled biochemical systems maintain the balance of metabolic fluxes? Using a model derived from a representative glycolysis example, this work derives sufficient coordination conditions for guaranteeing the balance of metabolic fluxes in the coupled systems subjected to any fluctuations. For diffusion-like coupling, it is explicitly shown that the sufficient conditions are the linear summation of individual uncoupled systems. For this case, coupling strength is not a key factor affecting the balance of metabolic fluxes, although it may affect the emergence of certain dynamic patterns. When the sufficient coordination conditions are satisfied, coupled systems always settle onto stable finite states, independently of the nature (type, period or amplitude) of external signals. When they are not, external signals may force the stable states of coupled systems to lose their coordination, resulting in the coupled systems having no stable finite states which is inconsistent with most normal biological functions. Numerical simulations support the analytical results. The generalization of this result for other coupled nonlinear biochemical systems is discussed. Finally, the maintenance of such biological coordination is discussed in the context of genetic engineering and environmental fluctuations.