Sufficient conditions for coordination of a nonlinear biochemical system under external forcing

One of the fundamental properties of biochemical networks in cells is the p reservation of viability under conditions of stress and environmental pertu rbation. This requires that the system maintains coordination in the sense that a stable (time-dependent) state can form under such conditions. Althou gh this property emerges from the characteristics of the constitutive enzym es, the general conditions that must be satisfied by a network to maintain a viable state are not known. The essential features of enzymatic reactions are saturation kinetics and a nonlinear dependency of reaction rate on met abolite concentration. For a simple branched system we derive sufficient co nditions on these features that, if satisfied, imply that the resulting met abolic processes remain coordinated when the system is exposed to external perturbations of any type, amplitude, or frequency. Upon removal of the per turbation, the unperturbed state will be recovered. When the system does no t satisfy the sufficient conditions, it is shown that coordination depends on the nature of the perturbing signals. Furthermore, once coordination is lost, it cannot be retrieved by removal of the perturbing force and therefo re the system cannot settle to any finite state. These results are supporte d by numerical analysis using three types of external signals: namely, rect angular, sinusoidal, and noisy signals.