Stability Analysis of Biological Networks Through a Dynamical Flow Network Modelling Approach

We show how certain classes of biological networks, with arbitrary "rate functions", can be modelled as dynamical flow networks. This characterisation of a biological network allows us to construct a linear co-positive Lyapunov function whose drift can be computed explicitly, and hence to assess the stability as well as the Input-to-State Stability (ISS) properties of the system, by only analysing the properties of the rate functions in their limits. We also provide sufficient conditions for ISS with respect to small inputs when the rate functions are subject to saturation, as is the case for Michaelis-Menten and Hill functions. We exemplify our proposed method for stability analysis by considering a model for glucose absorption where one of the rate functions is non-monotonic.