Reaction Networks, Oscillatory Motifs and Parameter Estimation in Biochemical Systems

Abstract

We outline an approach to analysis of dynamics of biosystems formulated as reaction networks. In particular, we discuss stability analysis provided that stoichiometric equations are given for each reaction step together with power law rate expressions. Based on stoichiometry alone, the network at stationary state can be decomposed into elementary subnetworks (elementary modes, extreme currents, fluxes). Assuming power law kinetics, the capacity of the elementary subnetworks for displaying dynamical instabilities, such as bistability and oscillations, is evaluated. These subnetworks are then suitably combined to form the entire network satisfying certain stability constraints implied by experiments. Specifically, we assume that an experimentally measured biosystem represented by a reaction network displays an experimentally observed change from a steady state to oscillations. For the assumed reaction mechanism only a limited set kinetic parameters is known. In contrast, input/output parameters are known from the experiment. The set of unknown kinetic parameters may be estimated by finding a suitable linear combination of elementary modes via linear optimization so that the dynamics displayed by the model fits the experimentally observed behavior. Moreover, reaction network theory is useful in identifying subnetworks that are destabilizing the steady state to yield oscillations. Such subnetworks are called oscillatory motifs and possess a characteristic topology. As an example, we analyze a carbon-nitrogen metabolism of cyanobacteria and examine its oscillatory dynamics.