(513cu) Reaction Networks, Motifs for Oscillatory Dynamics, and Parameter Estimation in Complex Biochemical Mechanisms

Reaction network theories in general and the stoichiometric network analysis in particular are tools for stability analysis of open reacting systems provided that stoichiometric (chemical) equations are given for each reaction step together with power law rate expressions. Based on stoichiometry alone, elementary subnetworks (known also as elementary modes or extreme currents) are identified and their capacity for displaying dynamical instabilities, such as bistability and oscillations, is evaluated by examining the associated Jacobian matrix. This analysis is qualitative in the sense that only reaction orders are needed as input information. Such information is sufficient for determining the core part of the mechanism providing for oscillations, often referred to as an oscillatory motif. However, this network theory can be extended by formulating a set of constraint equations aimed at parameter estimation of the unknown/unspecified rate coefficients by applying convex optimization, which takes into account data obtained from experiments at the onset of oscillations or a bistable switch. We call this extension the constrained stoichiometric network analysis.

Based on this approach, we discuss two cases: i) the reaction pathways leading to experimentally observed oscillatory dynamics in the urea-urease reaction in the CSTR; ii) the reaction pathways representing rhythmic behavior in metabolic and circadian models of cyanobacteria in a photobioreactor. The former involves a detailed mass action kinetic description of an enzyme reaction, the latter combines an empirical power law model of metabolism with a KaiABC circadian clock model.