Reaction Network Analysis of Rhythmic Dynamics in Metabolic and Circadian Models of Cyanobacteria in a Photobioreactor

Reaction network analysis assumes that stoichiometric equations are given for each reaction step together with power law rate expressions. On output, 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 and does not assume the values of rate coefficients and concentrations of chemical components. The subnetworks are combined to form the entire network and its stability is deduced from the stability of the constituting subnetworks. This combination principle can be conveniently used for kinetic parameter estimation of unknown/unspecified rate coefficients by applying linear optimization to a set of constraint equations balancing linearly combined subnetworks using corresponding rate expressions. From the mathematical point of view, this is a special case of convex optimization. The search for optimum is complicated because of restrictions imposed by solvability conditions. We employ a machine learning algorithm to facilitate the numerical procedure.

The outlined theory is applied to an experimental system involving photosynthesizing diazotrophic cyanobacteria in photobioreactor. In particular, we focus on biochemical processes giving rise to experimentally observed change from a steady state to oscillatory dynamics. Depending on external conditions oscillations in cyanobacteria may come either from circadian cycles synchronized with external light/dark cycle or from an internal ultradian clock, which is active even in the absence of external environmental cues. For the former, we examine models of circadian clock associated with a network involving the KaiABC proteins and their regeneration via a transcriptional network, for the latter, a carbon-nitrogen metabolic model is analyzed. Next, for these biochemical model systems the set of unknown kinetic parameters is determined via the outlined convex optimization so that the dynamics displayed by the model fit the experimentally observed emergence of oscillations.