(38g) Reaction Network Analysis and Motifs for Rhythmic Dynamics in Metabolic and Circadian Models of Cyanobacteria in a Photobioreactor

Reaction network theories 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 [1]. This analysis is qualitative in the sense that only reaction orders are needed as input information, whereas rate coefficients and concentrations of chemical components may remain unspecified. In the next step, 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 the unknown/unspecified rate coefficients by applying linear optimization to a set of constraint equations balancing linearly combined subnetworks with the corresponding rate expressions [2]. From mathematical point of view, this is a special case of convex optimization.

From the application point of view, the outlined theory is applied to experimentally measured activity of photosynthesizing diazotrophic cyanobacteria in a photobioreactor [3]. In particular, we focus on biochemical processes giving rise to experimentally observed change from a steady state to oscillatory dynamics. The oscillations in cyanobacteria come from either circadian cycles synchronized with external light/dark cycle or from an internal ultradian clock [4], 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.

For these biochemical systems a reaction mechanism is assumed (or available from previous research) with only a limited set of known kinetic parameters, in addition to input/output parameters known from the experiment. Then the set of unknown kinetic parameters is estimated via linear optimization so that the dynamics displayed by the model coincides with the experimentally observed behavior (emergence of oscillations). Such an estimate may not yield the ultimate best fit, rather, it helps to locate a region in the parameter space, where the observed dynamics are reproduced by the model. This global approach is useful especially when the number of unknown parameters is large. Once a suitable parameter region is found, either standard least-square methods or other more refined algorithms involving deep learning may be used to fine tune the parameters values.

In addition, the reaction network theory is useful in identifying subnetworks that are at the core of destabilizing the steady state. In particular, such subnetworks provide prototypes/motifs of (bio)chemical oscillators, which possess a characteristic network topology [5]. Thus the search for dynamical instabilities in large networks typical for biosystems can be reduced to the search for motifs.

References:

[1] B. L. Clarke, Stability of complex reaction networks. Advances in Chemical Physics 43, 1-278 (1980).

[2] V. Radojkovic and I. Schreiber, Constrained Stoichiometric Network Analysis, Physical Chemistry Chemical Physics 20, 9910–9921 (2018).

[3] J. Červený, J. Šalagovič, F. Muzika, D. Šafránek and I. Schreiber, Influence of Circadian Clocks on Optimal Regime of Central C-N Metabolism of Cyanobacteria. In: Cyanobacteria: From Basic Science to Applications, Edited by A.K. Mishra, D.N. Tiwari and A.N. Rai, Elsevier, London, 2019, pp. 193-206.

[4] J. Červený, M. A. Sinetova, L. Valledor, L. A. Sherman, L. Nedbal, Ultradian metabolic rhythm in the diazotrophic cyanobacterium Cyanothece sp. ATCC 51142. Proc. Natl. Acad. Sci. 110 (32), 13210–13215 (2013).

[5] J. Ross, I. Schreiber and M. O. Vlad, Determination of Complex Reaction Mechanisms, Oxford University Press, Inc., New York, 2006.