Transitions and Thermodynamics on Species Graphs of Chemical Reaction Networks
Abstract: Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By scaling concentrations by conservation laws, we obtain a graph representation of transitions compatible with the S-graph, which allows us to treat the dynamics in CRNs as transitions between chemicals. We also define thermodynamic-like quantities on the S-graph from the introduced transitions and investigate their properties, including the relationship between specieswise forces, activities, and conventional thermodynamic quantities. Remarkably, we demonstrate that this formulation can be developed for a class of irreversible CRNs, while for reversible CRNs, it is related to conventional thermodynamic quantities associated with reactions. The behavior of these specieswise quantities is numerically validated using an oscillating system (Brusselator). Our work provides a novel methodology for studying dynamics on S-graphs, paving the way for a deeper understanding of the intricate interplay between the structure and dynamics of chemical reaction networks.
- J. Orth, I. Thiele, and B. Palsson, What is flux balance analysis?, Nature biotechnology 28, 245 (2010).
- K. Yoshimura and S. Ito, Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks, Phys. Rev. Lett. 127, 160601 (2021a).
- Y. Himeoka, S. A. Horiguchi, and T. J. Kobayashi, Stoichiometric rays: A simple method to compute the controllable set of enzymatic reaction systems (2024), arXiv:2403.02169 [physics.bio-ph] .
- D. J. Watts and S. H. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 393, 440–442 (1998).
- M. Newman, Networks (Oxford University Press, 2018).
- D. Angeli, P. De Leenheer, and E. Sontag, Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates, Journal of Mathematical Biology 61, 581–616 (2009).
- A. Wagner and D. A. Fell, The small world inside large metabolic networks, Proceedings of the Royal Society of London. Series B: Biological Sciences 268, 1803–1810 (2001).
- S. Klamt, U.-U. Haus, and F. Theis, Hypergraphs and cellular networks, PLOS Computational Biology 5, 1 (2009).
- Y. Himeoka and K. Kaneko, Enzyme oscillation can enhance the thermodynamic efficiency of cellular metabolism: consequence of anti-phase coupling between reaction flux and affinity, Physical Biology 13, 026002 (2016).
- P. Kim and C. Hyeon, Thermodynamic optimality of glycolytic oscillations, The Journal of Physical Chemistry B 125, 5740 (2021), pMID: 34038120, https://doi.org/10.1021/acs.jpcb.1c01325 .
- L. Fontanil and E. Mendoza, Common complexes of decompositions and complex balanced equilibria of chemical reaction networks, MATCH Communications in Mathematical and in Computer Chemistry 87, 329 (2022).
- M. Feinberg, Foundations of Chemical Reaction Network Theory (Springer International Publishing, 2019).
- S. Müller, C. Flamm, and P. F. Stadler, What makes a reaction network ”chemical”?, J Cheminform 14, 63 (2022).
- L. J. Grady and J. R. Polimeni, Discrete Calculus (Springer London, 2010).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Reports on Progress in Physics 75, 126001 (2012).
- K. Yoshimura and S. Ito, Information geometric inequalities of chemical thermodynamics, Phys. Rev. Res. 3, 013175 (2021b).
- D. T. Gillespie, The chemical Langevin equation, The Journal of Chemical Physics 113, 297 (2000), https://pubs.aip.org/aip/jcp/article-pdf/113/1/297/19042305/297_1_online.pdf .
- N. Ohga, S. Ito, and A. Kolchinsky, Thermodynamic bound on the asymmetry of cross-correlations, Phys. Rev. Lett. 131, 077101 (2023).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.