European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

On the abelian structure of noncompetitive chemical reaction networks.

MS154-03

15 Jul 2026, 11:50

20m

11.01 - HS (University of Graz)

Minisymposium Talk Systems Biology and Biochemical Networks Advanced Topics in Stochastic Chemical Reaction Networks

Speaker

Louis Faul (Université de Fribourg)

Description

Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks. A central contribution of this work is that noncompetitive CRNs are special instances of Abelian networks (ANs)—a well-established framework for self-organized criticality. CRNs of interest in biochemistry and systems biology are embedded in complex networks so that local CRNs have to respond to internal and environmental cues. We describe the network’s response to such perturbations using a Markov chain whose state space is the set of CRN’s static states, from where no reaction is possible. The addition of molecules to a static state induces reactions that move the system into a new static state. For noncompetitive CRNs of finite state space, we use AN theory to get that only a fraction of the static states are recurrent, suggesting that these states might be the biologically relevant configurations.

We obtain furthermore that the set of recurrent states is in one to one correspondence with the critical group of the AN. Overall, this work establishes a unified algebraic and probabilistic framework for analyzing the long-term behavior of noncompetitive CRNs.

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