arXiv subjects

Louis Faul

Publications and source records attributed to Louis Faul.

3 recordsLinked to original sources

arXiv2026

Stability and feasibility of Microbial Consumer-Resource Model

Microbial communities are ubiquitous in nature but how they grow on available resources is still poorly understood. Communities are complex systems harboring thousands of microbial species that interact through resource competition. The classical MacArthur consumer-resource model has been shown to underestimate formed community biomass. A recent new microbial consumer-resource model (MiCRM) considers the inclusion of inter-specific interactions mediated by metabolite exchange (cross-feeding) where the various bacterial growth byproducts can be reused by other species for their own growth. We study persistence, feasibility and stability for MiCRM under some simplifying assumptions using slow-fast approximation. We show e.g. the non-persistence of the microbial community when the number of resource species M is smaller than the number of consumer species S. We then study the stability of the slow steady state when the number or survivors S is smaller than M, and show that such equilibria are generically stable. We finally propose a stochastic slow-fast version of the model having fast Poisson steady state and study related extinction events.

q-bio.PE↗

arXiv2025

On the abelian structure of noncompetitive chemical reaction networks

Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states, where the CRN is inactive, are rate independent, and that can implement ReLU neural networks. CRNs of interest in biochemistry and systems biology are embedded in complex networks so that CRNs have to respond to internal and environmental cues. We describe the network's response to such perturbations using a new Markov chain that we call CRN sandpile Markov chain, whose state space is the set of static states. The transition mechanism of the CRN sandpile Markov chain is defined by adding a molecule of a randomly chosen species to a static state, and then letting the CRN state evolve toward a new static state. A central contribution of the present work is the observation that one can associate a natural Abelian Network (AN) to each noncompetitive CRN, and use AN theory to get new mathematical results on noncompetitive CRNs. For noncompetitive CRNs on a finite state space, we use AN theory to get that only a fraction of the static states are recurrent for the CRN sandpile Markov chain. We obtain furthermore that the set of recurrent states is in one to one correspondence with the critical group of the AN, which plays a major role in AN theory. Overall, this work establishes a unified algebraic and probabilistic framework for analyzing the long-term behavior of noncompetitive CRNs. We focus on a special class of noncompetitive CRNs called generalized toppling networks, and obtain new mathematical results both for the CRN and AN settings.

q-bio.MN↗

arXiv2025

Identifiability of SDEs for reaction networks

Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of the stochastic differential equations associated to the reaction network. We derive conditions under which the law of the diffusion approximation is identifiable and provide theorems for verifying identifiability in practice. Notably, our results show that some reaction networks have non-identifiable reaction rates, even when the law of the corresponding stochastic process is completely known. Moreover, we show that reaction networks with distinct graphical structures can generate the same diffusion law under specific choices of reaction rates. Finally, we compare our framework with identifiability results in the deterministic ODE setting and the discrete continuous-time Markov chain models for reaction networks.

math.PR↗