Mathematical Framework for Stochastic Reaction Networks in Compartmentalized Systems with Content-Dependent Fragmentation
Researchers have developed new sufficient conditions for non-explosivity and positive recurrence in stochastic reaction networks where compartment fragmentation rates depend on the contents of those compartments. The work extends a 2023 study by Anderson and Howells, which addressed compartment dynamics independent of contents, and builds on a general framework proposed by Duso and Zechner in PNAS (2020). These results strengthen the mathematical foundation for modeling biological processes such as cell division and intracellular transport.
A new preprint on arXiv presents mathematical advances in the theory of stochastic reaction networks (SRNs) with compartmentalized, content-dependent dynamics. Standard SRN models assume homogeneous environments, but cellular biochemistry is often compartmentalized — at the cell level or within organelles — making such assumptions inadequate. The authors focus on a model where the fragmentation rate of a compartment depends on the abundance of designated molecular species within it, a scenario not covered by prior theoretical results. Crucially, they demonstrate that the explosivity characterization established in Anderson and Howells (Bull. Math. Biol., 2023) does not carry over to this content-dependent setting, necessitating new analytical tools. Under the assumption that the underlying chemical reaction network (CRN) admits a linear Lyapunov function, the authors derive new sufficient conditions guaranteeing non-explosivity and positive recurrence of the stochastic process. The paper is positioned within the broader framework for compartmentalized chemistry with dynamic compartments introduced by Duso and Zechner (PNAS, 2020). The results have potential implications for quantitative modeling of cell division, vesicle dynamics, and intracellular transport.
What's missing
The paper assumes the existence of a linear Lyapunov function for the underlying CRN, but does not fully characterize which classes of CRNs satisfy this assumption or how restrictive it is in practice. The biological applicability of the mathematical conditions to specific experimental systems remains to be demonstrated. Additionally, the paper does not address whether the new sufficient conditions for non-explosivity are also necessary, leaving open the question of tightness of the results.
What different sources said
- arXiv q-bioCenter
Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation
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