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Stochastic reaction networks in dynamic compartment populations

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress towards addressing this problem in the context of concrete biological systems but general approaches remain lacking. In this work we propose a mathematical framework based on counting processes that allows us to study compartment populations with arbitrary interactions and internal biochemistry. We provide an efficient description of the population dynamics in terms of differential equations which capture moments of the population and their variability. We demonstrate the relevance of our approach using several case studies inspired by biological systems at different scales.