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To isolate intrinsic noise in growing, non-stationary reaction systems, the authors formulate a large-deviations framework by decomposing molecular abundance into intensive composition and extensive volume coordinates. They show that composition fluctuations satisfy a large-deviation principle with speed proportional to volume, governed by a contact Hamilton–Jacobi equation, while observable covariances decay with accumulated volume rather than physical time. This framework provides an exact stochastic null model to separate intrinsic discrete reaction noise from external variability in expanding autocatalytic and cellular networks.
Fluctuations in growing stochastic networks decay with accumulated volume rather than physical time, unlocking a contact Hamilton–Jacobi formulation that cleanly isolates intrinsic noise in non-stationary systems.
Growing biochemical systems are intrinsically noisy, with one important source of stochasticity arising from the discrete reaction events of the underlying biochemical network. Because growing systems do not generally admit stationary abundance distributions, it is unclear how to separate this intrinsic chemical noise from other sources of variability in population and single-cell data. Here we develop a large-deviation theory for exponentially growing stochastic chemical reaction networks by decomposing abundance into volume and composition. In these coordinates, balanced growth corresponds to a stable composition together with exponentially increasing volume. We show that composition fluctuations satisfy a large-deviation principle with speed equal to the volume of the growing system, and the corresponding quasipotential is selected by a solution of the contact Hamilton--Jacobi equation. We also derive a fluctuation theory for accumulated observables and show that their covariances decay with accumulated-volume, rather than with physical time. Applications to a minimal autocatalytic network and a coarse-grained cellular growth model demonstrate how the theory predicts composition quasipotentials, growth-rate fluctuations, and correlations between observables. The framework therefore provides a stochastic null model for single-cell heterogeneity generated by the intrinsic stochasticity of the underlying chemical reaction network.