Thermodynamic and Statistical Signatures of Modality Changes in Concentration Distributions Driven by Stochastic Switching Between Two Activity States

Abstract

Stochastic switching between gene expression states, coupled with production and degradation dynamics, governs the accumulation of mRNA and proteins in cells. The concentrations of these accumulated entities dictate the phenotypic distribution of genetically identical cells. The underlying accumulation dynamics are well-captured by a two-state promoter switching model, with statistical and thermodynamic properties quantified via the Fano factor and entropy production rates. However, how these measures correlate with concentration distributions and their shifts under varying kinetic parameters remains largely unexplored. To this end, we use chemical master equations to study a generalized model of mRNA accumulation dynamics in the presence of stochastic switching between two activity states and state-dependent production and degradation rates. We derive exact expressions for the steady-state probability distribution and analytically compute the mean concentration, Fano factor, and entropy production rate (EPR). Simplifying these expressions, we identify contributions arising from stochastic switching rates and relaxation dynamics toward equilibrium in each activity state. Next, using our theoretical results, we characterize the variation in the Fano factor and EPR as a function of mean expression during modality changes of the distributions mediated by the variation of switching rates. We also identify the conditions in kinetic parameters that achieve the highest Fano factor and entropy production rates. Our findings establish a generalized framework for examining stochastic accumulation dynamics, clarifying how kinetic parameters dictate molecular distributions, noise, and dissipation. These insights extend readily to broader contexts coupling stochastic switching with accumulation, including protein burst dynamics, phenotype-switching-mediated drug intake, and queuing theory.