Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching

TL;DR

This paper explores how cell population growth, epigenetic phenotype switching, and entropy production interact, revealing mechanisms of natural selection and steady states through analytical models.

Contribution

It introduces a theoretical framework linking fitness, switching, and entropy production in cell populations, with analytical results for different growth-switching regimes.

Findings

Fitness increases via natural selection and covariance with switching

Entropy production is sustained by deviations from switching equilibrium

Analytical solutions for growth-dominant and switching-dominant limits

Abstract

Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separatedly defined two important concepts in mathematical terms: the {\em fitness} in the former and the (non-adiabatic) {\em entropy production} in the latter. Both play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth thus continuous natural selection. As a form of Price's equation, the fitness increases with ($i$) natural selection through variations and $(ii)$ a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state | "the red queen" scenario. At the same time the growth keeps the proportions of subpopulations away from the "intrinsic" switching equilibrium of individual cells, thus leads to a continous entropy production. A covariance, between the per capita growth rate and the "chemical potential" of subpopulation, counter-acts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.