Phenotypic switching of populations of cells in a stochastic environment

Abstract

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

arXiv comment17 pages, 6 figures

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• Model reduction methods for classical stochastic systems with fast-switching environments: reduced master equations, stochastic differential equations, and applications
• Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations
• Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
• The Fitness Value of Information with Delayed Phenotype Switching: Optimal Performance with Imperfect Sensing
• Toward understanding of the role of reversibility of phenotypic switching in the evolution of resistance to therapy
• Exact computation of growth-rate fluctuations in random environment