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Title: Phenotypic switching of populations of cells in a stochastic environment

Abstract

We report that 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. Finally, we discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

Authors:
 [1]; ORCiD logo [2];  [1]
  1. Univ. of Manchester (United Kingdom)
  2. Univ. of Manchester (United Kingdom) ; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; National Institutes of Health (NIH)
OSTI Identifier:
1467329
Report Number(s):
LA-UR-17-25113
Journal ID: ISSN 1742-5468
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Statistical Mechanics
Additional Journal Information:
Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1742-5468
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; population dynamics; stochastic processes; gene expression and regulation

Citation Formats

Hufton, Peter Graham, Lin, Yen Ting, and Galla, Tobias. Phenotypic switching of populations of cells in a stochastic environment. United States: N. p., 2018. Web. doi:10.1088/1742-5468/aaa78e.
Hufton, Peter Graham, Lin, Yen Ting, & Galla, Tobias. Phenotypic switching of populations of cells in a stochastic environment. United States. doi:10.1088/1742-5468/aaa78e.
Hufton, Peter Graham, Lin, Yen Ting, and Galla, Tobias. Thu . "Phenotypic switching of populations of cells in a stochastic environment". United States. doi:10.1088/1742-5468/aaa78e. https://www.osti.gov/servlets/purl/1467329.
@article{osti_1467329,
title = {Phenotypic switching of populations of cells in a stochastic environment},
author = {Hufton, Peter Graham and Lin, Yen Ting and Galla, Tobias},
abstractNote = {We report that 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. Finally, we discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.},
doi = {10.1088/1742-5468/aaa78e},
journal = {Journal of Statistical Mechanics},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}

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