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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. https://doi.org/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. https://doi.org/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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Works referenced in this record:

Phenotypic Tolerance: Antibiotic Enrichment of Noninherited Resistance in Bacterial Populations
journal, April 2005


Non-inherited antibiotic resistance
journal, July 2006

  • Levin, Bruce R.; Rozen, Daniel E.
  • Nature Reviews Microbiology, Vol. 4, Issue 7
  • DOI: 10.1038/nrmicro1445

Phenotypic variation in bacteria: the role of feedback regulation
journal, April 2006

  • Smits, Wiep Klaas; Kuipers, Oscar P.; Veening, Jan-Willem
  • Nature Reviews Microbiology, Vol. 4, Issue 4
  • DOI: 10.1038/nrmicro1381

Stochastic switching to competence
journal, December 2008

  • Leisner, Madeleine; Stingl, Kerstin; Frey, Erwin
  • Current Opinion in Microbiology, Vol. 11, Issue 6
  • DOI: 10.1016/j.mib.2008.09.020

A Stochastic Single-Molecule Event Triggers Phenotype Switching of a Bacterial Cell
journal, October 2008


Persister cells, dormancy and infectious disease
journal, December 2006


Bacterial Persistence as a Phenotypic Switch
journal, September 2004

  • Balaban, Nathalie Q.; Merrin, Jack; Chait, Remy
  • Science, Vol. 305, Issue 5690, p. 1622-1625
  • DOI: 10.1126/science.1099390

Treatment of Staphylococcal Infections with Penicillin by Intermittent Sterilisation
journal, October 1944


Microbial phenotypic heterogeneity and antibiotic tolerance
journal, February 2007


The importance of being persistent: heterogeneity of bacterial populations under antibiotic stress
journal, July 2009


Formal Darwinism, the individual–as–maximizing–agent analogy and bet–hedging
journal, April 1999

  • Grafen, Alan
  • Proceedings of the Royal Society of London. Series B: Biological Sciences, Vol. 266, Issue 1421
  • DOI: 10.1098/rspb.1999.0708

Stochastic switching as a survival strategy in fluctuating environments
journal, March 2008

  • Acar, Murat; Mettetal, Jerome T.; van Oudenaarden, Alexander
  • Nature Genetics, Vol. 40, Issue 4
  • DOI: 10.1038/ng.110

Playing Dr Jekyll and Mr Hyde: combined mechanisms of phase variation in bacteria
journal, October 2001


Staphylococcus aureus phenotype switching: an effective bacterial strategy to escape host immune response and establish a chronic infection
journal, January 2011

  • Tuchscherr, Lorena; Medina, Eva; Hussain, Muzaffar
  • EMBO Molecular Medicine, Vol. 3, Issue 3
  • DOI: 10.1002/emmm.201000115

Stochastic Gene Expression in Fluctuating Environments
journal, May 2004


Colored extrinsic fluctuations and stochastic gene expression
journal, January 2008

  • Shahrezaei, Vahid; Ollivier, Julien F.; Swain, Peter S.
  • Molecular Systems Biology, Vol. 4, Issue 1
  • DOI: 10.1038/msb.2008.31

Effects of Input Noise on a Simple Biochemical Switch
journal, September 2011


Kinetics of Genetic Switching into the State of Bacterial Competence
journal, February 2009

  • Leisner, Madeleine; Kuhr, Jan-Timm; Rädler, Joachim O.
  • Biophysical Journal, Vol. 96, Issue 3
  • DOI: 10.1016/j.bpj.2008.10.034

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations
journal, February 2005

  • Samoilov, M.; Plyasunov, S.; Arkin, A. P.
  • Proceedings of the National Academy of Sciences, Vol. 102, Issue 7
  • DOI: 10.1073/pnas.0406841102

The Interplay of Intrinsic and Extrinsic Bounded Noises in Biomolecular Networks
journal, February 2013


Emergence of phenotype switching through continuous and discontinuous evolutionary transitions
journal, May 2015


Optimality and adaptation of phenotypically switching cells in fluctuating environments
journal, December 2015


The Inheritance of Phenotypes: an Adaptation to Fluctuating Environments
journal, July 1996

  • Lachmann, Michael; Jablonka, Eva
  • Journal of Theoretical Biology, Vol. 181, Issue 1
  • DOI: 10.1006/jtbi.1996.0109

Bacterial Persistence: A Model of Survival in Changing Environments
journal, January 2005


Individual histories and selection in heterogeneous populations
journal, July 2010

  • Leibler, S.; Kussell, E.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 29
  • DOI: 10.1073/pnas.0912538107

Exact Results for the Evolution of Stochastic Switching in Variable Asymmetric Environments
journal, January 2010


Switching between phenotypes and population extinction
journal, November 2011


Population Dynamics of Bacterial Persistence
journal, May 2013


Optimal Mixed Strategies in Stochastic Environments
journal, April 1995


Phenotypic Diversity, Population Growth, and Information in Fluctuating Environments
journal, September 2005


Stochastic gene expression in switching environments
journal, March 2007

  • Gander, Martin J.; Mazza, Christian; Rummler, Hansklaus
  • Journal of Mathematical Biology, Vol. 55, Issue 2
  • DOI: 10.1007/s00285-007-0083-9

Switching and Growth for Microbial Populations in Catastrophic Responsive Environments
journal, April 2010


Study of selected phenotype switching strategies in time varying environment
journal, March 2016


Intrinsic noise in systems with switching environments
journal, May 2016


Non-Cooperative Games
journal, September 1951

  • Nash, John
  • The Annals of Mathematics, Vol. 54, Issue 2
  • DOI: 10.2307/1969529

The fitness value of information
journal, February 2010


The Value of Information for Populations in Varying Environments
journal, March 2011


Delayed bet-hedging resilience strategies under environmental fluctuations
journal, May 2017


Exact stochastic simulation of coupled chemical reactions
journal, December 1977

  • Gillespie, Daniel T.
  • The Journal of Physical Chemistry, Vol. 81, Issue 25
  • DOI: 10.1021/j100540a008

Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model
journal, February 2016


Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models
journal, January 2016

  • Lin, Yen Ting; Galla, Tobias
  • Journal of The Royal Society Interface, Vol. 13, Issue 114
  • DOI: 10.1098/rsif.2015.0772

Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
journal, July 1984


Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
journal, October 2009

  • Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
  • Journal of Statistical Physics, Vol. 137, Issue 2
  • DOI: 10.1007/s10955-009-9850-x

Evolutionary Game Theory in Growing Populations
journal, October 2010


Evolutionary and population dynamics: A coupled approach
journal, November 2011


Staphylococcus aureus Persisters Tolerant to Bactericidal Antibiotics
journal, January 2012

  • Lechner, Sabrina; Lewis, Kim; Bertram, Ralph
  • Journal of Molecular Microbiology and Biotechnology, Vol. 22, Issue 4
  • DOI: 10.1159/000342449

Long-Term Dynamics of Adaptation in Asexual Populations
journal, November 2013


How should we define ‘fitness’ for general ecological scenarios?
journal, June 1992


Deterministic analysis of extrinsic and intrinsic noise in an epidemiological model
journal, May 2016


Hybrid stochastic simplifications for multiscale gene networks
journal, January 2009

  • Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu
  • BMC Systems Biology, Vol. 3, Issue 1
  • DOI: 10.1186/1752-0509-3-89

Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes
journal, March 2009

  • Zeiser, Stefan; Franz, Uwe; Liebscher, Volkmar
  • Journal of Mathematical Biology, Vol. 60, Issue 2
  • DOI: 10.1007/s00285-009-0264-9

Diversity in times of adversity: probabilistic strategies in microbial survival games
journal, May 2005

  • Wolf, Denise M.; Vazirani, Vijay V.; Arkin, Adam P.
  • Journal of Theoretical Biology, Vol. 234, Issue 2
  • DOI: 10.1016/j.jtbi.2004.11.020

Evolution of Stochastic Switching Rates in Asymmetric Fitness Landscapes
journal, May 2009


Measurement of Diversity
journal, April 1949


Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
journal, October 2002

  • Haseltine, Eric L.; Rawlings, James B.
  • The Journal of Chemical Physics, Vol. 117, Issue 15
  • DOI: 10.1063/1.1505860

Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
journal, March 2003

  • Rao, Christopher V.; Arkin, Adam P.
  • The Journal of Chemical Physics, Vol. 118, Issue 11
  • DOI: 10.1063/1.1545446

Stochastic population dynamics under regime switching
journal, October 2007


On hybrid competitive Lotka–Volterra ecosystems
journal, December 2009


Competitive Lotka–Volterra population dynamics with jumps
journal, December 2011

  • Bao, Jianhai; Mao, Xuerong; Yin, Geroge
  • Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue 17
  • DOI: 10.1016/j.na.2011.06.043

Extrinsic Noise Driven Phenotype Switching in a Self-Regulating Gene
journal, July 2013


Dynamics of simple gene-network motifs subject to extrinsic fluctuations
journal, December 2015


Cooperation Dilemma in Finite Populations under Fluctuating Environments
journal, December 2013


SOS Response Induces Persistence to Fluoroquinolones in Escherichia coli
journal, December 2009


Ciprofloxacin Causes Persister Formation by Inducing the TisB toxin in Escherichia coli
journal, February 2010


Works referencing / citing this record:

Bet-hedging strategies in expanding populations
journal, April 2019