Phenotypic switching of populations of cells in a stochastic environment
Authored by Tobias Galla, Yen Ting Lin, Peter G Hufton
Date Published: 2018
DOI: 10.1088/1742-5468/aaa78e
Sponsors:
United Kingdom Engineering and Physical Sciences Research Council (EPSRC)
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Model Documentation:
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Mathematical description
Model Code URLs:
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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 di. erential 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
hostpathogen games.
Tags
Population dynamics
Diversity
Heterogeneity
Regulation
information
stochastic processes
fitness
Strategies
Gene-expression
Survival
Fluctuating environments
Gene expression
Bacterial persistence
Chemical-kinetics