Stochastic gene expression in switching environments |
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Authors: | Martin J Gander Christian Mazza Hansklaus Rummler |
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Institution: | (1) Section de Mathématiques, University of Geneva, 2-4 Rue du Lièvre, CP64, 1211 Genève 4, Switzerland;(2) Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, 1700 Fribourg, Switzerland;(3) Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, 1700 Fribourg, Switzerland |
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Abstract: | Organisms are known to adapt to regularly varying environments. However, in most cases, the fluctuations of the environment
are irregular and stochastic, alternating between favorable and unfavorable regimes, so that cells must cope with an uncertain
future. A possible response is population diversification. We assume here that the cell population is divided into two groups,
corresponding to two phenotypes, having distinct growth rates, and that cells can switch randomly their phenotypes. In static
environments, the net growth rate is maximized when the population is homogeneously composed of cells having the largest growth
rate. In random environments, growth rates fluctuate and observations reveal that sometimes heterogeneous populations have
a larger net growth rate than homogeneous ones, a fact illustrated recently through Monte-Carlo simulations based on a birth
and migration process in a random environment. We study this process mathematically by focusing on the proportion f(t) of cells having the largest growth rate at time t, and give explicitly the related steady state distribution π. We also prove the convergence of empirical averages along trajectories
to the first moment , and provide efficient numerical methods for computing .
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Keywords: | Gene expression Fluctuating environment Steady state |
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