NDLI: Stochastic gene expression in switching environments

Content Provider	Springer Nature Link
Author	Rummler, Hansklaus Gander, Martin J. Mazza, Christian
Copyright Year	2007
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 $${\mathbb{E}_\pi(f)}$$ , and provide efficient numerical methods for computing $${\mathbb{E}_\pi(f)}$$ .
Ending Page	269
Page Count	21
Starting Page	249
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	2
Volume Number	55
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-03-23
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fluctuating environment Mathematical Biology in General Applications of Mathematics Gene expression Steady state Continuous-time Markov processes on general state spaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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