Abstract
A simple model of gene regulation in response to stochastically changing environmental conditions is developed and analyzed. The model consists of a differential equation driven by a continuous time 2-state Markov process. The density function of the resulting process converges to a beta distribution. We show that the moments converge to their stationary values exponentially in time. Simulations of a two-stage process where protein production depends on mRNA concentrations are also presented demonstrating that protein concentration tracks the environment whenever the rate of protein turnover is larger than the rate of environmental change. Single-celled organisms are therefore expected to have relatively high mRNA and protein turnover rates for genes that respond to environmental fluctuations.
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This paper was greatly improved by the comments of several anonymous reviewers. S. R. Proulx was funded by NSF grant EF-0742582 and by the Baker Center for Bioinformatics at Iowa State University.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Smiley, M.W., Proulx, S.R. Gene expression dynamics in randomly varying environments. J. Math. Biol. 61, 231–251 (2010). https://doi.org/10.1007/s00285-009-0298-z
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DOI: https://doi.org/10.1007/s00285-009-0298-z