Gene expression dynamics in randomly varying environments.
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.
Smiley
Michael W
MW
Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA, 50011, USA.
Proulx
Stephen R
SR
Ecology Evolution and Marine Biology, University of California, Santa Barbara, Santa Barbara, CA, 93106-9620, USA. stephen.proulx@gmail.com.
D000465:Algorithms; D003198:Computer Simulation; D004777:Environment; D005057:Eukaryotic Cells / Q000378:metabolism; D005786:Gene Expression Regulation / Q000502:physiology*; D008390:Markov Chains; D008957:Models, Genetic; D011387:Prokaryotic Cells / Q000378:metabolism; D011506:Proteins / Q000235:genetics / Q000378:metabolism; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism
D011506:Proteins; D012333:RNA, Messenger