Effect and evolution of gene expression noise on the fitness landscape

Daniel A. Charlebois

Phys. Rev. E 92, 022713 – Published 17 August 2015

Abstract

Gene expression is a stochastic process that affects cellular and population fitness. Noise in gene expression can enhance fitness by increasing cell to cell variability as well as the time cells spend in favorable expression states. Using a stochastic model of gene expression together with a fitness function that incorporates the costs and benefits of gene expression in a stressful environment, we show that the fitness landscape is shaped by gene expression noise in more complex ways than previously anticipated. We find that mutations modulating the properties of expression noise enable cell populations to optimize their position on the fitness landscape. Additionally, we find that low levels of expression noise evolve under conditions where the fitness benefits of expression exceed the fitness costs, and that high levels of expression noise evolve when the expression costs exceed the fitness benefits. The results presented in this study expand our understanding of the interplay between stochastic gene expression and fitness in selective environments.

Received 18 February 2015
Revised 6 July 2015

DOI:https://doi.org/10.1103/PhysRevE.92.022713

Authors & Affiliations

Daniel A. Charlebois^*

Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794-5252, USA

^*daniel.charlebois@stonybrook.edu

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Issue

Vol. 92, Iss. 2 — August 2015

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Images

Figure 1
Fitness function describing the cost and benefit of expressing a stress resistance protein. Top row panels show cellular fitness $(w)$ as a function of expression level $(x)$ for (a) no-cost, (b) low-cost, and (c) high-cost gene expression. Black lines represent expression cost, blue (gray) lines expression benefit, and dashed red (gray) lines the resulting cellular fitness. Bottom row panels correspond to the top row panel above them (in terms of the fitness function and gene expression cost and benefit) and show expression time series for low $(η = 0.03, τ = 10$ , and $c = 200$ : black lines and histograms) and high $(η = 0.1, τ = 100$ , and $c = 200$ : gray lines and histograms) expression noise $(η)$ and corresponding histograms depict the probability that a cell will have a given $x$ .
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Figure 2
Fitness landscapes generated using a step fitness function. Left: population fitness $(W)$ after 10 generations $(10 t_{D})$ of exposure to a stressful environment as a function of noise magnitude $(η)$ and relaxation time $(τ)$ when the critical threshold step-fitness function $(x_{c})$ is set to the mean expression level $(μ = 1000)$ . Similarly, center and right panels show $W$ when $x_{c}$ is set to values above $μ$ $(x_{c} = 1200$ and $x_{c} = 2300$ , respectively). Left panel was first published in Ref. [23].
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Figure 3
Fitness landscapes generated using a cost-benefit fitness function. Population fitness $(W)$ after 10 generations $(10 t_{D})$ is shown as a function of gene expression noise $(η)$ and relaxation time $(τ)$ for no-cost (left), low-cost (center), and high-cost (right) gene expression.
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Figure 4
Mutation of gene expression noise magnitude and relaxation time parameters optimizes stress resistance on the fitness landscape. The heat map for low-cost gene expression shows how population fitness $(W)$ (value indicated by the color bar) depends on gene expression noise $(η)$ and relaxation time $(τ)$ . The open circle and arrow respectively represent the initial position $(80.0, 0.800)$ and final position $(60.1, 0.0963)$ of the trajectory of a representative population that evolved over 1000 generations on the fitness landscape.
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Figure 5
Evolution of gene expression noise when fitness costs and benefits are considered. The heat map shows the final level of gene expression noise $(η)$ after 1000 generations of stress exposure without mutation (left) and with mutation (right) for various values of cost $(α_{c})$ and benefit $(α_{b})$ parameters (higher values of $α_{c}$ and $α_{b}$ respectively represent lower fitness costs and benefits of expressing a stress resistance gene). The color bars indicate the level of $η$ .
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