Optimization of gene expression by natural selection

Abstract

It is generally assumed that stabilizing selection promoting a phenotypic optimum acts to shape variation in quantitative traits across individuals and species. Although gene expression represents an intensively studied molecular phenotype, the extent to which stabilizing selection limits divergence in gene expression remains contentious. In this study, we present a theoretical framework for the study of stabilizing and directional selection using data from between-species divergence of continuous traits. This framework, based upon Brownian motion, is analytically tractable and can be used in maximum-likelihood or Bayesian parameter estimation. We apply this model to gene-expression levels in 7 species of Drosophila, and find that gene-expression divergence is substantially curtailed by stabilizing selection. However, we estimate the selective effect, s, of gene-expression change to be very small, approximately equal to Ns for a change of one standard deviation, where N is the effective population size. These findings highlight the power of natural selection to shape phenotype, even when the fitness effects of mutations are in the nearly neutral range.

Fig. 1.

Realizations of the OU process. Three individual realizations are shown for each of four different parameter values. The drift parameter σ determines the degree of mutational pressure randomly impacting the trait value, while λ determines the pull of selection toward some optimal trait value (in this case 0). In each realization, the starting value was sampled from the equilibrium distribution.

Fig. 2.

Average pairwise variance in expression level for Drosophila species. Each point represents the average variance between a species pair. This variance initially increases with time, but eventually saturates. In the absence of stabilizing selection, pairwise variance is expected to saturate at 1. Nonlinear regression fit of pairwise variance vs. time for the OU model is represented as a dashed line (λ = 26.14; σ = 4.14).

Fig. 3.

Fitness landscape of gene-expression level estimated from OU parameters. Expression level is measured in terms of standard deviations relative to other genes in the genome. Fitness is equal to −(λ/2σ²)(μ−z)², where z represents the current trait value. The quadratic shape of the fitness landscape is assumed by the OU model; the data provides the magnitude of curvature.

Fig. 4.

Effect of protein-sequence evolution on patterns of gene-expression divergence. Nonlinear regression was used to estimate the drift parameter σ and equilibrium variance σ²/2λ in sliding windows across gene rank ordered according to their rate of protein-sequence evolution. Each window consists of 1,125 genes, or 25% of the total set of genes in which reliable alignments could be made. Mean estimates are shown as solid lines and 95% CIs shown as gray boundaries. Fast-evolving genes show similar rates of drift, but significantly greater levels of equilibrium variance, compared to slow-evolving genes.