Energy-dependent fitness: a quantitative model for the evolution of yeast transcription factor binding sites

Abstract

We present a genomewide cross-species analysis of regulation for broad-acting transcription factors in yeast. Our model for binding site evolution is founded on biophysics: the binding energy between transcription factor and site is a quantitative phenotype of regulatory function, and selection is given by a fitness landscape that depends on this phenotype. The model quantifies conservation, as well as loss and gain, of functional binding sites in a coherent way. Its predictions are supported by direct cross-species comparison between four yeast species. We find ubiquitous compensatory mutations within functional sites, such that the energy phenotype and the function of a site evolve in a significantly more constrained way than does its sequence. We also find evidence for substantial evolution of regulatory function involving point mutations as well as sequence insertions and deletions within binding sites. Genes lose their regulatory link to a given transcription factor at a rate similar to the neutral point mutation rate, from which we infer a moderate average fitness advantage of functional over nonfunctional sites. In a wider context, this study provides an example of inference of selection acting on a quantitative molecular trait.

Fig. 1.

Phylogeny of the four yeast species S. cerevisiae (cer), S. paradoxus (par), S. mikatae (mik), and S. bayanus (bay). We study the statistics of functional binding sites conserved in all four species, as well as functional changes on any of the external branches to par, mik, and bay (shown as thick lines). Figure adapted from ref. .

Fig. 2.

Abf1 binding energy and binding assay distributions. (A) Histograms of site energies, as predicted by the Abf1 energy matrix for all cer intergenic sequence (dots), for neutral background sequence described by the distribution P₀(E) (line), and for the 361 Abf1 binding sites in the Q₄^no ensemble described by the distribution Q_f(E) (bars). (B) Comparison with ChIP-chip data of ref. : histogram of log intensities x of cer binding for all promoters (dots) and for the subset of promoters containing Q₄^no sites (bars), which are mostly in the tail of the distribution (≈80% in the regime < −1). (C) Fitness landscape for Abf1 binding sites. Binding range (E < Ẽ = 0.9): scaled landscape 2N F(E) = log[Q_f(E)/P₀(E)] by using energy data from Q₄^no functional sites and intergenic background sequence (dots), quadratic fit (dashed line). Nonbinding range (E > Ẽ): 2N F(E) is approximated as constant with difference 2N ΔF₀ to maximal binding.

Fig. 3.

Phenotype evolution of binding sites. (A) Histogram of cer–par energy differences ΔE = E_par − E_cer for conserved Abf1 binding sites in Q₄ (bars), giving the sum of counts from nonoverlapping sites (dark shaded part) and overlapping sites (light shaded part). Predicted distribution Ω^τ (ΔE), normalized to total number of nonoverlapping sites (solid line). (B and C) Same as A for cer--mik and cer–bay energy differences. (D) Energy divergence 〈(ΔE)²〉 (filled squares) and additive divergence δ² (dots, see text) for conserved nonoverlapping sites between cer and the other three species, plotted against evolutionary distance τ; predicted energy divergence 〈(ΔE)²〉 (τ) (solid line) and additive divergence δ²(τ) (dashed line). The large-τ limit of these functions reproduces (up to sampling effects) the site-to-site energy variance in cer (open square) by definition of the evolution model, and predicts the site-to-site linear variance (open dot). (E) Histogram of energy differences ΔE = E_par − E_cer for the seven three-species conserved sites in Q_cmb without functional ortholog in par (bars), events with indels are highlighted (black bars). Theoretical distribution of energy changes ωΩ_loss^τ (ΔE) for loss events caused by point mutations (dashed line). (F and G) Same for species-specific loss of function in mik (13 events) and in bay (23 events).