Evolutionary population genetics of promoters: predicting binding sites and functional phylogenies

Abstract

We study the evolution of transcription factor-binding sites in prokaryotes, using an empirically grounded model with point mutations and genetic drift. Selection acts on the site sequence via its binding affinity to the corresponding transcription factor. Calibrating the model with populations of functional binding sites, we verify this form of selection and show that typical sites are under substantial selection pressure for functionality: for cAMP response protein sites in Escherichia coli, the product of fitness difference and effective population size takes values 2NDeltaF of order 10. We apply this model to cross-species comparisons of binding sites in bacteria and obtain a prediction method for binding sites that uses evolutionary information in a quantitative way. At the same time, this method predicts the functional histories of orthologous sites in a phylogeny, evaluating the likelihood for conservation or loss or gain of function during evolution. We have performed, as an example, a cross-species analysis of E. coli, Salmonella typhimurium, and Yersinia pseudotuberculosis. Detailed lists of predicted sites and their functional phylogenies are available.

Fig. 1.

Cross-species energy transition probabilities for neutral evolution (blue) and for evolution under time-independent selection in the fitness landscape of Fig. 3a (red). Curves are shown for fixed initial energy E₁ = 8 and various evolutionary distances t. The third curve in each family belongs to the distance between aligned loci of E. coli and S. typhimurium. Typical loci evolve toward weaker binding under neutrality but maintain their binding energy under selection.

Fig. 2.

Functional phylogenies for two species at evolutionary distances t₁ and t₂, counted from their last common ancestor at time t_a = 0. Branch segments with neutral evolution are shown in blue with evolution under selection in red. (a) Neutral evolution of nonfunctional loci, described by the energy pair distribution . (b) Evolution of functional loci under time-independent selection, described by the distribution Q^t. (c) Evolution under time-dependent selection generating a functional locus in species 1 and a nonfunctional locus in species 2, described by the distribution . This mode involves either a gain of function between ancestor and 1 or a loss of function between ancestor and 2. The switching event at time t′ is denoted by a green arrow. The corresponding mode where the roles of the two species are interchanged is described by the distribution .

Fig. 3.

Energy statistics and fitness landscape for CRP-binding loci in E. coli.(a) Count histogram with energy bins of width 0.1 (black), expected background counts (blue), and excess counts above background (red), with a 30-fold zoom into the region E < 14. The color bar indicates the probability of functionalityρ_Q(E), ranging from 1 (red) to 0 (blue). (b) Decomposition of the counts (log-scale, left y axis) according to the single-species hidden Markov model: background distribution (1 - λ)P₀(E) (blue), distribution λQ(E) of functional loci (red), and total distribution W(E) (orange). The resulting fitness landscape ΔF(E) according to Eq. 6 is also shown in orange (thick curve, right y axis).

Fig. 4.

Binding energy pairs and functional histories for aligned loci in E. coli and S. typhimurium.(a) Dot plot of counts (E₁, E₂), including verified binding sites (light blue). The background color shading indicates the likelihood of functional histories, varying between blue (conserved neutrality), red (conserved function), and green (functional switching). Isoprobability lines (α = 0, Q, 0s, s0) are dotted. (b) Energy pair density obtained from the counts (filled contours), compared with the distribution W^t(E₁, E₂) (contour lines, W^t = 10^-7, 10^-6, 10^-5, 10^-4).