Dynamics of Transcription Factor Binding Site Evolution

Evolution has produced a remarkable diversity of living forms that manifests in qualitative differences as well as quantitative traits. An essential factor that underlies this variability is transcription factor binding sites, short pieces of DNA that control gene expression levels. Nevertheless, we lack a thorough theoretical understanding of the evolutionary times required for the appearance and disappearance of these sites. By combining a biophysically realistic model for how cells read out information in transcription factor binding sites with model for DNA sequence evolution, we explore these timescales and ask what factors crucially affect them. We find that the emergence of binding sites from a random sequence is generically slow under point and insertion/deletion mutational mechanisms. Strong selection, sufficient genomic sequence in which the sites can evolve, the existence of partially decayed old binding sites in the sequence, as well as certain biophysical mechanisms such as cooperativity, can accelerate the binding site gain times and make them consistent with the timescales suggested by comparative analyses of genomic data.

Published in the journal: . PLoS Genet 11(11): e32767. doi:10.1371/journal.pgen.1005639
Category: Research Article
doi: 10.1371/journal.pgen.1005639


Evolution has produced a remarkable diversity of living forms that manifests in qualitative differences as well as quantitative traits. An essential factor that underlies this variability is transcription factor binding sites, short pieces of DNA that control gene expression levels. Nevertheless, we lack a thorough theoretical understanding of the evolutionary times required for the appearance and disappearance of these sites. By combining a biophysically realistic model for how cells read out information in transcription factor binding sites with model for DNA sequence evolution, we explore these timescales and ask what factors crucially affect them. We find that the emergence of binding sites from a random sequence is generically slow under point and insertion/deletion mutational mechanisms. Strong selection, sufficient genomic sequence in which the sites can evolve, the existence of partially decayed old binding sites in the sequence, as well as certain biophysical mechanisms such as cooperativity, can accelerate the binding site gain times and make them consistent with the timescales suggested by comparative analyses of genomic data.


Evolution produces heritable phenotypic variation within and between populations and species on relatively short timescales. Part of this variation is due to differences in gene regulation, which determines how much of each gene product exists in every cell. These gene expression levels are heritable quantitative traits subject to natural selection [13]. While the importance of their variability for the observed phenotypic variation is still debated [4], it is believed to be crucial within closely related species or in populations whose proteins are functionally or structurally similar [5]. The genetic basis for gene expression differences is thought to be non-coding regulatory DNA, but our understanding of its evolution is still immature; this is due, in part, to the lack of precise knowledge about the mapping between the regulatory sequence and the resulting expression levels.

Transcriptional regulation is the most extensively studied mechanism of gene regulation. Transcription factor proteins (TFs) recognize and bind specific DNA sequences called binding sites, thereby affecting the expression of target genes. Eukaryotic regulatory sequences, i.e., enhancers and promoters, are typically between a hundred and several thousand base pairs (bp) in length [6], and can harbor many transcription factor binding sites (TFBSs), each typically consisting of 6–12 bp. The situation is different in prokaryotes: they lack enhancer regions and have one or a few TFBSs which are typically longer, between 10 to 20 bp in length [7, 8]. Differences in TF binding are thought to arise primarily due to changes in the regulatory sequence at the TF binding sites rather than changes in the cellular environment or the TF proteins themselves [10]. Nevertheless, a theoretical understanding of the relationship between the evolution of the regulatory sequence and the evolution of gene expression levels remains elusive, mostly because of the complex interaction of evolutionary forces and biophysical processes [11].

From the evolutionary perspective, the crucial question is whether and when these regulatory sequences can evolve rapidly enough so that new phenotypic variants can arise and fix in the population over typical speciation timescales. Comparative genomic studies in eukaryotes provide evidence for the evolutionary dynamics of TF binding, highlighting the possibility for rapid and flexible TFBS gain and loss between closely related species on timescales of as little as a few million years [12, 13]. Examples include quick gain and loss events that cause divergent gene expression [14], or the compensation of such events by turn-over at other genome locations [15]; gain and loss events sometimes occur even in the presence of strong constraints on expression levels [16, 17]. Furthermore, such events enabled new binding sites on sex chromosomes that arose as recently as 1–2 million years ago [18, 19]. There are examples of rapid regulatory DNA evolution across and within populations requiring shorter timescales, i.e. 10.000–100.000 years [2, 2022]. On the other hand, strict conservation has also been observed at orthologous regulatory locations even in distant species (e.g., [23]). Taken together, these facts suggest that the rates of TFBS evolution can extend over many orders of magnitude and differ greatly from the point mutation rate at a neutral site. To study the evolutionary dynamics of regulatory sequences and understand the relevant timescales, we set up a theoretical framework with a special focus on the interplay of both population genetic and biophysical factors, briefly outlined below.

Sequence innovations originate from diverse mutational mechanisms in the genome. While tandem repeats [24] or transposable elements [25] may be important in evolution, the better studied and more widespread mutation types still need to be better understood in the context of TFBS evolution. Specifically, we ask how the evolutionary dynamics are affected by single nucleotide (point) mutations, as well as by insertions and deletions (indels). New mutations in the population are selected or eliminated by the combined effects of selection and random genetic drift. Although the importance of selection [2628] and mutational closeness of the initial sequences [29, 30] for TF binding site evolution has already been reported, the belief in fast evolution via point mutations without selection (i.e., neutral evolution) persists in the literature (e.g., [5, 13]), mainly due to Stone & Wray’s (2001) misinterpretation of their own simulation results [31] (see Macarthur & Brookfield (2004) [29]). This likely reflects the current lack of theoretical understanding of TFBS evolution in the literature, even under the simplest case of directional selection. Basic population genetics shows that directional selection is expected to cause a change, e.g., yield a functional binding site, over times on the order of 1/(NsUb), where N is the population size, s is the selection advantage of a binding site, and Ub is the beneficial mutation rate [32]. This process can be extremely slow, especially under neutrality, if several mutational steps are needed to reach a sequence with sufficient binding energy to confer a selective advantage. As already pointed out by Berg et al. (2004) [32], this places strong constraints on the length of the binding sites, if they were to evolve from random sequences.

Several biophysical factors, such as TF concentration and the energetics of TF-DNA and TF-TF interactions, might play an important role in TFBS evolution. Quantitative models for TF sequence specificity [3338] and for thermodynamic (TD) equilibrium of TF occupancy on DNA [34, 3943] were developed in recent decades and, in parallel with developments in sequencing, have contributed to our understanding of TF-DNA interaction biophysics. These biophysical factors can shape the characteristics of the TFBS fitness landscape over genotype space in evolutionary models [8, 29, 32, 4447]. There are also intensive efforts to understand the mapping from promoter/enhancer sequences to gene expression [42, 4850]. Despite this recent attention, there have been relatively few attempts to understand the evolutionary dynamics of TFBS in full promoter/enhancer regions [29, 43, 5153], especially using biophysically realistic but still mathematically tractable models. Such models are necessary to gain a thorough theoretical understanding of binding site evolution.

Our aim in this study is to investigate the dynamics of TFBS evolution by focusing on the typical evolutionary rates for individual TFBS gain and loss events. We consider both a single binding site at an isolated DNA region and a full enhancer/promoter region, able to harbor multiple binding sites. In the following section, we lay out our modeling framework, which covers both population genetic and biophysical considerations, as outlined above. Using this framework, we try to understand i) what typical gain and loss rates are for a single TFBS site; ii) how quickly populations converge to a stationary distribution for a single TFBS; iii) how multiple TFBS evolve in enhancers and promoters; iv) how early history of the evolving sequences can change the evolutionary rates of TFBS; and v) how cooperativity between TFs affects the evolution of gene expression. We find that, under realistic parameter ranges, both gain and loss of a single binding site is slow, slower than the typical divergence time between species. Importantly, fast emergence of an isolated TFBS requires strong selection and favorable initial sequences in the mutational neighborhood of a strong TFBS. The evolutionary process approaches the equilibrium distribution very slowly, raising concerns about the use of equilibrium assumptions in theoretical work. We proceed to show that the dynamics of TFBS evolution in larger sequences can be understood approximately from the dynamics of single binding sites; the TFBS gain times are again slow if evolution starts from random sequence in the absence of strong selection or large regulatory sequence “real estate.” Finally, we identify two factors that can speed up the emergence of TFBS: the existence of an initial sequence distribution biased towards the mutational neighborhood of strongly binding sequences, which suggests that ancient evolutionary history can play a major role in the emergence of “novelties” [54]; and the biophysical cooperativity between transcription factors, which can partially account for the lack of observed correlation between identifiable binding sequences and transcriptional activity [11].


Population genetics

We consider a finite population of N diploid individuals whose genetic content consists of an evolvable L base pair (bp) contiguous regulatory sequence σ to which TFs can bind. Given that σi ∈ {A, C, G, T} where i = 1, 2, …, L indexes the position in regulatory sequence, there are 4L different regulatory sequences in the genotype space. Each TF is assumed to bind to a contiguous sequence of n bp within our focal region of L bp (Fig 1A and 1B). Regulatory sequences evolve under mutation, selection, and sampling drift. The rest of the genome is assumed to be identical for all individuals and is kept constant. In the first part of our study we consider the regulatory sequence comprised of a single TFBS (i.e. L = n). Later, we consider the evolution of a longer sequence (i.e. Ln) in which more than one TFBS can evolve. For simulations, we use a Wright-Fisher model where N diploid individuals are sampled from the previous generation after mutation and selection. Our analytical treatment is general and corresponds to setups where a diffusion approximation to allele frequency evolution is valid. We neglect recombination since typical regulatory sequences are short, L ≤ 1000. To be consistent with most of the population genetics literature we assume diploidy, but since we do not consider any dominance effects, our results also hold for a haploid population with 2N individuals.

Biophysics of transcription regulation.
Fig. 1. Biophysics of transcription regulation.
A) TFs bind to regulatory DNA regions (promoters and enhancers) in a sequence-specific manner to regulate transcriptional gene expression (mRNA production) level via different mechanisms, such as recruiting RNA polymerase (RNA-pol). B) A schematic of two types of mutational processes that we model: point mutations (left) and indel mutations (right). C) The mismatch binding model results in redundancy of genotype classes, with a binomial distribution (red) of genotypes in each mismatch class (some examples of degenerate sequences shown) D) The mapping from the TFBS regulatory sequence to gene expression level is determined by the thermodynamic occupancy (binding probability) of the binding site. If each of the k mismatches from the consensus sequence decreases the binding energy by ϵ, the occupancy of the binding site is πTD(k) = (1 + eβ(ϵkμ))−1, where μ is the chemical potential (related to free TF concentration). A typical occupancy curve is shown in black (ϵ = 2 kB T and μ = 4 kB T); the gray curves show the effect of perturbation to these parameters (ϵ = 1 kB T, ϵ = 3 kB T and μ = 6 kB T); the orange curve illustrates the case of two cooperatively binding TFs (kc = 0 and Ec = −3 kB T, see text for details). We pick two thresholds, shown in dashed lines, to define discrete binding classes: strong

Evolutionary dynamics simplify in the low mutation limit where the population consists of a single genotype during most of its evolutionary history (the fixed state population model). Desai & Fisher [55] have shown that the condition log 4 N Δ f Δ f ≪ 1 4 N U b Δ f needs to hold for a fixed state population assumption to be accurate. The term on the left is the establishment time of a mutant allele with a selective advantage Δf relative to the wild type; the term on the right-hand side is the waiting time for such an allele to appear, where Ub is the beneficial mutation rate per individual per generation. Note that, in binding site context, Ub refers to the rate of mutations which increase the fitness, for instance, by increasing binding strength. Its exact value depends on the current state of the genotype; nevertheless, typical value estimates help model the evolutionary dynamics. In multicellular eukaryotes, where most evidence for the evolution of TFBSs has been collected and which provide the motivation for this manuscript, the number of mutations per nucleotide site is typically low, e.g. 4Nu ∼ 0.01 in Drosophila and 4Nu ∼ 0.001 in humans [56], where u is the point mutation rate per generation per base pair. For a single binding site of typical length n ∼ 5–15, one therefore expects the fixed state population model to be accurate. For longer regulatory sequences, one expects that beneficial mutations are rare among all possible mutations, so that the fixed state population model can be assumed to hold as well.

Evolution under the fixed state assumption can be treated as a simple Markovian jump process. The transition rate from a regulatory sequence σ to another regulatory sequence σ′ in a diploid population is

where Δfσ′,σ = f(σ′) − f(σ) is the fitness difference and Uσ′,σ is the mutation rate from σ to σ′. The fixation probability Pfix of a mutation with fitness difference Δf in a diploid population of N individuals is

which is based on the diffusion approximation [57]. Note that the fixation probability scaled with 1/N approximates to 2NΔf when NΔf ≫ 1. Evolutionary dynamics therefore depend essentially on how regulatory sequences are mutationally connected in genotype space, and how fitnesses differ between neighboring genotypes, i.e., on the fitness landscape.

Directional selection on biophysically motivated fitness landscapes

In this study, we focus on directional selection by assuming that fitness f is proportional to gene expression level g which depends on regulatory sequence, i.e.

where s is the selection strength. It is important to note that this choice does not imply that directional selection is the only natural selection mechanism. It simply aims at obtaining the theoretical upper limits for the rates of gaining and losing binding sites.

To analyze a realistic but tractable mapping from the regulatory sequence to fitness, we primarily assume that the proxy for gene expression is the binding occupancy (binding probability) π at a single TF binding site, or the sum of the binding occupancies within an enhancer/promoter region (based on limited experimental support [84]). This corresponds to

where π(i) is the binding occupancy of a site starting at the nucleotide i in sequence σ, and s can be interpreted as the selective advantage of a strongest binding to a weakest binding at a site. We assume all binding sites have equal strength and direction in their contribution towards total gene activation. Sites acting as repressors in our simple model would enter into Eq (4) with a negative selection strength, s. Future studies developing mathematically tractable models should consider more realistic case of unequal contribution with combined activator and repressor sites responding differentially to various regulatory inputs [53]. Although one can postulate different scenarios that map TF occupancies in a long (Ln) promoter to gene expression, we chose the simplest case which allows us to make analytical calculations. Later we relax our assumption on noninteracting binding sites and consider the effects of several kinds of interactions on gene expression and thus on evolutionary dynamics.

The occupancy of the TF on its binding site is assumed to be in thermodynamic (TD) equilibrium [34, 3943]. While this might not always be realistic [58, 59], there is empirical support for this assumption (particularly in prokaryotes) [48, 60, 61], and more importantly, it is sufficient to capture the essential nonlinearity in this genotype-phenotype-fitness mapping [62]. In thermodynamic equilibrium, the binding occupancy at the site starting with the i-th position in regulatory sequence is given by

Here, μ is the chemical potential of the TF (related to its free concentration) [44, 64]; Ei is the sequence specific binding energy, where lower energy corresponds to tighter binding, and β = (kB T)−1. We compute the binding energy Ei by adopting an additive energy model which is considered to be valid at least up to a few mismatches from the consensus sequence [37, 38, 65, 66], i.e.

where ξ stands for the energy matrix whose ξσj,j element gives the energetic contribution of the nucleotide σj appearing at the j-th position within TFBS. With this, Eq (4) can be rewritten more formally as

To allow analytical progress, we make the “mismatch assumption,” i.e., the energy matrices contain identical ϵ > 0 entries for every non-consensus (mismatch) base pair; the consensus entries are set to zero by convention. A single binding sequence with k mismatches therefore has the binding energy E = . We will refer to ϵ as “specificity.” Specificity is provided by diverse interactions between DNA and TF, including specific hydrogen bonds, van der Waals forces, steric exclusions, unpaired polar atoms, etc. [63]. ϵ is expected to be in the range 1–3 kB T, which is consistent with theoretical arguments [44] as well as direct measurements [6567]. Note that we explicitly check the validity of the analytical results based on the mismatch assumption by comparing them against simulations using realistic energy matrices. The redundancy (i.e., normalized number of distinct sequences) of a mismatch class k at a single site in a random genome can be described by a binomial distribution ϕ (Fig 1C) where the probability of encountering a mismatch class k is

where α = 3/4 in the case of equiprobable distribution over the four nucleotides.

We focus on selection in a single environment, which in this framework corresponds to a single choice for the TF concentration. We therefore fix the chemical potential to a baseline value of μ = 4 kB T, which maps changes in the sequence (mismatch class k) to a full range of gene expression levels, as shown in Fig 1D. We subsequently vary μ systematically and report how its value affects the results.

After these preliminaries, the equilibrium binding probability of Eq (5) reduces to

This function has a sigmoid shape whose steepness depends on specificity ϵ and whose midpoint depends on the ratio of chemical potential to specificity, μ/ϵ (Fig 1D). To simplify discussion, we introduce two classes of sequences: genotypes are associated with “strong binding”


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