The population genetics of cooperative gene regulation

Abstract

Background: Changes in gene regulatory networks drive the evolution of phenotypic diversity both within and between species. Rewiring of transcriptional networks is achieved either by changes to transcription factor binding sites or by changes to the physical interactions among transcription factor proteins. It has been suggested that the evolution of cooperative binding among factors can facilitate the adaptive rewiring of a regulatory network.

Results: We use a population-genetic model to explore when cooperative binding of transcription factors is favored by evolution, and what effects cooperativity then has on the adaptive re-writing of regulatory networks. We consider a pair of transcription factors that regulate multiple targets and overlap in the sets of target genes they regulate. We show that, under stabilising selection, cooperative binding between the transcription factors is favoured provided the amount of overlap between their target genes exceeds a threshold. The value of this threshold depends on several population-genetic factors: strength of selection on binding sites, cost of pleiotropy associated with protein-protein interactions, rates of mutation and population size. Once it is established, we find that cooperative binding of transcription factors significantly accelerates the adaptive rewiring of transcriptional networks under positive selection. We compare our qualitative predictions to systematic data on Saccharomyces cerevisiae transcription factors, their binding sites, and their protein-protein interactions.

Conclusions: Our study reveals a rich set of evolutionary dynamics driven by a tradeoff between the beneficial effects of cooperative binding at targets shared by a pair of factors, and the detrimental effects of cooperative binding for non-shared targets. We find that cooperative regulation will evolve when transcription factors share a sufficient proportion of their target genes. These findings help to explain empirical pattens in datasets of transcription factors in Saccharomyces cerevisiae and, they suggest that changes to physical interactions between transcription factors can play a critical role in the evolution of gene regulatory networks.

Figure 1

Schematic of the population-genetic model. A schematic cartoon of our population-genetic model. (top) When cooperativity is absent different transcription factors (gray and red) must bind to sites at each of their targets independently. Each factor has a number of targets, K₁and K₂, and a number β(K1 + K2) of shared targets (bottom). When cooperativity is present, a physical interaction between transcription factors (blue line) can mitigate the need to bind independently at shared targets, but may cause misregulation at targets that are not shared, by causing the factor with which it interacts cooperatievly to misbind. Cooperatively is therefore advantageous between transcription factors that share many targets, but it may be deleterious at targets that are not shared.

Figure 2

Evolutionary parameters that permit cooperative regulation. Evolutionary parameters that permit the evolution of gene regulation by cooperative transcription factors. Threshold number of shared targets for gain (black) and loss (red) of cooperative binding to be advantageous in a population at equilibrium under stabilising selection. The black line shows the value of βabove which a new mutation that results in cooperative binding will invade in a population that lacks cooperative binding. The red line shows the value of βbelow which a mutation resulting in loss of cooperative binding will invade, in a population that has cooperative binding. For values of βthat lie in the gray region, the dynamics are bistable: a population with cooperative binding will preserve it, and one without binding will not gain binding. The threshold fraction of shared targets varies with (top left) strength of selection, s, (top right) strength of cooperativity in reducing the effects of deleterious mutations 1/h, (bottom left) the cost of pleiotropy t and (bottom right) the population size, N. Lines show our analytic equations (Equations 2 and 3), and points show the results of 10⁵replicate Monte-Carlo simulations. Parameter values (unless stated otherwise) are u_l=2×10⁻⁷, u_g=10⁻⁷, K₁ + K₂=100, s=10⁻³, h=10⁻¹, t=10⁻⁴and N=10⁴.

Figure 3

A schematic cartoon of rewiring. A schematic cartoon of rewiring with (left) and without (right) cooperative binding. Selection favours a change in the regulation of target genes from the red TF to the green TF. Rewiring requires an initially deleterious mutation at the red binding site before a green binding site can be acquired. The fitness of the different states is shown on the left hand side for each case. The reduced fitness of the intermediate state is less when cooperative binding is present than when it is absent.

Figure 4

Cooperative binding accelerates adaptation. Cooperative binding accelerates adaptation under positive selection. The ratio of waiting times before the arrival of novel adaptive binding sites for populations without ( $t_r^{\ast }$) and with (t_r) cooperative binding. Provided Ns > 1, cooperative binding reduces the adaptation time up to 10-fold, compared to populations that lack cooperative binding. The line shows our analytic expression, and points show the result of 10⁵replicate Monte-Carlo simulations. Parameter values u_l=2×10⁻⁷, u_g=10⁻⁷, K₁ + K₂=100, h=10⁻¹, t=10⁻⁴, N=10⁴, u_r=10⁻⁷.

Figure 5

Number of shared targets. Fraction of targets that are shared between pairs transcription factors in S. cerevisiae[26-28]. (left) The fraction of targets that are shared among paris of transcription factors that lack cooperative binding and (right) the fraction of targets that are shared among transcription factors that bind cooperatively. The fraction of targets that are shared is larger among cooperative factors (p < 2×10⁻¹⁶, Wilcoxon test).