Hybrid incompatibility arises in a sequence-based bioenergetic model of transcription factor binding

Abstract

Postzygotic isolation between incipient species results from the accumulation of incompatibilities that arise as a consequence of genetic divergence. When phenotypes are determined by regulatory interactions, hybrid incompatibility can evolve even as a consequence of parallel adaptation in parental populations because interacting genes can produce the same phenotype through incompatible allelic combinations. We explore the evolutionary conditions that promote and constrain hybrid incompatibility in regulatory networks using a bioenergetic model (combining thermodynamics and kinetics) of transcriptional regulation, considering the bioenergetic basis of molecular interactions between transcription factors (TFs) and their binding sites. The bioenergetic parameters consider the free energy of formation of the bond between the TF and its binding site and the availability of TFs in the intracellular environment. Together these determine fractional occupancy of the TF on the promoter site, the degree of subsequent gene expression and in diploids, and the degree of dominance among allelic interactions. This results in a sigmoid genotype-phenotype map and fitness landscape, with the details of the shape determining the degree of bioenergetic evolutionary constraint on hybrid incompatibility. Using individual-based simulations, we subjected two allopatric populations to parallel directional or stabilizing selection. Misregulation of hybrid gene expression occurred under either type of selection, although it evolved faster under directional selection. Under directional selection, the extent of hybrid incompatibility increased with the slope of the genotype-phenotype map near the derived parental expression level. Under stabilizing selection, hybrid incompatibility arose from compensatory mutations and was greater when the bioenergetic properties of the interaction caused the space of nearly neutral genotypes around the stable expression level to be wide. F2's showed higher hybrid incompatibility than F1's to the extent that the bioenergetic properties favored dominant regulatory interactions. The present model is a mechanistically explicit case of the Bateson-Dobzhansky-Muller model, connecting environmental selective pressure to hybrid incompatibility through the molecular mechanism of regulatory divergence. The bioenergetic parameters that determine expression represent measurable properties of transcriptional regulation, providing a predictive framework for empirical studies of how phenotypic evolution results in epistatic incompatibility at the molecular level in hybrids.

Keywords: Dobzhansky–Muller interactions; adaptive landscape; cis–trans coevolution; genotype–phenotype map; regulatory evolution; speciation.

Figure 1

“Lock and key” model of a two-locus regulatory interaction. Expression depends on the fit between the transcription factor, encoded at the first locus, and a binding site in the regulatory region of the second locus. Alleles of the transcription factor and the binding site are represented as binary strings. A perfect match results in the maximum level of expression (but not necessarily the highest fitness).

Figure 2

Effects of the bioenergetic parameters ΔG₁ and E_diff on the genotype–phenotype (G–P) map and the corresponding fitness landscape. ΔG₁ and E_diff are in units of k_bT. (A) Effect on the G–P map. Horizontal axis: the number of mismatched bits between the binding site and the transcription factor’s binding motif. Vertical axis: the phenotype, which in this case is the expression level normalized to a scale of zero to one. ΔG₁ values, in steps of 0.0825 k_bT, were chosen for each E_diff so as to hold constant the expression produced by n = 12 substitutions. (See Figure S1 for the independent effects of these parameters.) (B) The fitness landscapes for the bioenergetic parameter combinations in A, in this case with environmental fitness parameters set to P_opt = 1 and σ_s = 0.05. Horizontal axis: Δ mismatches is the number of mismatches responsible for the difference between an individual’s phenotype P and the optimal phenotype P_opt. The bioenergetic parameters that determine expression level, and therefore the transition from genotype to phenotype, extend further to drive the relationship between genotype and fitness under a given environmental selection regime.

Figure 3

The effects of the slope the G–P map (phenotypic effect of one mutation) and population size on median F₂ misregulation and corresponding fitness. Open boxes correspond to directional selection from minimal expression (12 mismatches) toward maximal expression (zero mismatches). Shaded boxes correspond to stabilizing selection at maximal expression (zero mismatches). Box plots show median, quartiles, and full ranges. Population size has no effect under directional selection, but smaller populations are more likely to evolve misregulation under stabilizing selection. The slope of the G–P map is represented by the effect of one mutation, which here is the phenotypic difference between a genotype with zero mismatches and a genotype with one mismatch (visible in Figure 2A). Steeper slopes increase hybrid misregulation under directional selection, but decrease misregulation under stabilizing selection. The effect is the same for directional selection toward intermediate expression (not shown). Hybrid fitness follows Equation 4.

Figure 4

Effect of allelic dominance on median net phenotypic misregulation in F₁ (open bars) and F₂ (shaded bars) crosses following directional selection from minimal expression (12 mismatches) toward maximal expression (0 mismatches). Dominance is manipulated by changing E_diff and ΔG₁ values and expressed as the average effect on an individual’s phenotype of removing one of its TF allele copies. Dominance is highest on the left. Hybrid fitness follows Equation 4. Box plots show median, quartiles, and full ranges. See Model for details.

Figure 5

(A) Evolution toward lower gene expression: each parent population evolves two mismatches between transcription factor and binding site in response to selection for reduced expression. F₁ hybrids may have higher gene expression than either parent population due to reconstructed ancestral matches and accidental matches at derived sites. (B) Evolution toward higher gene expression: each parent evolves new matches between transcription factor and binding site in response to selection for increased expression. Incompatible alleles arise in the F₁ because each parent evolved a different fit between transcription factor and binding site.

Figure 6

Asymmetric expression of parental orthologs in the F₁ hybrid resulting from cis-by-trans regulatory divergence, when the relative amount of divergence in cis compared to trans differs between species. In the above example, divergence occurred under selection for reduced expression. More spurious matches resulted between the binding site of species 1 and the transcription factor of species 2 (top right interaction in the hybrid) than in the inverse interaction (bottom right). Depending on allelic dominance, the overall expression level in the F₁ generation may be nearly the same in hybrids as in the parent species.