Fig 1.
Schematic representation of protein expression and fitness of gene heterozygotes.
Here, the strengths of two enhancer alleles are represented by their ability to attract transcription factors. Four genotypes are represented: weaker enhancer homozygote (a), stronger enhancer homozygote (d) and enhancer locus heterozygotes (b) and (c). In enhancer locus heterozygotes, the stronger enhancer is either associated with the deleterious gene allele (b) or with the viable gene allele (c). Corresponding fitnesses are indicated. Note that we consider here a case where the total amount of proteins produced is constant.
Fig 2.
Variation of fitness (W, y-axis) as a function of the percentage of defective proteins noted %a (x-axis, from 0% in AA homozygotes to 100% in aa homozygotes) in different genotypes, where E1 and E2 are the weaker and stronger enhancer alleles respectively (e2 > e1).
This function is necessarily monotonic and concave when deleterious mutations are recessive (h < ½).
Fig 3.
Ratio of fixation probabilities of mutations altering enhancer strength relative to that of a neutral mutation.
In red, the mutant enhancer is three times stronger than the wild type; and in blue, three times weaker. Simulated and analytically predicted values (see methods) are represented by dots and lines, respectively. Values are reported for the case where enhancer strength evolution does not alter overall protein expression (model 1, see text), for various recombination rates between the enhancer and the gene (x-axis), for weak (s = 0.01, squares) or strong selection (s = 0.1, circles) and partial recessivity (h = 0.25). Results are illustrated for Npop u = 1 (where Npop is the population size and u the gene mutation rate). Results for higher Npop u just need to be multiplied by a factor equal to Npop u. For instance the relative fixation probability for Npop u = 10 of tightly linked stronger enhancers would be ~20 or ~30, for s = 0.01 or s = 0.1, respectively. Weaker enhancers (blue) are always selected against, while stronger enhancers (red) are selectively favored provided that they are closely linked to the gene, and disfavored otherwise.
Fig 4.
Comparative doubling times of enhancer strength escalation in models considering different selection pressures acting on overall gene expression.
Y-axis indicates doubling times of enhancer strength (the expected number of generations needed to double the initial enhancer strength) according to the mutation size standard deviation on enhancers (x-axis). Because in all models presented, enhancer strength increases open-endedly in average, this doubling time measures the rate of escalation (see methods). The mutation size standard deviation on enhancer strength (σE) is a measure of the magnitude of mutational input (see methods). In model 2 (plain lines), overall expression of one gene is involved in a dosage relationship with the overall expression of another gene. Overall expression is determined by one enhancer locus per gene, and any departure from optimal dosage is costly. In model 3 (dashed lines), the absolute amount of protein produced is under stabilizing selection, but expression level is influenced by both an enhancer and a TF locus. In both models, stabilizing selection intensity is scaled by the intensity of selection at the gene locus (see methods). Deceleration of ER process due to stabilizing selection is illustrated for γ values equal to 0 (in red), 1 (in green), 5 (in blue) and 10 (in purple). Doubling times were obtained using stochastic simulations (see methods).
Fig 5.
Comparative rate of enhancer strength escalation in models with or without self-fertilization.
Axes and simulation methods are the same than for Fig 4. Selfing rate ps is 0, 0.2 and 0.7 on blue, red and green curves, respectively. In all three cases, enhancer strength escalation is faster with larger mutational variance σE2 on the enhancer locus. Self-fertilization slows down the ER process.
Fig 6.
Fixation probabilities ratios of stronger enhancers (3:1 strength ratio compared to the resident allele) relative to that of neutral mutation (from Eq 7).
Results were obtained for different recombination rates between the enhancer and the gene as indicated on the figure. Other parameter values are s = 0.01, h = 0.25.