Phenotype selection due to mutational robustness.

The mutation-selection mechanism of Darwinian evolution gives rise not only to adaptation to environmental conditions but also to the enhancement of robustness against mutations. When two or more phenotypes have the same fitness value, the robustness distribution for different phenotypes can vary. Thus, we expect that some phenotypes are favored in evolution and that some are hardly selected because of a selection bias for mutational robustness. In this study, we investigated this selection bias for phenotypes in a model of gene regulatory networks (GRNs) using numerical simulations. The model had one input gene accepting a signal from the outside and one output gene producing a target protein, and the fitness was high if the output for the full signal was much higher than that for no signal. The model exhibited three types of responses to changes in the input signal: monostable, toggle switch, and one-way switch. We regarded these three response types as three distinguishable phenotypes. We constructed a randomly generated set of GRNs using the multicanonical Monte Carlo method originally developed in statistical physics and compared it to the outcomes of evolutionary simulations. One-way switches were strongly suppressed during evolution because of their lack of mutational robustness. By examining one-way switch GRNs in detail, we found that mutationally robust GRNs obtained by evolutionary simulations and non-robust GRNs obtained by McMC have different network structures. While robust GRNs have a common core motif, non-robust GRNs lack this motif. The bistability of non-robust GRNs is considered to be realized cooperatively by many genes, and these cooperative genotypes have been suppressed by evolution.