Translational and orientational glass transitions in the large-dimensional limit : a generalized replicated liquid theory and an application to patchy colloids
Shintaro Nagata, Macoto Kikuchi
Gene regulatory networks (GRNs) are complex systems in which many genes mutually regulate their expressions for changing the cell state adaptively to the environmental conditions. Besides the functions, the GRNs utilized by living systems possess several kinds of robustness. Here, the robustness means that the GRNs do not lose their functions when exposed to mutation or noises. Both the adaptive response and the robustness have been acquired through the evolution. In this respect, real GRNs are rare among “all the possible GRNs”. In this study, we explore the fitness landscape of GRNs and investigate how the robustness emerge in the “well-fitted” GRNs. For that purpose, we employ the Multi-Canonical Monte Carlo method, which can sample GRNs randomly in wide range of fitness. We consider a toy model of GRNs having one input gene and one output gene. The difference in the expression levels between the input states “on” and “off” is taken as the fitness. Thus the more sensitively a GRN responds to the input, the fitter it is. We show the following properties for the GRNs in the “fittest ensemble”: (1) They distinguish two different states of the input by switching the fixed points. Thus they exhibit bistability, which necessarily emerges as the fitness becomes high. (2) They are robust against noises thanks to the bistability. (3) Many GRNs in the fittest ensemble are robust against mutation. These properties are universal irrespective of the evolutionary pathway, because we did not perform evolutionary simulations.