Robustness, evolvability, and accessibility in the signal-integration space of gene regulatory circuits

Gene expression is commonly modulated by a set of regulating gene products, which bind to a gene’s cis-regulatory region. This region encodes an input-output function, referred to as signal-integration logic, that maps a specific combination of regulatory signals (inputs) to a particular gene expression state (output). The space of all possible signalintegration functions (genotypes) is vast and highly redundant: for the same set of inputs, many functions yield the same expression output (phenotype). Here, we exhaustively characterize signal-integration space within a computational model of genetic regulation. Our goal is to understand how the inherent redundancy of signal-integration space affects the relationship between robustness and evolvability in regulatory circuits. Among a number of results, we show that robust phenotypes are (i) evolvable, (ii) easily identified by random mutation, and (iii) mutationally biased toward other robust phenotypes. We then explore the implications of these results for mutation-based evolution by conducting an ensemble of random walks between randomly chosen source and target phenotypes. We demonstrate that the time required to identify the target phenotype is independent of the properties of the source phenotype.