Evolutionary potential of a duplicated repressor-operator pair: Simulating pathways using mutation data

Ample evidence has accumulated for the evolutionary importance of duplication events. However, little is known about the ensuing step-by-step divergence process and the selective conditions that allow it to progress. Here we present a computational study on the divergence of two repressors after duplication. A central feature of our approach is that intermediate phenotypes can be quantified through the use of in vivo measured repression strengths of Escherichia coli lac mutants. Evolutionary pathways are constructed by multiple rounds of single base pair substitutions and selection for tight and independent binding. Our analysis indicates that when a duplicated repressor co-diverges together with its binding site, the fitness landscape allows funneling to a new regulatory interaction with early increases in fitness. We find that neutral mutations do not play an essential role, which is important for substantial divergence probabilities. By varying the selective pressure we can pinpoint the necessary ingredients for the observed divergence. Our findings underscore the importance of coevolutionary mechanisms in regulatory networks, and should be relevant for the evolution of protein-DNA as well as protein-protein interactions.