Evolutionary Potential of a Duplicated Repressor-Operator Pair: Simulating Pathways Using Mutation Data

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Abstract
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. The evolution of a new trait critically depends on the existence of a path of viable intermediates. Generally speaking, fitness decreasing steps in this path hamper evolution, whereas fitness increasing steps accelerate it. Unfortunately, intermediates are hard to catch in action since they occur only transiently, which is why they have largely been neglected in evolutionary studies. The novelty of this study is that intermediate phenotypes can be predicted using published measurements of Escherichia coli mutants. Using this approach, the evolution of a small genetic network is simulated by computer. Following the duplication of one of its components, a new protein-DNA interaction develops via the accumulation of point mutations and selection. The resulting paths reveal a high potential to obtain a new regulatory interaction, in which neutral drift plays an almost negligible role. This study provides a mechanistic rationale for why such rapid divergence can occur and under which minimal selective conditions. In addition it yields a quantitative prediction for the minimum number of essential mutations.