Initially put forward by Stevens in 1951 [1
] and later advocated by Ohno in his seminal work [2
], gene duplication followed by functional divergence is now seen as a general mechanism for acquiring new functions [3
]. Also, regulatory networks are thought to be shaped significantly by genetic duplication [4
]. For instance, sequence analysis of transcription factor families points to various historical duplication events [5
]. However, very little is known about the subsequent mutational divergence pathways or about the corresponding stepwise phenotypical changes that are subject to selection. While these issues have not yet been explored experimentally, related generic aspects of mutational plasticity have been addressed theoretically [7
]. However, a central obstacle in studying mutational pathways through computer simulations remains the unknown relation between the sequence and binding affinity, for which, in general, a rather abstract mapping has to be assumed. To describe the formation of a new regulatory interaction after a duplication event, which is our current aim, such an abstract approach would be particularly speculative.
Here we reason that many characteristics of the adaptation of real protein-DNA contacts are hidden in the extensive body of mutational data that has been accumulated over many years (e.g., [12
] for the Escherichia coli lac
system). These measured repression values can be used as fitness landscapes, in which pathways can be explored by computing consecutive rounds of single base pair substitutions and selection. Here we develop this approach to study the divergence of duplicate repressors and their binding sites. More specifically, we focus on the creation of a new and unique protein-DNA recognition, starting from two identical repressors and two identical operators. We consider selective conditions that favor the evolution toward independent regulation. Interestingly, such regulatory divergence is inherently a coevolutionary process, where repressors and operators must be optimized in a coordinated fashion.
The mere presence of a selective pressure is clearly not a sufficient condition to achieve a new function. Rather, the evolutionary potential and limitations can be seen as governed by the shape of the actual fitness landscape and the evolutionary search within it. Studying these intrinsic limitations to divergence represents the overall aim of this work. Many open questions arise when considering the formation of a new protein-DNA interaction, which may be viewed as the construction of a new lock and uniquely matching key. For instance, how should the protein be modified step-by-step to recognize a new DNA-binding site that also does not yet exist, or vice versa? One would expect that complementary mutations need to occur in the protein and DNA-binding site. Does this mean that temporary losses in fitness must be endured when taking single-mutation steps? And, how many mutations must minimally accumulate before a noticeable new recognition is obtained on which selection can act? The latter is an important point: mutations conferring a selective advantage spread more readily through a population [15
], resulting in a drastic increase of the divergence probability. These questions are addressed by exhaustively searching the landscape for optimal pathways, as well as by complementary population dynamics simulations.
Previously it has been shown that lac
repressor mutants indeed exist that can bind exclusively to mutant lac
]. Our simulations reveal that a duplicated repressor-operator pair can readily evolve to achieve such independence of binding, while monotonously increasing its fitness in a step-by-step process. Moreover, simply following the fittest mutants does predominantly guide the system to the desired global optimum, which indicates funnel-like features in the fitness landscape. A detailed analysis of the subsequent network changes indicates a generic sequence of events, of which we study the underlying mechanisms by varying the applied selective pressure. Next, we show that the trajectories we find in the optimal pathway simulations are not rare exceptions, since similar trajectories are followed using a probabilistic scheme for accepting a mutation. The results further suggest the feasibility of studying regulatory divergence in laboratory evolution experiments, and finally we make a comparison to alternative models for the creation of new regulatory interactions.