Rational evolutionary design: The theory of in vitro protein evolution

Abstract

Directed evolution uses a combination of powerful search techniques to generate proteins with improved properties. Part of the success is due to the stochastic element of random mutagenesis; improvements can be made without a detailed description of the complex interactions that constitute function or stability. However, optimization is not a conglomeration of random processes. Rather, it requires both knowledge of the system that is being optimized and a logical series of techniques that best explores the pathways of evolution (Eigen et al., 1988). The weighing of parameters associated with mutation, recombination, and screening to achieve the maximum fitness improvement is the beginning of rational evolutionary design. The optimal mutation rate is strongly influenced by the finite number of mutants that can be screened. A smooth fitness landscape implies that many mutations can be accumulated without disrupting the fitness. This has the effect of lowering the required library size to sample a higher mutation rate. As the sequence ascends the fitness landscape, the optimal mutation rate decreases as the probability of discovering improved mutations also decreases. Highly coupled regions require that many mutations be simultaneously made to generate a positive mutant. Therefore, positive mutations are discovered at uncoupled positions as the fitness of the parent increases. The benefit of recombination is twofold: it combines good mutations and searches more sequence space in a meaningful way. Recombination is most beneficial when the number of mutants that can be screened is limited and the landscape is of an intermediate ruggedness. The structure of schema in proteins leads to the conclusion that many cut points are required. The number of parents and their sequence identity are determined by the balance between exploration and exploitation. Many disparate parents can explore more space, but at the risk of losing information. The required screening effort is related to the number of uphill paths, which decreases more rapidly for rugged landscapes. Noise in the fitness measurements causes a dramatic increase in the required mutant library size, thus implying a smaller optimal mutation rate. Because of strict limitations on the number of mutants that can be screened, there is motivation to optimize the content of the mutant library. By restricting mutations to regions of the gene that are expected to show improvement, a greater return can be made with the same number of mutants. Initial studies with subtilisin E have shown that structurally tolerant positions tend to be where positive activity mutants are made during directed evolution. Mutant fitness information is produced by the screening step that has the potential to provide insight into the structure of the fitness landscape, thus aiding the setting of experimental parameters. By analyzing the mutant fitness distribution and targeting specific regions of the sequence, in vitro evolution can be accelerated. However, when expediting the search, there is a trade-off between rapid improvement and the quality of the long-term solution. The benefit of neutrality has yet to be captured with in vitro protein evolution. Neutral theory predicts the punctuated emergence of novel structure and function, however, with current methods, the required time scale is not feasible. Utilizing neutral evolution to accelerate the discovery of new functional and structural solutions requires a theory that predicts the behavior of mutational pathways between networks. Because the transition from neutral to adaptive evolution requires a multi-mutational switch, increasing the mutation rate decreases the time required for a punctuated change to occur. By limiting the search to the less coupled region of the sequence (smooth portion of the fitness landscape), the required larger mutation rate can be tolerated. Advances in directed evolution will be achieved when the driving forces behind such proce