The design and development of new proteins has considerable practical application in medicine, industry, and basic science. Methods for design include computational de-novo design, abzymes, and evolutionary techniques where a parent protein or a family of proteins with related function is used to seed a search in sequence space. Such searches are complicated, however, by the limits of high-throughput experimental techniques to 10^3 – 10^10 sequences, so each screen is able to explore only a tiny fraction of the 20^n possible amino-acid sequences for a protein of length n. Protein engineering studies using this class of evolutionary techniques have met with varying degrees of success, making it difficult to draw conclusions about the relative effectiveness of different approaches. It is unclear the extent to which this variability reflects differences in the challenges attempted, in the technology applied, in the sizes or properties of the space of proteins searched, or something about the fundamental adaptability or designability of the parent protein.

From the perspective of protein design, designability is relevant as both the number of sequences allowed for a given structure and the accessibility of these sequences by different protein engineering techniques. We have computationally explored the allowed sequence space for three small proteins, allowing us to design, simulate, and evaluate strategies for protein design via directed evolution. Structure-based protein design onto rigid backbone structures allows us to generate long lists of allowed sequences for these proteins. Some sequences are stable for a given protein backbone structure while others are not, meaning that depending on the search and screening strategies, entire regions of sequence space may be inaccessible. Using computational simulations of error-prone PCR experiments, we have explored these sequence spaces using different experimental strategies. For example, evolutionary design procedures that make mostly single DNA mutations will sample the sequence space nearby the wild-type sequence very well. A new useful protein might be selected from a library of these nearby sequences, if they are allowed for the given protein structure. However, if the goal function requires a new sequence with multiple cooperative mutations, such a method is unlikely to reach that sequence before it generates more sequences than can be screened experimentally. Techniques that sample sequence space more broadly have been useful for finding new proteins with multiple, cooperative mutations. Genetic recombination, focused mutagenesis, and computational design techniques have all been successful in finding design solutions more distant from the wild type sequence.

Our computational approach allows us to explore these experimental strategies in detail. Structure-based protein design allows us to observe how the constraints of different backbone conformations influence the number and type of allowed protein sequences. We have made maps of these allowed sequences showing the relationships between them in terms of mutation distance and found that for some proteins the allowed sequences are close together in mutational space and in others more separated clusters of sequences are prevalent. We tested different error-prone PCR strategies and found that using our sequence space maps to guide the choice of wild type starting sequence can help generate more diverse libraries for screening. We are in the process of exploring complementary strategies that require less computational effort and would therefore be more useful for evolutionary design experimentalists.

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