Recombinatoric exploration of novel folded structures: A heteropolymer-based model of protein evolutionary landscapes

The role of recombination in evolution is compared with that of point mutations (substitutions) in the context of a simple, polymer physics-based model mapping between sequence (genotype) and conformational (phenotype) spaces. Crossovers and point mutations of lattice chains with a hydrophobic polar code are investigated. Sequences encoding for a single ground-state conformation are considered viable and used as model proteins. Point mutations lead to diffusive walks on the evolutionary landscape, whereas crossovers can “tunnel” through barriers of diminished fitness. The degree to which crossovers allow for more efficient sequence and structural exploration depends on the relative rates of point mutations versus that of crossovers and the dispersion in fitness that characterizes the ruggedness of the evolutionary landscape. The probability that a crossover between a pair of viable sequences results in viable sequences is an order of magnitude higher than random, implying that a sequence's overall propensity to encode uniquely is embodied partially in local signals. Consistent with this observation, certain hydrophobicity patterns are significantly more favored than others among fragments (i.e., subsequences) of sequences that encode uniquely, and examples reminiscent of autonomous folding units in real proteins are found. The number of structures explored by both crossovers and point mutations is always substantially larger than that via point mutations alone, but the corresponding numbers of sequences explored can be comparable when the evolutionary landscape is rugged. Efficient structural exploration requires intermediate nonextreme ratios between point-mutation and crossover rates.