Large phenotype jumps in biomolecular evolution

By defining the phenotype of a biopolymer by its active three-dimensional shape, and its genotype by its primary sequence, we propose a model that predicts and characterizes the statistical distribution of a population of biopolymers with a specific phenotype that originated from a given genotypic sequence by a single mutational event. Depending on the ratio $g_0$ that characterizes the spread of potential energies of the mutated population with respect to temperature, three different statistical regimes have been identified. We suggest that biopolymers found in nature are in a critical regime with $g_0\simeq 1–6,$ corresponding to a broad, but not too broad, phenotypic distribution resembling a truncated Lévy flight. Thus the biopolymer phenotype can be considerably modified in just a few mutations. The proposed model is in good agreement with the experimental distribution of activities determined for a population of single mutants of a group-I ribozyme.