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By defining the phenotype of a biopolymer by its active three-dimensionalshape, and its genotype by its primary sequence, we propose a model thatpredicts and characterizes the statistical distribution of a population ofbiopolymers with a specific phenotype, that originated from a given genotypicsequence by a single mutational event. Depending on the ratio g0 thatcharacterizes the spread of potential energies of the mutated population withrespect to temperature, three different statistical regimes have beenidentified. We suggest that biopolymers found in nature are in a criticalregime with g0 in the range 1-6, corresponding to a broad, but not too broad,phenotypic distribution resembling a truncated Levy flight. Thus the biopolymerphenotype can be considerably modified in just a few mutations. The proposedmodel is in good agreement with the experimental distribution of activitiesdetermined for a population of single mutants of a group I ribozyme.Comment: to appear in Phys. Rev. E; 7 pages, 6 figures; longer discussion in  VII, new fig.

Large phenotype jumps in biomolecular evolution