The distribution of structures in evolving protein populations

Proteins exhibit a nonuniform distribution of structures. A number of models have been advanced to explain this observation by considering the distribution of designabilities, that is, the fraction of all sequences that could successfully fold into any particular structure. It has been postulated that more designable structures should be more common, although the exact nature of this relationship has not been addressed. We find that the nonuniform distribution of protein structures found in nature can be explained by the interplay of evolution and population dynamics with the designability distribution. The relative frequency of different structures has a greater-than-linear dependence on designability, making the distribution of observed protein structures more uneven than the distribution of designabilities. The distribution of structures is also affected by additional factors such as the topology of the sequence space and the similarity of other structures.