Native protein sequences are close to optimal for their structures

How large is the volume of sequence space that is compatible with a given p rotein structure? starting from random sequences, low free energy sequences were generated for 108 protein backbone structures by using a Monte Carlo optimization procedure and a free energy function based primarily on Lennar d-Jones packing interactions and the Lazaridis-Karplus implicit solvation m odel. Remarkably, in the designed sequences 51% of the core residues and 27 % of all residues were identical to the amino acids in the corresponding po sitions in the native sequences. The lowest free energy sequences obtained for ensembles of native-like backbone structures were also similar to the n ative sequence. Furthermore. both the individual residue frequencies and th e covariances between pairs of positions observed in the very large SH3 dom ain family were recapitulated in core sequences designed for SH3 domain str uctures. Taken together, these results suggest that the volume of sequence space optimal for a protein structure is surprisingly restricted to a regio n around the native sequence.