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Understanding the features of the protein conformational space represents a key component to characterize protein structural evolution at the molecular level. This problem is approached in a twofold manner; simple lattice models are used to represent protein structures with the ability of a protein sequence to fold into the lowest energy native conformation, quantified as the foldability, which measures the fitness of the sequence. Alternatively, a self-consistent mean-field based theory is developed to evaluate the protein neutrality through random single-point and multiple-point mutations by calculating the pair-wise probability profile of the amino acid residues in a library of sequences, consistent with a particular foldability criterion. The theory predicts the change in sequence plasticity with the foldability criterion and also correlates the effect of hydrophobic residues on the variation of the free energy surface of the protein as a function of the number of cumulative mutations. The results obtained from the theory are compared with the exact enumeration results of 3 × 3 × 3 lattice protein and also with some small real proteins chosen from the protein databank. An excellent match of the results obtained from theory and exact enumeration with those of real proteins validates the range of applicability of the theory. The theory may provide a new perspective in de novo protein design, in-vivo/in-vitro protein evolution and site-directed mutagenesis experiments.

Statistical theory of neutral protein evolution by random site mutations