Using an elementary physical model for protein folding, of self-avoiding short copolymer chains on two-dimensional square lattices, we address two questions regarding the evolution and origins of globular proteins. (i) How will protein native structures and stabilities be affected by single-and double-site mutations? (ii) What is the probability that a randomly chosen sequence of amino acids will be compact and globular under folding conditions? For a large number of different sequences, we search the conformational space exhaustively to find unequivocally the "native" conformation(s), of global minimum free energy, for each sequence. We find that replacing nonpolar residues in the core by polar residues is generally destabilizing, that surface sites are less sensitive than core sites, that some mutations increase the degeneracy of native states, and that overall it is most probable that a mutation will be neutral, having no effect on the native structure. These results support a "Continuity Principle," that small changes in sequence seldom have large effects on structure or stability of the native state. The simulations also show that (i) the number of "convergent" sequences (different sequences coding for the same native structure) is extremely large and (ii) most sequences become quite dense under folding conditions. This implies that the probability of formation of a globular protein from a random sequence of amino acids by prebiotic or mutational methods is significantly greater than zero.

Lau, K. F., & Dill, K. A. (1990). Theory for protein mutability and biogenesis. Proceedings of the National Academy of Sciences, 87(2), 638–642.