Treating sequence dependence of protein stability in a mean-field model

Several statistical mechanical theories of protein stability have recently been developed, based on mean-field approximations, random energy models, or related assumptions. None of these models treats how protein stability depends on the monomer sequence: they only treat sequences as being random. Here, as a first approximation to sequence effects, we develop theory for how the compact conformations of copolymer chains of two monomer types A and B depend on 4 composition quantities: the numbers of AA, AB, BA, and BB segments. We apply this to improving the "reconfiguration term" of a mean-field treatment of protein stability [K. A. Dill (1985), Biochemistry, Vol. 24, pp. 1501-1509]. Reconfiguration refers to the change of a compact chain from a random conformation to one with an optimal hydrophobic core. By comparison with exhaustive enumeration studies, we find that the theory gives improved estimates for reconfiguration properties in compact copolymers. One interesting result is that for a chain of a given length and hydrophobic (H)/polar (P) composition, some hydrophobic clustering in the sequence (PHHHHP. . .)is more stabilizing than if hydrophobic and polar residues are perfectly alternating (HPHP . . .).