At the point of transition of the coil to the lowest-energy fold, an N-residue chain folds normally in approximately exp(N2/3) ns. Therefore, a 100-residue chain finds its most stable fold within minutes rather than in 10(100) ps = 10(80) years, according to the famous paradoxical estimate of Levinthal.
A theoretical study has shown that the occurrence of various structural elements in stable folds of random copolymers is exponentially dependent on the own energy of the element. A similar occurrence-on-energy dependence is observed in globular proteins from the level of amino acid conformations to the level of overall architectures. Thus, the structural features stabilized by many random sequences are typical of globular proteins while the features rarely observed in proteins are those which are stabilized by only a minor part of the random sequences.
Whether knowledge-based intra-molecular inter-residue potentials are valid to represent inter-molecular interactions takmg place at protein-protein interfaces has been questioned in several studies. Differences in the chain connectivity effect and in residue packing geometry between interfaces and single chain monomers have been pointed out as possible sources of distinct energetics for the two cases. In the present study, the interfacial regions of protein-protein complexes are examined to extract inter-molecular inter-residue potentials, using the same statistical methods as those previously adopted for intra-molecular residue pairs. Two sets of energy parameters are derived, corresponding to solvent-mediation and "average residue" mediation. The former set is shown to be highly correlated (correlation coefficient 0.89) with that previously obtained for inter-residue interactions within single chain monomers, while the latter exhibits a weaker correlation (0.69) with its intra-molecular counterpart. In addition to the close similarity of intra-and inter-molecular solvent-mediated potentials, they are shown to be significantly more residue-specific and thereby discriminative compared to the residue-mediated ones, indicating that solvent-mediation plays a major role in controlling the effective inter-residue interactions, either at interfaces, or within single monomers. Based on this observation, a reduced set of energy parameters comprising 20 one-body and 3 two-body terms is proposed (as opposed to the 20 X 20 tables of inter-residue potentials), which reproduces the conventional 20 X 20 tables with a correlation coefficient of 0.99.
A small number of folding patterns describe in outline most of the known protein globules, the same folds being found in non-homologous proteins with different functions. We show that the 'popular' folding patterns are those which, due to some thermodynamic advantages of their structure, can be stabilized by a lot of random sequences. In contrast, the folds which are rarely or never observed in natural globular proteins can be stabilized only by a tiny number of random sequences. The advantageous folds are few, they tolerate various primary structures, and therefore they can and ought to perform different functions. A connection between the inherent 'weak points' of protein folding patterns and positions of active sites are discussed.
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