Spin glasses and the statistical mechanics of protein folding.

Abstract

The theory of spin glasses was used to study a simple model of protein folding. The phase diagram of the model was calculated, and the results of dynamics calculations are briefly reported. The relation of these results to folding experiments, the relation of these hypotheses to previous protein folding theories, and the implication of these hypotheses for protein folding prediction schemes are discussed.The mechanism of globular-protein folding remains a central problem of molecular biology (1). Folding is the final stage in the translation of genetic information to a working protein and is one of the simplest examples of biological selforganization. A complete understanding of protein folding should lead to a scheme for predicting three-dimensional protein structure from one-dimensional sequence information, which would have important applications in biotechnology. Even falling short of a complete theory, there are many puzzling features of the kinetics and thermodynamics of protein folding that require qualitative explanation. In this paper we hope to highlight these features and to explain how some hypotheses drawn from the theory of spin glasses can illuminate some features of protein folding in a very simplified model.Physicochemical studies of protein folding have a long history (1-5). Despite these studies, a unified account of the dynamics of the process has failed to arise. Thermodynamically near physiological conditions the smaller proteins often exhibit all-or-none behavior, going discontinuously from the unfolded phase to the folded phase. This is reminiscent of a phase transition in a finite system (5). In larger proteins, deviations from this behavior have been ascribed to the domain structure of proteins. Farther away from physiological conditions more complex behavior has been observed, suggesting that a third "misfolded" or "collapsed" phase for protein molecules exists.The kinetic behavior of protein folding is more complicated than the thermodynamic behavior. Generally multiexponential kinetics is observed and in some cases discrete intermediates inferred (6). The range of time scale is puzzling. Refolding of denatured protein into a biologically active form takes 1 msec to 100 sec or longer. This period of time may be viewed in two different ways. On one hand the time is much too short for an exhaustive random search for the minimum free-energy structure; on the other hand it is clearly much longer than a simple "downhill run" to the minimum freeenergy structure. Nucleation models suggested by the all-ornone character of the thermodynamics also do not fit the kinetics.In the absence of microscopic models the solution of the time-scale problem has been attributed to the existence of "folding pathways." The relative slowness of folding is ascribed to the existence of many local minima of the free energy (7).We should also bear in mind that the in vivo studies of folding may give a biased view of the biological process. Robust, easily foldable proteins are the easiest to study. In vivo,...

Funnels, pathways, and the energy landscape of protein folding: A synthesis

“…This is a natural starting assumption for thinking about heteropolymer dynamics since one expects this behavior generically for heterogeneous systems. The implications of the roughness of heteropolymer energy landscapes for protein folding were first discussed by Bryngelson and Wolynes who postulated that the energies of the states of a random heteropolymer could be approximately modeled by a set of random, independent energies [4]. This model is known as the random energy model in the theory of spin glasses [45][46][47].…”

Analysis of PIN1 WW domain through a simple statistical mechanics model

“…In addition, the comparison to experiments requires an accumulation of folding events to gain a enough large statistics further narrowing the route to the to full-atom techniques. These limitations suggest resorting to minimalist models which adopt a less accurate description of protein chains, residue-residue and residue-solvent interactions [3,4,5,6,7]. Approximate representations reduce the computational costs and, with a certain amount of uncertainty, allow to follow all the stages which bring a protein into its native fold.…”

Determinants of protein side‐chain packing

“…This conclusion corresponds to the consistency principle of G6 (1983) or the principle of minimum frustration of Bryngelson and Wolynes (1987). These concepts state that the shortrange interactions governing secondary structure propensities are consistent (or not in conflict) with the long-range interactions.…”