Recent experiments, advances in theory, and analogies to other complex systems such as glasses and spin glasses yield insight into protein dynamics. The basis of the understanding is the observation that the energy landscape is complex: Proteins can assume a large number of nearly isoenergetic conformations (conformational substates). The concepts that emerge from studies of the conformational substates and the motions between them permit a quantitative discussion of one simple reaction, the binding of small ligands such as carbon monoxide to myoglobin.

The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation, that is, to the energy landscape. The statistical energy landscape approach explains when and why unique behaviors, such as specific folding pathways, occur in some proteins and more generally explains the distinction between folding processes common to all sequences and those peculiar to individual sequences. This approach also gives new, quantitative insights into the interpretation of experiments and simulations of protein folding thermodynamics and kinetics. Specifically, the picture provides simple explanations for folding as a two‐state first‐order phase transition, for the origin of metastable collapsed unfolded states and for the curved Arrhenius plots observed in both laboratory experiments and discrete lattice simulations. The relation of these quantitative ideas to folding pathways, to uniexponential vs. multiexponential behavior in protein folding experiments and to the effect of mutations on folding is also discussed. The success of energy landscape ideas in protein structure prediction is also described. The use of the energy landscape approach for analyzing data is illustrated with a quantitative analysis of some recent simulations, and a qualitative analysis of experiments on the folding of three proteins. The work unifies several previously proposed ideas concerning the mechanism protein folding and delimits the regions of validity of these ideas under different thermodynamic conditions. © 1995 Wiley‐Liss, Inc.

The energy landscape theory of protein folding is a statistical description of a protein's potential surface. It assumes that folding occurs through organizing an ensemble of structures rather than through only a few uniquely defined structural intermediates. It suggests that the most realistic model of a protein is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure. This statistical description has been developed using tools from the statistical mechanics of disordered systems, polymers, and phase transitions of finite systems. We review here its analytical background and contrast the phenomena in homopolymers, random heteropolymers, and protein-like heteropolymers that are kinetically and thermodynamically capable of folding. The connection between these statistical concepts and the results of minimalist models used in computer simulations is discussed. The review concludes with a brief discussion of how the theory helps in the interpretation of results from fast folding experiments and in the practical task of protein structure prediction.

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,...

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We review the Random First Order Transition Theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature Tg. These include: the viscosity catastrophe and heat capacity jump at Tg, and their connection; the non-exponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractral cooperative rearrangements; deviations from the Stokes-Einstein relation close to Tg; aging, and its correlation with fragility; the excess density of states at cryogenic temperatures due to two level tunneling systems and the Boson Peak. Contents

Protein folding and binding are kindred processes. Many proteins in the cell are unfolded, so folding and function are coupled. This paper investigates how binding kinetics is influenced by the folding of a protein. We find that a relatively unstructured protein molecule can have a greater capture radius for a specific binding site than the folded state with its restricted conformational freedom. In this scenario of binding, the unfolded state binds weakly at a relatively large distance followed by folding as the protein approaches the binding site: the ''fly-casting mechanism.'' We illustrate this scenario with the hypothetical kinetics of binding a single repressor molecule to a DNA site and find that the binding rate can be significantly enhanced over the rate of binding of a fully folded protein.W e often glibly state that a protein must be folded to function. The reasoning underlying this statement is that organizing complex networks of chemical reactions in the cell requires these reactions to be highly specific. This specificity is achieved ultimately by having a high degree of geometrical precision in molecular binding-the famous ''lock and key.'' Geometric precision accompanies the increased rigidity of a biomolecule once it has folded; thus, apparently, folding is required for specific function. It does come as a surprise, then, that many proteins in the cell appear to be unfolded most of the time (see ref. 1 and refs. therein). Several ideas about potential biological advantages of being unfolded have been proposed. For example, the rapid turnover of unfolded proteins because of proteolytic degradation may be required for cell-cycle regulation (2). Thermodynamic arguments have also been made suggesting that coupling folding and binding may allow greater equilibrium distinctions for binding to different sites (3). In this note, we investigate whether too much rigidity may conflict with the need for biomolecules to move during their function and is therefore a kinetic disadvantage. There is much evidence for residual flexibility in the folded state, which must be thought of as having an ensemble of conformations (4). Still, the range of motions allowed in the folded state, as measured by Debye-Waller factors (5), is more restricted than those allowed in an unfolded molecule, thus slowing the exploration of configuration space. Here, we illustrate, by means of a specific example of operator binding to DNA, how the speed of molecular recognition can be enhanced by having folding (necessary for the required specificity) occur during binding rather than before.Folding and binding are kindred phenomena. The similarity of binding and folding is clear at the thermodynamic level, where both processes involve accurately locating molecular fragments with respect to each other, reducing the configurational entropy, and simultaneously lowering the free energy by the exclusion of solvent and formation of hydrogen bonds and salt bridges (6, 7). At the structural level, the similarity between packing patterns between ...