General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics-fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.Keywords: chain collapse; hydrophobic interactions; lattice models; protein conformations; protein folding; protein stabilityWe review the principles of protein structure, stability, and folding kinetics from the perspective of simple exact models. We focus on the "folding code''-how the tertiary structure and folding pathway of a protein are encoded in its amino acid sequence. Although native proteins are specific, compact, and often remarkably symmetrical structures, ordinary synthetic polymers in solution, glasses, or melts adopt large ensembles of more expanded conformations, with little intrachain organization. With simple exact models, we ask what are the fundamental causes of the differences between proteins and other polymers-What makes proteins special?One view of protein folding assumes that the "local" interactions among the near neighbors in the amino acid sequence, the interactions that form helices and turns, are the main determinants of protein structure. This assumption implies that isolated helices form early in the protein folding pathway and then assemble into the native tertiary structure (see Fig. 1). It is the premise behind the paradigm, primary + secondary -+ tertiary structure, that seeks computer algorithms to predict secondary structures from the sequence, and then to assemble them into the tertiary native structure.Here we review a simple model of an alternative view, its basis in experimental results, and its implications. We show how the nonlocal interactions that drive collapse processes in heteropolymers can give rise to protein structure, stability, and folding kinetics. This perspective is based on evidence that the folding code is not predominantly localized in short windows of the amino acid sequence. It...

Oxidized and reduced hen lysozyme denatured in 8 M urea at low pH have been studied in detail by NMR methods. 15N correlated NOESY and TOCSY experiments have provided near complete sequential assignment for both 1H and 15N resonances. Over 900 NOEs, including 130 (i, i + 2) and 23 (i, i + 3) NOEs, could be identified by analysis of the NOESY spectra of the denatured states, and 3J(HN, Halpha) coupling constants and 15N relaxation rates have been measured. The coupling constant and NOE data were analyzed by comparisons with theoretical predictions from a random coil polypeptide model based on amino acid specific phi,psi distributions extracted from the protein data bank. There is significant agreement between predicted and experimental NMR parameters suggesting that local conformations of the denatured states are largely determined by short-range interactions within the polypeptide chain. This result is supported by the observation that the chemical shift, coupling constant, and NOE data are little affected by whether or not the four disulfide bridge cross-links are formed in the denatured protein. The relaxation data, however, show significant differences between the oxidized and reduced protein. Analysis of the relaxation data in terms of simple dynamics models provides evidence for weak clustering of hydrophobic groups near tryptophan residues and increased barriers to motion in the more compact conformers formed when the polypeptide chain is cross-linked by the disulfide bridges. Using this information, a structural description of these denatured states is given in terms of an ensemble of conformers, which have a complex relationship between their local and global characteristics.

How does a protein find its native state without a globally exhaustive search? We propose the "HZ" (hydrophobic zipper) hypothesis: hydrophobic contacts act as constraints that bring other contacts into spatial proximity, which then further constrain and zip up the next contacts, etc.In contrast to helix-coil cooperativity, HZ-heteropolymer collapse cooperatvity is driven by nonlocal interactions, causes sheet and irregular conformations in addition to helices, leads to secondary structurs concurrentiy with early hydrophobic core formation, is much more sequence dependent than helixcoil processes, and involves compact intermediate states that have much secondary-but little tertiary-structure. Hydrophobic contacts in the 1992 Protein Data Bank have the type of "topologial localness" predicted by the hypothesis. The HZ paths for amino acid sequences that mimic crambin and bovine pancreatic trypsin inhibitor are quickly found by computer; the best configurations thus reached have single hydrophobic cores that are within about 3 kcal/mol of the global minimum. This hypothesis shows how proteins could find globally optimal states without exhautive search.What is the origin of cooperativity in protein folding? Some proteins fold reversibly (1, 2), independently of pathway (3-5), to a unique native state. These native states must be at the global minimum of free energy that is accessible on the experimental time scale. To guarantee that a computational strategy finds the global optimum requires a search time that scales exponentially with chain length (6, 7). However, Levinthal (8) and Wetlaufer (9) pointed out that proteins fold much too fast (by at least tens of orders of magnitude) to involve an exhaustive search. Hence, the kinetics/thermodynamics paradox: how can a protein find a globally optimal state without a globally exhaustive search? It follows that the folding problem is not so much a problem of exhaustive computational searching as it is the question of what is the physical basis of cooperativity by which proteins avoid exhaustive searching of conformational space. This view has led to important experiments on protein-folding mechanisms and pathways (10-23).The main paradigm for cooperativity in biopolymers is the helix-coil theory (24-27). "Cooperativity" describes how a globally optimal state can be found without a global search, hence cooperativity involves conformational choices that must be local in some sense. The nature of "localness" is at the heart of cooperativity. For helix-coil processes, the global minimum (the helix) is found by local processes by which each individual tetrapeptide in the sequence finds a hydrogen-bonded helical conformation; the partition function for the whole chain is a product of partition functions for individual helical units (24)(25)(26)(27). Such processes are local in two respects. (i) Monomers i andj that seek to form a helical hydrogen-bonding contact are "sequence-local" (S-local)-i.e., near neighbors in the sequence (j = i + 3 for a-helices,