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...

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What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain "freezing" or ordering, Le., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements ( m ) have different frequencies, and the frequencies have different dependencies on compactness. m m contacts contribute significantly only at high densities, suggesting that mainchain hydrogen bonding in proteins may be promoted by compactness. The distributions of mrn, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.Keywords: conformational entropy; lattice model; protein stability; side-chain freezing; side-chain packing When a polymer becomes compact, as when a protein folds to its native state, the main chain loses degrees of freedom, incurring a large loss of entropy. Main-chain configurational entropy is a strong force opposing the stability of native proteins (Dill, 1985(Dill, , 1990. How do side chains contribute to the configurational entropy of protein conformations? Is there "side-chain freezing," i.e., a large sharp loss of degrees of freedom as the side chains pack into compact native conformations? We explore these issues with a simple model that can be studied rigorously.The inference that side-chain packing is important to protein stability has been drawn from several lines of evidence. Side chains in the hydrophobic cores of proteins are tightly packed (Richards, 1974(Richards, , 1977Richards & Lim, 1994) and proteins have low compressibilities (Klapper, 1971;Eden et al., 1982;Gavish et al., 1983;Kundrot & Richards, 1987). Many core side-chain motions are hindered or eliminated in native proteins (Gurd & Rothgeb, 1979;Wagner, 1983;McCammon & Harvey, 1987). Side-chain packing may also be important to the kinetics of folding. Ptitsyn (1987) and Ptitsyn et al. (1990) is critical. Rey and Skolnick (1993) have shown that the addition of model side chains to a model main chain in a computer simulation of protein folding reduces the number of pathways that lead to the native state, and Handel et al. (1993) have shown that it is not easy to design sequences that can fold to conformations with immobilized side chains.We can imagine a range of models of how sid...

What is the basis for the two-state cooperativity of protein folding? Since the 1950s, three main models have been put forward. 1. In 'helix-coil' theory, cooperativity is due to local interactions among near neighbours in the sequence. Helix-coil cooperativity is probably not the principal basis for the folding of globular proteins because it is not two-state, the forces are weak, it does not account for sheet proteins, and there is no evidence that helix formation precedes the formation of a hydrophobic core in the following pathways. 2. In the 'sidechain packing' model, cooperativity is attributed to the jigsaw-puzzle-like complementary fits of sidechains. This too is probably not the basis of folding cooperativity because exact models and experiments on homopolymers with sidechains give no evidence that sidechain freezing is two-state, sidechain complementarities in proteins are only weak trends, and the molten globule model predicted by this model is far more native-like than experiments indicate. 3. In the 'hydrophobic core collapse' model, cooperativity is due to the assembly of non-polar residues into a good core. Exact model studies show that this model gives two-state behaviour for some sequences of hydrophobic and polar monomers. It is based on strong forces. There is considerable experimental evidence for the kinetics this model predicts: the development of hydrophobic clusters and cores is concurrent with secondary structure formation. It predicts compact denatured states with sizes and degrees of disorder that are in reasonable agreement with experiments.

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