Protein chains coil into alpha-helices and beta-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold. For the past 40 years, alpha-helix formation has been extensively investigated in synthetic and natural peptides, including by nanosecond kinetic studies. In contrast, the mechanism of formation of beta structures has not been studied experimentally. The minimal beta-structure element is the beta-hairpin, which is also the basic component of antiparallel beta-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a beta-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 micros at room temperature, which is about 30 times slower than the rate of alpha-helix formation. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a beta-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

Using an empirical analysis of experimental data we have estimated a set of energy contributions which accounts for the stability of isolated alpha-helices. With this database and an algorithm based on statistical mechanics, we describe the average helical behaviour in solution of 323 peptides and the helicity per residue of those peptides analyzed by nuclear magnetic resonance. Moreover the algorithm successfully detects the alpha-helical tendency, in solution, of a peptide corresponding to a beta-strand of ubiquitin.

An elementary statistical mechanical model was used to calculate the folding rates for 22 proteins from their known three-dimensional structures. In this model, residues come into contact only after all of the intervening chain is in the native conformation. An additional simplifying assumption is that native structure grows from localized regions that then fuse to form the complete native molecule. The free energy function for this model contains just two contributions-conformational entropy of the backbone and the energy of the inter-residue contacts. The matrix of interresidue interactions is obtained from the atomic coordinates of the three-dimensional structure. For the 18 proteins that exhibit two-state equilibrium and kinetic behavior, profiles of the free energy versus the number of native peptide bonds show two deep minima, corresponding to the native and denatured states. For four proteins known to exhibit intermediates in folding, the free energy profiles show additional deep minima. The calculated rates of folding the two-state proteins, obtained by solving a diffusion equation for motion on the free energy profiles, reproduce the experimentally determined values surprisingly well. The success of these calculations suggests that folding speed is largely determined by the distribution and strength of contacts in the native structure. We also calculated the effect of mutations on the folding kinetics of chymotrypsin inhibitor 2, the most intensively studied two-state protein, with some success.The classical protein folding problem has been to predict the three-dimensional structure from the amino acid sequence. A second interesting problem is to use the known threedimensional structure to predict the kinetics and mechanism of folding. This has taken on new importance with the recognition that many human diseases are caused by the aggregation of partially folded or misfolded proteins (1). Several developments over the past decade have made the theoretical prediction of folding kinetics a realistic goal. The first is the acquisition of detailed experimental data on 18 small single-domain proteins of known structure that show two-state equilibrium and kinetic behavior, which was first observed for chymotrypsin inhibitor 2 (CI2) by Jackson and Fersht (2). These studies provide the experimental results (3) necessary for testing theoretical models. Second, the energy landscape approach, beginning with the work of Bryngelson and Wolynes (4), has provided a coherent description of both real folding experiments and computer simulations of folding (5-13). A major simplifying result of this approach is the finding that diffusion on a one-dimensional free energy surface can reproduce folding rates observed in computer simulations of simplified representations of proteins (14, 15). The implication is that folding rates of real proteins could be obtained by calculating a sufficiently accurate free energy as a function of an appropriate reaction coordinate (16-18). Finally, Baker and coworkers made a key obse...

Theory predicts the existence of barrierless protein folding. Without barriers, folding should be noncooperative and the degree of native structure should be coupled to overall protein stability. We investigated the thermal unfolding of the peripheral subunit binding domain from Escherichia coli's 2-oxoglutarate dehydrogenase multienzyme complex (termed BBL) with a combination of spectroscopic techniques and calorimetry. Each technique probed a different feature of protein structure. BBL has a defined three-dimensional structure at low temperatures. However, each technique showed a distinct unfolding transition. Global analysis with a statistical mechanical model identified BBL as a downhill-folding protein. Because of BBL's biological function, we propose that downhill folders may be molecular rheostats, in which effects could be modulated by altering the distribution of an ensemble of structures.

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a ␤-hairpin, the minimal structural element of the antiparallel ␤-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, ␤-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 2 15 possible conformations and 15 ؋ 2 15 possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the ␤-hairpin peptide.As is evident from the presentations at this Colloquium, the continuous discovery of thousands of new gene sequences is producing a revolution in all aspects of protein physics, chemistry, and biology. Foremost among these is the protein-folding problem. C. B. Anfinsen, in his Nobel Prize winning experiments at the National Institutes of Health (1), showed that a denatured protein can refold spontaneously to form a biologically functional (native) structure. From this result, Anfinsen concluded that the information for determining the threedimensional structure is somehow encoded in the amino acid sequence. This work has led to the realization that it should in principle be possible to calculate the three-dimensional structure of a protein from its amino acid sequence. Calculating the structure from the sequence has become known as the first part of the protein-folding problem and currently engages a large number of theoretical and computational scientists. The second part of the protein-folding problem is to understand how a protein folds. That is, what are the kinetics and mechanism (or mechanisms) of protein folding? This question is in many ways more challenging because for in vitro folding the ultimate answer is a description of the distribution of three-dimensional structures as a function of time, as the polypeptide progresses from a nearly random set of structures to the unique, compact native protein. An additional motivation for kinetic studies is their relation to the evolution of protein sequences. Evolution preserves protein sequences that correspond to structures with functions that are important to the organism. Theoretical studies by Wolynes and coworkers (2) have suggested how rapid folding to the native structure is yet another evolutionary pressure.The experimental investigation of the kinetics and mechanism of protein folding has been aided by several recent theoretical and technological advances. The theoretical advances include analytical approaches (2-4)...

This review describes how kinetic experiments using techniques with dramatically improved time resolution have contributed to understanding mechanisms in protein folding. Optical triggering with nanosecond laser pulses has made it possible to study the fastest-folding proteins as well as fundamental processes in folding for the first time. These include formation of alpha-helices, beta-sheets, and contacts between residues distant in sequence, as well as overall collapse of the polypeptide chain. Improvements in the time resolution of mixing experiments and the use of dynamic nuclear magnetic resonance methods have also allowed kinetic studies of proteins that fold too fast (greater than approximately 10(3) s-1) to be observed by conventional methods. Simple statistical mechanical models have been extremely useful in interpreting the experimental results. One of the surprises is that models originally developed for explaining the fast kinetics of secondary structure formation in isolated peptides are also successful in calculating folding rates of single domain proteins from their native three-dimensional structure.

Protein folding is an inherently complex process involving coordination of the intricate networks of weak interactions that stabilize native three-dimensional structures. In the conventional paradigm, simple protein structures are assumed to fold in an all-or-none process that is inaccessible to experiment. Existing experimental methods therefore probe folding mechanisms indirectly. A widely used approach interprets changes in protein stability and/or folding kinetics, induced by engineered mutations, in terms of the structure of the native protein. In addition to limitations in connecting energetics with structure, mutational methods have significant experimental uncertainties and are unable to map complex networks of interactions. In contrast, analytical theory predicts small barriers to folding and the possibility of downhill folding. These theoretical predictions have been confirmed experimentally in recent years, including the observation of global downhill folding. However, a key remaining question is whether downhill folding can indeed lead to the high-resolution analysis of protein folding processes. Here we show, with the use of nuclear magnetic resonance (NMR), that the downhill protein BBL from Escherichia coli unfolds atom by atom starting from a defined three-dimensional structure. Thermal unfolding data on 158 backbone and side-chain protons out of a total of 204 provide a detailed view of the structural events during folding. This view confirms the statistical nature of folding, and exposes the interplay between hydrogen bonding, hydrophobic forces, backbone conformation and side-chain entropy. From the data we also obtain a map of the interaction network in this protein, which reveals the source of folding cooperativity. Our approach can be extended to other proteins with marginal barriers (less than 3RT), providing a new tool for the study of protein folding.

We have measured the kinetics of the helix-coil transition for the synthetic 21-residue peptide Ac-WAAAH+(AAAR+A)3A-NH2 initiated by nanosecond laser temperature jumps. This peptide was designed with tryptophan in position 1 and histidine in position 5 so that the side chains interact when the backbone of residues 1−5 is α-helical. Histidine, when protonated, efficiently quenches tryptophan fluorescence providing a probe for the presence of helical structure. The kinetics measured throughout the melting transition are well-described by a single-exponential relaxation, with a rate of 3.3 × 106 s-1 at 301 K, the midpoint of the helix−coil transition. The rate increases with increasing temperature with an apparent activation energy of approximately 8 kcal/mol. To interpret these results we have fitted the equilibrium and kinetic data with the statistical mechanical model of Muñoz et al. (Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 5872−5879). This model includes both variable helix propensities and side chain−side chain interactions. The model accounts for the single-exponential kinetics by predicting that approximately 90% of the change in the tryptophan fluorescence results from melting of stretches of helix which include residues 1−5 by passage over a nucleation free energy barrier. The measured temperature dependence is reproduced by introducing damping from solvent friction and an activation barrier for the individual helix propagation and melting steps. This barrier is somewhat larger than that which results from the loss in conformational entropy or breaking of hydrogen bonds. The model provides a description of the kinetics of the helix-coil transition which is consistent with the results of other experimental studies as well as molecular dynamics simulations.