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.

How fast can a protein possibly fold? This question has stimulated experimentalists to seek fast folding proteins and to engineer them to fold even faster. Proteins folding at or near the speed limit are prime candidates for all-atom molecular dynamics simulations. They may also have no free energy barrier, allowing the direct observation of intermediate structures on the pathways from the unfolded to the folded state. Both experimental and theoretical approaches predict a speed limit of approximately N/100micros for a generic N-residue single-domain protein, with alpha proteins folding faster than beta or alphabeta. The predicted limits suggest that most known ultrafast folding proteins can be engineered to fold more than ten times faster.

Nanosecond lasers were used to measure the rate of conformational changes in myoglobin after ligand dissociation at ambient temperatures. At low solvent viscosities the rate is independent of viscosity, but at high viscosities it depends on approximately the inverse first power of the viscosity. Kramers theory for unimolecular rate processes can be used to explain this result if the friction term is modified to include protein as well as solvent friction. The theory and experiment suggest that the dominant factor in markedly reducing the rate of conformational changes in myoglobin at low temperatures (less than 200 K) is the very high viscosity (greater than 10(7) centipoise) of the glycerol-water solvent. That is, at low temperatures conformational substates may not be "frozen" so much as "stuck."

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Formation of a specific contact between two residues of a polypeptide chain is an important elementary process in protein folding. Here we describe a method for studying contact formation between tryptophan and cysteine based on measurements of the lifetime of the tryptophan triplet state. With tryptophan at one end of a flexible peptide and cysteine at the other, the triplet decay rate is identical to the rate of quenching by cysteine. We show that this rate is also close to the diffusion-limited rate of contact formation. The length dependence of this end-to-end contact rate was studied in a series of Cys-(Ala-Gly-Gln) k-Trp peptides, with k varying from 1 to 6. The rate decreases from ϳ1͞(40 ns) for k ‫؍‬ 1 to ϳ1͞(140 ns) for k ‫؍‬ 6, approaching the length dependence expected for a random coil (n ؊3͞2 ) for the longest peptides.T o understand how proteins fold, it is essential to know the time scales and mechanisms of its elementary processes (1). The formation of a contact between two residues in an unfolded polypeptide chain is one of the most fundamental of these processes and is central to many aspects of protein-folding mechanisms. Most helical segments in proteins are unstable in isolation (2, 3) and require interactions with residues in other parts of the chain to form stable folded structures. Similarly, interaction between side chains on opposite strands of an antiparallel ␤ sheet are required for stability (4). Initiation of a parallel ␤ sheet requires a contact between residues distant in sequence. Because of its central role in protein folding, it is important to develop kinetic methods to investigate contact formation. Here we describe a technique with nanosecond time resolution and apply it to the investigation of the end-to-end contact formation rate in a flexible peptide.An initial glimpse of the kinetics of contact formation was obtained in a study of unfolded cytochrome c (5-7). In these experiments, photodissociation of carbon monoxide from the heme with a nanosecond laser pulse was used to initiate an intramolecular ligand-binding process. CO dissociation opens up a binding site at the heme iron, permitting binding kinetics to be measured by time-resolved absorption spectroscopy. This study showed that intramolecular methionine binding is very close to diffusion limited. The measured binding rate of ϳ1͞(40 s) is therefore also the rate of forming a contact, in this case between positions separated by ϳ50 residues in the sequence. An obvious limitation of this technique, however, is that it is restricted to very few proteins (a subset of heme proteins). A more generic method for measuring contact formation was clearly needed.One such method has been introduced recently by Bieri et al. (8), who attached thioxanthone at one end of a f lexible peptide and naphthalene near the other. On optical excitation, the triplet state of thioxanthone forms and transfers its excitation energy to naphthalene on close contact in an apparently diffusion-limited process. The rate at which the thioxanthone tr...

The kinetics of the helix<==>coil transition of an alanine-based peptide following a laser-induced temperature jump were monitored by the fluorescence of an N-terminal probe, 4-(methylamino)benzoic acid (MABA). This probe forms a peptide hydrogen bond to the helix backbone, which changes its fluorescence quantum yield. The MABA fluorescence intensity decreases in a single exponential relaxation, with relaxation times that are weakly temperature dependent, exhibiting a maximum value of approximately 20 ns near the midpoint of the melting transition. We have developed a new model, the kinetic version of the equilibrium 'zipper' model for helix<==>coil transitions to explain these results. In this 'kinetic zipper' model, an enormous reduction in the number of possible species results from the assumption that each molecule contains either no helical residues or a single contiguous region of helix (the single-sequence approximation). The decay of the fraction of N-terminal residues that are helical, calculated from numerical solutions of the kinetic equations which describe the model, can be approximately described by two exponential relaxations having comparable amplitudes. The shorter relaxation time results from rapid unzipping (and zipping) of the helix ends in response to the temperature jump, while the longer relaxation time results from equilibration of helix-containing and non-helix-containing structures by passage over the nucleation free energy barrier. The decay of the average helix content is dominated by the slower process. The model therefore explains the experimental observation that relaxation for the N-terminal fluorescent probe is approximately 8-fold faster than that for the infrared probe of Williams et al. [(1996) Biochemistry 35, 691-697], which measures the average helix content, but does not account for the absence of observable amplitude for the slow relaxation in the fluorescence experiments (<10% slow phase). If we assume that the activation barrier for the coil-->helix rate is purely entropic, the model can also explain the maximum in the temperature dependence of the relaxation time for the fluorescent probe. Parameters that best reproduce the melting curves and the ratio of relaxation times predict a value of the cooperativity parameter sigma which is approximately 3-fold larger than previously reported values obtained from fitting equilibrium data only. The helix growth rate of approximately 10(8) s-1 that reproduces the experimental relaxation times is approximately 100-fold slower than those observed in molecular dynamics simulations. These parameters can be used to simulate the kinetically cooperative formation of a helix from the all-coil state.

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)...