An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein-the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models-a three-state chemical-kinetics model, a physicalkinetics model, and an Ising-like theoretical model that considers 10 5 possible conformations (microstates). In both the physicalkinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 10 5 microstates. The analysis of the data on site-directed mutants using the chemicalkinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-byresidue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical-or physical-kinetics models.fluorescence ͉ funneled energy landscape ͉ Ising-like model ͉ laser temperature jump ͉ polypeptide A major challenge to advancing our understanding of how proteins fold is the development of an analytical theoretical model capable of calculating the quantities directly measured in both equilibrium and kinetic experiments. We have approached this problem experimentally by studying a small ultrafast folding protein, the 35-residue subdomain from the villin headpiece (1-7) (Fig. 1). It is the smallest naturally occurring protein that autonomously folds into a globular structure (8-10), so it should have one of the simplest protein-folding mechanisms, which may therefore be amenable to understanding in depth by a theoretical model. Moreover, because folding of this protein occurs in a few microseconds, close to the proposed theoretical speed limit (4, 11), it can be investigated in detail by molecular-dynamics simulations. Our theoretical approach is to calculate the experimentally measured quantities with an Ising-like statistical mechanical model (12, 13), originally developed to explain our results on the ␤-hairpin from the protein GB1 (14,15), and similar to models of Baker, Finkelstein,. The key simplifying feature of these models is that they explicitly consider only interactions between residues that are in contact in the native structur...

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.funneled energy landscape ͉ Ising-like model ͉ Kramers ͉ polypeptide ͉ viscosity D espite the complexity of the protein folding process, the kinetics and mechanisms of folding can be usefully and accurately described by diffusion over barriers on a lowdimensional free-energy surface (1-5). For ultrafast-folding proteins, the barriers are small and the rates may be affected by the variation of the diffusion coefficient along the reaction coordinate. In addition to solvent friction, the diffusion coefficient is determined by internal friction, which reflects the ''roughness'' of the energy landscape that arises from drag because of intrachain interactions and escape from local minima on the energy surface (1, 4, 6, 7). Both theoretical studies (1,8) and simulations (4, 9, 10) indicate that the internal friction depends on position along the reaction coordinate, but there have been no experiments that address this important issue in the physics of protein folding. In this work, we obtain a quantitative measure of the contribution of internal friction to the dynamics of folding from experiments on the viscosity dependence of the kinetics for the ultrafast-folding villin subdomain. Fitting the data with an Ising-like theoretical model, moreover, yields information on the position dependence of the diffusion coefficient. Unlike all previous studies of the viscosity dependence of protein-folding kinetics (11-17), we carried out experiments under conditions where there is no effect of the viscogen on the equilibrium thermal unfolding, as was done in a previous study of ␣-helix and ␤-hairpin formation (18).For barriers Ͼϳ 3RT separating folded and unfolded states, Kramers theory (19) predicts that the relaxation rate, 1/ , is given by:where is the relaxation time, f and u are the folding and unfolding times, ⌬G f ‡ is the free energy barrier to folding, ⌬G u ‡ is the free energy barrier to unfolding, R is the gas constant, T is the absolute temperature, ( u ) 2 is the curvature in the unfolded free energy well, ( f ) 2 is the curvature in the folded free energy well, ( ‡ ) 2 is the curvature a...

Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, α(3)D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross-correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin size increases, a phenomenon with similarities to NMR exchange broadening. When comparable populations of folded and unfolded molecules are present, this method yields rate coefficients in very good agreement with those obtained with the maximum likelihood method. As a first step toward characterizing transition paths, the Viterbi algorithm was used to locate the most probable transition points in the photon trajectories.

The interactions of partially unfolded proteins provide insight into protein folding and protein aggregation. In this work, we studied partially unfolded hen egg lysozyme interactions in solutions containing up to 7 M guanidinium chloride (GdnHCl). The osmotic second virial coefficient (B(22)) of lysozyme was measured using static light scattering in GdnHCl aqueous solutions at 20 degrees C and pH 4.5. B(22) is positive in all solutions, indicating repulsive protein-protein interactions. At low GdnHCl concentrations, B(22) decreases with rising ionic strength: in the absence of GdnHCl, B(22) is 1.1 x 10(-3) mLmol/g(2), decreasing to 3.0 x 10(-5) mLmol/g(2) in the presence of 1 M GdnHCl. Lysozyme unfolds in solutions at GdnHCl concentrations higher than 3 M. Under such conditions, B(22) increases with ionic strength, reaching 8.0 x 10(-4) mLmol/g(2) at 6.5 M GdnHCl. Protein-protein hydrodynamic interactions were evaluated from concentration-dependent diffusivity measurements, obtained from dynamic light scattering. At moderate GdnHCl concentrations, lysozyme interparticle interactions are least repulsive and hydrodynamic interactions are least attractive. The lysozyme hydrodynamic radius was calculated from infinite-dilution diffusivity and did not change significantly during protein unfolding. Our results contribute toward better understanding of protein interactions of partially unfolded states in the presence of a denaturant; they may be helpful for the design of protein refolding processes that avoid protein aggregation.

Although it has been known for more than 60 years that the cause of sickle cell disease is polymerization of a hemoglobin mutant, hydroxyurea is the only drug approved for treatment by the US Food and Drug Administration. This drug, however, is only partially successful, and the discovery of additional drugs that inhibit fiber formation has been hampered by the lack of a sensitive and quantitative cellular assay. Here, we describe such a method in a 96-well plate format that is based on laser-induced polymerization in sickle trait cells and robust, automated image analysis to detect the precise time at which fibers distort ("sickle") the cells. With this kinetic method, we show that small increases in cell volume to reduce the hemoglobin concentration can result in therapeutic increases in the delay time prior to fiber formation. We also show that, of the two drugs (AES103 and GBT440) in clinical trials that inhibit polymerization by increasing oxygen affinity, one of them (GBT440) also inhibits sickling in the absence of oxygen by two additional mechanisms.sickle cell | drugs | hemoglobin S | treatment | screening assay

Protein aggregation is a challenge to the successful manufacture of protein therapeutics; it can impose severe limitations on purification yields and compromise formulation stability. Advances in computer power, and the wealth of computational studies pertaining to protein folding, have facilitated the development of molecular simulation as a tool to investigate protein misfolding and aggregation. Here, we highlight the successes of protein aggregation studies carried out in silico, with a particular emphasis on studies related to biotechnology. To conclude, we discuss future prospects for the field, and identify several biotechnology-related problems that would benefit from molecular simulation.

Determining the rate of forming the truly folded conformation of ultrafast folding proteins is an important issue for both experiments and simulations. The double-norleucine mutant of the 35-residue villin subdomain is the focus of recent computer simulations with atomistic molecular dynamics because it is currently the fastest folding protein. The folding kinetics of this protein have been measured in laser temperature-jump experiments using tryptophan fluorescence as a probe of overall folding. The conclusion from the simulations, however, is that the rate determined by fluorescence is significantly larger than the rate of overall folding. We have therefore employed an independent experimental method to determine the folding rate. The decay of the tryptophan triplet-state in photoselection experiments was used to monitor the change in the unfolded population for a sequence of the villin subdomain with one amino acid difference from that of the laser temperature-jump experiments, but with almost identical equilibrium properties. Folding times obtained in a two-state analysis of the results from the two methods at denaturant concentrations varying from 1.5-6.0 M guanidinium chloride are in excellent agreement, with an average difference of only 20%. Polynomial extrapolation of all the data to zero denaturant yields a folding time of 220 ðþ100, − 70Þ ns at 283 K, suggesting that under these conditions the barrier between folded and unfolded states has effectively disappeared-the so-called "downhill scenario." tryptophan triplet lifetime | villin headpiece subdomain | downhill protein folding | laser temperature jump

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