Protein Folding as Biased Conformational Diffusion

Motion of a disordered polypeptide chain as studied by paramagnetic relaxation enhancements, 15N relaxation, and molecular dynamics simulations: how fast is segmental diffusion in denatured ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental (15)N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional (15)N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual H(N) atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49-0.55 × 10(-6) cm(2)/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and H(N) moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10(-6) cm(2)/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2-6.0 × 10(-6) cm(2)/s.

What can solid state NMR contribute to our understanding of protein folding?

Complete understanding of the folding process that connects a structurally disordered state of a protein to an ordered, biochemically functional state requires detailed characterization of intermediate structural states with high resolution and site specificity. While the intrinsically inhomogeneous and dynamic nature of unfolded and partially folded states limits the efficacy of traditional X-ray diffraction and solution NMR in structural studies, solid state NMR methods applied to frozen solutions can circumvent the complications due to molecular motions and conformational exchange encountered in unfolded and partially folded states. Moreover, solid state NMR methods can provide both qualitative and quantitative structural information at the site-specific level, even in the presence of structural inhomogeneity. This article reviews relevant solid state NMR methods and their initial applications to protein folding studies. Using either chemical denaturation to prepare unfolded states at equilibrium or a rapid freezing apparatus to trap non-equilibrium, transient structural states on a sub-millisecond time scale, recent results demonstrate that solid state NMR can contribute essential information about folding processes that is not available from more familiar biophysical methods.

A critical assessment of putative gatekeeper interactions in the villin headpiece helical subdomain

The helical subdomain of the villin headpiece (HP36) is one of the smallest naturally occurring proteins that folds cooperatively. Its small size, rapid folding, and simple three-helix topology have made it an extraordinary popular model system for computational, theoretical, and experimental studies of protein folding. Aromatic-proline interactions involving Trp64 and Pro62 have been proposed to play a critical role in specifying the subdomain fold by acting as gatekeeper residues. Note that the numbering corresponds to full-length headpiece. Mutation of Pro62 has been shown to lead to a protein that does not fold, but this may arise for two different reasons: The residue may make interactions that are critical for the specificity of the fold or the mutation may simply destabilize the domain. In the first case, the protein cannot fold, while in the second, the small fraction of molecules that do fold adopt the correct structure. The modest stability of the wild type prevents a critical analysis of these interactions because even moderately destabilizing mutations lead to a very small folded state population. Using a hyperstable variant of HP36, denoted DM HP36, as our new wild type, we characterized a set of mutants designed to assess the role of the putative gatekeeper interactions. Four single mutants, DM Pro62Ala, DM Trp64Leu, DM Trp64Lys, and DM Trp64Ala, and a double mutant, DM Pro62Ala Trp64Leu, were prepared. All mutants are less stable than DM HP36, but all are well folded as judged by CD and (1)H NMR. All of the mutants display sigmoidal thermal unfolding and urea-induced unfolding curves. Double-mutant cycle analysis shows that the interactions between Pro62 and Trp64 are weak but favorable. Interactions involving Pro62 and proline-aromatic interactions are, thus, not required for specifying the subdomain fold. The implications for the design and thermodynamics of miniature proteins are discussed.

Native like structure in the unfolded state of the villin headpiece helical subdomain, an ultrafast folding protein

The villin headpiece subdomain, HP36, is the smallest naturally occurring protein that folds cooperatively. Its small size, rapid folding, and simple three-helix topology have made it an extremely popular system for computational studies of protein folding. The role of unfolded state structure in rapid folding is an area of active investigation, but relatively little is known about the properties of unfolded states under native conditions. A peptide fragment, HP21, which contains the first and second helices of HP36 has been shown to be a good model for structure in the unfolded state of the intact domain but a detailed description of the conformational propensities of HP21 is lacking and the balance between native and nonnative interactions is not known. A series of three-dimensional NMR experiments were performed on (13)C, (15)N-labeled HP21 to investigate in detail its conformational propensities. Analysis of (13)C(alpha), (13)C(beta), (13)CO chemical shifts, Deltadelta(13)C(alpha) - Deltadelta(13)C(beta) secondary shifts, the secondary structure propensity scores, NOEs, (15)N R(2) values and comparison of experimental chemical shifts with those of HP36 and with chemical shifts calculated using the SHIFTS and SHIFTX programs all indicate that there is significant native like structure in the HP21 ensemble, and thus by implication in the unfolded state of HP36.

Using an amino acid fluorescence resonance energy transfer pair to probe protein unfolding: application to the villin headpiece subdomain and the LysM domain

Previously, we have shown that p-cyanophenylalanine (Phe CN) and tryptophan (Trp) constitute an efficient fluorescence resonance energy transfer (FRET) pair that has several advantages over commonly used dye pairs. Here, we aim to examine the general applicability of this FRET pair in protein folding-unfolding studies by applying it to the urea-induced unfolding transitions of two small proteins, the villin headpiece subdomain (HP35) and the lysin motif (LysM) domain. Depending on whether Phe CN is exposed to solvent, we are able to extract either qualitative information about the folding pathway, as demonstrated by HP35, which has been suggested to unfold in a stepwise manner, or quantitative thermodynamic and structural information, as demonstrated by LysM, which has been shown to be an ideal two-state folder. Our results show that the unfolding transition of HP35 reported by FRET occurs at a denaturant concentration lower than that measured by circular dichroism (CD) and that the loop linking helix 2 and helix 3 remains compact in the denatured state, which are consistent with the notion that HP35 unfolds in discrete steps and that its unfolded state contains residual structures. On the other hand, our FRET results on the LysM domain allow us to develop a model for extracting structural and thermodynamic parameters about its unfolding, and we find that our results are in agreement with those obtained by other methods. Given the fact that Phe CN is a non-natural amino acid and, thus, amenable to incorporation into peptides and proteins via existing peptide synthesis and protein expression methods, we believe that the FRET method demonstrated here is widely applicable to protein conformational studies, especially to the study of relatively small proteins.

Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data

Differential scanning calorimetry was used to measure the temperature dependence of the absolute heat capacity of the 35-residue subdomain of the villin headpiece, a protein that folds in 5 mus and is therefore assumed to have a small free-energy barrier separating folded and unfolded states. To obtain an estimate of the barrier height from the calorimetric data, two models, a variable-barrier model and an Ising-like model, were used to fit the heat capacity in excess of the folded state over the temperature range 15-125 degrees C. The variable-barrier model is based on an empirical mathematical form for the density of states, with four adjustable parameters and the enthalpy (H) as a reaction coordinate. The Ising-like model is based on the inter-residue contact map of the X-ray structure with exact enumeration of approximately 10(5) possible conformations, with two adjustable parameters in the partition function, and either the fraction of native contacts (Q) or the number of ordered residues (P) as reaction coordinates. The variable-barrier model provides an excellent fit to the data and yields a barrier height at the folding temperature ranging from 0.4 to 1.1 kcal mol(-1), while the Ising-like model provides a less good fit and yields barrier heights of 2.3 +/- 0.1 kcal mol(-1) and 2.1 +/- 0.1 kcal mol(-1) for the Q and P reaction coordinates, respectively. In both models, the barrier to folding increases with increasing temperature. Assuming a sufficiently large activation energy for diffusion on the free-energy surfaces, both models are consistent with the observation of a temperature-independent folding rate in previously published laser temperature-jump experiments. Analysis of this kinetic data, using an approximate form for the pre-exponential factor of Kramers theory and the 70 ns relaxation time for the fast phase that precedes the unfolding/refolding relaxation to determine the diffusion coefficient, results in a barrier height of 1.6 +/- 0.3 kcal mol-1 for an unspecified reaction coordinate. Although no independent test of the validity of the H, Q, or P reaction coordinates is given, the barrier-height estimates obtained with the three reaction coordinates are in quite good agreement with the value derived from a Kramers analysis of the kinetics that makes no assumptions about the reaction coordinate. However, the higher estimates obtained using Q or P appear more consistent with the finding of barrier-crossing kinetics of a villin mutant that folds in 700 ns, corresponding to a 1.3 kcal mol-1 reduction in the folding barrier relative to wild-type. All of the results suggest that the free-energy barrier to folding is sufficiently low that it should be possible to engineer this protein or find solution conditions that would eliminate the barrier to create the "downhill" folding scenario of Wolynes and Onuchic.

Optimum folding pathways for growing protein chains

The folding of a protein is studied as it grows residue by residue from the N-terminus and enters an environment that stabilizes the folded state. This mode of folding of a growing chain is different from refolding where the full chain folds from a disordered initial configuration to the native state. We propose a sequential dynamic optimization method that computes the evolution of optimum folding pathways as amino acid residues are added to the peptide chain one by one. The dynamic optimization formulation is deterministic and uses Newton's equations of motion and a Go-type potential that establishes the native contacts and excluded volume effects. The method predicts the optimal energy-minimizing path among all the alternative feasible pathways. As two examples, the folding of the chicken villin headpiece, a 36-residue protein, and chymotrypsin inhibitor 2 (CI2), a 64-residue protein, are studied. Results on the villin headpiece show significant differences from the refolding of the same chain studied previously. Results on CI2 mostly agree with the results of refolding experiments and computational work.

Global optimization and folding pathways of selected alpha-helical proteins

The results of basin-hopping global optimization simulations are presented for four small, alpha-helical proteins described by a coarse-grained potential. A step-taking scheme that incorporates the local conformational preferences extracted from a large number of high-resolution protein structures is compared with an unbiased scheme. In addition, the discrete path sampling method is used to investigate the folding of one of the proteins, namely, the villin headpiece subdomain. Folding times from kinetic Monte Carlo simulations and iterative calculations based on a Markovian first-step analysis for the resulting stationary-point database are in good mutual agreement, but differ significantly from the experimental values, probably because the native state is not the global free energy minimum for the potential employed.

Reconciling the solution and X-ray structures of the villin headpiece helical subdomain: molecular dynamics simulations and double mutant cycles reveal a stabilizing cation-pi interaction

The 36-residue helical subdomain of the villin headpiece, HP36, is one of the smallest cooperatively folded proteins, folding on the microsecond time scale. The domain is an extraordinarily popular model system for both experimental and computational studies of protein folding. The structure of HP36 has been determined using X-ray crystallography and NMR spectroscopy, with the resulting structures exhibiting differences in helix packing, van der Waals contacts, and hydrogen bonding. It is important to determine the solution structure of HP36 with as much accuracy as possible since this structure is widely used as a reference for simulations and experiments. We complement the existing data by using all-atom molecular dynamics simulations with explicit solvent to evaluate which of the experimental models is the better representation of HP36 in solution. After simulation for 50 ns initiated with the NMR structure, we observed that the protein spontaneously adopts structures with a backbone conformation, core packing, and C-capping motif on the third helix that are more consistent with the crystal structure. We also examined hydrogen bonding and side chain packing interactions between D44 and R55 and between F47 and R55, respectively, which were observed in the crystal structure but not in the NMR-based solution structure. Simulations showed large fluctuations in the distance between D44 and R55, while the distance between F47 and R55 remained stable, suggesting the formation of a cation-pi interaction between those residues. Experimental double mutant cycles confirmed that the F47-R55 pair has a larger energetic coupling than the D44-R55 interaction. Overall, these combined experimental and computational studies show that the X-ray crystal structure is the better reference structure for HP36 in solution at neutral pH. Our analysis also shows how detailed molecular dynamics simulations combined with experimental validation can help bridge the gap between NMR and crystallographic methods.

Residue Specific Resolution of Protein Folding Dynamics Using Isotope-Edited Infrared Temperature Jump Spectroscopy†

A major difficulty in experimental studies of protein folding is the lack of nonperturbing, residue specific probes of folding. Here, we demonstrate the ability to resolve protein folding dynamics at the level of a single residue using 13C=18O isotope-edited infrared spectroscopy. A single 13C=18O isotopic label was incorporated into the backbone of the 36 residue, three-helix bundle villin headpiece subdomain (HP36). The label was placed in a solvent protected region of the second alpha-helix of the protein. The 13C=18O isotopic label shifted the carbonyl stretching frequency to 1572.1 cm-1 in the folded state, well removed from the 12C=16O band of the unlabeled protein backbone. The unique IR signature of the 13C=18O label was exploited to probe the equilibrium thermal unfolding transition using temperature-dependent FTIR spectroscopy. The folding/unfolding dynamics were monitored using temperature-jump (T-jump) IR spectroscopy. The equilibrium unfolding studies showed conformational changes suggestive of a loss of helical structure in helix 2 prior to the global unfolding of the protein. T-jump relaxation kinetics probing both the labeled site and the 12C=16O band were found to be biphasic with similar relaxation rates. The slow relaxation phase (approximately 2 x 10(5) s-1) corresponds to the global folding transition. The location of the label, a buried position in helix 2, provides an important probe of the origin of the fast relaxation phase (approximately 10(7) s-1). This phase has significant amplitude for the labeled position even though it is well protected from solvent in the folded structure. The fast phase likely represents a rapid pre-equilibrium that involves solvent penetration around the label and possible partial unfolding of helix 2 prior to the global unfolding transition. This work represents the first experimental study of ultrafast folding dynamics with residue specific resolution.

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.

Quantifying Polypeptide Conformational Space: Sensitivity to Conformation and Ensemble Definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.

NMR Characterization of a Peptide Model Provides Evidence for Significant Structure in the Unfolded State of the Villin Headpiece Helical Subdomain

The villin headpiece subdomain (HP36) is the smallest naturally occurring protein that folds cooperatively. The protein folds on a microsecond time scale. Its small size and very rapid folding have made it a popular target for biophysical studies of protein folding. Temperature-dependent one-dimensional (1D) NMR studies of the full-length protein together with CD and 1D NMR studies of the 21-residue peptide fragment (HP21) derived from HP36 have shown that there is significant structure in the unfolded state of HP36 and have demonstrated that HP21 is a good model of these interactions. Here, we characterized the model peptide HP21 in detail by two-dimensional NMR. Strongly upfield shifted C(alpha) protons, the magnitude of the 3J(NH,alpha) coupling constants, and the pattern of backbone-backbone and backbone-side chain NOEs indicate that the ensemble of structures populated by HP21 contains alpha-helical structure and native as well as non-native hydrophobic contacts. The hydrogen-bonded secondary structure inferred from the NOEs is, however, not sufficient to confer significant protection against amide H-D exchange. These studies indicate that there is significant secondary structure and hydrophobic clustering in the unfolded state of HP36. The implications for the folding of HP36 are discussed.

Multistate Folding of the Villin Headpiece Domain

The villin headpiece (HP67) is a 67 residue, monomeric protein derived from the C-terminal domain of villin. Wild-type HP67 (WT HP67) is the smallest fragment of villin that retains strong in vitro actin-binding activity. WT HP67 is made up of two subdomains, which form a tightly packed interface. The C-terminal subdomain of WT HP67, denoted HP35, is rich in helical structure, folds in isolation, and has been widely used as a model system for folding studies. In contrast, very little is known about the folding of the intact villin headpiece domain. Here, NMR, CD and H/2H amide exchange measurements are used to follow the pH, thermal and urea-induced unfolding of WT HP67 and a mutant (HP67 H41Y) in which a buried conserved histidine in the N-terminal subdomain, His41, has been mutated to Tyr. Although most small proteins display two-state equilibrium unfolding, the results presented here demonstrate that unfolding of the villin headpiece is a multistate process. The presence of a folded N-terminal subdomain is shown to stabilize the C-terminal subdomain, increasing the midpoints of the thermal and urea-induced unfolding transitions and increasing protection factors for H/2H exchange. Histidine 41 has been shown to act as a pH-dependent switch in wild-type HP67: the N-terminal subdomain is unfolded when His41 is protonated, while the C-terminal subdomain remains folded irrespective of the protonation state of His41. Mutation of His41 to Tyr eliminates the segmental pH-dependent unfolding of the headpiece. The mutation stabilizes both domains, but folding is still multistate, indicating that His41 is not solely responsible for the unusual equilibrium unfolding behavior of villin headpiece domain.

Efficient high level expression of peptides and proteins as fusion proteins with the N-terminal domain of L9: application to the villin headpiece helical subdomain

The efficient expression of small to midsize polypeptides and small marginally stable proteins can be difficult. A new protein fusion system is developed to allow the expression of peptides and small proteins. The polypeptide of interest is linked via a Factor Xa cleavage sequence to the C-terminus of the N-terminal domain of the ribosomal protein L9 (NTL9). NTL9 is a small (56 residue) basic protein. The C-terminus of the protein is part of an alpha-helix which extends away from the globular structure thus additional domains can be fused without altering the fold of NTL9. NTL9 expresses at high levels, is extremely soluble, and remains fully folded over a wide temperature and pH range. The protein has a high net positive charge, facilitating purification of fusion proteins by ion exchange chromatography. NTL9 fusions can also be easily purified by reverse phase HPLC. As a test case we demonstrate the high level expression of a small, 36 residue, three helix bundle, the villin headpiece subdomain. This protein is widely used as a model system for folding studies and the development of a simple expression system should facilitate experimental studies of the subdomain. The yield of purified fusion protein is 70 mg/L of culture and the yield of purified villin headpiece subdomain is 24 mg/L of culture. We also demonstrate the use of the fusion system to express a smaller marginally folded peptide fragment of the villin headpiece domain.

Effect of modulating unfolded state structure on the folding kinetics of the villin headpiece subdomain

Equilibrium Fourier transform infrared (FTIR) and temperature-jump (T-jump) IR spectroscopic techniques were used to study the thermodynamics and kinetics of the unfolding and folding of the villin headpiece helical subdomain (HP36), a small three-helix protein. A double phenylalanine mutant (HP36 F47L, F51L) that destabilizes the hydrophobic core of this protein also was studied. The double mutant is less stable than wild type (WT) and has been shown to contain less residual secondary structure and tertiary contacts in its unfolded state. The relaxation kinetics after a T-jump perturbation were studied for both HP36 and HP36 F47L, F51L. Both proteins exhibited biphasic relaxation kinetics in response to a T-jump. The folding times for the WT (3.23 micros at 60.2 degrees C) and double phenylalanine mutant (3.01 micros at 49.9 degrees C) at the approximate midpoints of their thermal unfolding transitions were found to be similar. The folding time for the WT was determined to be 3.34 mus at 49.9 degrees C, similar to the folding time of the double phenylalanine mutant at that temperature. The double phenylalanine mutant, however, unfolds faster with an unfolding time of 3.01 micros compared with 6.97 micros for the WT at 49.9 degrees C.

High-Resolution Crystal Structures of Villin Headpiece and Mutants with Reduced F-Actin Binding Activity,

Villin-type headpiece domains are approximately 70 amino acid modular motifs found at the C terminus of a variety of actin cytoskeleton-associated proteins. The headpiece domain of villin, a protein found in the actin bundles of the brush border epithelium, is of interest both as a compact F-actin binding domain and as a model folded protein. We have determined the high-resolution crystal structures of chicken villin headpiece (HP67) at 1.4 A resolution as well as two mutants, R37A and W64Y, at 1.45 and 1.5 A resolution, respectively. Replacement of R37 causes a 5-fold reduction in F-actin binding affinity in sedimentation assays. Replacement of W64 results in a much more drastic reduction in F-actin binding affinity without significant changes in headpiece structure or stability. The detailed comparison of these crystal structures with each other and to our previously determined NMR structures of HP67 and the 35-residue autonomously folding subdomain in villin headpiece, HP35, provides the details of the headpiece fold and further defines the F-actin binding site of villin-type headpiece domains.

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.

Determination of ultrafast protein folding rates from loop formation dynamics

Quenching of the triplet state of tryptophan by contact with cysteine can be used to measure the kinetics of loop formation in unfolded proteins. Here we show that cysteine quenching dynamics also provide a novel method for measuring folding rates when the exchange between folded and unfolded states is faster than the unquenched triplet lifetime (approximately 100 micros). We use this technique to investigate folding/unfolding kinetics of the 35 residue headpiece subdomain of the protein villin, which contains a single tryptophan residue and was engineered to contain a cysteine residue at the N terminus. At intermediate concentrations of denaturant the time-course of the triplet decay consists of two relaxations, the rates and amplitudes of which reveal the fast kinetics for folding and unfolding of this protein. The folding rates extracted using a simple kinetic model are close to those reported previously from laser-induced temperature-jump experiments that employ the change in tryptophan fluorescence as a probe. However, the results differ significantly from those reported from dynamic NMR line shape analysis on a variant with methionine at the N terminus, an issue that remains to be resolved. The analysis of the triplet quenching kinetics also shows that the quenching rates in the unfolded state increase with decreasing denaturant concentration, indicating a compaction of the unfolded protein.

The protein folding 'speed limit'

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.

Distributions in protein conformation space: implications for structure prediction and entropy

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 A, is 10(-14). A high-resolution structural prediction, say to 2 A, is immensely more difficult (10(-57)). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium alpha-carbon displacements in the native ensemble would be 0.3-0.5 A based on T Delta S of 1.42 kcal/(mol residue).

Peptide Models Provide Evidence for Significant Structure in the Denatured State of a Rapidly Folding Protein: The Villin Headpiece Subdomain

The villin headpiece subdomain is a cooperatively folded 36-residue, three-alpha-helix protein. The domain is one of the smallest naturally occurring sequences which has been shown to fold. Recent experimental studies have shown that it folds on the 10-micros time scale. Its small size, simple topology, and very rapid folding have made it an attractive target for computational studies of protein folding. We present temperature-dependent NMR studies that provide evidence for significant structure in the denatured state of the headpiece subdomain. A set of peptide fragments derived from the headpiece were also characterized in order to determine if there is a significant tendency to form a locally stabilized structure in the denatured state. Peptides corresponding to each of the three isolated helices and to the connection between the first and second helices were largely unstructured. A longer peptide fragment which contains the first and second helices shows considerable structure, as judged by NMR and CD. Concentration-dependent CD measurements and analytical ultracentrifugation experiments indicate that the structure is not due to self-association. NMR studies indicate that the structure is stabilized by tertiary interactions involving phenylalanines and Val 50. A peptide in which two of the three phenylalanines are changed to leucine is considerably less structured, confirming the importance of the phenylalanines. This work indicates that there is significant structure in the denatured state of this rapidly folding protein.

Assessment of the role of computations in structural biology

Computations are now an integrated part of structural biology and are used in data gathering, data processing, and data storage as well as in a full spectrum of theoretical pursuits. In this review, we focus on areas of great promise and call attention to important issues of internal consistency and error analysis.

Experimental tests of villin subdomain folding simulations

We have used laser temperature-jump to investigate the kinetics and mechanism of folding the 35 residue subdomain of the villin headpiece. The relaxation kinetics are biphasic with a sub-microsecond phase corresponding to a helix-coil transition and a slower microsecond phase corresponding to overall unfolding/refolding. At 300 K, the folding time is 4.3(+/-0.6) micros, making it the fastest folding, naturally occurring protein, with a rate close to the theoretical speed limit. This time is in remarkable agreement with the prediction of 5 (+11,-3) micros by Zagrovic et al. from atomistic molecular dynamics simulations using an implicit solvent model. We test their prediction that replacement of the C-terminal phenylalanine residue with alanine will increase the folding rate by removing a transient non-native interaction. We find that the alanine substitution has no effect on the folding rate or on the equilibrium constant. Implications of this result for the validity of the simulated folding mechanism are discussed.

Dynamic NMR line-shape analysis demonstrates that the villin headpiece subdomain folds on the microsecond time scale

There is considerable interest in small proteins that fold very rapidly. These proteins have become attractive targets for both theoretical and computational studies. The independently folded 36-residue villin headpiece subdomain has been the subject of a number of such studies and is predicted to fold quickly. We demonstrate using dynamic NMR line-shape analysis that the protein folds on the time scale of 10 mus. Folding rates were directly estimated between 56 and 78 degrees C using resolved protein resonances from three different residues at both 500 and 700 MHz. The rates estimated using different residues and different field strengths agree well with each other. The estimated folding rate lies between 0.5 and 2.0 x 105 s-1 over this temperature range. The folding rate depends only weakly on temperature.