Nanosecond folding dynamics of a three-stranded beta-sheet

We studied conformational stability and folding kinetics of a three-stranded beta-sheet containing two rigid turns. Static infrared measurements indicate that this beta-sheet undergoes a broad but cooperative thermal unfolding transition with a midpoint at approximately 53 degrees C. Interestingly, time-resolved infrared experiments show that its relaxation kinetics in response to a temperature-jump (T-jump) occur on the nanosecond time scale (e.g., the relaxation time is approximately 140 ns at 35.0 degrees C), thereby suggesting that the conformational relaxation encounters only a small free energy barrier or even proceeds in a downhill manner. Further Langevin dynamics simulations suggest that the observed T-jump relaxation kinetics could be modeled by a conformational diffusion process along a single-well free energy profile, which allowed us to determine the effective diffusion constant and also the roughness of the folding energy landscape.     

Infrared study of the stability and folding kinetics of a 15-residue beta-hairpin

The thermal stability and folding kinetics of a 15-residue beta-hairpin (SESYINPDGTWTVTE) have been studied by using infrared (IR) spectroscopy coupled with laser-induced temperature-jump (T-jump) technique for rapid folding-unfolding initiation. An alternative method based on analyzing IR difference spectra was also introduced to obtain thermodynamic properties of beta-sheets, which complements the commonly used circular dichroism (CD) and fluorescence techniques. Equilibrium IR measurements indicate that the thermal unfolding of this beta-hairpin is fairly broad. However, it can be described by a two-state transition with a thermal melting temperature of approximately 29 degrees C. Time-resolved IR measurements following a T-jump, probed at 1634 cm(-1), indicate that the folding of this beta-hairpin follows first-order kinetics and is amazingly fast. At 300 K, the folding time is approximately 0.8 micros, which is only 2-3 times slower than that of alpha-helix formation. Additionally, the energetic barrier for folding is small (approximately 2 kcal mol(-1)). These results, in conjunction with results from other studies, support a view that the details of native contacts play a dominant role in the kinetics of beta-hairpin folding.     

Beta-hairpin folding by a model amyloid peptide in solution and at an interface

The development of specific agents against amyloidoses requires an understanding of the conformational distribution of fibrillogenic peptides at a microscopic level. Here, I present molecular dynamics simulations of the model amyloid peptide LSFD with sequence LSFDNSGAITIG-NH2 in explicit water and at a water/vapor interface for a total time scale of approximately 1.8 micros. An extended structure was used as initial peptide configuration. At approximately 290 K, solvated LSFD was kinetically trapped in diverse misfolded beta-sheet/coil conformations. At 350 K, in contrast, the same type II' beta-hairpin in equilibrium with less ordered but also U-shaped conformations was observed for the core residues DNSGAITI in solution and at the interface in multiple independent simulations. The most stable structural unit of the beta-hairpin was the two residue turn (GA). The core residues exhibited a well-defined folded state in which the beta-hairpin was stabilized by a hydrogen bond between the side chain of Asn-385 and the main chain carbonyl group of Gly-387. My results suggest that beta-sheet conformations indicated from previous Fourier-transform infrared spectroscopy measurements immediately after preparation of the peptide solution may not arise from protofilaments as speculated by others but are a property of LSFD monomers. In addition, combined with previous results from X-ray scattering, my findings suggest that interfacial aggregation of LSFD implies a transition from U-shaped to extended peptide conformations. This work including the first simulations of reversible beta-hairpin folding at an interface is an essential step toward a microscopic understanding of interfacial peptide folding and self-assembly. Knowledge of the main conformation of the peptide core may facilitate the design of possible inhibitors of LSFD aggregation as a test ground for future computational therapeutic strategies against amyloid diseases.     

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.     

Effective stochastic dynamics on a protein folding energy landscape

We present an approach to protein folding kinetics using stochastic reaction-coordinate dynamics, in which the effective drift velocities and diffusion coefficients are determined from microscopic simulation data. The resultant Langevin equation can then be used to directly simulate the folding process. Here, we test this approach by applying it to a toy two-state dynamical system and to a funnellike structure-based (Go-type) model. The folding time predictions agree very well with full simulation results. Therefore, we have in hand a fast numerical tool for calculating the folding kinetic properties, even when full simulations are not feasible. In addition, the local drift and diffusion coefficients provide an alternative way to compute the free energy profile in cases where only local sampling can be achieved.     

Kinetics of folding and binding of an intrinsically disordered protein: the inhibitor of yeast aspartic proteinase YPrA

The 68 residue peptide IA 3 is an intrinsically unstructured protein that serves as an endogenous inhibitor of the yeast aspartic proteinase A (YPrA). Although unstructured in free solution, IA 3 forms an N-terminal alpha helix as it binds to YPrA, leading to subnanomolar inhibition of the protease. Equilibrium structural and inhibition studies provide little insight into the mechanism and kinetics of the coupled folding and binding interaction. We have used laser temperature jump spectroscopy to study the kinetics of folding of free IA 3 and of the interaction between IA 3 and YPrA. Inducing folding with trifluoroethanol cosolvent allows us to determine the folding rate (kf approximately 0.3 (micros)(-1)) and the unfolding rate (ku approximately 3 (micros)(-1)) for free IA 3 in water at 25 degrees C. A substantially faster relaxation process is observed in the presence of the proteinase; this process appears to be the kinetic signature of an intermediate binding step in the coupled folding and binding interaction of IA 3 and YPrA.     

Structural and pathway complexity of beta-strand reorganization within aggregates of human transthyretin(105-115) peptide

Interstrand conformational rearrangements of human transthyretin peptide (TTR(105-115)) within dimeric aggregates were simulated by means of molecular dynamics (MD) with implicit solvation model for a total length of 48 micros. The conformations sampled in the MD simulations were clustered to identify free energy minima without any projections of free energy surface. A connected graph was constructed with nodes (=clusters) and edges corresponding to free energy minima and transitions between nodes, respectively. This connected graph which reflects the complexity of the free energy surface was used to extract the transition disconnectivity graph, which reflects the overall free energy barriers between pairs of free energy minima but does not contain information on transition paths. The routes of transitions between important free energy minima were obtained by further processing the original graph and the MD data. We have found that both parallel and antiparallel aggregates are populated. The parallel aggregates with different alignment patterns are separated by nonnegligible free energy barriers. Multiroutes exist in the interstrand conformational reorganization. Most visited routes do not dominant the kinetics, while less visited routes contribute a little each but they are numerous and their total contributions are actually dominant. There are various kinds of reptation motions, including those through a beta-bulge, side-chain aided reptation, and flipping or rotation of a hairpin formed by one strand.     

Stretched versus compressed exponential kinetics in α-helix folding

In a recent paper (J. Bredenbeck, J. Helbing, J.R. Kumita, G.A. Woolley, P. Hamm, α-helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time resolved IR spectroscopy, Proc. Natl. Acad. Sci USA 102 (2005) 2379), we have investigated the folding of a photo-switchable α-helix with a kinetics that could be fit by a stretched exponential function exp(−(t/τ)^β). The stretching factor β became smaller as the temperature was lowered, a result which has been interpreted in terms of activated diffusion on a rugged energy surface. In the present paper, we discuss under which conditions diffusion problems occur with stretched exponential kinetics (β < 1) and under which compressed exponential kinetics is obtained (β > 1). We show that diffusion problems do have a strong tendency to yield stretched exponential kinetics, yet, that there are conditions (strong perturbation from equilibrium, performing the experiment in the folding direction) under which compressed exponential kinetics would be expected instead. We discuss the kinetics on free energy surfaces predicted by simple initiation-propagation models (zipper models) of α-helix folding, as well as by folding funnel models. We show that our recent experiment has been performed under condition for which models with strong downhill driving force, such as the zipper model, would predict compressed, rather than stretched exponential kinetics, in disagreement with the experimental observation. We therefore propose that the free energy surface along a reaction coordinate that governs the folding kinetics must be relatively flat and has a shape similar to a 1D golf course. We discuss how this conclusion can be unified with the thermodynamically well established zipper model by introducing an additional kinetic reaction coordinate.     

Probing the complete folding trajectory of a DNA hairpin using dual beam fluorescence fluctuation spectroscopy

The conformational fluctuations of dye-quencher labeled DNA hairpin molecules in aqueous solution were investigated using dual probe beam fluorescence fluctuation spectroscopy. The measurements revealed the flow and diffusion times of the DNA molecules through two spatially offset optical probe regions, the absolute and relative concentrations of each conformational substate of the DNA, and the kinetics of the DNA hairpin folding and unfolding reactions in the 1 micros to 10 ms time range. A DNA hairpin containing a 21-nucleotide polythymine loop and a 4-base pair stem exhibited double exponential relaxation kinetics, with time constants of 84 and 393 micros. This confirms that folding and melting of the DNA hairpin structure is not a two state process but proceeds by way of metastable intermediate states. The fast time constant corresponds to formation and unfolding of an intermediate, and the slow time constant is due to formation and disruption of the fully base-paired stem. This is consistent with a previous study of a similar DNA hairpin with a 5-base pair stem, in which the fast reaction was attributed to the fluctuations of an intermediate DNA conformation [J. Am. Chem. Soc. 2006, 128, 1240-1249]. In that case, reactions involving the native conformation could not be observed directly due to the limited observation time range of the fluorescence correlation spectroscopy experiment. The intermediate states of the DNA hairpins are suggested to be due to a collapsed ensemble of folded hairpins containing various partially folded or misfolded conformations.     

Expanding the realm of ultrafast protein folding: gpW, a midsize natural single-domain with alpha+beta topology that folds downhill

All ultrafast folding proteins known to date are either very small in size (less than 45 residues), have an alpha-helix bundle topology, or have been artificially engineered. In fact, many of them share two or even all three features. Here we show that gpW, a natural 62-residue alpha+beta protein expected to fold slowly in a two-state fashion, folds in microseconds (i.e., from tau = 33 micros at 310 K to tau = 1.7 micros at 355 K). Thermodynamic analyses of gpW reveal probe dependent thermal denaturation, complex coupling between two denaturing agents, and differential scanning calorimetry (DSC) thermogram characteristic of folding over a negligible thermodynamic folding barrier. The free energy surface analysis of gpW folding kinetics also produces a marginal folding barrier of about thermal energy ( RT) at the denaturation midpoint. From these results we conclude that gpW folds in the downhill regime and is close to the global downhill limit. This protein seems to be poised toward downhill folding by a loosely packed hydrophobic core with low aromatic content, large stabilizing contributions from local interactions, and abundance of positive charges on the native surface. These special features, together with a complex functional role in bacteriophage lambda assembly, suggest that gpW has been engineered to fold downhill by natural selection.     

Simple continuous and discrete models for simulating replica exchange simulations of protein folding

The efficiency of temperature replica exchange (RE) simulations hinge on their ability to enhance conformational sampling at physiological temperatures by taking advantage of more rapid conformational interconversions at higher temperatures. While temperature RE is a parallel simulation technique that is relatively straightforward to implement, kinetics in the RE ensemble is complicated, and there is much to learn about how best to employ RE simulations in computational biophysics. Protein folding rates often slow down above a certain temperature due to entropic bottlenecks. This "anti-Arrhenius" behavior represents a challenge for RE. However, it is far from straightforward to systematically explore the impact of this on RE by brute force molecular simulations, since RE simulations of protein folding are very difficult to converge. To understand some of the basic mechanisms that determine the efficiency of RE, it is useful to study simplified low dimensionality systems that share some of the key characteristics of molecular systems. Results are presented concerning the efficiency of temperature RE on a continuous two-dimensional potential that contains an entropic bottleneck. Optimal efficiency was obtained when the temperatures of the replicas did not exceed the temperature at which the harmonic mean of the folding and unfolding rates is maximized. This confirms a result we previously obtained using a discrete network model of RE. Comparison of the efficiencies obtained using the continuous and discrete models makes it possible to identify non-Markovian effects, which slow down equilibration of the RE ensemble on the more complex continuous potential. In particular, the rate of temperature diffusion and also the efficiency of RE is limited by the time scale of conformational rearrangements within free energy basins.     

Overcoming entropic barrier with coupled sampling at dual resolutions

An enhanced sampling method is proposed for ab initio protein folding simulations. The new method couples a high-resolution model for accuracy and a low-resolution model for efficiency. It aims to overcome the entropic barrier found in the exponentially large protein conformational space when a high-resolution model, such as an all-atom molecular mechanics force field, is used. The proposed method is designed to satisfy the detailed balance condition so that the Boltzmann distribution can be generated in all sampling trajectories in both high and low resolutions. The method was tested on model analytical energy functions and ab initio folding simulations of a beta-hairpin peptide. It was found to be more efficient than replica-exchange method that is used as its building block. Analysis with the analytical energy functions shows that the number of energy calculations required to find global minima and to converge mean potential energies is much fewer with the new method. Ergodic measure shows that the new method explores the conformational space more rapidly. We also studied imperfect low-resolution energy models and found that the introduction of errors in low-resolution models does decrease its sampling efficiency. However, a reasonable increase in efficiency is still observed when the global minima of the low-resolution models are in the vicinity of the global minimum basin of the high-resolution model. Finally, our ab initio folding simulation of the tested peptide shows that the new method is able to fold the peptide in a very short simulation time. The structural distribution generated by the new method at the equilibrium portion of the trajectory resembles that in the equilibrium simulation starting from the crystal structure.     

Site-specific relaxation kinetics of a tryptophan zipper hairpin peptide using temperature-jump IR spectroscopy and isotopic labeling

Two antiparallel beta-strands connected by a turn make beta-hairpins an ideal model system to analyze the interactions and dynamics of beta-sheets. Site-specific conformational dynamics were studied by temperature-jump IR spectroscopy and isotopic labeling in a model based on the tryptophan zipper peptide, Trpzip2, developed by Cochran et al. (Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 5578). The modified Trpzip2C peptides have nearly identical equilibrium spectral behavior as Trpzip2 showing that they also form well-characterized beta-hairpin conformations in aqueous solution. Selective introduction of 13C=O groups on opposite strands lead to distinguishable cross-strand coupling of the labeled residues as monitored in the amide I' band. These frequency patterns reflect theoretical predictions, and the coupled 13C=O band loses intensity with increase in temperature and unfolding of the hairpin. Thermal relaxation kinetics were analyzed for unlabeled and cross-strand isotopically labeled variants. T-jumps of approximately 10 degrees C induce relaxation times of a few microseconds that decrease with increase of the peptide temperature. Differences in kinetic behavior for the loss of beta-strand and gain of disordered structure can be used to distinguish localized structure dynamics by comparison of nonlabeled and labeled amide I' components. Analysis of the data supports multistate dynamic and equilibrium behavior, but because of this process it is not possible to clearly define a folding and unfolding rate. Nonetheless, site-specific relaxation kinetics could be seen to be consistent with a hydrophobic collapse hypothesis for hairpin folding.     

Force-momentum-based self-guided Langevin dynamics: a rapid sampling method that approaches the canonical ensemble

The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.     

Mapping the cytochrome C folding landscape

The solution to the riddle of how a protein folds is encoded in the conformational energy landscape for the constituent polypeptide. Employing fluorescence energy transfer kinetics, we have mapped the S.cerevisiae iso-1 cytochrome c landscape by monitoring the distance between a C-terminal fluorophore and the heme during folding. Within 1 ms after denaturant dilution to native conditions, unfolded protein molecules have evolved into two distinct and rapidly equilibrating populations: a collection of collapsed structures with an average fluorophore-heme distance (r) of 27 A and a roughly equal population of extended polypeptides with r > 50 A. Molecules with the native fold appear on a time scale regulated by heme ligation events ( approximately 300 ms, pH 7). The experimentally derived landscape for folding has a narrow central funnel with a flat upper rim on which collapsed and extended polypeptides interchange rapidly in a search for the native structure.     

Diffusive dynamics on multidimensional rough free energy surfaces

The dynamics of processes relevant to chemistry and biophysics on rough free energy landscapes is investigated using a recently developed algorithm to solve the Smoluchowski equation. Two different processes are considered: ligand rebinding in MbCO and protein folding. For the rebinding dynamics of carbon monoxide (CO) to native myoglobin (Mb) from locations around the active site, the two-dimensional free energy surface (FES) is constructed using extensive molecular dynamics simulations. The surface describes the minima in the A state (bound MbCO), CO in the distal pocket and in the Xe4 pocket, and the transitions between these states and allows to study the diffusion of CO in detail. For the folding dynamics of protein G, a previously determined two-dimensional FES was available. To follow the diffusive dynamics on these rough free energy surfaces, the Smoluchowski equation is solved using the recently developed hierarchical discrete approximation method. From the relaxation of the initial nonequilibrium distribution, experimentally accessible quantities such as the rebinding time for CO or the folding time for protein G can be calculated. It is found that the free energy barrier for CO in the Xe4 pocket and in the distal pocket (B state) closer to the heme iron is approximately 6 kcal/mol which is considerably larger than the inner barrier which separates the bound state and the B state. For the folding of protein G, a barrier of approximately 10 kcal/mol between the unfolded and the folded state is consistent with folding times of the order of milliseconds.     

Early intermediate in human prion protein folding as evidenced by ultrarapid mixing experiments

An important step toward understanding the mechanism of the PrP(C)-to-PrP(Sc) conversion is to elucidate the folding pathway(s) of the prion protein. On the basis of stopped-flow measurements, we recently proposed that the prion protein folds via a transient intermediate formed on the submillisecond time scale, and mutations linked to familial diseases result in a pronounced increase in the population of this intermediate. Here, we have extended these studies to continuous-flow measurements using a capillary mixing system with a time resolution of approximately 100 micros. This allowed us to directly observe two distinct phases in folding of the recombinant human prion protein 90-231, providing unambiguous evidence for rapid accumulation of an early intermediate (with a time constant of approximately 50 micros), followed by a rate-limiting folding step (with a time constant of approximately 700 micros). The present study also clearly demonstrates that the population of the intermediate is significantly increased at mildly acidic pH and in the presence of urea. A similar three-state folding behavior was observed for the Gerstmann-Straussler-Scheinker disease-associated F198S mutant, in which case the population of an intermediate was greatly increased as compared to that of the wild-type protein. Overall, the present data strongly suggest that this partially structured intermediate may be a direct monomeric precursor of the misfolded PrP(Sc) oligomer.     

Temperature jump and fast photochemical oxidation probe submillisecond protein folding

We report a new mass-spectrometry-based approach for studying protein-folding dynamics on the submillisecond time scale. The strategy couples a temperature jump with fast photochemical oxidation of proteins (FPOP), whereby folding/unfolding is followed by changes in oxidative modifications by OH radical reactions. Using a flow system containing the protein barstar as a model, we altered the protein's equilibrium conformation by applying the temperature jump and demonstrated that its reactivity with OH free radicals serves as a reporter of the conformational change. Furthermore, we found that the time-dependent increase in mass resulting from free-radical oxidation is a measure of the rate constant for the transition from the unfolded to the first intermediate state. This advance offers the promise that, when extended with mass-spectrometry-based proteomic analysis, the sites and kinetics of folding/unfolding can also be followed on the submillisecond time scale.     

A computational study of the correlations between structure and dynamics in free and surface-immobilized single polymer chains

The correlations between structure and dynamics in free and surface-immobilized polymers were investigated via Langevin dynamics simulations of a free-jointed homopolymer. A detailed analysis was performed for a polymer in free solution and a polymer attached to a surface. The cases of repulsive and attractive surfaces, as well as poor and good solvents, were considered. The analysis focuses on properties that are particularly relevant to single molecule measurements, namely: (1) the distribution of end-to-end distance, (2) the correlations between the conformational structure and the time scale of its motion, (3) the correlations, at equilibrium, between the end-to-end distance and its displacement, and (4) the correlation between the initial coil conformation and the collapse pathway into the globular state. The differences and similarities between this model and a previously considered model of a protein, with two-state folding kinetics and a well-defined native state, are also discussed.     

Interstrand side chain--side chain interactions in a designed beta-hairpin: significance of both lateral and diagonal pairings

The contributions of interstrand side chain-side chain contacts to beta-sheet stability have been examined with an autonomously folding beta-hairpin model system. RYVEV(D)PGOKILQ-NH2 ((D)P = D-proline, O = ornithine) has previously been shown to adopt a beta-hairpin conformation in aqueous solution, with a two-residue loop at D-Pro-Gly. In the present study, side chains that display interstrand NOEs (Tyr-2, Lys-9, and Leu-11) are mutated to alanine or serine, and the conformational impact of the mutations is assessed. In the beta-hairpin conformation Tyr-2 and Leu-11 are directly across from one another (non-hydrogen bonded pair). This "lateral" juxtaposition of two hydrophobic side chains appears to contribute to beta-hairpin conformational stability, which is consistent with results from other beta-sheet model studies and with statistical analyses of interstrand residue contacts in protein crystal structures. Interaction between the side chains of Tyr-2 and Lys-9 also stabilizes the beta-hairpin conformation. Tyr-2/Lys-9 is a "diagonal" interstrand juxtaposition because these residues are not directly across from one another in terms of the hydrogen bonding registry between the strands. This diagonal interaction arises from the right-handed twist that is commonly observed among beta-sheets. Evidence of diagonal side chain-side chain contacts has been observed in other autonomously folding beta-sheet model systems, but we are not aware of other efforts to determine whether a diagonal interaction contributes to beta-sheet stability.