Ultrafast Folding Protein Research Articles

Measuring internal friction of an ultrafast-folding protein

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.

Microscopic Reversibility of Protein Folding in Molecular Dynamics Simulations of the Engrailed Homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.

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.

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.

Relaxation Rate for an Ultrafast Folding Protein Is Independent of Chemical Denaturant Concentration

The connection between free-energy surfaces and chevron plots has been investigated in a laser temperature jump kinetic study of a small ultrafast folding protein, the 35-residue subdomain from the villin headpiece. Unlike all other proteins that have been studied so far, no measurable dependence of the unfolding/refolding relaxation rate on denaturant concentration was observed over a wide range of guanidinium chloride concentration. Analysis with a simple Ising-like theoretical model shows that this denaturant-invariant relaxation rate can be explained by a large movement of the major free energy barrier, together with a denaturant- and reaction coordinate-dependent diffusion coefficient.

A pre-existing hydrophobic collapse in the unfolded state of an ultrafast folding protein

Insights into the conformational passage of a polypeptide chain across its free energy landscape have come from the judicious combination of experimental studies and computer simulations. Even though some unfolded and partially folded proteins are now known to possess biological function or to be involved in aggregation phenomena associated with disease states, experimentally derived atomic-level information on these structures remains sparse as a result of conformational heterogeneity and dynamics. Here we present a technique that can provide such information. Using a 'Trp-cage' miniprotein known as TC5b (ref. 5), we report photochemically induced dynamic nuclear polarization NMR pulse-labelling experiments that involve rapid in situ protein refolding. These experiments allow dipolar cross-relaxation with hyperpolarized aromatic side chain nuclei in the unfolded state to be identified and quantified in the resulting folded-state spectrum. We find that there is residual structure due to hydrophobic collapse in the unfolded state of this small protein, with strong inter-residue contacts between side chains that are relatively distant from one another in the native state. Prior structuring, even with the formation of non-native rather than native contacts, may be a feature associated with fast folding events in proteins.

Sub-microsecond Protein Folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.

Improvement on a simplified model for protein folding simulation

Improvements were made on a simplified protein model--the Ramachandran model-to achieve better computer simulation of protein folding. To check the validity of such improvements, we chose the ultrafast folding protein Engrailed Homeodomain as an example and explored several aspects of its folding. The engrailed homeodomain is a mainly alpha-helical protein of 61 residues from Drosophila melanogaster. We found that the simplified model of Engrailed Homeodomain can fold into a global minimum state with a tertiary structure in good agreement with its native structure.

Internal friction in the ultrafast folding of the tryptophan cage

Protein folding is a diffusional process, and the speed of folding is controlled by the frictional forces that act on the polypeptide chain. Several previous studies have suggested that the bulk viscosity of the solvent is the only important source of friction in folding reactions. By contrast, our studies of the folding dynamics of the Tryptophan Cage, a small, ultrafast-folding protein, show clear evidence for additional frictional forces that are independent of the solvent viscosity. The nature of this internal friction appears qualitatively different for the folding vs. unfolding reactions. We expect that this phenomenon could significantly influence the rate of many folding processes that proceed on sufficiently fast (∼μs) time scales. In particular, it may limit folding speeds to values substantially slower than the diffusion limits estimated from simple contact-formation studies in polypeptides.

High-resolution x-ray crystal structures of the villin headpiece subdomain, an ultrafast folding protein.

The 35-residue subdomain of the villin headpiece (HP35) is a small ultrafast folding protein that is being intensely studied by experiments, theory, and simulations. We have solved the x-ray structures of HP35 and its fastest folding mutant [K24 norleucine (nL)] to atomic resolution and compared their experimentally measured folding kinetics by using laser temperature jump. The structures, which are in different space groups, are almost identical to each other but differ significantly from previously solved NMR structures. Hence, the differences between the x-ray and NMR structures are probably not caused by lattice contacts or crystal/solution differences, but reflect the higher accuracy of the x-ray structures. The x-ray structures reveal important details of packing of the hydrophobic core and some additional features, such as cross-helical H bonds. Comparison of the x-ray structures indicates that the nL substitution produces only local perturbations. Consequently, the finding that the small stabilization by the mutation is completely reflected in an increased folding rate suggests that this region of the protein is as structured in the transition state as in the folded structure. It is therefore a target for engineering to increase the folding rate of the subdomain from approximately 0.5 micros(-1) for the nL mutant to the estimated theoretical speed limit of approximately 3 micros(-1).

Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

We report the application of Langevin dynamics to the physics-based united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (alpha; 46 residues), 1GAB (alpha; 47 residues), 1LQ7 (alpha; 67 residues), 1CLB (alpha; 75 residues), 1E0L (beta; 28 residues), and 1E0G (alpha+beta; 48 residues), and 1IGD (alpha+beta; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All alpha-helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative alpha-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800+ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.

Internal friction in the ultrafast folding of the tryptophan cage

Abstract Protein folding is a diffusional process, and the speed of folding is controlled by the frictional forces that act on the polypeptide chain. Several previous studies have suggested that the bulk viscosity of the solvent is the only important source of friction in folding reactions. By contrast, our studies of the folding dynamics of the Tryptophan Cage, a small, ultrafast-folding protein, show clear evidence for additional frictional forces that are independent of the solvent viscosity. The nature of this internal friction appears qualitatively different for the folding vs. unfolding reactions. We expect that this phenomenon could significantly influence the rate of many folding processes that proceed on sufficiently fast (∼μs) time scales. In particular, it may limit folding speeds to values substantially slower than the diffusion limits estimated from simple contact-formation studies in polypeptides.

Methods for molecular dynamics simulations of protein folding/unfolding in solution

All atom molecular dynamics simulations have become a standard method for mapping equilibrium protein dynamics and non-equilibrium events like folding and unfolding. Here, we present detailed methods for performing such simulations. Generic protocols for minimization, solvation, simulation, and analysis derived from previous studies are also presented. As a measure of validation, our water model is compared with experiment. An example of current applications of these methods, simulations of the ultrafast folding protein Engrailed Homeodomain are presented including the experimental evidence used to verify their results. Ultrafast folders are an invaluable tool for studying protein behavior as folding and unfolding events measured by experiment occur on timescales accessible with the high-resolution molecular dynamics methods we describe. Finally, to demonstrate the prospect of these methods for folding proteins, a temperature quench simulation of a thermal unfolding intermediate of the Engrailed Homeodomain is described.

The complete folding pathway of a protein from nanoseconds to microseconds.

Combining experimental and simulation data to describe all of the structures and the pathways involved in folding a protein is problematical. Transition states can be mapped experimentally by phi values, but the denatured state is very difficult to analyse under conditions that favour folding. Also computer simulation at atomic resolution is currently limited to about a microsecond or less. Ultrafast-folding proteins fold and unfold on timescales accessible by both approaches, so here we study the folding pathway of the three-helix bundle protein Engrailed homeodomain. Experimentally, the protein collapses in a microsecond to give an intermediate with much native alpha-helical secondary structure, which is the major component of the denatured state under conditions that favour folding. A mutant protein shows this state to be compact and contain dynamic, native-like helices with unstructured side chains. In the transition state between this and the native state, the structure of the helices is nearly fully formed and their docking is in progress, approximating to a classical diffusion-collision model. Molecular dynamics simulations give rate constants and structural details highly consistent with experiment, thereby completing the description of folding at atomic resolution.

Ultrafast folding of WW domains without structured aromatic clusters in the denatured state.

Ultrafast-folding proteins are important for combining experiment and simulation to give complete descriptions of folding pathways. The WW domain family comprises small proteins with a three-stranded antiparallel beta-sheet topology. Previous studies on the 57-residue YAP 65 WW domain indicate the presence of residual structure in the chemically denatured state. Here we analyze three minimal core WW domains of 38-44 residues. There was little spectroscopic or thermodynamic evidence for residual structure in either their chemically or thermally denatured states. Folding and unfolding kinetics, studied by using rapid temperature-jump and continuous-flow techniques, show that each domain folds and unfolds very rapidly in a two-state transition through a highly compact transition state. Folding half-times were as short as 17 micros at 25 degrees C, within an order of magnitude of the predicted maximal rate of loop formation. The small size and topological simplicity of these domains, in conjunction with their very rapid two-state folding, may allow us to reduce the difference in time scale between experiment and theoretical simulation.