Application of the diffusion-collision model to the folding of three-helix bundle proteins

The B domain of protein A retains residual structures in 6 M guanidinium chloride as revealed by hydrogen/deuterium-exchange NMR spectroscopy

The characterization of residual structures persistent in unfolded proteins is an important issue in studies of protein folding, because the residual structures present, if any, may form a folding initiation site and guide the subsequent folding reactions. Here, we studied the residual structures of the isolated B domain (BDPA) of staphylococcal protein A in 6 M guanidinium chloride. BDPA is a small three-helix-bundle protein, and until recently its folding/unfolding reaction has been treated as a simple two-state process between the native and the fully unfolded states. We employed a dimethylsulfoxide (DMSO)-quenched hydrogen/deuterium (H/D)-exchange 2D NMR techniques with the use of spin desalting columns, which allowed us to investigate the H/D-exchange behavior of individually identified peptide amide (NH) protons. We obtained H/D-exchange protection factors of the 21 NH protons that form an α-helical hydrogen bond in the native structure, and the majority of these NH protons were significantly protected with a protection factor of 2.0-5.2 in 6 M guanidinium chloride, strongly suggesting that these weakly protected NH protons form much stronger hydrogen bonds under native folding conditions. The results can be used to deduce the structure of an early folding intermediate, when such an intermediate is shown by other methods. Among three native helical regions, the third helix in the C-terminal side was highly protected and stabilized by side-chain salt bridges, probably acting as the folding initiation site of BDPA. The present results are discussed in relation to previous experimental and computational findings on the folding mechanisms of BDPA.

Folding with a protein's native shortcut network

A complex network approach to protein folding is proposed, wherein a protein's contact map is reconceptualized as a network of shortcut edges, and folding is steered by a structural characteristic of this network. Shortcut networks are generated by a known message passing algorithm operating on protein residue networks. It is found that the shortcut networks of native structures (SCN0s) are relevant graph objects with which to study protein folding at a formal level. The logarithm form of their contact order (SCN0_lnCO) correlates significantly with folding rate of two-state and nontwo-state proteins. The clustering coefficient of SCN0s (C_SCN0 ) correlates significantly with folding rate, transition-state placement and stability of two-state folders. Reasonable folding pathways for several model proteins are produced when C_SCN0 is used to combine protein segments incrementally to form the native structure. The folding bias captured by C_SCN0 is detectable in non-native structures, as evidenced by Molecular Dynamics simulation generated configurations for the fast folding Villin-headpiece peptide. These results support the use of shortcut networks to investigate the role protein geometry plays in the folding of both small and large globular proteins, and have implications for the design of multibody interaction schemes in folding models. One facet of this geometry is the set of native shortcut triangles, whose attributes are found to be well-suited to identify dehydrated intraprotein areas in tight turns, or at the interface of different secondary structure elements.

Fast helix formation in the B domain of protein A revealed by site-specific infrared probes

Comparison of experimental and computational protein folding studies can be difficult because of differences in structural resolution. Isotope-edited infrared spectroscopy offers a direct measure of structural changes involved in protein folding at the single-residue level. Here we demonstrate the increased resolution of site-specific infrared probes to the peptide backbone in the B domain of staphylococcal protein A (BdpA). (13)C═(18)O-labeled methionine was incorporated into each of the helices using recombinant protein expression. Laser-induced temperature jumps coupled with infrared spectroscopy were used to probe changes in the peptide backbone on the submillisecond time scale. The relaxation kinetics of the buried helices, solvated helices, and labeled positions were measured independently by probing the corresponding bands assigned in the amide I region. Using these wavelength-dependent measurements, we observe a fast nanosecond phase and slower microsecond phase at each position. We find at least partial formation of helices 1-3 in the fast intermediate state that precedes the transition state. These measurements provide direct, time-resolved experimental evidence of the early formation of partial helical structure in helices 1 and 3, supporting folding models proposed by computer simulations.

General mechanism of two-state protein folding kinetics

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.

Computational and theoretical methods for protein folding

A computational approach is essential whenever the complexity of the process under study is such that direct theoretical or experimental approaches are not viable. This is the case for protein folding, for which a significant amount of data are being collected. This paper reports on the essential role of in silico methods and the unprecedented interplay of computational and theoretical approaches, which is a defining point of the interdisciplinary investigations of the protein folding process. Besides giving an overview of the available computational methods and tools, we argue that computation plays not merely an ancillary role but has a more constructive function in that computational work may precede theory and experiments. More precisely, computation can provide the primary conceptual clues to inspire subsequent theoretical and experimental work even in a case where no preexisting evidence or theoretical frameworks are available. This is cogently manifested in the application of machine learning methods to come to grips with the folding dynamics. These close relationships suggested complementing the review of computational methods within the appropriate theoretical context to provide a self-contained outlook of the basic concepts that have converged into a unified description of folding and have grown in a synergic relationship with their computational counterpart. Finally, the advantages and limitations of current computational methodologies are discussed to show how the smart analysis of large amounts of data and the development of more effective algorithms can improve our understanding of protein folding.

Conformational dynamics is more important than helical propensity for the folding of the all α-helical protein Im7

Im7 folds via an on-pathway intermediate that contains three of the four native α-helices. The missing helix, helix III, is the shortest and its failure to be formed until late in the pathway is related to frustration in the structure. Im7H3M3, a 94-residue variant of the 87-residue Im7 in which helix III is the longest of the four native helices, also folds via an intermediate. To investigate the structural basis for this we calculated the frustration in the structure of Im7H3M3 and used NMR to investigate its dynamics. We found that the native state of Im7H3M3 is highly frustrated and in equilibrium with an intermediate state that lacks helix III, similar to Im7. Model-free analysis identified residues with chemical exchange contributions to their relaxation that aligned with the residues predicted to have highly frustrated interactions, also like Im7. Finally, we determined properties of urea-denatured Im7H3M3 and identified four clusters of interacting residues that corresponded to the α-helices of the native protein. In Im7 the cluster sizes were related to the lengths of the α-helices with cluster III being the smallest but in Im7H3M3 cluster III was also the smallest, despite this region forming the longest helix in the native state. These results suggest that the conformational properties of the urea-denatured states promote formation of a three-helix intermediate in which the residues that form helix III remain non-helical. Thus it appears that features of the native structure are formed early in folding linked to collapse of the unfolded state.

Right- and left-handed three-helix proteins. II. Similarity and differences in mechanical unfolding of proteins

Here, we study mechanical properties of eight 3-helix proteins (four right-handed and four left-handed ones), which are similar in size under stretching at a constant speed and at a constant force on the atomic level using molecular dynamics simulations. The analysis of 256 trajectories from molecular dynamics simulations with explicit water showed that the right-handed three-helix domains are more mechanically resistant than the left-handed domains. Such results are observed at different extension velocities studied (192 trajectories obtained at the following conditions: v = 0.1, 0.05, and 0.01 Å ps(-1) , T = 300 K) and under constant stretching force (64 trajectories, F = 800 pN, T = 300 K). We can explain this by the fact, at least in part, that the right-handed domains have a larger number of contacts per residue and the radius of cross section than the left-handed domains.

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.

Nearly symmetrical proteins: folding pathways and transition states

The folding pathways of the B domain of protein A have been the subject of many experimental and computational studies. Based on a statistical mechanical model, it has been suggested that the native state symmetry leads to multiple pathways, highly dependent on temperature and denaturant concentration. Experiments, however, have not confirmed this scenario. By considering four nearly symmetrical proteins, one of them being the above molecule, here we show that, if contact energies are properly taken into account, a different picture emerges from kinetic simulations of the above-mentioned model. This is characterized by a dominant folding pathway, which is consistent with the most recent experimental results. Given the simplicity of the model, we also report on a direct sampling of the transition state.

Dual folding pathways of an alpha/beta protein from all-atom ab initio folding simulations

Successful ab initio folding of proteins with both alpha-helix and beta-sheet requires a delicate balance among a variety of forces in the simulation model, which may explain that the successful folding of any alpha/beta proteins to within experimental error has yet to be reported. Here we demonstrate that it is an achievable goal to fold alpha/beta proteins with a force field emphasizing the balance between the two major secondary structures. Using our newly developed force field, we conducted extensive ab initio folding simulations on an alpha/beta protein full sequence design (FSD) employing both conventional molecular dynamics and replica exchange molecular dynamics in combination with a generalized-Born solvation model. In these simulations, the folding of FSD to the native state with high population (>64.2%) and high fidelity (C(alpha)-Root Mean Square Deviation of 1.29 A for the most sampled conformation when compared to the experimental structure) was achieved. The folding of FSD was found to follow two pathways. In the major pathway, the folding started from the formation of the helix. In the minor pathway, however, folding of the beta-hairpin started first. Further examination revealed that the helix initiated from the C-terminus and propagated toward the N-terminus. The formation of the hydrophobic contacts coincided with the global folding. Therefore the hydrophobic force does not appear to be the driving force of the folding of this protein.

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.

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102-14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape-based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C-terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.

Probing the folding transition state structure of the villin headpiece subdomain via side chain and backbone mutagenesis

Backbone-backbone hydrogen bonds are a common feature of native protein structures, yet their thermodynamic and kinetic influence on folding has long been debated. This is reflected by the disparity between current protein folding models, which place hydrogen bond formation at different stages along the folding trajectory. For example, previous studies have suggested that the denatured state of the villin headpiece subdomain contains a residual helical structure that may provide a bias toward the folded state by confining the conformational search associated with its folding. Although helical hydrogen bonds clearly stabilize the folded state, here we show, using an amide-to-ester mutation strategy, that the formation of backbone hydrogen bonds within helices is not rate-limiting in the folding of the subdomain, thereby suggesting that such hydrogen bonds are unlikely to be formed en route from the denatured to the transition state. On the other hand, elimination of hydrogen bonds within the turn region elicits a slower folding rate, consistent with the hypothesis that these residues are involved in the formation of a folding nucleus. While illustrating a potentially conserved aspect of helix-turn-helix folding, our results further underscore the inherent importance of turns in protein supersecondary structure formation.

ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions

A new implicit solvation model for use in Monte Carlo simulations of polypeptides is introduced. The model is termed ABSINTH for self-Assembly of Biomolecules Studied by an Implicit, Novel, and Tunable Hamiltonian. It is designed primarily for simulating conformational equilibria and oligomerization reactions of intrinsically disordered proteins in aqueous solutions. The paradigm for ABSINTH is conceptually similar to the EEF1 model of Lazaridis and Karplus (Proteins 1999, 35, 133). In ABSINTH, the transfer of a polypeptide solute from the gas phase into a continuum solvent is the sum of a direct mean field interaction (DMFI), and a term to model the screening of polar interactions. Polypeptide solutes are decomposed into a set of distinct solvation groups. The DMFI is a sum of contributions from each of the solvation groups, which are analogs of model compounds. Continuum-mediated screening of electrostatic interactions is achieved using a framework similar to the one used for the DMFI. Promising results are shown for a set of test cases. These include the calculation of NMR coupling constants for short peptides, the assessment of the thermal stability of two small proteins, reversible folding of both an alpha-helix and a beta-hairpin forming peptide, and the polymeric properties of intrinsically disordered polyglutamine peptides of varying lengths. The tests reveal that the computational expense for simulations with the ABSINTH implicit solvation model increase by a factor that is in the range of 2.5-5.0 with respect to gas-phase calculations.

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.

Quantifying the structural requirements of the folding transition state of protein A and other systems

The B-domain of protein A is a small three-helix bundle that has been the subject of considerable experimental and theoretical investigation. Nevertheless, a unified view of the structure of the transition-state ensemble (TSE) is still lacking. To characterize the TSE of this surprisingly challenging protein, we apply a combination of psi analysis (which probes the role of specific side-chain to side-chain contacts) and kinetic H/D amide isotope effects (which measures hydrogen-bond content), building upon previous studies using mutational phi analysis (which probes the energetic influence of side-chain substitutions). The second helix is folded in the TSE, while helix formation appears just at the carboxy and amino termini of the first and third helices, respectively. The experimental data suggest a homogenous yet plastic TS with a native-like topology. This study generalizes our earlier conclusion, based on two larger alpha/beta proteins, that the TSEs of most small proteins achieve approximately 70% of their native state's relative contact order. This high percentage limits the degree of possible TS heterogeneity and requires a reevaluation of the structural content of the TSE of other proteins, especially when they are characterized as small or polarized.

Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.

The complex folding pathways of protein A suggest a multiple-funnelled energy landscape

Folding proteins into their native states requires the formation of both secondary and tertiary structures. Many questions remain, however, as to whether these form into a precise order, and various pictures have been proposed that place the emphasis on the first or the second level of structure in describing folding. One of the favorite test models for studying this question is the B domain of protein A, which has been characterized by numerous experiments and simulations. Using the activation-relaxation technique coupled with a generic energy model (optimized potential for efficient peptide structure prediction), we generate more than 50 folding trajectories for this 60-residue protein. While the folding pathways to the native state are fully consistent with the funnel-like description of the free energy landscape, we find a wide range of mechanisms in which secondary and tertiary structures form in various orders. Our nonbiased simulations also reveal the presence of a significant number of non-native beta and alpha conformations both on and off pathway, including the visit, for a non-negligible fraction of trajectories, of fully ordered structures resembling the native state of nonhomologous proteins.

Loop-closure principles in protein folding

Simple theoretical concepts and models have been helpful to understand the folding rates and routes of single-domain proteins. As reviewed in this article, a physical principle that appears to underly these models is loop closure.

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.

A one-dimensional reaction coordinate for identification of transition states from explicit solvent P(fold)-like calculations

A properly identified transition state ensemble (TSE) in a molecular dynamics (MD) simulation can reveal a tremendous amount about how a protein folds and offer a point of comparison to experimentally derived Phi(F) values, which reflect the degree of structure in these transient states. In one such method of TSE identification, dubbed P(fold), MD simulations of individual protein structures taken from an unfolding trajectory are used to directly assess an input structure's probability of folding before unfolding, and P(fold) is, by definition, 0.5 for the TSE. Other, less computationally intensive methods, such as multidimensional scaling (MDS) of the pairwise root mean-squared deviation (RMSD) matrix of the conformations sampled in a thermal unfolding trajectory, have also been used to identify the TSE. Identification of the TSE is made from the original MD simulation without the need to run further simulations. Here we present a P(fold)-like study and describe methods for identification of the TSE through the derivation of a high fidelity, bounded, one-dimensional reaction coordinate for protein folding. These methods are applied to the engrailed homeodomain. The TSE identified by this approach is essentially identical to the TSE identified previously by MDS of the pairwise RMSD matrix. However, the cost of performing P(fold), or even our reduced P(fold)-like calculations, is at least 36,000 times greater than the MDS method.

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.

Folding time distributions as an approach to protein folding kinetics

A 27-residue lattice heteropolymer subject to Monte Carlo dynamics on a simple cubic lattice is studied over a range of temperatures. Folding time distributions are used to obtain information concerning the details of folding kinetics. The results are compared with those from methods based on mean force surfaces expressed in terms of a reduced set of variables and on a disconnectivity graph for the same system. A detailed analysis of the folding trajectories is given, and the importance of dead-end traps in determining the folding time is demonstrated. We show that the calculated folding kinetics can be modeled by a system of kinetic equations, with the essential rate constants determined from the Monte Carlo simulations and the resulting folding time distributions. The kinetic equations make possible an analysis of the variation of the importance of different channels with temperature. In particular, we show that the presence of intermediates may be masked in the folding time distributions, with the mean folding time being independent of the height of the barrier between the intermediates and collapsed globule state of the system. This and other results demonstrate that care has to be used in interpreting experimental folding data in terms of the underlying kinetics. Correspondingly, simulations are shown to have to satisfy certain requirements to obtain proper sampling of the dead-end traps.

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.

Ultrafast and downhill protein folding

Ultrafast folding proteins have served an important role in benchmarking molecular dynamics simulations and testing protein folding theories. These proteins are simple enough and fold fast enough that realistic simulations are possible, which facilitates the direct comparison of absolute folding rates and folding mechanisms with those observed experimentally. Such comparisons have achieved remarkable success, but have also revealed the shortcomings that remain in experiment, theory and simulation alike. Some ultrafast folding proteins may fold without encountering an activation barrier (downhill folding), allowing the exploration of the molecular timescale of folding and the roughness of the energy landscape. The biological significance of ultrafast folding remains uncertain, but its practical significance is crucial to progress in understanding how proteins fold.

Local structure formation in simulations of two small proteins

Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small alpha-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.

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.

Spinach on the ceiling: a theoretical chemist's return to biology

I was born in Vienna and came to the United States as a refugee in October 1938. This experience played an important role in my view of the world and my approach to science: It contributed to my realization that it was safe to stop working in fields that I felt I understood and to focus on different areas of research by asking questions that would teach me and others something new. I describe my experiences that led me from chemistry and physics back to my first love, biology, and outline some of the contributions I have made as part of my ongoing learning experience.

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.

Effects of denaturants on the dynamics of loop formation in polypeptides

Quenching of the triplet state of tryptophan by close contact with cysteine has been used to measure the reaction-limited and diffusion-limited rates of loop formation in disordered polypeptides having the sequence cys-(ala-gly-gln)j-trp (j=1-9). The decrease in the length-dependence of the reaction-limited rate for short chains in aqueous buffer, previously attributed to chain stiffness, is not observed at high concentrations of chemical denaturant (6 M GdmCl and 8 M urea), showing that denaturants increase chain flexibility. For long chains, both reaction-limited and diffusion-limited rates are significantly smaller in denaturant and exhibit a steeper length dependence. The results can be explained using end-to-end distributions from a wormlike chain model in which excluded volume interactions are incorporated by associating a 0.4-0.5 nm diameter hard sphere with the end of each virtual peptide bond. Fitting the data with this model shows that the denaturants reduce the persistence length from approximately 0.6 nm to approximately 0.4 nm, only slightly greater than the length of a peptide bond. The same model also describes the reported length dependence for the radii of gyration of chemically denatured proteins containing 50-400 residues. The end-to-end diffusion coefficients obtained from the diffusion-limited rates are smaller than the sum of the monomer diffusion coefficients and exhibit significant temperature dependence, suggesting that diffusion is slowed by internal friction arising from barriers to backbone conformational changes.

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.

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.

Flexibly varying folding mechanism of a nearly symmetrical protein: B domain of protein A

The folding pathway of the B domain of protein A is the pathway most intensively studied by computer simulations. Recent systematic measurement of Phi values by Sato et al., however, has shown that none of the published computational predictions is consistent with the detailed features of the experimentally observed folding mechanism. In this article we use a statistical mechanical model of folding to show that sensitive dependence of multiple transition state ensembles on temperature and the denaturant concentration is the key to resolving the inconsistency among simulations and the experiment. Such sensitivity in multiple transition state ensembles is a natural consequence of symmetry-breaking in a nearly symmetrical protein.

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.

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.

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.

The βαβαβ elementary supersecondary structure of the Rossmann fold from porcine lactate dehydrogenase exhibits characteristics of a molten globule

Protein classifications show that the Rossmann fold, which consists of two betaalphabetaalphabeta motifs (BABAB) related by a rough twofold axis, is the most populated alphabeta fold, and that the betaalphabeta submotif (BAB) is a widespread elementary structural arrangement. Herein, we report MD simulations, circular dichroism and NMR analyses on BAB and BABAB from porcine lactate dehydrogenase to evaluate their intrinsic stability. Our results demonstrate that BAB is not stable in solution and is not a folding nucleus. We also find that BABAB, despite its appearance of a functional and structural unit, is not an independent and thermodynamically stable folding unit. Rather, we show that BABAB retains most native secondary structure but very little tertiary structure, thus displaying characteristics of a molten globule.

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.

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).