The energy landscape of a fast-folding protein mapped by Ala-->Gly substitutions

DnaK response to expression of protein mutants is dependent on translation rate and stability

Chaperones play a central part in the quality control system in cells by clearing misfolded and aggregated proteins. The chaperone DnaK acts as a sensor for molecular stress by recognising short hydrophobic stretches of misfolded proteins. As the level of unfolded protein is a function of protein stability, we hypothesised that the level of DnaK response upon overexpression of recombinant proteins would be correlated to stability. Using a set of mutants of the λ-repressor with varying thermal stabilities and a fluorescent reporter system, the effect of stability on DnaK response and protein abundance was investigated. Our results demonstrate that the initial DnaK response is largely dependent on protein synthesis rate but as the recombinantly expressed protein accumulates and homeostasis is approached the response correlates strongly with stability. Furthermore, we observe a large degree of cell-cell variation in protein abundance and DnaK response in more stable proteins.

Engineered Metal-Binding Sites to Probe Protein Folding Transition States: Psi Analysis

The formation of the transition state ensemble (TSE) represents the rate-limiting step in protein folding. The TSE is the least populated state on the pathway, and its characterization remains a challenge. Properties of the TSE can be inferred from the effects on folding and unfolding rates for various perturbations. A difficulty remains on how to translate these kinetic effects to structural properties of the TSE. Several factors can obscure the translation of point mutations in the frequently used method, "mutational Phi analysis." We take a complementary approach in "Psi analysis," employing rationally inserted metal binding sites designed to probe pairwise contacts in the TSE. These contacts can be confidently identified and used to construct structural models of the TSE. The method has been applied to multiple proteins and consistently produces a considerably more structured and native-like TSE than Phi analysis. This difference has significant implications to our understanding of protein folding mechanisms. Here we describe the application of the method and discuss how it can be used to study other conformational transitions such as binding.

Mutational Analysis of Protein Folding Transition States: Phi Values

The analysis of protein folding reactions by monitoring the kinetic effects of specifically designed single-point mutations, the so-termed phi-value analysis, has been a favorite technique to experimentally probe the mechanisms of protein folding. The idea behind phi-value analysis is that the effects that mutations have on the folding and unfolding rate constants report on the energetic/structural features of the folding transition state ensemble (TSE), which is the highest point in the free energy surface connecting the native and unfolded states, and thus the rate limiting step that ultimately defines the folding mechanism. For single-domain, two-state folding proteins, the general procedure to perform the phi-value analysis of protein folding is relatively simple to implement in the lab. Once the mutations have been produced and purified, the researcher needs to follow a few specific guidelines to perform the experiments and to analyze the data so produced. In this chapter, a step-by-step description of how to measure and interpret the effects induced by site-directed mutations on the folding and unfolding rate constants of a protein of interest is provided. Some possible solutions to the most typical problems that arise when performing phi-value analysis in the lab are also provided.

Dissecting Multiple Pathways in the Relaxation Dynamics of Helix <==> Coil Transitions with Optimum Dimensionality Reduction

Fast kinetic experiments with dramatically improved time resolution have contributed significantly to understanding the fundamental processes in protein folding pathways involving the formation of a-helices and b-hairpin, contact formation, and overall collapse of the peptide chain. Interpretation of experimental results through application of a simple statistical mechanical model was key to this understanding. Atomistic description of all events observed in the experimental findings was challenging. Recent advancements in theory, more sophisticated algorithms, and a true long-term trajectory made way for an atomically detailed description of kinetics, examining folding pathways, validating experimental results, and reporting new findings for a wide range of molecular processes in biophysical chemistry. This review describes how optimum dimensionality reduction theory can construct a simplified coarse-grained model with low dimensionality involving a kinetic matrix that captures novel insights into folding pathways. A set of metastable states derived from molecular dynamics analysis generate an optimally reduced dimensionality rate matrix following transition pathway analysis. Analysis of the actual long-term simulation trajectory extracts a relaxation time directly comparable to the experimental results and confirms the validity of the combined approach. The application of the theory is discussed and illustrated using several examples of helix <==> coil transition pathways. This paper focuses primarily on a combined approach of time-resolved experiments and long-term molecular dynamics simulation from our ongoing work.

Co-translational folding of α-helical proteins: structural studies of intermediate-length variants of the λ repressor

Nascent polypeptide chains fold cotranslationally, but the atomic‐level details of this process remain unknown. Here, we report crystallographic, de novo modeling, and spectroscopic studies of intermediate‐length variants of the λ repressor N‐terminal domain. Although the ranges of helical regions of the half‐length variant were almost identical to those of the full‐length protein, the relative orientations of these helices in the intermediate‐length variants differed. Our results suggest that cotranslational folding of the λ repressor initially forms a helical structure with a transient conformation, as in the case of a molten globule state. This conformation subsequently matures during the course of protein synthesis.

Database

Structural data are available in the PDB under the accession numbers http://www.rcsb.org/pdb/search/structidSearch.do?structureId=5ZCA and http://www.rcsb.org/pdb/search/structidSearch.do?structureId=3WOA.

Differences in the mechanical unfolding pathways of apo- and copper-bound azurins

Metalloproteins carry out diverse biological functions including metal transport, electron transfer, and catalysis. At present, the influence of metal cofactors on metalloprotein stability is not well understood. Here, we report the mechanical stability and unfolding pathway of azurin, a cupredoxin family protein with β-barrel topology and type I copper-binding centre. Single-molecule force spectroscopy (SMFS) experiments reveal 2-state and 3-state unfolding pathways for apo-azurin. The intermediate in the 3-state pathway occurs at an unfolding contour length of 7.5 nm from the native state. Steered molecular dynamics (SMD) simulations show that apo-azurin unfolds via a first transition state (TS) where β2Β–β8 and β7–β8 strand pairs rupture to form the intermediate, which subsequently unfolds by the collective rupture of remaining strands. SMFS experiments on holo-azurin exhibit an additional 4-state pathway besides the 2-state and 3-state pathways. The unfolding contour length leading to the first intermediate is 6.7 nm suggesting a sequestration of ~1 nm polypeptide chain length by the copper. SMD simulations reveal atomistic details of the copper sequestration and predict a combined β4–β7 pair and copper coordination sphere rupture to create the third TS in the 4-state pathway. Our systematic studies provide detailed mechanistic insights on modulation of protein mechanical properties by metal-cofactors.

Helical Propensity Affects the Conformational Properties of the Denatured State of Cytochrome c'

Changing the helical propensity of a polypeptide sequence might be expected to affect the conformational properties of the denatured state of a protein. To test this hypothesis, alanines at positions 83 and 87 near the center of helix 3 of cytochrome c' from Rhodopseudomonas palustris were mutated to serine to decrease the stability of this helix. A set of 13 single histidine variants in the A83S/A87S background were prepared to permit assessment of the conformational properties of the denatured state using histidine-loop formation in 3 M guanidine hydrochloride. The data are compared with previous histidine-heme loop formation data for wild-type cytochrome c'. As expected, destabilization of helix 3 decreases the global stabilities of the histidine variants in the A83S/A87S background relative to the wild-type background. Loop stability versus loop size data yields a scaling exponent of 2.1 ± 0.2, similar to the value of 2.3 ± 0.2 obtained for wild-type cytochrome c'. However, the stabilities of all histidine-heme loops, which contain the helix 3 sequence segment, are increased in the A83S/A87S background compared to the wild-type background. Rate constants for histidine-heme loop breakage are similar for the wild-type and A83S/A87S variants. However, for histidine-heme loops that contain the helix 3 sequence segment, the rate constants for loop formation increase in the A83S/A87S background compared to the wild-type background. Thus, residual helical structure appears to stiffen the polypeptide chain slowing loop formation in the denatured state. The implications of these results for protein folding mechanisms are discussed.

Cooperative folding near the downhill limit determined with amino acid resolution by hydrogen exchange

The relationship between folding cooperativity and downhill, or barrier-free, folding of proteins under highly stabilizing conditions remains an unresolved topic, especially for proteins such as λ-repressor that fold on the microsecond timescale. Under aqueous conditions where downhill folding is most likely to occur, we measure the stability of multiple H bonds, using hydrogen exchange (HX) in a λYA variant that is suggested to be an incipient downhill folder having an extrapolated folding rate constant of 2 × 10(5) s(-1) and a stability of 7.4 kcal·mol(-1) at 298 K. At least one H bond on each of the three largest helices (α1, α3, and α4) breaks during a common unfolding event that reflects global denaturation. The use of HX enables us to both examine folding under highly stabilizing, native-like conditions and probe the pretransition state region for stable species without the need to initiate the folding reaction. The equivalence of the stability determined at zero and high denaturant indicates that any residual denatured state structure minimally affects the stability even under native conditions. Using our ψ analysis method along with mutational ϕ analysis, we find that the three aforementioned helices are all present in the folding transition state. Hence, the free energy surface has a sufficiently high barrier separating the denatured and native states that folding appears cooperative even under extremely stable and fast folding conditions.

Single-molecule chemo-mechanical unfolding reveals multiple transition state barriers in a small single-domain protein

A fundamental question in protein folding is whether proteins fold through one or multiple trajectories. While most experiments indicate a single pathway, simulations suggest proteins can fold through many parallel pathways. Here, we use a combination of chemical denaturant, mechanical force and site-directed mutations to demonstrate the presence of multiple unfolding pathways in a simple, two-state folding protein. We show that these multiple pathways have structurally different transition states, and that seemingly small changes in protein sequence and environment can strongly modulate the flux between the pathways. These results suggest that in vivo, the crowded cellular environment could strongly influence the mechanisms of protein folding and unfolding. Our study resolves the apparent dichotomy between experimental and theoretical studies, and highlights the advantage of using a multipronged approach to reveal the complexities of a protein's free-energy landscape.

Although most protein folding experiments can be explained by a single pathway, theoretical evidence suggests the presence of multiple pathways. Here, the authors resolve this using a combination of force, chemical denaturation and mutagenesis to modulate the flux between parallel pathways.

Benchmarking all-atom simulations using hydrogen exchange

Long-time molecular dynamics (MD) simulations are now able to fold small proteins reversibly to their native structures [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520]. These results indicate that modern force fields can reproduce the energy surface near the native structure. To test how well the force fields recapitulate the other regions of the energy surface, MD trajectories for a variant of protein G are compared with data from site-resolved hydrogen exchange (HX) and other biophysical measurements. Because HX monitors the breaking of individual H-bonds, this experimental technique identifies the stability and H-bond content of excited states, thus enabling quantitative comparison with the simulations. Contrary to experimental findings of a cooperative, all-or-none unfolding process, the simulated denatured state ensemble, on average, is highly collapsed with some transient or persistent native 2° structure. The MD trajectories of this protein G variant and other small proteins exhibit excessive intramolecular H-bonding even for the most expanded conformations, suggesting that the force fields require improvements in describing H-bonding and backbone hydration. Moreover, these comparisons provide a general protocol for validating the ability of simulations to accurately capture rare structural fluctuations.

Simplified protein models: predicting folding pathways and structure using amino acid sequences

We demonstrate the ability of simultaneously determining a protein's folding pathway and structure using a properly formulated model without prior knowledge of the native structure. Our model employs a natural coordinate system for describing proteins and a search strategy inspired by the observation that real proteins fold in a sequential fashion by incrementally stabilizing nativelike substructures or "foldons." Comparable folding pathways and structures are obtained for the twelve proteins recently studied using atomistic molecular dynamics simulations [K. Lindorff-Larsen, S. Piana, R. O. Dror, D. E. Shaw, Science 334, 517 (2011)], with our calculations running several orders of magnitude faster. We find that nativelike propensities in the unfolded state do not necessarily determine the order of structure formation, a departure from a major conclusion of the molecular dynamics study. Instead, our results support a more expansive view wherein intrinsic local structural propensities may be enhanced or overridden in the folding process by environmental context. The success of our search strategy validates it as an expedient mechanism for folding both in silico and in vivo.

De novo prediction of protein folding pathways and structure using the principle of sequential stabilization

Motivated by the relationship between the folding mechanism and the native structure, we develop a unified approach for predicting folding pathways and tertiary structure using only the primary sequence as input. Simulations begin from a realistic unfolded state devoid of secondary structure and use a chain representation lacking explicit side chains, rendering the simulations many orders of magnitude faster than molecular dynamics simulations. The multiple round nature of the algorithm mimics the authentic folding process and tests the effectiveness of sequential stabilization (SS) as a search strategy wherein 2° structural elements add onto existing structures in a process of progressive learning and stabilization of structure found in prior rounds of folding. Because no a priori knowledge is used, we can identify kinetically significant non-native interactions and intermediates, sometimes generated by only two mutations, while the evolution of contact matrices is often consistent with experiments. Moreover, structure prediction improves substantially by incorporating information from prior rounds. The success of our simple, homology-free approach affirms the validity of our description of the primary determinants of folding pathways and structure, and the effectiveness of SS as a search strategy.

Reducing lambda repressor to the core

Lambda repressor fragment λ(*)(6-85) is one of the fastest folding small protein fragments known to date. We hypothesized that removal of three out of five helices of λ(*)(6-85) would further reduce this protein to its smallest folding core. Molecular dynamics simulations singled out two energetically stable reduced structures consisting of only helices 1 and 4 connected by a short glycine/serine linker, as well as a less stable control. We investigated these three polypeptides and their fragments experimentally by using circular dichroism, fluorescence spectroscopy, and temperature jump relaxation spectroscopy to gain insight into their thermodynamic and kinetic properties. Based on the thermal melts, the order of peptide stability was in correspondence with theoretical predictions. The most stable two-helix bundle, λ(blue1), is a cooperatively folding miniprotein with the same melting temperature and folding rate as the full-length λ(*)(6-85) pseudo wild type and a well-defined computed structure.

Investigation of an anomalously accelerating substitution in the folding of a prototypical two-state protein

The folding rates of two-state single-domain proteins are generally resistant to small-scale changes in amino acid sequence. For example, having surveyed here over 700 single-residue substitutions in 24 well-characterized two-state proteins, we find that the majority (55%) of these substitutions affect folding rates by less than a factor of 2, and that only 9% affect folding rates by more than a factor of 8. Among those substitutions that significantly affect folding rates, we find that accelerating substitutions are an order of magnitude less common than those that decelerate the process. One of the most extreme outliers in this data set, an arginine-to-phenylalanine substitution at position 48 (R48F) of chymotrypsin inhibitor 2 (CI2), accelerates the protein's folding rate by a factor of 36 relative to that of the wild-type protein and is the most accelerating substitution reported to date in a two-state protein. In order to better understand the origins of this anomalous behavior, we have characterized the kinetics of multiple additional substitutions at this position. We find that substitutions at position 48 in CI2 fall into two distinct classes. The first, comprising residues that ablate the charge of the wild-type arginine but retain the hydrophobicity of its alkane chain, accelerate folding by at least 10-fold. The second class, comprising all other residues, produces folding rates within a factor of two of the wild-type rate. A significant positive correlation between hydrophobicity and folding rate across all of the residues we have characterized at this position suggests that the hydrophobic methylene units of the wild-type arginine play a significant role in stabilizing the folding transition state. Likewise, studies of the pH dependence of the histidine substitution indicate a strong correlation between folding rate and charge state. Thus, mutations that ablate the arginine's positive charge while retaining the hydrophobic contacts of its methylene units tend to dramatically accelerate folding. Previous studies have suggested that arginine 48 plays an important functional role in CI2, which may explain why it is highly conserved despite the anomalously large deceleration it produces in the folding of this protein.

A survey of lambda repressor fragments from two-state to downhill folding

We survey the two-state to downhill folding transition by examining 20 lambda(6-85)* mutants that cover a wide range of stabilities and folding rates. We investigated four new lambda(6-85)* mutants designed to fold especially rapidly. Two were engineered using the core remodeling of Lim and Sauer, and two were engineered using Ferreiro et al.'s frustratometer. These proteins have probe-dependent melting temperatures as high as 80 degrees C and exhibit a fast molecular phase with the characteristic temperature dependence of the amplitude expected for downhill folding. The survey reveals a correlation between melting temperature and downhill folding previously observed for the beta-sheet protein WW domain. A simple model explains this correlation and predicts the melting temperature at which downhill folding becomes possible. An X-ray crystal structure with a 1.64-A resolution of a fast-folding mutant fragment shows regions of enhanced rigidity compared to the full wild-type protein.

Slowing down downhill folding: a three-probe study

The mutant Tyr22Trp/Glu33Tyr/Gly46Ala/Gly48Ala of lambda repressor fragment lambda(6-85) was previously assigned as an incipient downhill folder. We slow down its folding in a cryogenic water-ethylene-glycol solvent (-18 to -28 degrees C). The refolding kinetics are probed by small-angle x-ray scattering, circular dichroism, and fluorescence to measure the radius of gyration, the average secondary structure content, and the native packing around the single tryptophan residue. The main resolved kinetic phase of the mutant is probe independent and faster than the main phase observed for the pseudo-wild-type. Excess helical structure formed early on by the mutant may reduce the formation of turns and prevent the formation of compact misfolded states, speeding up the overall folding process. Extrapolation of our main cryogenic folding phase and previous T-jump measurements to 37 degrees C yields nearly the same refolding rate as extrapolated by Oas and co-workers from NMR line-shape data. Taken together, all the data consistently indicate a folding speed limit of approximately 4.5 micros for this fast folder.

Analysis of the free-energy surface of proteins from reversible folding simulations

Computer generated trajectories can, in principle, reveal the folding pathways of a protein at atomic resolution and possibly suggest general and simple rules for predicting the folded structure of a given sequence. While such reversible folding trajectories can only be determined ab initio using all-atom transferable force-fields for a few small proteins, they can be determined for a large number of proteins using coarse-grained and structure-based force-fields, in which a known folded structure is by construction the absolute energy and free-energy minimum. Here we use a model of the fast folding helical λ-repressor protein to generate trajectories in which native and non-native states are in equilibrium and transitions are accurately sampled. Yet, representation of the free-energy surface, which underlies the thermodynamic and dynamic properties of the protein model, from such a trajectory remains a challenge. Projections over one or a small number of arbitrarily chosen progress variables often hide the most important features of such surfaces. The results unequivocally show that an unprojected representation of the free-energy surface provides important and unbiased information and allows a simple and meaningful description of many-dimensional, heterogeneous trajectories, providing new insight into the possible mechanisms of fast-folding proteins.

The process of protein folding is a complex transition from a disordered to an ordered state. Here, we simulate a specific fast-folding protein at the point at which the native and denatured states are at equilibrium and show that obtaining an accurate description of the mechanisms of folding and unfolding is far from trivial. Using simple quantities which quantify the degree of native order is, in the case of this protein, clearly misleading. We show that an unbiased representation of the free-energy surface can be obtained; using such a representation we are able to redesign the landscape and thus modify, upon site-specific “mutations”, the folding and unfolding rates. This leads us to formulate a hypothesis to explain the very fast folding of many proteins.

Different members of a simple three-helix bundle protein family have very different folding rate constants and fold by different mechanisms

The 15th, 16th, and 17th repeats of chicken brain alpha-spectrin (R15, R16, and R17, respectively) are very similar in terms of structure and stability. However, R15 folds and unfolds 3 orders of magnitude faster than R16 and R17. This is unexpected. The rate-limiting transition state for R15 folding is investigated using protein engineering methods (Phi-value analysis) and compared with previously completed analyses of R16 and R17. Characterisation of many mutants suggests that all three proteins have similar complexity in the folding landscape. The early rate-limiting transition states of the three domains are similar in terms of overall structure, but there are significant differences in the patterns of Phi-values. R15 apparently folds via a nucleation-condensation mechanism, which involves concomitant folding and packing of the A- and C-helices, establishing the correct topology. R16 and R17 fold via a more framework-like mechanism, which may impede the search to find the correct packing of the helices, providing a possible explanation for the fast folding of R15.

Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics

Energy landscape theory requires that the protein-folding mechanism is generally globally directed or funneled toward the native state. The collective nature of transition state ensembles further suggests that sufficient averaging of the native interactions can occur so that the knowledge of the native topology may suffice for predicting the mechanism. Nevertheless, while simple homogeneously weighted native topology-based models predict the folding mechanisms for many proteins, for other proteins knowledge of the native topology, by itself, seems not to suffice in determining the folding mechanism. Simulations of proteins with differing topologies reveal that the failure of homogeneously weighted topology-based models can, however, be completely understood within the framework of a funneled energy landscape and can be quantified by comparing the fluctuation of entropy cost for forming contacts to the expected fluctuations in contact energy. To be precise, we find the transition state ensembles of proteins with all-alpha topologies, which are more uniform in the specific entropy cost of contact formation, have transition state ensembles that are more readily perturbed by differences in energetic weights than are the transition state ensembles of proteins with significant amounts of beta-structure, where the specific entropy costs of contact formation are more widely distributed. This behavior is consistent with a random-field Ising model analogy that follows from the free energy functional approach to folding.

Capillarity-like growth of protein folding nuclei

A full structural description of transition state ensembles in protein folding includes the specificity of the ordered residues composing the folding nucleus as well as spatial density. To our knowledge, the spatial properties of the folding nucleus and interface of specific nuclei have yet to receive significant attention. We analyze folding routes predicted by a variational model in terms of a generalized formalism of the capillarity scaling theory that assumes the volume of the folded core of the nucleus grows with chain length as V(f) approximately N(3nu). For 27 two-state proteins studied, the scaling exponent nu ranges from 0.2 to 0.45 with an average of 0.33. This average value corresponds to packing of rigid objects, although generally the effective monomer size in the folded core is larger than the corresponding volume per particle in the native-state ensemble. That is, on average, the folded core of the nucleus is found to be relatively diffuse. We also study the growth of the folding nucleus and interface along the folding route in terms of the density or packing fraction. The evolution of the folded core and interface regions can be classified into three patterns of growth depending on how the growth of the folded core is balanced by changes in density of the interface. Finally, we quantify the diffuse versus polarized structure of the critical nucleus through direct calculation of the packing fraction of the folded core and interface regions. Our results support the general picture of describing protein folding as the capillarity-like growth of folding nuclei.

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.

Implementation of a k/k(0) method to identify long-range structure in transition states during conformational folding/unfolding of proteins

A previously introduced kinetic-rate constant (k/k(0)) method, where k and k(0) are the folding (unfolding) rate constants in the mutant and the wild-type forms, respectively, of a protein, has been applied to obtain qualitative information about structure in the transition state ensemble (TSE) of bovine pancreatic ribonuclease A (RNase A), which contains four native disulfide bonds. The method compares the folding (unfolding) kinetics of RNase A, with and without a covalent crosslink and tests whether the crosslinked residues are associated in the folding (unfolding) transition state (TS) of the noncrosslinked version. To confirm that the fifth disulfide bond has not introduced a significant structural perturbation, we solved the crystal structure of the V43C-R85C mutant to 1.6 A resolution. Our findings suggest that residues Val43 and Arg85 are not associated, and that residues Ala4 and Val118 may form nonnative contacts, in the folding (unfolding) TSE of RNase A.

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.

Tuning lambda6-85 towards downhill folding at its melting temperature

The five-helix bundle lambda6-85* is a fast two-state folder. Several stabilized mutants have been reported to fold kinetically near-downhill or downhill. These mutants undergo a transition to two-state folding kinetics when heated. It has been suggested that this transition is caused by increased hydrophobicity at higher temperature. Here we investigate two histidine-containing mutants of lambda6-85* to see if a weaker hydrophobic core can extend the temperature range of downhill folding. The very stable lambdaHA is the fastest-folding lambda repressor to date (k(f)(-1) approximately k(obs)(-1)=2.3 micros at 44 degrees C). It folds downhill at low temperature, but transits back to two-state folding at its unfolding midpoint. lambdaHG has a weakened hydrophobic core. It is less stable than some slower folding mutants of lambda6-85*, and it has more exposed hydrophobic surface area in the folded state. This mutant nonetheless folds very rapidly, and has the non-exponential folding kinetics of an incipient downhill folder even at the unfolding midpoint (k(m)(-1) approximately 2 micros, k(a)(-1)=15 micros at 56 degrees C). We also compare the thermodynamic melting transition of lambdaHG with the nominal two-state folding mutant lambdaQG, which has a similar melting temperature. Unlike lambdaQG, lambdaHG yields fluorescence wavelength-dependent cooperativities and probe-dependent melting temperatures. This result combined with previous work shows that the energy landscapes of lambda repressor mutants support all standard folding mechanisms.

Key Role of Coulombic Interactions for the Folding Transition State of the Cold Shock Protein

The cold shock protein CspB shows a five-stranded beta-sheet structure, and it folds rapidly via a native-like transition state. A previous Phi value analysis showed that most of the residues with Phi values close to one reside in strand beta1, and two of them, Lys5 and Lys7 are partially exposed charged residues. To elucidate how coulombic interactions of these two residues contribute to the energetic organisation of the folding transition state we performed comparative folding experiments in the presence of an ionic denaturant (guanidinium chloride) and a non-ionic denaturant (urea) and a double-mutant analysis. Lys5 contributes 6.6 kJ mol(-1) to the stability of the transition state, and half of it originates from screenable coulombic interactions. Lys7 contributes 5.3 kJ mol(-1), and 3.4 kJ mol(-1) of it are screened by salt. In the folded protein Lys7 interacts with Asp25, and the screenable coulombic interaction between these two residues is fully formed in the transition state. This suggests that long-range coulombic interactions such as those originating from Lys5 and Lys7 of CspB can be important for organizing and stabilizing native-like structure early in protein folding.

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.

Solvation of the folding-transition state in Pseudomonas aeruginosa azurin is modulated by metal: Solvation of azurin's folding nucleus

The role of water in protein folding, specifically its presence or not in the transition-state structure, is an unsolved question. There are two common classes of folding-transition states: diffuse transition states, in which almost all side chains have similar, rather low phi (phi) values, and polarized transition states, which instead display distinct substructures with very high phi-values. Apo-and zinc-forms of Pseudomonas aeruginosa azurin both fold in two-state equilibrium and kinetic reactions; while the apo-form exhibits a polarized transition state, the zinc form entails a diffuse, moving transition state. To examine the presence of water in these two types of folding-transition states, we probed the equilibrium and kinetic consequences of replacing core valines with isosteric threonines at six positions in azurin. In contrast to regular hydrophobic-to-alanine phi-value analysis, valine-to-threonine mutations do not disrupt the core packing but stabilize the unfolded state and can be used to assess the degree of solvation in the folding-transition state upon combination with regular phi-values. We find that the transition state for folding of apo-azurin appears completely dry, while that for zinc-azurin involves partially formed interactions that engage water molecules. This distinct difference between the apo-and holo-folding nuclei can be rationalized in terms of the shape of the free-energy barrier.

An on-pathway hidden intermediate and the early rate-limiting transition state of Rd-apocytochrome b562 characterized by protein engineering

The folding pathway of Rd-apocytochrome b562, a four-helix bundle protein, was characterized using Trp and Ala/Gly pair mutations. We found that the Trp mutants (F65W) of both the fully folded Rd-apocytochrome b562 and a partially unfolded intermediate with the N-terminal helix (helix I) unfolded, fold with identical folding rates, providing direct evidence for the conclusion that the rate-limiting transition state folds before the partially unfolded intermediate; and that this hidden intermediate is an on-pathway intermediate. We further characterized the helical structures formed in the rate-limiting transition state by measuring the folding/unfolding rates for Ala/Gly pair mutations at solvent-exposed positions. Little change in folding rates occurred for the Ala/Gly pair mutations at positions in helix I and the C-terminal regions of helix II and IV. In contrast, a significant difference in folding rates was observed for the Ala/Gly pair mutations in helix III and the N-terminal regions of helix II and IV, suggesting that helix III and the N-terminal regions of helix II and IV are formed in the rate-limiting transition state. These results complement those obtained from earlier studies and help to define the folding pathway of Rd-apocytochrome b562 in more detail.

A critical assessment of the topomer search model of protein folding using a continuum explicit-chain model with extensive conformational sampling

Recently, a series of closely related theoretical constructs termed the "topomer search model" (TSM) has been proposed for the folding mechanism of small, single-domain proteins. A basic assumption of the proposed scenarios is that the rate-limiting step in folding is an essentially unbiased, diffusive search for a conformational state called the native topomer defined by an overall native-like topological pattern. Successes in correlating TSM-predicted folding rates with that of real proteins have been interpreted as experimental support for the model. To better delineate the physics entailed, key TSM concepts are examined here using extensive Langevin dynamics simulations of continuum C(alpha) chain models. The theoretical native topomers of four experimentally well-studied two-state proteins are characterized. Consistent with the TSM perspective, we found that the sizes of the native topomers increase with experimental folding rate. However, a careful determination of the corresponding probabilities that the native topomers are populated during a random search fails to reproduce the previously predicted folding rates. Instead, our results indicate that an unbiased TSM search for the native topomer amounts to a Levinthal-like process that would take an impossibly long average time to complete. Furthermore, intraprotein contacts in all four native topomers considered exhibit no apparent correlation with the experimental phi-values determined from the folding kinetics of these proteins. Thus, the present findings suggest that certain basic, generic yet essential energetic features in protein folding are not accounted for by TSM scenarios to date.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

The Structure of the Major Transition State for Folding of an FF Domain from Experiment and Simulation

We have analysed the transition state of folding of the four-helix FF domain from HYPA/FBP11 by high-resolution experiment and simulation as part of a continuing effort to understand the principles of folding and the refinement of predictive methods. The major transition state for folding was subjected to a Phi-value analysis utilising 50 mutants. The transition state contained a nucleus for folding centred around the end of helix 1 (H1) and the beginning of helix 2 (H2). Secondary structure in this region was fully formed (PhiF=0.9-1) and tertiary interactions were well developed. Interactions in the distal part of the native structure were weak (PhiF=0-0.2). The hydrophobic core and other parts of the protein displayed intermediate Phi-values, suggesting that interactions coalesce as the end of H1 and beginning of H2 are in the process of being formed. The distribution of Phi-values resembled that of barnase, which folds via an intermediate, rather than that of CI2 which folds by a concerted nucleation-condensation mechanism. The overall picture of the transition state structure identified in molecular dynamics simulations is in qualitative agreement, with the turn connecting H1 and H2 being formed, a loosened core, and H4 partially unfolded and detached from the core. There are some differences in the details and interpretation of specific Phi-values.

Downhill protein folding: evolution meets physics

Proteins can be redesigned to fold downhill on a free energy surface characterized by only a few coordinates, confirming a principal prediction of the 'energy-landscape' model. Nonetheless, natural proteins have small but significant barriers. Spectroscopy and kinetics reveal potential biological causes for activation barriers during protein folding: evolution against protein aggregation and for protein function.

Kinetic equivalence of the heat and cold structural transitions of lambda6-85

Heat- and cold-denatured proteins are considered separate thermodynamic states because temperature tuning requires the protein to pass through two 'soft' first-order phase transitions. When both pressure and temperature changes are allowed, the heat- and cold-denatured states of proteins can be interconverted without going through the native state. This raises the question of whether these states are distinguished from one another by their folding kinetics. For the Tyr22Trp/Ala37Gly/Ala49Gly mutant of the 80 residue five-helix bundle protein lambda(6-85), we show that viscosity-corrected folding rates do not distinguish the cold- and heat-denatured states. We attribute this to a folding mechanism dominated by hydrophobic collapse. Our 'temperature-symmetric' approach offers an alternative to viscosity tuning with solvent additives in such cases.

Kinetics are probe-dependent during downhill folding of an engineered lambda6-85 protein

The Y22W/Q33Y/G46,48A mutant of the protein lambda6-85 folds in a few microseconds at room temperature. We find that its folding kinetics are probe-dependent under a strong bias toward the native state, a new signature for downhill folding. The IR- and fluorescence-detected relaxation time scales converge when the native bias is removed by raising the temperature, recovering activated two-state folding. Langevin dynamics simulations on one- and 2D free energy surfaces tunable from two-state to downhill folding reproduce the difference between the IR and fluorescence experiments, as well as the temperature and viscosity trends. In addition, the 2D surface reproduces the stretched exponential dynamics that we fit to the glucose solution experimental data at short times. Nonexponential dynamics at <10 micros is a signature either for local free energy minima along the reaction coordinate ("longitudinal roughness"), or for folding on a higher-dimensional free energy surface ("transverse roughness").

Variations in the fast folding rates of the lambda-repressor: a hybrid molecular dynamics study

The ability to predict the effects of mutations on protein folding rates and mechanisms would greatly facilitate folding studies. Using a realistic full atom potential coupled with a Gō-like potential biased to the native state structure, we have investigated the effects of point mutations on the folding rates of a small single domain protein. The hybrid potential provides a detailed level of description of the folding mechanism that we correlate to features of the folding energy landscapes of fast and slow mutants of an 80-residue-long fragment of the lambda-repressor. Our computational reconstruction of the folding events is compared to the recent experimental results of W. Y. Yang and M. Gruebele (see companion article) and T. G. Oas and co-workers on the lambda-repressor, and helps to clarify the differences observed in the folding mechanisms of the various mutants.

Fast folding of a helical protein initiated by the collision of unstructured chains

To examine whether helix formation necessarily precedes chain collision, we have measured the folding of a fully helical coiled coil that has been specially engineered to have negligible intrinsic helical propensity but high overall stability. The folding rate approaches the diffusion-limited value and is much faster than possible if folding is contingent on precollision helix formation. Therefore, the collision of two unstructured chains is the initial step of the dominant kinetic pathway, whereas helicity exerts its influence only at a later step. Folding from an unstructured encounter complex may be efficient and robust, which has implications for any biological process that couples folding to binding.

Folding lambda-repressor at its speed limit

We show that the five-helix bundle lambda(6-85) can be engineered and solvent-tuned to make the transition from activated two-state folding to downhill folding. The transition manifests itself as the appearance of additional dynamics faster than the activated kinetics, followed by the disappearance of the activated kinetics when the bias toward the native state is increased. Our fastest value of 1 micros for the "speed" limit of lambda(6-85) is measured at low concentrations of a denaturant that smooths the free-energy surface. Complete disappearance of the activated phase is obtained in stabilizing glucose buffer. Langevin dynamics on a rough free-energy surface with variable bias toward the native state provides a robust and quantitative description of the transition from activated to downhill folding. Based on our simulation, we estimate the residual energetic frustration of lambda(6-85) to be delta(2) G approximately 0.64 k(2)T(2). We show that lambda(6-86), as well as very fast folding proteins or folding intermediates estimated to lie near the speed limit, provide a better rate-topology correlation than proteins with larger energetic frustration. A limit of beta > or = 0.7 on any stretching of lambda(6-85) barrier-free dynamics suggests that a low-dimensional free-energy surface is sufficient to describe folding.

The Folding Transition State of the Cold Shock Protein is Strongly Polarized

The cold shock protein CspB from Bacillus subtilis consists of a three-stranded (beta1-beta3) and a two stranded (beta4-beta5) sheet, which form a closed beta barrel structure. CspB folds and unfolds rapidly in a two-state reaction, and the unfolded and the folded molecules interconvert with a time constant of 30 ms at the midpoint of the urea-induced transition (at 25 degrees C). The transition state of folding is native-like, as judged by the Tanford betaT value of > or =0.9. By using a mutational approach and Phi value analysis, we find that the folding transition state of CspB is energetically polarized. Despite the high betaT value, most Phi values are low. Values close to 1 were found for only a few residues, particularly in strand beta1 (Lys5, Val6, Lys7, Asn10). The interactions of the Asn10 side-chain with the backbone at positions 12 and 13 define the turn that connects the strands beta1 and beta2. Lys5 and Val6 in beta1 interact with residues in beta4, and their high Phi values indicate that an energetic linkage between beta1 and beta4 and thus between the two sheets exists already in the transition state. We compared our experimental Phi values with theoretical predictions of the folding pathway of cold shock proteins. Several of them suggest that the entire first sheet is formed in the transition state, and some identify the beta1-beta4 pairing as a crucial step in folding. Alternative paths that involve formation of the second sheet and beta3-beta5 pairing reactions were, however, suggested as well. The calculations gave coarse-grained pictures that are limited in resolution to the two sheets of CspB or to the elements of secondary structure. They did not identify the key residues with the high Phi values within these structural elements.

Conformational Heterogeneity of an Equilibrium Folding Intermediate Quantified and Mapped by Scanning Mutagenesis

It is challenging to experimentally define an energy landscape for protein folding that comprises multiple partially unfolded states. Experimental results are often ambiguous as to whether a non-native state is conformationally homogeneous. Here, we tested an approach combining systematic mutagenesis and a Brønsted-like analysis to reveal and quantify conformational heterogeneity of folding intermediate states. Using this method, we resolved an otherwise apparently homogeneous equilibrium folding intermediate of Borrelia burgdorferi OspA into two conformationally distinct species and determined their relative populations. Furthermore, we mapped the structural differences between these intermediate species, which are consistent with the non-native species that we previously proposed based on native-state hydrogen exchange studies. When treated as a single state, the intermediate ensemble exhibited fractional Phi-values for mutations and Hammond-type behaviors that are often observed for folding transition states. We found that a change in relative population of the two species within the intermediate ensemble explains these properties well, suggesting that fractional Phi-values and Hammond-type behaviors exhibited by folding intermediates and transition states may arise more often from conformational heterogeneity than from a single partial structure. Our results are consistent with the presence of multiple minima in a rugged energy landscape predicted from theoretical studies. The method described here provides a promising means to probe a complex folding energy landscape.

Heterogeneous Folding of the trpzip Hairpin: Full Atom Simulation and Experiment

The beta-hairpin trpzip2 can be tuned continuously from a two-state folder to folding on a rough energy landscape without a dominant refolding barrier. At high denaturant concentration, this extremely stable peptide exhibits a single apparent "two-state" transition temperature when monitored by different spectroscopic techniques. However, under optimal folding conditions the hairpin undergoes an unusual folding process with three clusters of melting transitions ranging from 15 degrees C to 160 degrees C, as monitored by 12 different experimental and computational observables. We explain this behavior in terms of a rough free energy landscape of the unfolded peptide caused by multiple tryptophan interactions and alternative backbone conformations. The landscape is mapped out by potentials of mean force derived from replica-exchange molecular dynamics simulations. Implications for deducing cooperativity from denaturant titrations, for the origin of folding cooperativity, and for the folding of thermophilic proteins are pointed out. trpzip is an excellent small tunable model system for the glass-like folding transitions predicted by landscape theory.