Tuning lambda6-85 towards downhill folding at its melting temperature

Chemical interactions modulate λ6-85 stability in cells

Because steric crowding is most effective when the crowding agent is similar in size to the molecule that it acts upon and the average macromolecule inside cells is much larger than a small protein or peptide, steric crowding is not predicted to affect their folding inside cells. On the other hand, chemical interactions should perturb in-cell structure and stability because they arise from interactions between the surface of the small protein or peptide and its environment. Indeed, previous in vitro measurements of the λ-repressor fragment, λ6-85 , in crowding matrices comprised of Ficoll or protein crowders support these predictions. Here, we directly quantify the in-cell stability of λ6-85 and distinguish the contribution of steric crowding and chemical interactions to its stability. Using a FRET-labeled λ6-85 construct, we find that the fragment is stabilized by 5°C in-cells compared to in vitro. We demonstrate that this stabilization cannot be explained by steric crowding because, as anticipated, Ficoll has no effect on λ6-85 stability. We find that the in-cell stabilization arises from chemical interactions, mimicked in vitro by mammalian protein extraction reagent (M-PER™). Comparison between FRET values in-cell and in Ficoll confirms that U-2 OS cytosolic crowding is reproduced at macromolecule concentrations of 15% w/v. Our measurements validate the cytomimetic of 15% Ficoll and 20% M-PER™ that we previously developed for protein and RNA folding studies. However, because the in-cell stability of λ6-85 is reproduced by 20% v/v M-PER™ alone, we predict that this simplified mixture could be a useful tool to predict the in-cell behaviors of other small proteins and peptides.

Threading single proteins through pores to compare their energy landscapes

Protein function correlates with its structural dynamics. While theoretical approaches to studying protein energy landscapes are well developed, experimental methods that enable probing these landscapes of proteins remain challenging. We used solid-state nanopores to study the translocation behavior of three mutants of a helix bundle protein and quantified the number of energetically accessible conformational states for each mutant. We found that a slower-folding mutant with access to more conformational states translocates faster than a faster-folding mutant with a smaller number of accessible states, suggesting that ease of folding and ease of translocation are at odds in this case.

Translocation of proteins is correlated with structural fluctuations that access conformational states higher in free energy than the folded state. We use electric fields at the solid-state nanopore to control the relative free energy and occupancy of different protein conformational states at the single-molecule level. The change in occupancy of different protein conformations as a function of electric field gives rise to shifts in the measured distributions of ionic current blockades and residence times. We probe the statistics of the ionic current blockades and residence times for three mutants of the λ-repressor family in order to determine the number of accessible conformational states of each mutant and evaluate the ruggedness of their free energy landscapes. Translocation becomes faster at higher electric fields when additional flexible conformations are available for threading through the pore. At the same time, folding rates are not correlated with ease of translocation; a slow-folding mutant with a low-lying intermediate state translocates faster than a faster-folding two-state mutant. Such behavior allows us to distinguish among protein mutants by selecting for the degree of current blockade and residence time at the pore. Based on these findings, we present a simple free energy model that explains the complementary relationship between folding equilibrium constants and translocation rates.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

A Disordered Loop Mediates Heterogeneous Unfolding of an Ordered Protein by Altering the Native Ensemble

The high flexibility of long disordered or partially structured loops in folded proteins allows for entropic stabilization of native ensembles. Destabilization of such loops could alter the native ensemble or promote alternate conformations within the native ensemble if the ordered regions themselves are held together weakly. This is particularly true of downhill folding systems that exhibit weak unfolding cooperativity. Here, we combine experimental and computational methods to probe the response of the native ensemble of a helical, downhill folding domain PDD, which harbors an 11-residue partially structured loop, to perturbations. Statistical mechanical modeling points to continuous structural changes on both temperature and mutational perturbations driven by entropic stabilization of partially structured conformations within the native ensemble. Long time-scale simulations of the wild-type protein and two mutants showcase a remarkable conformational switching behavior wherein the parallel helices in the wild-type protein sample an antiparallel orientation in the mutants, with the C-terminal helix and the loop connecting the helices displaying high flexibility, disorder, and non-native interactions. We validate these computational predictions via the anomalous fluorescence of a native tyrosine located at the interface of the helices. Our observations highlight the role of long loops in determining the unfolding mechanisms, sensitivity of the native ensembles to mutational perturbations and provide experimentally testable predictions that can be explored in even two-state folding systems.

A new way to recognize downhill folding based on generalized path length

The protein folding is an important scientific problem and many methods were designed to elucidate the protein folding and obtain insight into the molecular mechanism. A novel means is presented to identify the downhill pathways of protein folding in this paper. This method is based on barrier energy profile projected onto the generalized path length (GPL) with Breadth-first searching (BFS) algorithm. We show the effectiveness of this approach by constructing the barrier energy profile of trpzip2 and comparing with other methods.

Switching Protein Conformational Substates by Protonation and Mutation

Protein modules that regulate the availability and conformational status of transcription factors determine the rapidity, duration, and magnitude of cellular response to changing conditions. One such system is the single-gene product Cnu, a four-helix bundle transcription co-repressor, which acts as a molecular thermosensor regulating the expression of virulence genes in enterobacteriaceae through modulation of its native conformational ensemble. Cnu and related genes have also been implicated in pH-dependent expression of virulence genes. We hypothesize that protonation of a conserved buried histidine (H45) in Cnu promotes large electrostatic frustration, thus disturbing the H-NS, a transcription factor, binding face. Spectroscopic and calorimetric methods reveal that H45 exhibits a suppressed p K_a of ∼5.1, the protonation of which switches the conformation to an alternate native ensemble in which the fourth helix is disordered. The population redistribution can also be achieved through a mutation H45V, which does not display any switching behavior at pH values greater than 4. The Wako-Saitô-Muñoz-Eaton (WSME) statistical mechanical model predicts specific differences in the conformations and fluctuations of the fourth and first helices of Cnu determining the observed pH response. We validate these predictions through fluorescence lifetime measurements of a sole tryptophan, highlighting the presence of both native and non-native interactions in the regions adjoining the binding face of Cnu. Our combined experimental-computational study thus shows that Cnu acts both as a thermo- and pH-sensor orchestrated via a subtle but quantifiable balance between the weak packing of a structural element and protonation of a buried histidine that promotes electrostatic frustration.

Protein Folding Cooperativity and Thermodynamic Barriers of the Simplest β-Sheet Fold: A Survey of WW Domains

Theory and experiments have shown that microsecond folding proteins exhibit characteristic thermodynamic properties that reflect the limited cooperativity of folding over marginal barriers (downhill folding). Those studies have mostly focused on proteins with large α-helical contents and small size, which tend to be the fastest folders. A key open question is whether such properties are also present in the fastest all-β proteins. We address this issue by investigating the unfolding thermodynamics of a collection of WW domains as representatives of the simplest β-sheet fold. WW domains are small microsecond folders, although they do not fold as fast as their α-helical counterparts. In previous work on the NEDD4-WW4 domain, we reported deviations from two-state thermodynamics that were less apparent and thus suggestive of an incipient downhill scenario. Here we investigate the unfolding thermodynamics of four other WW domains (NEDD4-WW3, YAP65-WW1(L30K), FBP11-WW1, and FBP11-WW2) by performing all of the thermodynamic tests for downhill folding that have been previously developed on α-helical proteins. This set of five WW domains shares low sequence identity and include examples from two specificity classes, thus providing a comprehensive survey. Thermodynamic analysis of the four new WW domains consistently reveals all of the properties of downhill folding equilibria, which are in all cases more marked than what we found before in NEDD4-WW4. Our results show that fast-folding all-β proteins do share limited cooperativity and gradual unfolding thermodynamics with fast α-helical proteins and suggest that the free energy barrier to folding of natural proteins is mostly determined by size and fold topology and much less by the specific amino acid sequence.

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.

pH-Dependent cooperativity and existence of a dry molten globule in the folding of a miniprotein BBL

Solution pH plays an important role in protein dynamics, stability, and folding; however, detailed mechanisms remain poorly understood. Here we use continuous constant pH molecular dynamics in explicit solvent with pH replica exchange to describe the pH profile of the folding cooperativity of a miniprotein BBL, which has drawn intense debate in the past. Our data reconciled the two opposing hypotheses (downhill vs. two-state) and uncovered a sparsely populated unfolding intermediate. As pH is lowered from 7 to 5, the folding barrier vanishes. As pH continues to decrease, the unfolding barrier lowers and denaturation is triggered by the protonation of Asp162, consistent with experimental evidence. Interestingly, unfolding proceeded via an intermediate, with intact secondary structure and a compact, unlocked hydrophobic core shielded from solvent, lending support to the recent hypothesis of a universal dry molten globule in protein folding. Our work demonstrates that constant pH molecular dynamics is a unique tool for testing this and other hypotheses to advance the knowledge in protein dynamics, stability, and folding.

Roles of conformational disorder and downhill folding in modulating protein-DNA recognition

Transcription factors are thought to efficiently search for their target DNA site via a combination of conventional 3D diffusion and 1D diffusion along the DNA molecule mediated by non-specific electrostatic interactions. This process requires the DNA-binding protein to quickly exchange between a search competent and a target recognition mode, but little is known as to how these two binding modes are encoded in the conformational properties of the protein. Here, we investigate this issue on the engrailed homeodomain (EngHD), a DNA-binding domain that folds ultrafast and exhibits a complex conformational behavior consistent with the downhill folding scenario. We explore the interplay between folding and DNA recognition using a coarse-grained computational model that allows us to manipulate the folding properties of the protein and monitor its non-specific and specific binding to DNA. We find that conformational disorder increases the search efficiency of EngHD by promoting a fast gliding search mode in addition to sliding. When gliding, EngHD remains loosely bound to DNA moving linearly along its length. A partially disordered EngHD also binds more dynamically to the target site, reducing the half-life of the specific complex via a spring-loaded mechanism. These findings apply to all conditions leading to partial disorder. However, we also find that at physiologically relevant temperatures EngHD is well folded and can only obtain the conformational flexibility required to accelerate 1D diffusion when it folds/unfolds within the downhill scenario (crossing a marginal free energy barrier). In addition, the conformational flexibility of native downhill EngHD enables its fast reconfiguration to lock into the specific binding site upon arrival, thereby affording finer control of the on- and off-rates of the specific complex. Our results provide key mechanistic insights into how DNA-binding domains optimize specific DNA recognition through the control of their conformational dynamics and folding mechanism.

Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico. All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats.

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.

Can Local Probes Go Global? A Joint Experiment-Simulation Analysis of λ(6-85) Folding

The process of protein folding is known to involve global motions in a cooperative affair; the structure of most of the protein sequences is gained or lost over a narrow range of temperature, denaturant, or pressure perturbations. At the same time, recent simulations and experiments reveal a complex structural landscape with a rich set of local motions and conformational changes. We couple experimental kinetic and thermodynamic measurements with specifically tailored analysis of simulation data to isolate local versus global folding probes. We find that local probes exhibit lower melting temperatures, smaller surface area changes, and faster kinetics compared to global ones. We also see that certain local probes of folding match the global behavior more closely than others. Our work highlights the importance of using multiple probes to fully characterize protein folding dynamics by theory and experiment.

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.

Comparing Fast Pressure Jump and Temperature Jump Protein Folding Experiments and Simulations

The unimolecular folding reaction of small proteins is now amenable to a very direct mechanistic comparison between experiment and simulation. We present such a comparison of microsecond pressure and temperature jump refolding kinetics of the engineered WW domain FiP35, a model system for β-sheet folding. Both perturbations produce experimentally a faster and a slower kinetic phase, and the "slow" microsecond phase is activated. The fast phase shows differences between perturbation methods and is closer to the downhill limit by temperature jump, but closer to the transiently populated intermediate limit by pressure jump. These observations make more demands on simulations of the folding process than just a rough comparison of time scales. To complement experiments, we carried out several pressure jump and temperature jump all-atom molecular dynamics trajectories in explicit solvent, where FiP35 folded in five of the six simulations. We analyzed our pressure jump simulations by kinetic modeling and found that the pressure jump experiments and MD simulations are most consistent with a 4-state kinetic mechanism. Together, our experimental and computational data highlight FiP35's position at the boundary where activated intermediates and downhill folding meet, and we show that this model protein is an excellent candidate for further pressure jump molecular dynamics studies to compare experiment and modeling at the folding mechanism level.

Dependence of internal friction on folding mechanism

An outstanding challenge in protein folding is understanding the origin of "internal friction" in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

Statistical analyses of protein folding rates from the view of quantum transition

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism. Especially, the temperature dependence of the folding rate remains unsolved in the literature. Starting from the assumption that protein folding is an event of quantum transition between molecular conformations, we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies. The non-Arrhenius temperature relation for 16 proteins, whose experimental data had previously been available, was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation. A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory. The statistical comparisons of the folding rates for 65 two-state proteins were carried out, and the theoretical vs. experimental correlation coefficient was 0.73. Moreover, the maximum and the minimum folding rates given by the theory were consistent with the experimental results.

Probing the origins of two-state folding

Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior is likely for any system with an overwhelmingly populated native state. We show two-state folding is a natural consequence of such two-state thermodynamics, and is strengthened by increasing the population of the native state. Further, the model exhibits hub-like behavior, with slow interconversions between unfolded states. Despite this, the unfolded state equilibrates quickly relative to the folding time. This apparent paradox is readily understood through this model. Finally, our results compare favorable with measurements of folding rates as a function of chain length and Keq, providing new insight into these relations.

Observation of complete pressure-jump protein refolding in molecular dynamics simulation and experiment

Density is an easily adjusted variable in molecular dynamics (MD) simulations. Thus, pressure-jump (P-jump)-induced protein refolding, if it could be made fast enough, would be ideally suited for comparison with MD. Although pressure denaturation perturbs secondary structure less than temperature denaturation, protein refolding after a fast P-jump is not necessarily faster than that after a temperature jump. Recent P-jump refolding experiments on the helix bundle λ-repressor have shown evidence of a <3 μs burst phase, but also of a ~1.5 ms "slow" phase of refolding, attributed to non-native helical structure frustrating microsecond refolding. Here we show that a λ-repressor mutant is nonetheless capable of refolding in a single explicit solvent MD trajectory in about 19 μs, indicating that the burst phase observed in experiments on the same mutant could produce native protein. The simulation reveals that after about 18.5 μs of conformational sampling, the productive structural rearrangement to the native state does not occur in a single swift step but is spread out over a brief series of helix and loop rearrangements that take about 0.9 μs. Our results support the molecular time scale inferred for λ-repressor from near-downhill folding experiments, where transition-state population can be seen experimentally, and also agrees with the transition-state transit time observed in slower folding proteins by single-molecule spectroscopy.

Fast protein folding kinetics

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Isomerization- and temperature-jump-induced dynamics of a photoswitchable β-hairpin

Conformational changes in proteins and peptides can be initiated by diverse processes. This raises the question how the variation of initiation mechanisms is connected to differences in folding or unfolding processes. In this work structural dynamics of a photoswitchable β-hairpin model peptide were initiated by two different mechanisms: temperature jump (T-jump) and isomerization of a backbone element. In both experiments the structural changes were followed by time-resolved IR spectroscopy in the nanosecond to microsecond range. When the photoisomerization of the azobenzene backbone switch initiated the folding reaction, pronounced absorption changes related to folding into the hairpin structure were found with a time constant of about 16 μs. In the T-jump experiment kinetics with the same time constant were observed. For both initiation processes the reaction dynamics revealed the same strong dependence of the reaction time on temperature. The highly similar transients in the microsecond range show that the peptide dynamics induced by T-jump and isomerization are both determined by the same mechanism and exclude a downhill-folding process. Furthermore, the combination of the two techniques allows a detailed model for folding and unfolding to be presented: The isomerization-induced folding process ends in a transition-state reaction scheme, in which a high energetic barrier of 48 kJ mol(-1) separates unfolded and folded structures.

Engineering folding dynamics from two-state to downhill: application to λ-repressor

One strategy for reaching the downhill folding regime, primarily exploited for the λ_6–85 protein fragment, consists of cumulatively introducing mutations that speed up folding. This is an experimentally demanding process where chemical intuition usually serves as a guide for the choice of amino acid residues to mutate. Such an approach can be aided by computational methods that screen for protein engineering hot spots. Here we present one such method that involves sampling the energy landscape of the pseudo-wild-type protein and investigating the effect of point mutations on this landscape. Using a novel metric for the cooperativity, we identify those residues leading to the least cooperative folding. The folding dynamics of the selected mutants are then directly characterized and the differences in the kinetics are analyzed within a Markov-state model framework. Although the method is general, here we present results for a coarse-grained topology-based simulation model of λ-repressor, whose barrier is reduced from an initial value of ∼4k_BT at the midpoint to ∼1k_BT, thereby reaching the downhill folding regime.

Dodine as a protein denaturant: the best of two worlds?

Traditional denaturants such as urea and guanidinium ion unfold proteins in a cooperative "all-or-none" fashion. However, their high working concentration in combination with their strong absorption in the far ultraviolet region make it impossible to measure high quality circular dichroism or infrared spectra, which are commonly used to detect changes in protein secondary structure. On the other hand, detergents such as dodecyl sulfate destabilize native protein conformation at low millimolar concentrations and are UV transparent, but they denature proteins more gradually than guanidinium or urea. In this work, we studied the denaturation properties of the fungicide dodecylguanidinium acetate (dodine), which combines both denaturants into one. We show that dodine unfolds some small proteins at millimolar concentrations, facilitates temperature denaturation, and is transparent enough at its working concentration, unlike guanidinium, to measure full range circular dichroism spectra. Our results also suggest that dodine allows fine-tuning of the protein's unfolded state, unlike traditional "all-or-none" denaturants.

Microsecond folding experiments and simulations: a match is made

For the past two decades, protein folding experiments have been speeding up from the second or millisecond time scale to the microsecond time scale, and full-atom simulations have been extended from the nanosecond to the microsecond and even millisecond time scale. Where the two meet, it is now possible to compare results directly, allowing force fields to be validated and refined, and allowing experimental data to be interpreted in atomistic detail. In this perspective we compare recent experiments and simulations on the microsecond time scale, pointing out the progress that has been made in determining native structures from physics-based simulations, refining experiments and simulations to provide more quantitative underlying mechanisms, and tackling the problems of multiple reaction coordinates, downhill folding, and complex underlying structure of unfolded or misfolded states.

Eigenvalues of the homogeneous finite linear one step master equation: applications to downhill folding

Motivated by the observed time scales in protein systems said to fold "downhill," we have studied the finite, linear master equation, with uniform rates forward and backward as a model of the downhill process. By solving for the system eigenvalues, we prove the claim that in situations where there is no free energy barrier a transition between single- and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

GPU/CPU Algorithm for Generalized Born/Solvent-Accessible Surface Area Implicit Solvent Calculations

Molecular dynamics methodologies comprise a vital research tool for structural biology. Molecular dynamics has benefited from technological advances in computing, such as multi-core CPUs and graphics processing units (GPUs), but harnessing the full power of hybrid GPU/CPU computers remains difficult. The generalized Born/solvent-accessible surface area implicit solvent model (GB/SA) stands to benefit from hybrid GPU/CPU computers, employing the GPU for the GB calculation and the CPU for the SA calculation. Here, we explore the computational challenges facing GB/SA calculations on hybrid GPU/CPU computers and demonstrate how NAMD, a parallel molecular dynamics program, is able to efficiently utilize GPUs and CPUs simultaneously for fast GB/SA simulations. The hybrid computation principles demonstrated here are generally applicable to parallel applications employing hybrid GPU/CPU calculations.

Structural Characterization of λ-Repressor Folding from All-Atom Molecular Dynamics Simulations

The five-helix bundle λ-repressor fragment is a fast-folding protein. A length of 80 amino acid residues puts it on the large end among all known microsecond folders and its size poses a computational challenge for molecular dynamics (MD) studies. We simulated the folding of a novel λ-repressor fast-folding mutant (λ-HG) in explicit solvent using an all-atom description. By means of a recently developed tempering method, we observed reversible folding and unfolding of λ-repressor in a 10-microsecond trajectory. The folding kinetics was also investigated through a set of MD simulations run at different temperatures that together covered more than 125 microseconds. The protein was seen to fold into a native-like topology at intermediate temperature and a slow-folding pathway was identified. The simulations suggest new experimental observables for better monitoring the folding process, and a novel mutation expected to accelerate λ-repressor folding.

Exploring one-state downhill protein folding in single molecules

A one-state downhill protein folding process is barrierless at all conditions, resulting in gradual melting of native structure that permits resolving folding mechanisms step-by-step at atomic resolution. Experimental studies of one-state downhill folding have typically focused on the thermal denaturation of proteins that fold near the speed limit (ca. 10(6) s(-1)) at their unfolding temperature, thus being several orders of magnitude too fast for current single-molecule methods, such as single-molecule FRET. An important open question is whether one-state downhill folding kinetics can be slowed down to make them accessible to single-molecule approaches without turning the protein into a conventional activated folder. Here we address this question on the small helical protein BBL, a paradigm of one-state downhill thermal (un)folding. We decreased 200-fold the BBL folding-unfolding rate by combining chemical denaturation and low temperature, and carried out free-diffusion single-molecule FRET experiments with 50-μs resolution and maximal photoprotection using a recently developed Trolox-cysteamine cocktail. These experiments revealed a single conformational ensemble at all denaturing conditions. The chemical unfolding of BBL was then manifested by the gradual change of this unique ensemble, which shifts from high to low FRET efficiency and becomes broader at increasing denaturant. Furthermore, using detailed quantitative analysis, we could rule out the possibility that the BBL single-molecule data are produced by partly overlapping folded and unfolded peaks. Thus, our results demonstrate the one-state downhill folding regime at the single-molecule level and highlight that this folding scenario is not necessarily associated with ultrafast kinetics.

Crowding effects on the small, fast-folding protein lambda6-85

The microsecond folder lambda6-85 is a small (9.2 kDa = 9200 amu) five helix bundle protein. We investigated the stability of lambda6-85 in two different low-fluorescence crowding matrices: the large 70 kDa carbohydrate Ficoll 70, and the small 14 kDa thermophilic protein SubL. The same thermal stability of secondary structure was measured by circular dichroism in aqueous buffer, and at a crowding fraction phi = 15 +/- 1% of Ficoll 70. Tryptophan fluorescence detection (probing a tertiary contact) yielded the same thermal stability in Ficoll, but 4 degrees C lower in aqueous buffer. Temperature-jump kinetics revealed that the relaxation rate, corrected for bulk viscosity, was very similar in Ficoll and in aqueous buffer. Thus viscosity, hydrodynamics and crowding seem to compensate one another. However, a new fast phase was observed in Ficoll, attributed to crowding-induced downhill folding. We also measured the stability of lambda6-85 in phi = 14 +/- 1% SubL, which acts as a smaller more rigid crowder. Significantly greater stabilization (7 to 13 degrees C depending on probe) was observed than in the Ficoll matrix. The results highlight the importance of crowding agent choice for studies of small, fast-folding proteins amenable to comparison with molecular dynamics simulations.

Unifying model for two-state and downhill protein folding

A protein-folding model is proposed at the amino acid level, in which the folding process is divided into two successive stages: the rate-determining step, dominated by the "stochastic interactions"of solvent molecules, and the rapid phase, dominated by the "order interactions"among atoms in polypeptide. The master equation approach is used to investigate the folding kinetics, and an analytical treatment of the master equation yields a simple three-parameter expression for folding time. It is found that both two-state and downhill protein-folding kinetics can be described by a unifying model.

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saitô-Muñoz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.

Navigating the downhill protein folding regime via structural homologues

Proteins that fold over free-energy barriers <or= 3RT are classified as downhill folders. This regime is characterized by equilibrium unfolding that is proportionally broader and more complex the lower the folding barrier. Downhill proteins are also expected to fold up in a few microseconds. However, the relationship between rate and equilibrium signatures is affected by other factors such as protein size and folding topology. Here we perform a direct comparison of the kinetics and equilibrium unfolding of two structural homologues: BBL and PDD. BBL folds-unfolds in just approximately 1 micros at 335 K and displays the equilibrium signatures expected for a protein at the bottom of the downhill folding regime. PDD, which has the same 3D structure and size, folds-unfolds approximately 8 times more slowly and, concomitantly, exhibits all the downhill equilibrium signatures to a lesser degree. Our results demonstrate that the equilibrium signatures of downhill folding are proportional to the changes in folding rate once structural and size-scaling effects are factored out. This conclusion has two important implications: (1) it confirms that the quantitative analysis of equilibrium experiments in ultrafast folding proteins does provide direct information about free-energy barriers, a result that is incompatible with the conventional view of protein folding as a highly activated process, and (2) it advocates for equilibrium-kinetic studies of homologous proteins as a powerful tool to navigate the downhill folding regime via comparative analysis. The latter should prove extremely useful for the investigation of sequence, functional, and evolutionary determinants of protein folding barriers.

Folding of a helix at room temperature is critically aided by electrostatic polarization of intraprotein hydrogen bonds

We report direct folding of a 17-residue helix protein (pdb:2I9M) by standard molecular dynamics simulation (single trajectory) at room temperature with implicit solvent. Starting from a fully extended structure, 2I9M successfully folds into the native conformation within 16 ns using adaptive hydrogen bond-specific charges to take into account the electrostatic polarization effect. Cluster analysis shows that conformations in the native state cluster have the highest population (78.4%) among all sampled conformations. Folding snapshots and the secondary structure analysis demonstrate that the folding of 2I9M begins at terminals and progresses toward the center. A plot of the free energy landscape indicates that there is no significant free energy barrier during folding, which explains the observed fast folding speed. For comparison, exactly the same molecular dynamics simulation but carried out under existing AMBER charges failed to fold 2I9M into native-like structures. The current study demonstrates that electrostatic polarization of intraprotein hydrogen bonding, which stabilizes the helix, is critical to the successful folding of 2I9m.

Evidence, from simulations, of a single state with residual native structure at the thermal denaturation midpoint of a small globular protein

The folding of the B-domain of staphylococcal protein A has been studied by coarse-grained canonical and multiplexed replica-exchange molecular dynamics simulations with the UNRES force field in a broad range of temperatures (270 K < or = T < or = 350 K). In canonical simulations, the folding was found to occur either directly to the native state or through kinetic traps, mainly the topological mirror image of the native three-helix bundle. The latter folding scenario was observed more frequently at low temperatures. With increase of temperature, the frequency of the transitions between the folded and misfolded/unfolded states increased and the folded state became more diffuse with conformations exhibiting increased root-mean-square deviations from the experimental structure (from about 4 A at T = 300 K to 8.7 A at T = 325 K). An analysis of the equilibrium conformational ensemble determined from multiplexed replica exchange simulations at the folding-transition temperature (T(f) = 325 K) showed that the conformational ensemble at this temperature is a collection of conformations with residual secondary structures, which possess native or near-native clusters of nonpolar residues in place, and not a 50-50% mixture of fully folded and fully unfolded conformations. These findings contradict the quasi-chemical picture of two- or multistate protein folding, which assumes an equilibrium between the folded, unfolded, and intermediate states, with equilibrium shifting with temperature but with the native conformations remaining essentially unchanged. Our results also suggest that long-range hydrophobic contacts are the essential factor to keep the structure of a protein thermally stable.

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Protein folded states are kinetic hubs

Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them positioned to potentially provide a deeper understanding of molecular kinetics that can lead to experimentally testable hypotheses. Here we use existing MSMs for the villin headpiece and NTL9, which were constructed from atomistic simulations, to accomplish this goal. In addition, we provide simpler, humanly comprehensible networks that capture the essence of molecular kinetics and reproduce qualitative phenomena like the apparent two-state folding often seen in experiments. Together, these models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states (many unfolded basins that interconvert more rapidly with the native state than with one another) yet often still appear two-state. Most importantly, we find that protein native states are hubs that can be reached quickly from any other state. However, metastability and a web of nonnative states slow the average folding rate. Experimental tests for these findings and their implications for other fields, like protein design, are also discussed.

A natural missing link between activated and downhill protein folding scenarios

We propose protein PTB1 : 4W as a good candidate for engineering into a downhill folder. PTB1 : 4W has a probe-dependent thermal unfolding curve and sub-millisecond T-jump relaxation kinetics on more than one time scale. Its refolding rate in denaturant is a non-linear function of denaturant concentration (curved chevron plot). Yet at high denaturant concentration its unfolding is probe-independent, and the folding kinetics can be fitted to a single exponential decay. The domain appears to fold via a mechanism between downhill folding and activated folding over several small barriers, and when denaturant is added, one of these barriers greatly increases and simplifies the observed folding to apparent two-state kinetics. We predict the simplest free energy function consistent with the thermal denaturation and kinetics experiments by using the singular value Smoluchowski dynamics (SVSD) model. PTB1 : 4W is a natural 'missing link' between downhill and activated folding. We suggest mutations that could move the protein into the downhill folding limit.

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.