Ultrafast Folding Protein Research Articles

Quantifying the energy landscape in weakly and strongly disordered frictional media.

We investigate the "roughness" of the energy landscape of a system that diffuses in a heterogeneous medium with a random position-dependent friction coefficient α(x). This random friction acting on the system stems from spatial inhomogeneity in the surrounding medium and is modeled using the generalized Caldira-Leggett model. For a weakly disordered medium exhibiting a Gaussian random diffusivity D(x) = kBT/α(x) characterized by its average value ⟨D(x)⟩ and a pair-correlation function ⟨D(x1)D(x2)⟩, we find that the renormalized intrinsic diffusion coefficient is lower than the average one due to the fluctuations in diffusivity. The induced weak internal friction leads to increased roughness in the energy landscape. When applying this idea to diffusive motion in liquid water, the dissociation energy for a hydrogen bond gradually approaches experimental findings as fluctuation parameters increase. Conversely, for a strongly disordered medium (i.e., ultrafast-folding proteins), the energy landscape ranges from a few to a few kcal/mol, depending on the strength of the disorder. By fitting protein folding dynamics to the escape process from a metastable potential, the decreased escape rate conceptualizes the role of strong internal friction. Studying the energy landscape in complex systems is helpful because it has implications for the dynamics of biological, soft, and active matter systems.

Effects of altered backbone composition on the folding kinetics and mechanism of an ultrafast-folding protein.

Sequence-encoded protein folding is a ubiquitous biological process that has been successfully engineered in a range of oligomeric molecules with artificial backbone chemical connectivity. A remarkable aspect of protein folding is the contrast between the rapid rates at which most sequences in nature fold and the vast number of conformational states possible in an unfolded chain with hundreds of rotatable bonds. Research efforts spanning several decades have sought to elucidate the fundamental chemical principles that dictate the speed and mechanism of natural protein folding. In contrast, little is known about how protein mimetic entities transition between an unfolded and folded state. Here, we report effects of altered backbone connectivity on the folding kinetics and mechanism of the B domain of Staphylococcal protein A (BdpA), an ultrafast-folding sequence. A combination of experimental biophysical analysis and atomistic molecular dynamics simulations performed on the prototype protein and several heterogeneous-backbone variants reveal the interplay among backbone flexibility, folding rates, and structural details of the transition state ensemble. Collectively, these findings suggest a significant degree of plasticity in the mechanisms that can give rise to ultrafast folding in the BdpA sequence and provide atomic level insights into how protein mimetic chains adopt an ordered folded state.

Compliant mechanical response of the ultrafast folding protein EnHD under force

Ultrafast folding proteins have become an important paradigm in the study of protein folding dynamics. Due to their low energetic barriers and fast kinetics, they are amenable for study by both experiment and simulation. However, single molecule force spectroscopy experiments on these systems are challenging as these proteins do not provide the mechanical fingerprints characteristic of more mechanically stable proteins, which makes it difficult to extract information about the folding dynamics of the molecule. Here, we investigate the unfolding of the ultrafast protein Engrailed Homeodomain (EnHD) by single-molecule atomic force microscopy experiments. Constant speed experiments on EnHD result in featureless transitions typical of compliant proteins. However, in the force-ramp mode we recover sigmoidal curves that we interpret as a very compliant protein that folds and unfolds many times over a marginal barrier. This is supported by a simple theoretical model and coarse-grained molecular simulations. Our results show the ability of force to modulate the unfolding dynamics of ultrafast folding proteins.

Reversible two-state folding of the ultrafast protein gpW under mechanical force

Ultrafast folding proteins have limited cooperativity and thus are excellent models to resolve, via single-molecule experiments, the fleeting molecular events that proteins undergo during folding. Here we report single-molecule atomic force microscopy experiments on gpW, a protein that, in bulk, folds in a few microseconds over a marginal folding barrier (∼1 kBT). Applying pulling forces of only 5 pN, we maintain gpW in quasi-equilibrium near its mechanical unfolding midpoint and detect how it interconverts stochastically between the folded and an extended state. The interconversion pattern is distinctly binary, indicating that, under an external force, gpW (un)folds over a significant free-energy barrier. Using molecular simulations and a theoretical model we rationalize how force induces such barrier in an otherwise downhill free-energy surface. Force-induced folding barriers are likely a general occurrence for ultrafast folding biomolecules studied with single-molecule force spectroscopy.

Instrumental Effects in the Dynamics of an Ultrafast Folding Protein under Mechanical Force.

The analysis and interpretation of single molecule force spectroscopy (smFS) experiments is often complicated by hidden effects from the measuring device. Here we investigate these effects in our recent smFS experiments on the ultrafast folding protein gpW, which has been previously shown to fold without crossing a free energy barrier in the absence of force (i.e., downhill folding). Using atomic force microscopy (AFM) smFS experiments, we found that a very small force of ∼5 pN brings gpW near its unfolding midpoint and results in two-state (un)folding patterns that indicate the emergence of a force-induced free energy barrier. The change in the folding regime is concomitant with a 30,000-fold slowdown of the folding and unfolding times, from a few microseconds that it takes gpW to (un)fold at the midpoint temperature to seconds in the AFM. These results are puzzling because the barrier induced by force in the folding free energy landscape of gpW is far too small to account for such a difference in time scales. Here we use recently developed theoretical methods to resolve the origin of the strikingly slow dynamics of gpW under mechanical force. We find that, while the AFM experiments correctly capture the equilibrium distance distribution, the measured dynamics are entirely controlled by the response of the cantilever and polyprotein linker, which is much slower than the protein conformational dynamics. This interpretation is likely applicable to the folding of other small biomolecules in smFS experiments, and becomes particularly important in the case of systems with fast folding dynamics and small free energy barriers, and for instruments with slow response times.

How the Barrierless Folding Helps DNA Recognition: Theoretical Investigation on Ultrafast Folding Protein Engrailed Homeodomain

Engrailed homeodomain (EngHD), a 3-helix bundle fast-folding protein, has been found to play a critical role in transcription regulation during its binding to DNA. Evidence shows that protein efficiently recognizes the short target DNA sequence from the enormous pool of binding sites via the process of “facilitated diffusion”, including sliding and hopping. During the facilitated diffusion, protein is supposed to go through “speed” mode, where protein nonspecifically interacts with DNA in fast diffusion, and “stability” mode, where protein strongly and specifically scans the base pairs in DNA with slow displacement.

Modern Analysis of Protein Folding by Differential Scanning Calorimetry.

Differential scanning calorimetry (DSC) is a very powerful tool for investigating protein folding and stability because its experimental output reflects the energetics of all conformations that become minimally populated during thermal unfolding. Accordingly, analysis of DSC experiments with simple thermodynamic models has been key for developing our understanding of protein stability during the past five decades. The discovery of ultrafast folding proteins, which have naturally broad conformational ensembles and minimally cooperative unfolding, opens the possibility of probing the complete folding free energy landscape, including those conformations at the top of the barrier to folding, via DSC. Exploiting this opportunity requires high-quality experiments and the implementation of novel analytical methods based on statistical mechanics. Here, we cover the recent exciting developments in this front, describing the new analytical procedures in detail as well as providing experimental guidelines for performing such analysis.

β-Structure within the Denatured State of the Helical Protein Domain BBL

Protein denatured states are the origin of both healthy and toxic conformational species. Denatured states of ultrafast folding proteins are of interest in mechanistic studies because they are energetically close to the kinetic bottleneck of folding. However, their transient nature makes them elusive to experiment. Here, we generated the denatured state of the helical domain BBL that is poised to fold in microseconds by a single-point mutation and combined circular dichroism spectroscopy, single-molecule fluorescence fluctuation analysis, and computer simulation to characterize its structure and dynamics. Circular dichroism showed a largely unfolded ensemble with marginal helix but significant β-sheet content. Main-chain structure and dynamics were unaffected by side-chain interactions that stabilize the native state, as revealed by site-directed mutagenesis and nanosecond loop closure kinetics probed by fluorescence correlation spectroscopy. Replica-exchange and constant-temperature molecular dynamics simulations showed a highly collapsed, hydrogen-bonded denatured state containing turn and β-sheet structure and few nucleating helices in an otherwise unfolded ensemble. An irregular β-hairpin element that connects helices in the native fold was poised to be formed. The surprising observation of β-structure in regions that form helices in the native state is reconciled by a generic low-energy pathway from the northwest quadrant of Ramachandran space to the helical basin present under folding conditions, proposed recently. Our results show that, indeed, rapid nucleation of helix emanates from β-structure formed early within a collapsed ensemble of unfolded conformers.

Accelerated Monte-Carlo Simulations for All-Atom Protein Folding

Recent advances in the computational description of proteins facilitate the atomic-level characterization of fast folding proteins using molecular-dynamics simulations[1]. However, due to the femtosecond timestep of an MD simulation, 10 ˆ 10 computationally expensive energy evaluations are required to reach timescales of the order of single folding events even for ultrafast-folding proteins. Stochastic simulation techniques can overcome this limiting factor by generating thermodynamic conformational ensembles without incorporating atomic vibrations, but most of these methods are inherently sequential. Here we investigate a parallel extension to the conventional Metropolis-Hastings algorithm, the Multiple-Try-Metropolis, enabling parallel simulation of reversible Markov-chains[2,3]. We successfully characterize the thermodynamic landscape of the Villin-headpiece-subdomain using a generalized MTM approach adapted to protein systems. We parameterized the polypeptide using the AMBER99SB-STAR-ILDN-forcefield with an implicit solvent model. In our simulations we could observe approximately two folding transitions per day on standard hardware, with a total of 109 transition events during 3∗10 ˆ 9 energy evaluations. The MTM approach thus facilitates the efficient thermodynamic characterization of proteins on common computer architectures. The comparison with experimental resolved folding times of 8µs translates to a time equivalent of 16ps per MTM step.[1] Shaw, Science-2010.[2] Liu, JASA-2000.[3] Pandolfi, JMLR-2010.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Ultrafast folding kinetics and cooperativity of villin headpiece in single-molecule force spectroscopy

In this study we expand the accessible dynamic range of single-molecule force spectroscopy by optical tweezers to the microsecond range by fast sampling. We are able to investigate a single molecule for up to 15 min and with 300-kHz bandwidth as the protein undergoes tens of millions of folding/unfolding transitions. Using equilibrium analysis and autocorrelation analysis of the time traces, the full energetics as well as real-time kinetics of the ultrafast folding of villin headpiece 35 and a stable asparagine 68 alanine/lysine 70 methionine variant can be measured directly. We also performed Brownian dynamics simulations of the response of the bead-DNA system to protein-folding fluctuations. All key features of the force-dependent deflection fluctuations could be reproduced: SD, skewness, and autocorrelation function. Our measurements reveal a difference in folding pathway and cooperativity between wild-type and stable variant of headpiece 35. Autocorrelation force spectroscopy pushes the time resolution of single-molecule force spectroscopy to ∼10 µs thus approaching the timescales accessible for all atom molecular dynamics simulations.

Probing Free-Energy Surfaces with Differential Scanning Calorimetry

Many aspects of protein folding can be understood in terms of projections of the highly dimensional energy landscape onto a few (or even only one) particularly relevant coordinates. These free-energy surfaces can be probed conveniently from experimental differential scanning calorimetry (DSC) thermograms, as DSC provides a direct relation with the protein partition function. Free-energy surfaces thus obtained are consistent with two fundamental scenarios predicted by the energy-landscape perspective: (a) well-defined macrostates separated by significant free-energy barriers, in some cases, and, in many other cases, (b) marginal or even vanishingly small barriers, which furthermore show a good correlation with kinetics for fast- and ultrafast-folding proteins. Overall, the potential of DSC to assess free-energy surfaces for a wide variety of proteins makes it possible to address fundamental issues, such as the molecular basis of the barrier modulations produced by natural selection in response to functional requirements or to ensure kinetic stability.

Making connections between ultrafast protein folding kinetics and molecular dynamics simulations

Determining the rate of forming the truly folded conformation of ultrafast folding proteins is an important issue for both experiments and simulations. The double-norleucine mutant of the 35-residue villin subdomain is the focus of recent computer simulations with atomistic molecular dynamics because it is currently the fastest folding protein. The folding kinetics of this protein have been measured in laser temperature-jump experiments using tryptophan fluorescence as a probe of overall folding. The conclusion from the simulations, however, is that the rate determined by fluorescence is significantly larger than the rate of overall folding. We have therefore employed an independent experimental method to determine the folding rate. The decay of the tryptophan triplet-state in photoselection experiments was used to monitor the change in the unfolded population for a sequence of the villin subdomain with one amino acid difference from that of the laser temperature-jump experiments, but with almost identical equilibrium properties. Folding times obtained in a two-state analysis of the results from the two methods at denaturant concentrations varying from 1.5-6.0 M guanidinium chloride are in excellent agreement, with an average difference of only 20%. Polynomial extrapolation of all the data to zero denaturant yields a folding time of 220 (+100,-70) ns at 283 K, suggesting that under these conditions the barrier between folded and unfolded states has effectively disappeared--the so-called "downhill scenario."

Measuring Sub-Microsceond Protein Folding Kinetics with Independent Probes

Determining the rate of forming the truly folded conformation of ultrafast folding proteins has been an important issue for both experiment and simulation. The double-norleucine mutant of the 35-residue villin subdomain has been the focus of recent computer simulations with atomistic molecular dynamics because it is currently the fastest folding protein, with folding times less than 1 microsecond as measured by tryptophan fluorescence in laser temperature jump experiments. However, the molecular dynamics simulations reported folding times much longer than the times for fluorescence changes. To establish the folding time with greater certainty, we have therefore employed an independent method. In this experiment the decay of the tryptophan triplet state measured by triplet-triplet absorption spectroscopy monitors the change in the population of the unfolded state. The experimental rates from the two methods will be critically compared with each other and with the rates from simulations.T.C. and M.B. made equal contributions to this work.

Folding of the Pit1 homeodomain near the speed limit

Current questions in protein folding mechanisms include how fast can a protein fold and are there energy barriers for the folding and unfolding of ultrafast folding proteins? The small 3-helical engrailed homeodomain protein folds in 1.7 μs to form a well-characterized intermediate, which rearranges in 17 μs to native structure. We found that the homologous pituitary-specific transcription factor homeodomain (Pit1) folded in a similar manner, but in two better separated kinetic phases of 2.3 and 46 μs. The greater separation and better fluorescence changes facilitated a detailed kinetic analysis for the ultrafast phase for formation of the intermediate. Its folding rate constant changed little with denaturant concentration or mutation but unfolding was very sensitive to denaturant and energy changes on mutation. The folding rate constant of 3 × 10(5) s(-1) in water decreased with increasing viscosity, and was extrapolated to 4.4 × 10(5) s(-1) at zero viscosity. Thus, the formation of the intermediate was partly rate limited by chain diffusion and partly by an energy barrier to give a very diffuse transition state, which was followed by the formation of structure. Conversely, the unfolding reaction required the near complete disruption of the tertiary structure of the intermediate in a highly cooperative manner, being exquisitely sensitive to individual mutations. The folding is approaching, but has not reached, the downhill-folding scenario of energy landscape theory. Under folding conditions, there is a small energy barrier between the denatured and transition states but a larger barrier between native and transition states.

The Effect of Electrostatics on the Marginal Cooperativity of an Ultrafast Folding Protein

Proteins fold up by coordinating the different segments of their polypeptide chain through a network of weak cooperative interactions. Such cooperativity results in unfolding curves that are typically sigmoidal. However, we still do not know what factors modulate folding cooperativity or the minimal amount that ensures folding into specific three-dimensional structures. Here, we address these issues on BBL, a small helical protein that folds in microseconds via a marginally cooperative downhill process (Li, P., Oliva, F. Y., Naganathan, A. N., and Muñoz, V. (2009) Proc. Natl. Acad. Sci. USA. 106, 103-108). Particularly, we explore the effects of salt-induced screening of the electrostatic interactions in BBL at neutral pH and in acid-denatured BBL. Our results show that electrostatic screening stabilizes the native state of the neutral and protonated forms, inducing complete refolding of acid-denatured BBL. Furthermore, without net electrostatic interactions, the unfolding process becomes much less cooperative, as judged by the broadness of the equilibrium unfolding curve and the relaxation rate. Our experiments show that the marginally cooperative unfolding of BBL can still be made twice as broad while the protein retains its ability to fold into the native three-dimensional structure in microseconds. This result demonstrates experimentally that efficient folding does not require cooperativity, confirming predictions from theory and computer simulations and challenging the conventional biochemical paradigm. Furthermore, we conclude that electrostatic interactions are an important factor in determining folding cooperativity. Thus, electrostatic modulation by pH-salt and/or mutagenesis of charged residues emerges as an attractive tool for tuning folding cooperativity.

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.

ϕ-Value Analysis for Ultrafast Folding Proteins by NMR Relaxation Dispersion

Proteins that fold rapidly, on the (sub-) microsecond time scale, offer the prospect of direct comparison between experimental data and molecular dynamics simulations. However, experimental studies for such proteins frequently are hindered because folding rates are too fast to measure using conventional stopped-flow methods. To overcome this impediment, NMR spin relaxation dispersion experiments are used to quantify mutational effects on kinetics (DeltaDeltaG(o)), stability (DeltaDeltaG(o)), and phi-values (DeltaDeltaG(dagger)/DeltaDeltaG(o)) for proteins exhibiting chemical exchange line broadening that is fast on the NMR chemical shift time scale. The accuracy of phi-value analysis is enhanced because mutational effects on denatured or intermediate states can be detected through changes in line broadening. The transition and intermediate states of the villin headpiece domain, HP67, are characterized in varying solvent conditions to validate the method.

Native like structure in the unfolded state of the villin headpiece helical subdomain, an ultrafast folding protein

The villin headpiece subdomain, HP36, is the smallest naturally occurring protein that folds cooperatively. Its small size, rapid folding, and simple three-helix topology have made it an extremely popular system for computational studies of protein folding. The role of unfolded state structure in rapid folding is an area of active investigation, but relatively little is known about the properties of unfolded states under native conditions. A peptide fragment, HP21, which contains the first and second helices of HP36 has been shown to be a good model for structure in the unfolded state of the intact domain but a detailed description of the conformational propensities of HP21 is lacking and the balance between native and nonnative interactions is not known. A series of three-dimensional NMR experiments were performed on (13)C, (15)N-labeled HP21 to investigate in detail its conformational propensities. Analysis of (13)C(alpha), (13)C(beta), (13)CO chemical shifts, Deltadelta(13)C(alpha) - Deltadelta(13)C(beta) secondary shifts, the secondary structure propensity scores, NOEs, (15)N R(2) values and comparison of experimental chemical shifts with those of HP36 and with chemical shifts calculated using the SHIFTS and SHIFTX programs all indicate that there is significant native like structure in the HP21 ensemble, and thus by implication in the unfolded state of HP36.

The Folding Mechanism of BBL: Plasticity of Transition-State Structure Observed within an Ultrafast Folding Protein Family

Studies on members of protein families with similar structures but divergent sequences provide insights into the effects of sequence composition on the mechanism of folding. Members of the peripheral subunit-binding domain (PSBD) family fold ultrafast and approach the smallest size for cooperatively folding proteins. Φ-Value analysis of the PSBDs E3BD and POB reveals folding via nucleation–condensation through structurally very similar, polarized transition states. Here, we present a Φ-value analysis of the family member BBL and found that it also folds by a nucleation–condensation mechanism. The mean Φ values of BBL, E3BD, and POB were near identical, indicating similar fractions of non-covalent interactions being formed in the transition state. Despite the overall conservation of folding mechanism in this protein family, however, the pattern of Φ values determined for BBL revealed a larger dispersion of the folding nucleus across the entire structure, and the transition state was less polarized. The observed plasticity of transition-state structure can be rationalized by the different helix-forming propensities of PSBD sequences. The very strong helix propensity in the first helix of BBL, relative to E3BD and POB, appears to recruit more structure formation in that helix in the transition state at the expense of weaker interactions in the second helix. Differences in sequence composition can modulate transition-state structure of even the smallest natural protein domains.

Chemical, physical, and theoretical kinetics of an ultrafast folding protein

An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein--the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models--a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 10(5) possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 10(5) microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models.