Nanosecond folding dynamics of a three-stranded beta-sheet

Folding Kinetics and Volume Variation of the β-Hairpin Peptide Chignolin upon Ultrafast pH-Jumps

In-depth characterization of fundamental folding steps of small model peptides is crucial for a better understanding of the folding mechanisms of more complex biomacromolecules. We have previously reported on the folding/unfolding kinetics of a model α-helix. Here, we study folding transitions in chignolin (GYDPETGTWG), a short β-hairpin peptide previously used as a model to study conformational changes in β-sheet proteins. Although previously suggested, until now, the role of the Tyr2-Trp9 interaction in the folding mechanism of chignolin was not clear. In the present work, pH-dependent conformational changes of chignolin were characterized by circular dichroism (CD), nuclear magnetic resonance (NMR), ultrafast pH-jump coupled with time-resolved photoacoustic calorimetry (TR-PAC), and molecular dynamics (MD) simulations. Taken together, our results present a comprehensive view of chignolin's folding kinetics upon local pH changes and the role of the Tyr2-Trp9 interaction in the folding process. CD data show that chignolin's β-hairpin formation displays a pH-dependent skew bell-shaped curve, with a maximum close to pH 6, and a large decrease in β-sheet content at alkaline pH. The β-hairpin structure is mainly stabilized by aromatic interactions between Tyr2 and Trp9 and CH-π interactions between Tyr2 and Pro4. Unfolding of chignolin at high pH demonstrates that protonation of Tyr2 is essential for the stability of the β-hairpin. Refolding studies were triggered by laser-induced pH-jumps and detected by TR-PAC. The refolding of chignolin from high pH, mainly due to the protonation of Tyr2, is characterized by a volume expansion (10.4 mL mol-1), independent of peptide concentration, in the microsecond time range (lifetime of 1.15 μs). At high pH, the presence of the deprotonated hydroxyl (tyrosinate) hinders the formation of the aromatic interaction between Tyr2 and Trp9 resulting in a more disorganized and dynamic tridimensional structure of the peptide. This was also confirmed by comparing MD simulations of chignolin under conditions mimicking neutral and high pH.

Characterization of Homogeneous and Heterogeneous Amyloid-β42 Oligomer Preparations with Biochemical Methods and Infrared Spectroscopy Reveals a Correlation between Infrared Spectrum and Oligomer Size

Soluble oligomers of the amyloid-β(1-42) (Aβ42) peptide, widely considered to be among the relevant neurotoxic species involved in Alzheimer’s disease, were characterized with a combination of biochemical and biophysical methods. Homogeneous and stable Aβ42 oligomers were prepared by treating monomeric solutions of the peptide with detergents. The prepared oligomeric solutions were analyzed with blue native and sodium dodecyl sulfate polyacrylamide gel electrophoresis, as well as with infrared (IR) spectroscopy. The IR spectra indicated a well-defined β-sheet structure of the prepared oligomers. We also found a relationship between the size/molecular weight of the Aβ42 oligomers and their IR spectra: The position of the main amide I′ band of the peptide backbone correlated with oligomer size, with larger oligomers being associated with lower wavenumbers. This relationship explained the time-dependent band shift observed in time-resolved IR studies of Aβ42 aggregation in the absence of detergents, during which the oligomer size increased. In addition, the bandwidth of the main IR band in the amide I′ region was found to become narrower with time in our time-resolved aggregation experiments, indicating a more homogeneous absorption of the β-sheets of the oligomers after several hours of aggregation. This is predominantly due to the consumption of smaller oligomers in the aggregation process.

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.

Enhanced Sensitivity to Local Dynamics in Peptides by Use of Temperature-Jump IR Spectroscopy and Isotope Labeling

Site-specific isotopic labeling of molecules is a widely used approach in IR spectroscopy to resolve local contributions to vibrational modes. The induced frequency shift of the corresponding IR band depends on the substituted masses, as well as on hydrogen bonding and vibrational coupling. The impact of these different factors was analyzed with a designed three-stranded β-sheet peptide and by use of selected ¹³ C isotope substitutions at multiple positions in the peptide backbone. Single-strand labels give rise to isotopically shifted bands at different frequencies, depending on the specific sites; this demonstrates sensitivity to the local environment. Cross-strand double- and triple-labeled peptides exhibited two resolved bands that could be uniquely assigned to specific residues, the equilibrium IR spectra of which indicated only weak local-mode coupling. Temperature-jump IR laser spectroscopy was applied to monitor structural dynamics and revealed an impressive enhancement of the isotope sensitivity to both local positions and coupling between them, relative to that of equilibrium FTIR spectroscopy. Site-specific relaxation rates were altered upon the introduction of additional cross-strand isotopes. Likewise, the rates for the global β-sheet dynamics were affected in a manner dependent on the distinct relaxation behavior of the labeled oscillator. This study reveals that isotope labels provide not only local structural probes, but rather sense the dynamic complexity of the molecular environment.

Insight into the internal structure of amyloid-β oligomers by isotope-edited Fourier transform infrared spectroscopy

Isotope-edited infrared spectroscopy reveals the structural unit of amyloid-β oligomers.

Isotopically Site-Selected Dynamics of a Three-Stranded β-Sheet Peptide Detected with Temperature-Jump Infrared-Spectroscopy

Infrared detected temperature-jump (T-jump) spectroscopy and site-specific isotopic labeling were applied to study a model three-stranded β-sheet peptide with the goal of individually probing the dynamics of strand and turn structural elements. This peptide had two ^DPro-Gly (pG) turn sequences to stabilize the two component hairpins, which were labeled with ¹³C═O on each of the Gly residues to resolve them spectroscopically. Labeling the second turn on the amide preceding the ^DPro (Xxx-^DPro amide) provided an alternate turn label as a control. Placing ¹³C═O labels on specific in-strand residues gave shifted modes that overlap the Xxx-^DPro amide I' modes. Their impact could be separated from the turn dynamics by a novel difference transient analysis approach. Fourier-transform infrared spectra were modeled with density functional theory-computations which showed the local, isotope-selected vibrations were effectively uncoupled from the other amide I modes. Our T-jump dynamics results, combined with nuclear magnetic resonance structures and equilibrium spectral measurements, showed the first turn to be most stable and best formed with the slowest dynamics, whereas the second turn and first strand (N-terminus) had similar dynamics, and the third strand (C-terminus) had the fastest dynamics and was the least structured. The relative dynamics of the strands, Xxx-^DPro amides, and ¹³C-labeled Gly residues on the turns also qualitatively corresponded to molecular dynamics (MD) simulations of turn and strand fluctuations. MD trajectories indicated the turns to be bistable, with the first turn being Type I' and the second turn flipping from I' to II'. The differences in relaxation times for each turn and the separate strands revealed that the folding process of this turn-stabilized β-sheet structure proceeds in a multistep process.

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.

Folding of a Zinc-Finger ββα-Motif Investigated Using Two-Dimensional and Time-Resolved Vibrational Spectroscopy

Small proteins provide good model systems for studying the fundamental forces that control protein folding. Here, we investigate the folding dynamics of the 28-residue zinc-finger mutant FSD-1, which is designed to form a metal-independent folded ββα-motif, and which provides a testing ground for proteins containing a mixed α/β fold. Although the folding of FSD-1 has been actively studied, the folding mechanism remains largely unclear. In particular, it is unclear in what stage of folding the α-helix is formed. To address this issue we investigate the folding mechanism of FSD-1 using a combination of temperature-dependent UV circular dichroism (UV-CD), Fourier transform infrared (FTIR) spectroscopy, two-dimensional infrared (2D-IR) spectroscopy, and temperature-jump (T-jump) transient-IR spectroscopy. Our UV-CD and FTIR data show different thermal melting transitions, indicating multistate folding behavior. Temperature-dependent 2D-IR spectra indicate that the α-helix is the most stable structural element of FSD-1. To investigate the folding/unfolding re-equilibration dynamics of FSD-1, the conformational changes induced by a nanosecond T-jump are probed with transient-IR and transient dispersed-pump-probe (DPP) IR spectroscopy. We observe biexponential T-jump relaxation kinetics (with time constants of 80 ± 13 ns and 1300 ± 100 ns at 322 K), confirming that the folding involves an intermediate state. The IR and dispersed-pump-probe IR spectra associated with the two kinetic components suggest that the folding of FSD-1 involves early formation of the α-helix, followed by the formation of the β-hairpin and hydrophobic contacts.

Structural features and molecular aggregations of designed triple-stranded β-sheets in single crystals

Design, synthesis, single-crystal conformations and molecular aggregations of hybrid triple-stranded β-sheets, and their structural analogy with protein structures are reported.

Effect of viscogens on the kinetic response of a photoperturbed allosteric protein

By covalently binding a photoswitchable linker across the binding groove of the PDZ2 domain, a small conformational change can be photo-initiated that mimics the allosteric transition of the protein. The response of its binding groove is investigated with the help of ultrafast pump-probe IR spectroscopy from picoseconds to tens of microseconds. The temperature dependence of that response is compatible with diffusive dynamics on a rugged energy landscape without any prominent energy barrier. Furthermore, the dependence of the kinetics on the concentration of certain viscogens, sucrose, and glycerol, has been investigated. A pronounced viscosity dependence is observed that can be best fit by a power law, i.e., a fractional viscosity dependence. The change of kinetics when comparing sucrose with glycerol as viscogen, however, provides strong evidence that direct interactions of the viscogen molecule with the protein do play a role as well. This conclusion is supported by accompanying molecular dynamics simulations.

Kinetics study on the HIV-1 ectodomain protein quaternary structure formation reveals coupling of chain folding and self-assembly in the refolding cascade

Entry of HIV-1 into the target cell is mediated by the envelope glycoprotein consisting of noncovalently associated surface subunit gp120 and transmembrane subunit gp41. To form a functional gp41 complex, the protein undergoes hairpin formation and self-assembly. The fusion event can be inhibited by gp41-derived peptides at nanomolar concentration and is highly dependent on the time of addition, implying a role of folding kinetics on the inhibitory action. Oligomerization of the gp41 ectodomain was demonstrated by light scattering measurements. Kinetic study by stopped-flow fluorescence and absorption measurements (i) revealed a multistate folding pathway and stable intermediates; (ii) showed a dissection of fast and slow components for early and late stages of folding, respectively, with 3 orders of magnitude difference in the time scale; (iii) showed the slow process was attributed to misfolding and unzipping of the hairpin; and (iv) showed retardation of the native hairpin formation is assumed to lead to coupling of the correctly registered hairpin and self-assembly. This coupling allows the deduction on the time scale of intrachain folding (0.1-1 s) for the protein. The folding reaction was illustrated by a free energy profile to explain the temporal dichotomy of fast and slow steps of folding as well as effective inhibition by gp41-derived peptide.

Protein folding: understanding the role of water and the low Reynolds number environment as the peptide chain emerges from the ribosome and folds

The mechanism of protein folding during early stages of the process has three determinants. First, moving water molecules obey the rules of low Reynolds number physics without an inertial component. Molecular movement is instantaneous and size insensitive. Proteins emerging from the ribosome move and rotate without an external force if they change shape, forming and propagating helical structures that increases translocational efficiency. Forward motion ceases when the shape change or propelling force ceases. Second, application of quantum field theory to water structure predicts the spontaneous formation of low density coherent units of fixed size that expel dissolved atmospheric gases. Structured water layers with both coherent and non-coherent domains, form a sheath around the new protein. The surface of exposed hydrophobic amino acids is protected from water contact by small nanobubbles of dissolved atmospheric gases, 5 or 6 molecules on average, that vibrate, attracting even widely separated resonating nanobubbles. This force results from quantum effects, appearing only when the system is within and interacts with an oscillating electromagnetic field. The newly recognized quantum force sharply bends the peptide and is part of a dynamic field determining the pathway of protein folding. Third, the force initiating the tertiary folding of proteins arises from twists at the position of each hydrophobic amino acid, that minimizes surface exposure of the hydrophobic amino acids and propagates along the protein. When the total bend reaches 360°, the leading segment of water sheath intersects the trailing segment. This steric self-intersection expels water from overlapping segments of the sheath and by Newton׳s second law moves the polypeptide chain in an opposite direction. Consequently, with very few exceptions that we enumerate and discuss, tertiary structures are absent from proteins without hydrophobic amino acids, which control the early stages of protein folding and the overall shape of protein. Consequently, proteins only adopt a limited number of forms. The formation of quaternary structures is not necessarily prevented by the absence of hydrophobic amino acids.

Discriminating trpzip2 and trpzip4 peptides' folding landscape using the two-dimensional infrared spectroscopy: a simulation study

We analyzed, based on the theoretical spectroscopic modeling, how the differences in the folding landscapes of two β-hairpin peptides trpzip2 and trpzip4 are reflected in their thermal unfolding infrared measurements. The isotope-edited equilibrium FTIR and two dimensional infrared spectra of the two peptides were calculated, using the nonlinear exciton propagation method, at a series of temperatures. The spectra calculations were based on the configuration distributions generated using the GB(OBC) implicit solvent MD simulation and the integrated tempering sampling technique. Conformational analysis revealed the different local thermal stabilities for these two peptides, which suggested the different folding landscapes. Our study further suggested that the ellipticities of the isotope peaks in the coherent IR signals are more sensitive to these local stability differences compared with other spectral features such as the peak intensities. Our technique can thus be combined with the relevant experimental measurements to achieve a better understanding of the peptide folding behaviors.

Modeling the thermal unfolding 2DIR spectra of a β-hairpin peptide based on the implicit solvent MD simulation

We simulated the equilibrium isotope-edited FTIR and 2DIR spectra of a β-hairpin peptide trpzip2 at a series of temperatures. The simulation was based on the configuration distributions generated using the GB(OBC) implicit solvent model and the integrated tempering sampling (ITS) technique. A soaking procedure was adapted to generate the peptide in explicit solvent configurations for the spectroscopy calculations. The nonlinear exciton propagation (NEP) method was then used to calculate the spectra. Agreeing with the experiments, the intensities and ellipticities of the isotope-shifted peaks in our simulated signals have the site-specific temperature dependences, which suggest the inhomogeneous local thermal stabilities along the peptide chain. Our simulation thus proposes a cost-effective means to understand a peptide's conformational change and related IR spectra across its thermal unfolding transition.

Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip

Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.

Atomic-level description of ubiquitin folding

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.

Mutational effects on the folding dynamics of a minimized hairpin

The fold stabilities and folding dynamics of a series of mutants of a model hairpin, KTW-NPATGK-WTE (HP7), are reported. The parent system and the corresponding DPATGK loop species display submicrosecond folding time constants. The mutational studies revealed that ultrafast folding requires both some prestructuring of the loop and a favorable interaction between the chain termini in the transition state. In the case of YY-DPETGT-WY, another submicrosecond folding species [Davis, C. M., Xiao, S., Raleigh, D. P., and Dyer, R. B. (2012) J. Am. Chem. Soc. 134, 14476-14482], a hydrophobic cluster provides the latter. In the case of HP7, the Coulombic interaction between the terminal NH3(+) and CO2(-) units provides this; a C-terminal Glu to amidated Ala mutation results in a 5-fold retardation of the folding rate. The effects of mutations within the reversing loop indicate the balance between loop flexibility (favoring fast conformational searching) and turn formation in the unfolded state is a major factor in determining the folding dynamics. The -NAAAKX- loops examined display no detectable turn formation propensity in other hairpin constructs but do result in stable analogues of HP7. Peptide KTW-NAAAKK-WTE displays the same fold stability as HP7, but both the folding and unfolding time constants are greater by a factor of 20.

Using thioamides to site-specifically interrogate the dynamics of hydrogen bond formation in β-sheet folding

Thioamides are sterically almost identical to their oxoamide counterparts, but they are weaker hydrogen bond acceptors. Therefore, thioamide amino acids are excellent candidates for perturbing the energetics of backbone-backbone H-bonds in proteins and hence should be useful in elucidating protein folding mechanisms in a site-specific manner. Herein, we validate this approach by applying it to probe the dynamic role of interstrand H-bond formation in the folding kinetics of a well-studied β-hairpin, tryptophan zipper. Our results show that reducing the strength of the peptide's backbone-backbone H-bonds, except the one directly next to the β-turn, does not change the folding rate, suggesting that most native interstrand H-bonds in β-hairpins are formed only after the folding transition state.

Molecular origin of Gerstmann-Sträussler-Scheinker syndrome: insight from computer simulation of an amyloidogenic prion peptide

Prion proteins become pathogenic through misfolding. Here, we characterize the folding of a peptide consisting of residues 109-122 of the Syrian hamster prion protein (the H1 peptide) and of a more amyloidogenic A117V point mutant that leads in humans to an inheritable form of the Gerstmann-Sträussler-Scheinker syndrome. Atomistic molecular dynamics simulations are performed for 2.5 μs. Both peptides lose their α-helical starting conformations and assume a β-hairpin that is structurally similar in both systems. In each simulation several unfolding/refolding events occur, leading to convergence of the thermodynamics of the conformational states to within 1 kJ/mol. The similar stability of the β-hairpin relative to the unfolded state is observed in the two peptides. However, substantial differences are found between the two unfolded states. A local minimum is found within the free energy unfolded basin of the A117V mutant populated by misfolded collapsed conformations of comparable stability to the β-hairpin state, consistent with increased amyloidogenicity. This population, in which V117 stabilizes a hydrophobic core, is absent in the wild-type peptide. These results are supported by simulations of oligomers showing a slightly higher stability of the associated structures and a lower barrier to association for the mutated peptide. Hence, a single point mutation carrying only two additional methyl groups is here shown to be responsible for rather dramatic differences of structuring within the unfolded (misfolded) state.

Simulating the T-jump-triggered unfolding dynamics of trpzip2 peptide and its time-resolved IR and two-dimensional IR signals using the Markov state model approach

We proposed a computational protocol of simulating the T-jump peptide unfolding experiments and the related transient IR and two-dimensional IR (2DIR) spectra based on the Markov state model (MSM) and nonlinear exciton propagation (NEP) methods. MSMs partition the conformation space into a set of nonoverlapping metastable states, and we can calculate spectra signal for each of these states using the NEP method. Thus the overall spectroscopic observable for a given system is simply the sum of spectra of different metastable states weighted by their populations. We show that results from MSMs constructed from a large number of simulations have a much better agreement with the equilibrium experimental 2DIR spectra compared to that generated from straightforward MD simulations starting from the folded state. This indicates that a sufficient sampling of important relevant conformational states is critical for calculating the accurate spectroscopic observables. MSMs are also capable of simulating the unfolding relaxation dynamics upon the temperature jump. The agreement of the simulation using MSMs and NEP with the experiment not only provides a justification for our protocol, but also provides the physical insight of the underlying spectroscopic observables. The protocol we developed has the potential to be extended to simulate a wide range of fast triggering plus optical detection experiments for biomolecules.

Studying submicrosecond protein folding kinetics using a photolabile caging strategy and time-resolved photoacoustic calorimetry

Kinetic measurement of protein folding is limited by the method used to trigger folding. Traditional methods, such as stopped flow, have a long mixing dead time and cannot be used to monitor fast folding processes. Here, we report a compound, 4-(bromomethyl)-6,7-dimethoxycoumarin, that can be used as a "photolabile cage" to study the early stages of protein folding. The folding process of a protein, RD1, including kinetics, enthalpy, and volume change, was studied by the combined use of a phototriggered caging strategy and time-resolved photoacoustic calorimetry. The cage caused unfolding of the photolabile protein, and then a pulse UV laser (∼10(-9) s) was used to break the cage, leaving the protein free to refold and allowing the resolving of two folding events on a nanosecond time scale. This strategy is especially good for monitoring fast folding proteins that cannot be studied by traditional methods.

Computational design and experimental testing of the fastest-folding β-sheet protein

One of the most important and elusive goals of molecular biology is the formulation of a detailed, atomic-level understanding of the process of protein folding. Fast-folding proteins with low free-energy barriers have proved to be particularly productive objects of investigation in this context, but the design of fast-folding proteins was previously driven largely by experiment. Dramatic advances in the attainable length of molecular dynamics simulations have allowed us to characterize in atomic-level detail the folding mechanism of the fast-folding all-β WW domain FiP35. In the work reported here, we applied the biophysical insights gained from these studies to computationally design an even faster-folding variant of FiP35 containing only naturally occurring amino acids. The increased stability and high folding rate predicted by our simulations were subsequently validated by temperature-jump experiments. The experimentally measured folding time was 4.3 μs at 80 °C-about three times faster than the fastest previously known protein with β-sheet content and in good agreement with our prediction. These results provide a compelling demonstration of the potential utility of very long molecular dynamics simulations in redesigning proteins well beyond their evolved stability and folding speed.

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.

[Prediction of the spatial structure of proteins: emphasis on membrane targets]

Knowledge of the spatial structure of proteins is a prerequisite for both awareness of their functional mechanisms and the framework for rational drug discovery and design. Meanwhile, direct structural determination is often hampered or impractical due to the complexity, expensiveness, and limited capabilities of experimental techniques. These issues are especially pronounced for integral membrane proteins. On numerous occasions, the theoretical prediction of protein structures may facilitate the process by exploiting physical or empirical principles. This paper surveys modern techniques for the prediction of the spatial structure of proteins using computer algorithms, and the main emphasis is placed on the most "complex" targets - membrane proteins (MPs). The first part of the review describes de novo methods based on empirical physical principles; in the second part, a comparative modeling philosophy, which accounts for the structure of related proteins, is described. Special focus is made regarding pharmacologically relevant classes of G-coupled receptors, receptor tyrosine ki-nases, and other MPs. Algorithms for the assessment of the models quality and potential fields of application of computer models are discussed.

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

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

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.

A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D

We present fluorescence-detected measurements of the temperature-jump relaxation kinetics of the designed three-helix bundle protein alpha(3)D taken under solvent conditions identical to previous infrared-detected kinetics. The fluorescence-detected rate is similar to the IR-detected rate only at the lowest temperature where we could measure it (326 K). The fluorescence-detected rate decreases by a factor of 3 over the 326-344 K temperature range, whereas the IR-detected rate remains nearly constant over the same range. To investigate this probe dependence, we tested an extensive set of physically reasonable one-dimensional (1D) free energy surfaces by Langevin dynamics simulation. The simulations included coordinate- and temperature-dependent roughness, diffusion coefficients, and IR/fluorescence spectroscopic signatures. None of these can reproduce the IR and fluorescence data simultaneously, forcing us to the conclusion that a 1D free energy surface cannot accurately describe the folding of alpha(3)D. This supports the hypothesis that alpha(3)D has a multidimensional free energy surface conducive to downhill folding at 326 K, and that it is already an incipient downhill folder with probe-dependent kinetics near its melting point.

Characterization of the cofactor-induced folding mechanism of a zinc-binding peptide using computationally designed mutants

Metals are the most commonly encountered protein cofactors, and they play important structural and functional roles in biology. In many cases, metal binding provides a major driving force for a polypeptide chain to fold. While there are many studies on the structure, stability, and function of metal-binding proteins, there are few studies focusing on understanding the kinetic mechanism of metal-induced folding. Herein, the Zn(2+)-induced folding kinetics of a small zinc-binding protein are studied; the CH1(1) peptide is derived from the first cysteine/histidine-rich region (CH1 domain) of the protein interaction domains of the transcriptional coregulator CREB-binding protein. Computational design is used to introduce tryptophan and histidine mutations that are structurally consistent with CH1(1); these mutants are studied using stopped-flow tryptophan fluorescence experiments. The Zn(2+)-induced CH1(1) folding kinetics are consistent with two parallel pathways, where the initial binding of Zn(2+) occurs at two sites. However, the initially formed Zn(2+)-bound complexes can proceed either directly to the folded state where zinc adopts a tetrahedral coordination or to an off-pathway misligated intermediate. While elimination of those ligands responsible for misligation simplifies the folding kinetics, it also leads to a decrease in the zinc binding constant. Therefore, these results suggest why these nonnative zinc ligands in the CH1(1) motif are conserved in several distantly related organisms and why the requirement for function can lead to kinetic frustration in folding. In addition, the loop closure rate of the CH1(1) peptide is determined based on the proposed model and temperature-dependent kinetic measurements.

Protein dynamics: from molecules, to interactions, to biology

Proteins have a remarkably rich diversity of dynamical behaviors, and the articles in this issue of the International Journal of Molecular Sciences are a testament to that fact. From the picosecond motions of single sidechains probed by NMR or fluorescence spectroscopy, to aggregation processes at interfaces that take months, all time scales play a role. Proteins are functional molecules, so by their nature they always interact with their environment. This environment includes water, other biomolecules, or larger cellular structures. In a sense, it also includes the protein molecule itself: proteins are large enough to fold and interact with themselves. These interactions have been honed by evolution to produce behaviors completely different from those of random polymers.

Probing the nanosecond dynamics of a designed three-stranded beta-sheet with a massively parallel molecular dynamics simulation

Recently a temperature-jump FTIR study of a designed three-stranded sheet showing a fast relaxation time of approximately 140 +/- 20 ns was published. We performed massively parallel molecular dynamics simulations in explicit solvent to probe the structural events involved in this relaxation. While our simulations produce similar relaxation rates, the structural ensemble is broad. We observe the formation of turn structure, but only very weak interaction in the strand regions, which is consistent with the lack of strong backbone-backbone NOEs in previous structural NMR studies. These results suggest that either (D)P(D)P-II folds at time scales longer than 240 ns, or that (D)P(D)P-II is not a well-defined three-stranded beta-sheet. This work also provides an opportunity to compare the performance of several popular forcefield models against one another.

How general is the nucleation-condensation mechanism?

We investigate the structures of the major folding transition states of nine proteins by correlation of published Phi-values with inter-residue contact maps. Combined with previous studies on six proteins, the analysis suggests that at least 10 of the 15 small globular proteins fold via a nucleation-condensation mechanism with a concurrent build-up of secondary and tertiary structure contacts, but a structural consolidation that is clearly nonuniformly distributed over the molecule and most intense in a single structural region suggesting the occurrence of a single folding nucleus. However, on average helix- and sheet-forming residues show somewhat larger Phi-values in the major transition state, suggesting that secondary structure formation is one important driving force in the nucleation-condensation in many proteins and that secondary-structure forming residues tend to be more prominent in folding nuclei. We synthesize the combined information on these 10 of 15 proteins into a unified nucleation-condensation mechanism which also accounts for effects described by the framework, hydrophobic collapse, zipper, and funnel models.

Viscosity scaling for the glassy phase of protein folding

Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.

Consistent free energy landscapes and thermodynamic properties of small proteins based on a single all-atom force field employing an implicit solvation

We have attempted to improve the PARAM99 force field in conjunction with the generalized Born (GB) solvation model with a surface area correction for more consistent protein folding simulations. For this purpose, using an extended alphabeta training set of five well-studied molecules with various folds (alpha, beta, and betabetaalpha), a previously modified version of PARAM99/GBSA is further refined, such that all native states of the five training species correspond to their lowest free energy minimum states. The resulting modified force field (PARAM99MOD5/GBSA) clearly produces reasonably acceptable conformational free energy surfaces of the training set with correct identifications of their native states in the free energy minimum states. Moreover, due to its well-balanced nature, this new force field is expected to describe secondary structure propensities of diverse folds in a more consistent manner. Remarkably, temperature dependent behaviors simulated with the current force field are in good agreement with the experiment. This agreement is a significant improvement over the existing standard all-atom force fields. In addition, fundamentally important thermodynamic quantities, such as folding enthalpy (DeltaH) and entropy (DeltaS), agree reasonably well with the experimental data.

The protein folding problem

The "protein folding problem" consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

Loop-closure principles in protein folding

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

Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece

We have performed molecular dynamics simulations on a set of nine unfolded conformations of the fastest-folding protein yet discovered, a variant of the villin headpiece subdomain (HP-35 NleNle). The simulations were generated using a new distributed computing method, yielding hundreds of trajectories each on a time scale comparable to the experimental folding time, despite the large (10,000 atom) size of the simulation system. This strategy eliminates the need to assume a two-state kinetic model or to build a Markov state model. The relaxation to the folded state at 300 K from the unfolded configurations (generated by simulation at 373 K) was monitored by a method intended to reflect the experimental observable (quenching of tryptophan by histidine). We also monitored the relaxation to the native state by directly comparing structural snapshots with the native state. The rate of relaxation to the native state and the number of resolvable kinetic time scales both depend upon starting structure. Moreover, starting structures with folding rates most similar to experiment show some native-like structure in the N-terminal helix (helix 1) and the phenylalanine residues constituting the hydrophobic core, suggesting that these elements may exist in the experimentally relevant unfolded state. Our large-scale simulation data reveal kinetic complexity not resolved in the experimental data. Based on these findings, we propose additional experiments to further probe the kinetics of villin folding.

Dehydration-driven solvent exposure of hydrophobic surfaces as a driving force in peptide folding

Recent work has shown that the nature of hydration of pure hydrophobic surfaces changes with the length scale considered: water hydrogen-bonding networks adapt to small exposed hydrophobic species, hydrating or "wetting" them at relatively high densities, whereas larger hydrophobic areas are "dewetted" [Chandler D (2005), Nature 29:640-647]. Here we determine whether this effect is also present in peptides by examining the folding of a beta-hairpin (the 14-residue amyloidogenic prion protein H1 peptide), using microsecond time-scale molecular dynamics simulations. Two simulation models are compared, one explicitly including the water molecules, which may thus adapt locally to peptide configurations, and the other using a popular continuum approximation, the generalized Born/surface area implicit solvent model. The results obtained show that, in explicit solvent, peptide conformers with high solvent-accessible hydrophobic surface area indeed also have low hydration density around hydrophobic residues, whereas a concomitant higher hydration density around hydrophilic residues is observed. This dewetting effect stabilizes the fully folded beta-hairpin state found experimentally. In contrast, the implicit solvent model destabilizes the fully folded hairpin, tending to cluster hydrophobic residues regardless of the size of the exposed hydrophobic surface. Furthermore, the rate of the conformational transitions in the implicit solvent simulation is almost doubled with respect to that of the explicit solvent. The results suggest that dehydration-driven solvent exposure of hydrophobic surfaces may be a significant factor determining peptide conformational equilibria.

The protein folding problem: when will it be solved?

The protein folding problem can be viewed as three different problems: defining the thermodynamic folding code; devising a good computational structure prediction algorithm; and answering Levinthal's question regarding the kinetic mechanism of how proteins can fold so quickly. Once regarded as a grand challenge, protein folding has seen much progress in recent years. Folding codes are now being used to successfully design proteins and non-biological foldable polymers; aided by the Critical Assessment of Techniques for Structure Prediction (CASP) competition, protein structure prediction has now become quite good. Even the once-challenging Levinthal puzzle now seems to have an answer--a protein can avoid searching irrelevant conformations and fold quickly by making local independent decisions first, followed by non-local global decisions later.