Understanding beta-hairpin formation.

The kinetics of formation of protein structural motifs (e.g., alpha-helices and beta-hairpins) can provide information about the early events in protein folding. A recent study has used fluorescence measurements to monitor the folding thermodynamics and kinetics of a 16-residue beta-hairpin. In the present paper, we obtain the free energy surface and conformations involved in the folding of an atomistic model for the beta-hairpin from multicanonical Monte Carlo simulations. The results suggest that folding proceeds by a collapse that is downhill in free energy, followed by rearrangement to form a structure with part of the hydrophobic cluster; the hairpin hydrogen bonds propagate outwards in both directions from the partial cluster. Such a folding mechanism differs from the published interpretation of the experimental results, which is based on a helix-coil-type phenomenological model.     

Submillisecond events in protein folding.

The pathway of protein folding is now being analyzed at the resolution of individual residues by kinetic measurements on suitably engineered mutants. The kinetic methods generally employed for studying folding are typically limited to the time range of > or = 1 ms because the folding of denatured proteins is usually initiated by mixing them with buffers that favor folding, and the dead time of rapid mixing experiments is about a millisecond. We now show that the study of protein folding may be extended to the microsecond time region by using temperature-jump measurements on the cold-unfolded state of a suitable protein. We are able to detect early events in the folding of mutants of barstar, the polypeptide inhibitor of barnase. A preliminary characterization of the fast phase from spectroscopic and phi-value analysis indicates that it is a transition between two relatively solvent-exposed states with little consolidation of structure.     

Direct observation of ultrafast folding and denatured state dynamics in single protein molecules

Single-molecule fluorescence resonance energy transfer (smFRET) experiments are extremely useful in studying protein folding but are generally limited to time scales of greater than ≈100 μs and distances greater than ≈2 nm. We used single-molecule fluorescence quenching by photoinduced electron transfer, detecting short-range events, in combination with fluorescence correlation spectroscopy (PET-FCS) to investigate folding dynamics of the small binding domain BBL with nanosecond time resolution. The kinetics of folding appeared as a 10-μs decay in the autocorrelation function, resulting from stochastic fluctuations between denatured and native conformations of individual molecules. The observed rate constants were probe independent and in excellent agreement with values derived from conventional temperature-jump (T-jump) measurements. A submicrosecond relaxation was detected in PET-FCS data that reported on the kinetics of intrachain contact formation within the thermally denatured state. We engineered a mutant of BBL that was denatured under the reaction conditions that favored folding of the parent wild type (“D_phys”). D_phys had the same kinetic signature as the thermally denatured state and revealed segmental diffusion with a time constant of intrachain contact formation of 500 ns. This time constant was more than 10 times faster than folding and in the range estimated to be the “speed limit” of folding. D_phys exhibited significant deviations from a random coil. The solvent viscosity and temperature dependence of intrachain diffusion showed that chain motions were slaved by the presence of intramolecular interactions. PET-FCS in combination with protein engineering is a powerful approach to study the early events and mechanism of ultrafast protein folding.     

Toward a better understanding of protein folding pathways.

Experimental observations of how unfolded proteins refold to their native three-dimensional structures contrast with many popular theories of protein folding mechanisms. The available experimental evidence (ignoring slow cis-trans peptide bond isomerization) is largely consistent with the following general scheme: under folding conditions, unfolded protein molecules rapidly equilibrate between different conformations prior to complete refolding. This rapid prefolding equilibrium favors certain compact conformations that have somewhat lower free energies than the other unfolded conformations. Some of the favored conformations are important for productive folding. The rate-limiting step occurs late in the pathway and involves a high-energy, distorted form of the native conformation; there appears to be a single transition state through which essentially all molecules refold. Consequently, proteins are not assembled via a large number of independent pathways, nor is folding initiated by a nucleation event in the unfolded protein followed by rapid growth of the folded structure. The known folding pathways involving disulfide bond formation follow the same general principles. An exceptional folding mechanism for reduced ribonuclease A proposed by Scheraga et al. (Scheraga, H.A., Konishi, Y., Rothwarf, D.M. & Mui, P.W. (1987) Proc. Natl. Acad. Sci. USA 84, 5740-5744) is shown to result from experimental shortcomings, an incorrect kinetic analysis, and a failure to consider the kinetics of unfolding.     

Effect of glycosylation on protein folding: a close look at thermodynamic stabilization

Glycosylation is one of the most common posttranslational modifications to occur in protein biosynthesis, yet its effect on the thermodynamics and kinetics of proteins is poorly understood. A minimalist model based on the native protein topology, in which each amino acid and sugar ring was represented by a single bead, was used to study the effect of glycosylation on protein folding. We studied in silico the folding of 63 engineered SH3 domain variants that had been glycosylated with different numbers of conjugated polysaccharide chains at different sites on the protein's surface. Thermal stabilization of the protein by the polysaccharide chains was observed in proportion to the number of attached chains. Consistent with recent experimental data, the degree of thermal stabilization depended on the position of the glycosylation sites, but only very weakly on the size of the glycans. A thermodynamic analysis showed that the origin of the enhanced protein stabilization by glycosylation is destabilization of the unfolded state rather than stabilization of the folded state. The higher free energy of the unfolded state is enthalpic in origin because the bulky polysaccharide chains force the unfolded ensemble to adopt more extended conformations by prohibiting formation of a residual structure. The thermodynamic stabilization induced by glycosylation is coupled with kinetic stabilization. The effects introduced by the glycans on the biophysical properties of proteins are likely to be relevant to other protein polymeric conjugate systems that regularly occur in the cell as posttranslational modifications or for biotechnological purposes.     

Competition between native topology and nonnative interactions in simple and complex folding kinetics of natural and designed proteins

We compared folding properties of designed protein Top7 and natural protein S6 by using coarse-grained chain models with a mainly native-centric construct that accounted also for nonnative hydrophobic interactions and desolvation barriers. Top7 and S6 have similar secondary structure elements and are approximately equal in length and hydrophobic composition. Yet their experimental folding kinetics were drastically different. Consistent with experiment, our simulated folding chevron arm for Top7 exhibited a severe rollover, whereas that for S6 was essentially linear, and Top7 model kinetic relaxation was multiphasic under strongly folding conditions. The peculiar behavior of Top7 was associated with several classes of kinetic traps in our model. Significantly, the amino acid residues participating in nonnative interactions in trapped conformations in our Top7 model overlapped with those deduced experimentally. These affirmations suggest that the simple ingredients of native topology plus sequence-dependent nonnative interactions are sufficient to account for some key features of protein folding kinetics. Notably, when nonnative interactions were absent in the model, Top7 chevron rollover was not correctly predicted. In contrast, nonnative interactions had little effect on the quasi linearity of the model folding chevron arm for S6. This intriguing distinction indicates that folding cooperativity is governed by a subtle interplay between the sequence-dependent driving forces for native topology and the locations of favorable nonnative interactions entailed by the same sequence. Constructed with a capability to mimic this interplay, our simple modeling approach should be useful in general for assessing a designed sequence’s potential to fold cooperatively.     

Cytochrome c′ folding triggered by electron transfer: Fast and slow formation of four-helix bundles

Reduced (Fe(II)) Rhodopseudomonas palustris cytochrome c' (Cyt c') is more stable toward unfolding ([GuHCl](1/2) = 2.9(1) M) than the oxidized (Fe(III)) protein ([GuHCl](1/2) = 1.9(1) M). The difference in folding free energies (Delta Delta G(f) degrees = 70 meV) is less than half of the difference in reduction potentials of the folded protein (100 mV vs. NHE) and a free heme in aqueous solution ( approximately -150 mV). The spectroscopic features of unfolded Fe(II)-Cyt c' indicate a low-spin heme that is axially coordinated to methionine sulfur (Met-15 or Met-25). Time-resolved absorption measurements after CO photodissociation from unfolded Fe(II)(CO)-Cyt c' confirm that methionine can bind to the ferroheme on the microsecond time scale [k(obs) = 5(2) x 10(4) s(-1)]. Protein folding was initiated by photoreduction (two-photon laser excitation of NADH) of unfolded Fe(III)-Cyt c' ([GuHCl] = 2.02--2.54 M). Folding kinetics monitored by heme absorption span a wide time range and are highly heterogeneous; there are fast-folding ( approximately 10(3) s(-1)), intermediate-folding (10(2)-10(1) s(-1)), and slow-folding (10(-1) s(-1)) populations, with the last two likely containing methionine-ligated (Met-15 or Met-25) ferrohemes. Kinetics after photoreduction of unfolded Fe(III)-Cyt c' in the presence of CO are attributable to CO binding [1.4(6) x 10(3) s(-1)] and Fe(II)(CO)-Cyt c' folding [2.8(9) s(-1)] processes; stopped-flow triggered folding of Fe(III)-Cyt c' (which does not contain a protein-derived sixth ligand) is adequately described by a single kinetics phase with an estimated folding time constant of approximately 4 ms [Delta G(f) degrees = -33(3) kJ mol(-1)] at zero denaturant.     

Mutations as trapdoors to two competing native conformations of the Rop-dimer

Conformational transitions play a central role in regulating protein function. Structure-based models with multiple basins have been used to understand the mechanisms governing these transitions. A model able to accommodate multiple folding basins is proposed to explore the mutational effects in the folding of the Rop-dimer (Rop). In experiments, Rop mutants show unusually strong increases in folding rates with marginal effects on stability. We investigate the possibility of two competing conformations representing a parallel (P) and the wild-type antiparallel (AP) arrangement of the monomers as possible native conformations. We observe occupation of both distinct states and characterize the transition pathways. An interesting observation from the simulations is that, for equivalent energetic bias, the transition to the P basin (non-wild-type basin) shows a lower free-energy barrier. Thus, the rapid kinetics observed in experiments appear to be the result of two competing states with different kinetic behavior, triggered upon mutation by the opening of a trapdoor arising from Rop's symmetric structure. The general concept of having competing conformations for the native state goes beyond explaining Rop's mutational behaviors and can be applied to other systems. A switch between competing native structures might be triggered by external factors to allow, for example, allosteric control or signaling.     

Protein folding pathways from replica exchange simulations and a kinetic network model

We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large ( approximately 10(6)) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the alpha-helix/beta-hairpin interconversion.     

Electrostatic mechanism of nucleosomal array folding revealed by computer simulation

Although numerous experiments indicate that the chromatin fiber displays salt-dependent conformations, the associated molecular mechanism remains unclear. Here, we apply an irregular Discrete Surface Charge Optimization (DiSCO) model of the nucleosome with all histone tails incorporated to describe by Monte Carlo simulations salt-dependent rearrangements of a nucleosomal array with 12 nucleosomes. The ensemble of nucleosomal array conformations display salt-dependent condensation in good agreement with hydrodynamic measurements and suggest that the array adopts highly irregular 3D zig-zag conformations at high (physiological) salt concentrations and transitions into the extended "beads-on-a-string" conformation at low salt. Energy analyses indicate that the repulsion among linker DNA leads to this extended form, whereas internucleosome attraction drives the folding at high salt. The balance between these two contributions determines the salt-dependent condensation. Importantly, the internucleosome and linker DNA-nucleosome attractions require histone tails; we find that the H3 tails, in particular, are crucial for stabilizing the moderately folded fiber at physiological monovalent salt.     

A structure-based method for derivation of all-atom potentials for protein folding

A method for deriving all-atom protein folding potentials is presented and tested on a three-helix bundle protein, as well as on hairpin and helical sequences. The potentials obtained are composed of a contact term between pairs of atoms, and a local density term for each atom, mimicking solvent exposure preferences. Using this potential in an all-atom protein folding simulation, we repeatedly folded the three-helix bundle, with the lowest energy conformations having a C(alpha) distance rms from the native structure of less than 2 A. Similar results were obtained for the hairpin and helices by using different potentials. We derived potentials for several different proteins and found a high correlation between the derived parameters, suggesting that a potential of this form eventually could be found that folds multiple, unrelated proteins at the atomic level of detail.     

Kinetics and thermodynamics of folding in model proteins.

Monte Carlo simulations on a class of lattice models are used to probe the thermodynamics and kinetics of protein folding. We find two transition temperatures: one at T theta, when chains collapse from a coil to a compact phase, and the other at Tf (< T theta), when chains adopt a conformation corresponding to their native state. The kinetics are probed by several correlation functions and are interpreted in terms of the underlying energy landscape. The transition from the coil to the native state occurs in three distinct stages. The initial stage corresponds to a random collapse of the protein chain. At intermediate times tau c, during which much of the native structure is acquired, there are multiple pathways. For longer times tau r (>> tau c) the decay is exponential, suggestive of a late transition state. The folding time scale (approximately tau r) varies greatly depending on the model. Implications of our results for in vitro folding of proteins are discussed.     

Protein folding by distributed computing and the denatured state ensemble

The distributed computing (DC) paradigm in conjunction with the folding@home (FH) client server has been used to study the folding kinetics of small peptides and proteins, giving excellent agreement with experimentally measured folding rates, although pathways sampled in these simulations are not always consistent with the folding mechanism. In this study, we use a coarse-grain model of protein L, whose two-state kinetics have been characterized in detail by using long-time equilibrium simulations, to rigorously test a FH protocol using approximately 10,000 short-time, uncoupled folding simulations starting from an extended state of the protein. We show that the FH results give non-Poisson distributions and early folding events that are unphysical, whereas longer folding events experience a correct barrier to folding but are not representative of the equilibrium folding ensemble. Using short-time, uncoupled folding simulations started from an equilibrated denatured state ensemble (DSE), we also do not get agreement with the equilibrium two-state kinetics because of overrepresented folding events arising from higher energy subpopulations in the DSE. The DC approach using uncoupled short trajectories can make contact with traditionally measured experimental rates and folding mechanism when starting from an equilibrated DSE, when the simulation time is long enough to sample the lowest energy states of the unfolded basin and the simulated free-energy surface is correct. However, the DC paradigm, together with faster time-resolved and single-molecule experiments, can also reveal the breakdown in the two-state approximation due to observation of folding events from higher energy subpopulations in the DSE.     

Lattice model for rapidly folding protein-like heteropolymers.

Protein folding is a relatively fast process considering the astronomical number of conformations in which a protein could find itself. Within the framework of a lattice model, we show that one can design rapidly folding sequences by assigning the strongest attractive couplings to the contacts present in a target native state. Our protein design can be extended to situations with both attractive and repulsive contacts. Frustration is minimized by ensuring that all the native contacts are again strongly attractive. Strikingly, this ensures the inevitability of folding and accelerates the folding process by an order of magnitude. The evolutionary implications of our findings are discussed.     

UDP-Glc:glycoprotein glucosyltransferase recognizes structured and solvent accessible hydrophobic patches in molten globule-like folding intermediates

Protein folding in the cell involves the action of different molecular chaperones and folding-facilitating enzymes. In the endoplasmic reticulum (ER), the folding status of glycoproteins is stringently controlled by a glucosyltranferase enzyme (GT) that creates monoglucosylated structures recognized by ER resident lectins (calnexincalreticulin, CNXCRT). GT serves as a folding sensor because it only glucosylates misfolded or partly folded glycoproteins. Nevertheless, the molecular mechanism behind this recognition process remains largely unknown. In this paper we explore the structural determinants for GT recognition by using a single domain model protein. For this purpose we used a family of chemically glycosylated proteins derived from chymotrypsin inhibitor-2 as GT substrates. Structural characterization of species showing higher glucose acceptor capacity suggests that GT recognizes solvent accessible hydrophobic patches in molten globule-like conformers mimicking intermediate folding stages of nascent glycoproteins. It was further confirmed that BiP (binding protein, a chaperone of the heat shock protein 70 family) preferentially recognized neoglycoproteins displaying extended conformations, thus providing a molecular rationale for the sequential BiP-CNXCRT interaction with folding glycoproteins observed in vivo.     

Multiple stepwise refolding of immunoglobulin domain I27 upon force quench depends on initial conditions

Mechanical folding trajectories for polyproteins starting from initially stretched conformations generated by single-molecule atomic force microscopy experiments [Fernandez, J. M. & Li, H. (2004) Science 303, 1674-1678] show that refolding, monitored by the end-to-end distance, occurs in distinct multiple stages. To clarify the molecular nature of folding starting from stretched conformations, we have probed the folding dynamics, upon force quench, for the single I27 domain from the muscle protein titin by using a C(alpha)-Go model. Upon temperature quench, collapse and folding of I27 are synchronous. In contrast, refolding from stretched initial structures not only increases the folding and collapse time scales but also decouples the two kinetic processes. The increase in the folding times is associated primarily with the stretched state to compact random coil transition. Surprisingly, force quench does not alter the nature of the refolding kinetics, but merely increases the height of the free-energy folding barrier. Force quench refolding times scale as tau(F) approximately tau(F)(0)exp(f(q)Deltax(f)/k(B)T), where Deltax(f) approximately 0.6 nm is the location of the average transition state along the reaction coordinate given by end-to-end distance. We predict that tau(F) and the folding mechanism can be dramatically altered by the initial and/or final values of force. The implications of our results for design and analysis of experiments are discussed.     

Integrating folding kinetics and protein function: biphasic kinetics and dual binding specificity in a WW domain

Because of the association of beta-sheet formation with the initiation and propagation of amyloid diseases, model systems have been sought to further our understanding of this process. WW domains have been proposed as one such model system. Whereas the folding of the WW domains from human Yes-associated protein (YAP) and Pin have been shown to obey single-exponential kinetics, the folding of the WW domain from formin-binding protein (FBP) 28 has been shown to proceed via biphasic kinetics. From an analysis of free-energy landscapes from atomic-level molecular dynamics simulations, the biphasic folding kinetics observed in the FBP WW domain may be traced to the ability of this WW domain to adopt two slightly different forms of packing in its hydrophobic core. This conformational change is propagated along the peptide backbone and affects the position of a tryptophan residue shown in other WW domains to play a key role in binding. The WW domains of Pin and YAP do not support more than one type of packing each, leading to monophasic folding kinetics. The ability of the FBP WW domain to assume two different types of packing may, in turn, explain the capacity of this WW domain to bind two classes of ligand, a property that is not shared by other WW domains. These findings lead to the hypothesis that lability with respect to conformations separated by an observable barrier as a requirement for function is incompatible with the ability of a protein to fold via single-exponential kinetics.     

Constructing, verifying, and dissecting the folding transition state of chymotrypsin inhibitor 2 with all-atom simulations

Experimentally, protein engineering and phi-value analysis is the method of choice to characterize the structure in folding transition state ensemble (TSE) of any protein. Combining experimental phi values and computer simulations has led to a deeper understanding of how proteins fold. In this report, we construct the TSE of chymotrypsin inhibitor 2 from published phi values. Importantly, we verify, by means of multiple independent simulations, that the conformations in the TSE have a probability of approximately 0.5 to reach the native state rapidly, so the TSE consists of true transition states. This finding validates the use of transition state theory underlying all phi-value analyses. Also, we present a method to dissect and study the TSE by generating conformations that have a disrupted alpha-helix (alpha-disrupted states) or disordered beta-strands 3 and 4 (beta-disrupted states). Surprisingly, the alpha-disrupted states have a stronger tendency to fold than the beta-disrupted states, despite the higher phi values for the alpha-helix in the TSE. We give a plausible explanation for this result and discuss its implications on protein folding and design. Our study shows that, by using both experiments and computer simulations, we can gain many insights into protein folding.     

Phi-value analysis of a three-state protein folding pathway by NMR relaxation dispersion spectroscopy

Experimental studies of protein folding frequently are consistent with two-state folding kinetics. However, recent NMR relaxation dispersion studies of several fast-folding mutants of the Fyn Src homology 3 (SH3) domain have established that folding proceeds through a low-populated on-pathway intermediate, which could not be detected with stopped-flow experiments. The dispersion experiments provide precise kinetic and thermodynamic parameters that describe the folding pathway, along with a detailed site-specific structural characterization of both the intermediate and unfolded states from the NMR chemical shifts that are extracted. Here we describe NMR relaxation dispersion Phi-value analysis of the A39V/N53P/V55L Fyn SH3 domain, where the effects of suitable point mutations on the energy landscape are quantified, providing additional insight into the structure of the folding intermediate along with per-residue structural information of both rate-limiting transition states that was not available from previous studies. In addition to the advantage of delineating the full three-state folding pathway, the use of NMR relaxation dispersion as opposed to stopped-flow kinetics to quantify Phi values facilitates their interpretation because the obtained chemical shifts monitor any potential structural changes along the folding pathway that might be introduced by mutation, a significant concern in their analysis. Phi-Value analysis of several point mutations of A39V/N53P/V55L Fyn SH3 establishes that the beta(3)-beta(4)-hairpin already is formed in the first transition state, whereas strand beta(1), which forms nonnative interactions in the intermediate, does not fully adopt its native conformation until after the final transition state. The results further support the notion that on-pathway intermediates can be stabilized by nonnative contacts.