Ultrafast and downhill protein folding

Ultrafast folding proteins have served an important role in benchmarking molecular dynamics simulations and testing protein folding theories. These proteins are simple enough and fold fast enough that realistic simulations are possible, which facilitates the direct comparison of absolute folding rates and folding mechanisms with those observed experimentally. Such comparisons have achieved remarkable success, but have also revealed the shortcomings that remain in experiment, theory and simulation alike. Some ultrafast folding proteins may fold without encountering an activation barrier (downhill folding), allowing the exploration of the molecular timescale of folding and the roughness of the energy landscape. The biological significance of ultrafast folding remains uncertain, but its practical significance is crucial to progress in understanding how proteins fold.     

Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.     

Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.     

Force Field Bias in Protein Folding Simulations

Long timescale (>1 μs) molecular dynamics simulations of protein folding offer a powerful tool for understanding the atomic-scale interactions that determine a protein's folding pathway and stabilize its native state. Unfortunately, when the simulated protein fails to fold, it is often unclear whether the failure is due to a deficiency in the underlying force fields or simply a lack of sufficient simulation time. We examine one such case, the human Pin1 WW domain, using the recently developed deactivated morphing method to calculate free energy differences between misfolded and folded states. We find that the force field we used favors the misfolded states, explaining the failure of the folding simulations. Possible further applications of deactivated morphing and implications for force field development are discussed.     

Helix nucleation kinetics from molecular simulations in explicit solvent

We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possibly complicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.     

Exposing the kinetic traps in RNA folding.

Large ribozymes fold on a 'glacial' timescale compared to the folding of their protein counterparts. The sluggish folding exhibited by large RNAs results from the formation of kinetically trapped, misfolded intermediates, which are nonessential features of the folding mechanism. Newly developed mutant ribozymes that avoid kinetic traps should facilitate the study of the RNA folding problem.     

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.     

Molecular dynamics simulations of peptides and proteins with amplified collective motions

We present a novel method that uses the collective modes obtained with a coarse-grained model/anisotropic network model to guide the atomic-level simulations. Based on this model, local collective modes can be calculated according to a single configuration in the conformational space of the protein. In the molecular dynamics simulations, the motions along the slowest few modes are coupled to a higher temperature by the weak coupling method to amplify the collective motions. This amplified-collective-motion (ACM) method is applied to two test systems. One is an S-peptide analog. We realized the refolding of the denatured peptide in eight simulations out of 10 using the method. The other system is bacteriophage T4 lysozyme. Much more extensive domain motions between the N-terminal and C-terminal domain of T4 lysozyme are observed in the ACM simulation compared to a conventional simulation. The ACM method allows for extensive sampling in conformational space while still restricting the sampled configurations within low energy areas. The method can be applied in both explicit and implicit solvent simulations, and may be further applied to important biological problems, such as long timescale functional motions, protein folding/unfolding, and structure prediction.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Energy landscape distortions and the mechanical unfolding of proteins

Molecular simulations and an energy landscape analysis are used to examine the stretching of a model protein. A mapping of the energy landscape shows that stretching the protein causes energy minima and energy barriers to flatten out and disappear, and new energy minima to be created. The implications of these landscape distortions depend on the timescale regime under which the protein is stretched. When the timescale for thermally activated processes is longer than the timescale of stretching, the disappearances of energy barriers provide the mechanism for protein unfolding. When the timescale for thermally activated processes is shorter than the timescale of stretching, the landscape distortions influence the stretching process by changing the number and types of energy minima in which the system can exist.     

Residual structure in a peptide fragment of the outer membrane protein X under denaturing conditions: a molecular dynamics study

The Escherichia coli outer membrane protein X (OmpX) contains two polypeptide segments that present nonrandom residual structure in 8 M aqueous urea, whereas the remainder of the protein is in a flexibly disordered conformation (Tafer et al. in Biochemistry 43:860–869, 2004). In the present study, the results of two long-timescale (0.4 μs) unrestrained explicit-solvent molecular dynamics (MD) simulations of a tetradecapeptide representative of one of these two segments in 8 M aqueous urea are reported and analyzed. The two simulations were initiated either from the conformation of the corresponding segment in an NMR model structure of the unfolded protein or from an entirely extended configuration. The sampled conformational ensembles agree qualitatively with the experimentally observed NOEs, but not quantitatively, suggesting that a number of relevant configurations were not visited on the 2 × 0.4 μs timescale. Major conformational transitions occur on the 0.1 μs timescale, and the ensembles corresponding to the two independent simulations overlap only to a limited extent. However, both simulations show in multiple events the reversible formation and disruption of α-helical secondary structure (characteristic of the urea-denatured state) and β-turn secondary structure (characteristic of the native state). Events of helix formation are correlated with the appearance of hydrogen bonds between two side chains (Asp75–Ser78) and of a persistent hydrophobic contact (Trp76–Tyr80). They also evidence a peculiar helix stabilization and N-terminal capping role for a negatively charged residue (Asp75). These features are in good qualitative agreement with the NMR model for the structured state of the corresponding segment in the urea-denatured protein. The analysis of the simulations provides a detailed picture of the structural and dynamic features of the considered peptide at atomic resolution that is of high relevance in the understanding of the OmpX folding process.     

Apoflavodoxin (un)folding followed at the residue level by NMR

The denaturant-induced (un)folding of apoflavodoxin from Azotobacter vinelandii has been followed at the residue level by NMR spectroscopy. NH groups of 21 residues of the protein could be followed in a series of 1H-15N heteronuclear single-quantum coherence spectra recorded at increasing concentrations of guanidinium hydrochloride despite the formation of protein aggregate. These NH groups are distributed throughout the whole apoflavodoxin structure. The midpoints of unfolding determined by NMR coincide with the one obtained by fluorescence emission spectroscopy. Both techniques give rise to unfolding curves with transition zones at significantly lower denaturant concentrations than the one obtained by circular dichroism spectroscopy. The NMR (un)folding data support a mechanism for apoflavodoxin folding in which a relatively stable intermediate is involved. Native apoflavodoxin is shown to cooperatively unfold to a molten globule-like state with extremely broadened NMR resonances. This initial unfolding step is slow on the NMR chemical shift timescale. The subsequent unfolding of the molten globule is faster on the NMR chemical shift timescale and the limited appearance of 1H-15N HSQC cross peaks of unfolded apoflavodoxin in the denaturant range studied indicates that it is noncooperative.     

A Second Look at Mini-Protein Stability: Analysis of FSD-1 Using Circular Dichroism, Differential Scanning Calorimetry, and Simulations

Mini-proteins that contain <50 amino acids often serve as model systems for studying protein folding because their small size makes long timescale simulations possible. However, not all mini-proteins are created equal. The stability and structure of FSD-1, a 28-residue mini-protein that adopted the ββα zinc-finger motif independent of zinc binding, was investigated using circular dichroism, differential scanning calorimetry, and replica-exchange molecular dynamics. The broad melting transition of FSD-1, similar to that of a helix-to-coil transition, was observed by using circular dichroism, differential scanning calorimetry, and replica-exchange molecular dynamics. The N-terminal β-hairpin was found to be flexible. The FSD-1 apparent melting temperature of 41°C may be a reflection of the melting of its α-helical segment instead of the entire protein. Thus, despite its attractiveness due to small size and purposefully designed helix, sheet, and turn structures, the status of FSD-1 as a model system for studying protein folding should be reconsidered.     

Multiscale simulation of the interaction of calreticulin-thrombospondin-1 complex with a model membrane microdomain

Cell surface calreticulin (CRT) binding to thrombospondin-1 (TSP1), regulates cell adhesion, migration, anoikis resistance, and collagen production. Due to the essential role of membrane microdomains in CRT-mediated focal adhesion disassembly, we previously studied the effect of raft-like bilayers on TSP1–CRT interactions with all-atom molecular dynamics (AAMD) simulations. However, the simulated systems of protein on the surface of the bilayer(s) in the explicit solvent are too large for long timescale AAMD simulations due to computational expense. In this study, we adopted a multiscale modeling approach of combining AAMD, coarse-grained molecule dynamics (CGMD), and reversed AAMD (REV AAMD) simulations to investigate the interactions of single CRT or of the TSP1–CRT complex with a membrane microdomain at microsecond timescale. Results showed that CRT conformational stabilization by binding of TSP1 in AAMD simulation was undetectable in CGMD simulation, but it was recovered in REV AAMD simulation. Similarly, interactions of the CRT N-domain and TSP1 with the membrane microdomain were lost in CGMD simulations but they were re-gained in the REV AAMD simulations. There was the higher coordination of the CRT P-domain in the TSP1–CRT complex with the lipid components of membrane microdomain compared to that of single CRT, which could directly affect the conformation of CRT and further mediate CRT recruitment of LDL receptor-related protein for signaling events. This study provides structural and molecular insights into TSP1–CRT interactions in a membrane microdomain environment and demonstrates the feasibility of using multiscale simulations to investigate the interactions between protein and membrane microdomains at a long timescale.     

Accelerated molecular dynamics simulations of the octopamine receptor using GPUs: discovery of an alternate agonist‐binding position

Octopamine receptors (OARs) perform key biological functions in invertebrates, making this class of G‐protein coupled receptors (GPCRs) worth considering for insecticide development. However, no crystal structures and very little research exists for OARs. Furthermore, GPCRs are large proteins, are suspended in a lipid bilayer, and are activated on the millisecond timescale, all of which make conventional molecular dynamics (MD) simulations infeasible, even if run on large supercomputers. However, accelerated Molecular Dynamics (aMD) simulations can reduce this timescale to even hundreds of nanoseconds, while running the simulations on graphics processing units (GPUs) would enable even small clusters of GPUs to have processing power equivalent to hundreds of CPUs. Our results show that aMD simulations run on GPUs can successfully obtain the active and inactive state conformations of a GPCR on this reduced timescale. Furthermore, we discovered a potential alternate active‐state agonist‐binding position in the octopamine receptor which has yet to be observed and may be a novel GPCR agonist‐binding position. These results demonstrate that a complex biological system with an activation process on the millisecond timescale can be successfully simulated on the nanosecond timescale using a simple computing system consisting of a small number of GPUs. Proteins 2016; 84:1480–1489. © 2016 Wiley Periodicals, Inc.     

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Experiment and theory highlight role of native state topology in SH3 folding.

We use a combination of experiments, computer simulations and simple model calculations to characterize, first, the folding transition state ensemble of the src SH3 domain, and second, the features of the protein that determine its folding mechanism. Kinetic analysis of mutations at 52 of the 57 residues in the src SH3 domain revealed that the transition state ensemble is even more polarized than suspected earlier: no single alanine substitution in the N-terminal 15 residues or the C-terminal 9 residues has more than a two-fold effect on the folding rate, while such substitutions at 15 sites in the central three-stranded beta-sheet cause significant decreases in the folding rate. Molecular dynamics (MD) unfolding simulations and ab initio folding simulations on the src SH3 domain exhibit a hierarchy of folding similar to that observed in the experiments. The similarity in folding mechanism of different SH3 domains and the similar hierarchy of structure formation observed in the experiments and the simulations can be largely accounted for by a simple native state topology-based model of protein folding energy landscapes.     

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.