Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

Kinetic partitioning mechanism governs the folding of the third FnIII domain of tenascin-C: evidence at the single-molecule level

Statistical mechanics and molecular dynamics simulations proposed that the folding of proteins can follow multiple parallel pathways on a rugged energy landscape from unfolded state en route to their folded native states. Kinetic partitioning mechanism is one of the possible mechanisms underlying such complex folding dynamics. Here, we use single-molecule atomic force microscopy technique to directly probe the multiplicity of the folding pathways of the third fibronectin type III domain from the extracellular matrix protein tenascin-C (TNfn3). By stretching individual (TNfn3)₈ molecules, we forced TNfn3 domains to undergo mechanical unfolding and refolding cycles, allowing us to directly observe the folding pathways of TNfn3. We found that, after being mechanically unraveled and then relaxed to zero force, TNfn3 follows multiple parallel pathways to fold into their native states. The majority of TNfn3 fold into the native state in a simple two-state fashion, while a small percentage of TNfn3 were found to be trapped into kinetically stable folding intermediate states with well-defined three-dimensional structures. Furthermore, the folding of TNfn3 was also influenced by its neighboring TNfn3 domains. Complex misfolded states of TNfn3 were observed, possibly due to the formation of domain-swapped dimeric structures. Our studies revealed the ruggedness of the folding energy landscape of TNfn3 and provided direct experimental evidence that the folding dynamics of TNfn3 are governed by the kinetic partitioning mechanism. Our results demonstrated the unique capability of single-molecule AFM to probe the folding dynamics of proteins at the single-molecule level.     

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.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

Ten-microsecond molecular dynamics simulation of a fast-folding WW domain

All-atom molecular dynamics (MD) simulations of protein folding allow analysis of the folding process at an unprecedented level of detail. Unfortunately, such simulations have not yet reached their full potential both due to difficulties in sufficiently sampling the microsecond timescales needed for folding, and because the force field used may yield neither the correct dynamical sequence of events nor the folded structure. The ongoing study of protein folding through computational methods thus requires both improvements in the performance of molecular dynamics programs to make longer timescales accessible, and testing of force fields in the context of folding simulations. We report a ten-microsecond simulation of an incipient downhill-folding WW domain mutant along with measurement of a molecular time and activated folding time of 1.5 microseconds and 13.3 microseconds, respectively. The protein simulated in explicit solvent exhibits several metastable states with incorrect topology and does not assume the native state during the present simulations.     

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.     

Fast in silico protein folding by introduction of alternating hydrogen bond potentials

We accelerate protein folding in all-atom molecular dynamics simulations by introducing alternating hydrogen bond potentials as a supplement to the force field. The alternating hydrogen bond potentials result in accelerated hydrogen bond reordering, which leads to rapid formation of secondary structure elements. The method does not require knowledge of the native state but generates the potentials based on the development of the tertiary structure in the simulation. In protein folding, the formation of secondary structure elements, especially α-helix and β-sheet, is very important, and we show that our method can fold both efficiently and with great speed.     

Folding Pathways of the Tetrahymena Ribozyme

Like many structured RNAs, the Tetrahymena group I intron ribozyme folds through multiple pathways and intermediates. Under standard conditions in vitro, a small fraction reaches the native state (N) with k_obs ≈ 0.6 min^− 1, while the remainder forms a long-lived misfolded conformation (M) thought to differ in topology. These alternative outcomes reflect a pathway that branches late in folding, after disruption of a trapped intermediate (I_trap). Here we use catalytic activity to probe the folding transitions from I_trap to the native and misfolded states. We show that mutations predicted to weaken the core helix P3 do not increase the rate of folding from I_trap but they increase the fraction that reaches the native state rather than forming the misfolded state. Thus, P3 is disrupted during folding to the native state but not to the misfolded state, and P3 disruption occurs after the rate-limiting step. Interestingly, P3-strengthening mutants also increase native folding. Additional experiments show that these mutants are rapidly committed to folding to the native state, although they reach the native state with approximately the same rate constant as the wild-type ribozyme (~ 1 min^− 1). Thus, the P3-strengthening mutants populate a distinct pathway that includes at least one intermediate but avoids the M state, most likely because P3 and the correct topology are formed early. Our results highlight multiple pathways in RNA folding and illustrate how kinetic competitions between rapid events can have long-lasting effects because the “choice” is enforced by energy barriers that grow larger as folding progresses.     

Ab initio folding of proteins with all-atom discrete molecular dynamics

Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. We performed folding simulations of six small proteins (20-60 residues) with distinct native structures by the replica exchange method. In all cases, native or near-native states were reached in simulations. For three small proteins, multiple folding transitions are observed, and the computationally characterized thermodynamics are in qualitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes and applied to protein engineering and design of protein-protein interactions.     

Tackling Force-Field Bias in Protein Folding Simulations: Folding of Villin HP35 and Pin WW Domains in Explicit Water

The ability to fold proteins on a computer has highlighted the fact that existing force fields tend to be biased toward a particular type of secondary structure. Consequently, force fields for folding simulations are often chosen according to the native structure, implying that they are not truly “transferable.” Here we show that, while the AMBER ff03 potential is known to favor helical structures, a simple correction to the backbone potential (ff03^∗) results in an unbiased energy function. We take as examples the 35-residue α-helical Villin HP35 and 37 residue β-sheet Pin WW domains, which had not previously been folded with the same force field. Starting from unfolded configurations, simulations of both proteins in Amber ff03^∗ in explicit solvent fold to within 2.0 Å RMSD of the experimental structures. This demonstrates that a simple backbone correction results in a more transferable force field, an important requirement if simulations are to be used to interpret folding mechanism.     

On the origins of the weak folding cooperativity of a designed ββα ultrafast protein FSD-1

FSD-1, a designed small ultrafast folder with a ββα fold, has been actively studied in the last few years as a model system for studying protein folding mechanisms and for testing of the accuracy of computational models. The suitability of this protein to describe the folding of naturally occurring α/β proteins has recently been challenged based on the observation that the melting transition is very broad, with ill-resolved baselines. Using molecular dynamics simulations with the AMBER protein force field (ff96) coupled with the implicit solvent model (IGB = 5), we shed new light into the nature of this transition and resolve the experimental controversies. We show that the melting transition corresponds to the melting of the protein as a whole, and not solely to the helix-coil transition. The breadth of the folding transition arises from the spread in the melting temperatures (from ∼325 K to ∼302 K) of the individual transitions: formation of the hydrophobic core, β-hairpin and tertiary fold, with the helix formed earlier. Our simulations initiated from an extended chain accurately predict the native structure, provide a reasonable estimate of the transition barrier height, and explicitly demonstrate the existence of multiple pathways and multiple transition states for folding. Our exhaustive sampling enables us to assess the quality of the Amber ff96/igb5 combination and reveals that while this force field can predict the correct native fold, it nonetheless overstabilizes the α-helix portion of the protein (Tm = ∼387K) as well as the denatured structures.     

In silico chaperonin-like cycle helps folding of proteins for structure prediction

Currently, one of the most serious problems in protein-folding simulations for de novo structure prediction is conformational sampling of medium-to-large proteins. In vivo, folding of these proteins is mediated by molecular chaperones. Inspired by the functions of chaperonins, we designed a simple chaperonin-like simulation protocol within the framework of the standard fragment assembly method: in our protocol, the strength of the hydrophobic interaction is periodically modulated to help the protein escape from misfolded structures. We tested this protocol for 38 proteins and found that, using a certain defined criterion of success, our method could successfully predict the native structures of 14 targets, whereas only those of 10 targets were successfully predicted using the standard protocol. In particular, for non-α-helical proteins, our method yielded significantly better predictions than the standard approach. This chaperonin-inspired protocol that enhanced de novo structure prediction using folding simulations may, in turn, provide new insights into the working principles underlying the chaperonin system.     

Structural analysis of kinetic folding intermediates for a TIM barrel protein, indole-3-glycerol phosphate synthase, by hydrogen exchange mass spectrometry and Gō model simulation

The structures of partially folded states appearing during the folding of a (βα)₈ TIM barrel protein, the indole-3-glycerol phosphate synthase from Sulfolobus solfataricus (sIGPS), was assessed by hydrogen exchange mass spectrometry (HX-MS) and Gō model simulations. HX-MS analysis of the peptic peptides derived from the pulse-labeled product of the sub-millisecond folding reaction from the urea-denatured state revealed strong protection in the (βα)₄ region, modest protection in the neighboring (βα)_1-3 and (βα)₅β₆ segments and no significant protection in the remaining N and C-terminal segments. These results demonstrate that this species is not a collapsed form of the unfolded state under native-favoring conditions nor is it the native state formed via fast-track folding. However, the striking contrast of these results with the strong protection observed in the (βα)_2-5β₆ region after 5 s of folding demonstrates that these species represent kinetically distinct folding intermediates that are not identical as previously thought. A re-examination of the kinetic folding mechanism by chevron analysis of fluorescence data confirmed distinct roles for these two species: the burst-phase intermediate is predicted to be a misfolded, off-pathway intermediate, while the subsequent 5 s intermediate corresponds to an on-pathway equilibrium intermediate. Comparison with the predictions using a C^α Gō model simulation of the kinetic folding reaction for sIGPS shows good agreement with the core of the structure offering protection against exchange in the on-pathway intermediate(s). Because the native-centric Gō model simulations do not explicitly include sequence-specific information, the simulation results support the hypothesis that the topology of TIM barrel proteins is a primary determinant of the folding free energy surface for the productive folding reaction. The early misfolding reaction must involve aspects of non-native structure not detected by the Gō model simulation.     

Ubr1 and Ubr2 Function in a Quality Control Pathway for Degradation of Unfolded Cytosolic Proteins

Quality control systems facilitate polypeptide folding and degradation to maintain protein homeostasis. Molecular chaperones promote folding, whereas the ubiquitin/proteasome system mediates degradation. We show here that Saccharomyces cerevisiae Ubr1 and Ubr2 ubiquitin ligases promote degradation of unfolded or misfolded cytosolic polypeptides. Ubr1 also catalyzes ubiquitinylation of denatured but not native luciferase in a purified system. This activity is based on the direct interaction of denatured luciferase with Ubr1, although Hsp70 stimulates polyubiquitinylation of the denatured substrate. We also report that loss of Ubr1 and Ubr2 function suppressed the growth arrest phenotype resulting from chaperone mutation. This correlates with increased protein kinase maturation and indicates partitioning of foldable conformers toward the proteasome. Our findings, based on the efficiency of this quality control system, suggest that the cell trades growth potential to avert the potential toxicity associated with accumulation of unfolded or misfolded proteins. Ubr1 and Ubr2 therefore represent E3 components of a novel quality control pathway for proteins synthesized on cytosolic ribosomes.     

The C-terminal Tails of the Bacterial Chaperonin GroEL Stimulate Protein Folding by Directly Altering the Conformation of a Substrate Protein

Many essential cellular proteins fold only with the assistance of chaperonin machines like the GroEL-GroES system of Escherichia coli. However, the mechanistic details of assisted protein folding by GroEL-GroES remain the subject of ongoing debate. We previously demonstrated that GroEL-GroES enhances the productive folding of a kinetically trapped substrate protein through unfolding, where both binding energy and the energy of ATP hydrolysis are used to disrupt the inhibitory misfolded states. Here, we show that the intrinsically disordered yet highly conserved C-terminal sequence of the GroEL subunits directly contributes to substrate protein unfolding. Interactions between the C terminus and the non-native substrate protein alter the binding position of the substrate protein on the GroEL apical surface. The C-terminal tails also impact the conformational state of the substrate protein during capture and encapsulation on the GroEL ring. Importantly, removal of the C termini results in slower overall folding, reducing the fraction of the substrate protein that commits quickly to a productive folding pathway and slowing several kinetically distinct folding transitions that occur inside the GroEL-GroES cavity. The conserved C-terminal tails of GroEL are thus important for protein folding from the beginning to the end of the chaperonin reaction cycle.     

Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model

We develop a coarse-grained protein model with a simplified amino acid interaction potential. Using this model, we perform discrete molecular dynamics folding simulations of a small 20-residue protein--Trp-cage--from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2-angstroms backbone root-mean-square distance from the corresponding NMR structures. The minimum root-mean-square distance of Trp-cage conformations in simulations can be <1 angstroms. Our findings suggest that, at least in the case of Trp-cage, a detailed all-atom protein model with a molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success of folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulation studies may be mainly due to the special stabilizing features specific to this miniprotein.