Dimerization of the p53 oligomerization domain: identification of a folding nucleus by molecular dynamics simulations

Dimerization of the p53 oligomerization domain involves coupled folding and binding of monomers. To examine the dimerization, we have performed molecular dynamics (MD) simulations of dimer folding from the rate-limiting transition state ensemble (TSE). Among 799 putative transition state structures that were selected from a large ensemble of high-temperature unfolding trajectories, 129 were identified as members of the TSE via calculation of a 50% transmission coefficient from at least 20 room-temperature simulations. This study is the first to examine the refolding of a protein dimer using MD simulations in explicit water, revealing a folding nucleus for dimerization. Our atomistic simulations are consistent with experiment and offer insight that was previously unobtainable.     

Topological frustration and the folding of interleukin-1 beta

The cytokine, interleukin-1beta (IL-1beta), adopts a beta-trefoil fold. It is known to be much slower folding than similarly sized proteins, despite having a low contact order. Proteins are sufficiently well designed that their folding is not dominated by local energetic traps. Therefore, protein models that encode only the folded structure and are energetically unfrustrated (Gō-type), can capture the essentials of the folding routes. We investigate the folding thermodynamics of IL-1beta using such a model and molecular dynamics (MD) simulations. We develop an enhanced sampling technique (a modified multicanonical method) to overcome the sampling problem caused by the slow folding. We find that IL-1beta has a broad and high free energy barrier. In addition, the protein fold causes intermediate unfolding and refolding of some native contacts within the protein along the folding trajectory. This "backtracking" occurs around the barrier region. Complex folds like the beta-trefoil fold and functional loops like the beta-bulge of IL-1beta can make some of the configuration space unavailable to the protein and cause topological frustration.     

Commitment and nucleation in the protein G transition state

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.     

Reconstruction of the src-SH3 protein domain transition state ensemble using multiscale molecular dynamics simulations

We use an integrated computational approach to reconstruct accurately the transition state ensemble (TSE) for folding of the src-SH3 protein domain. We first identify putative TSE conformations from free energy surfaces generated by importance sampling molecular dynamics for a fully atomic, solvated model of the src-SH3 protein domain. These putative TSE conformations are then subjected to a folding analysis using a coarse-grained representation of the protein and rapid discrete molecular dynamics simulations. Those conformations that fold to the native conformation with a probability (P(fold)) of approximately 0.5, constitute the true transition state. Approximately 20% of the putative TSE structures were found to have a P(fold) near 0.5, indicating that, although correct TSE conformations are populated at the free energy barrier, there is a critical need to refine this ensemble. Our simulations indicate that the true TSE conformations are compact, with a well-defined central beta sheet, in good agreement with previous experimental and theoretical studies. A structured central beta sheet was found to be present in a number of pre-TSE conformations, however, indicating that this element, although required in the transition state, does not define it uniquely. An additional tight cluster of contacts between highly conserved residues belonging to the diverging turn and second beta-sheet of the protein emerged as being critical elements of the folding nucleus. A number of commonly used order parameters to identify the transition state for folding were investigated, with the number of native Cbeta contacts displaying the most satisfactory correlation with P(fold) values.     

Unfolding transition state and intermediates of the tumor suppressor p16INK4a investigated by molecular dynamics simulations

The ankyrin repeat is one of the most common protein motifs and is involved in protein-protein interactions. It consists of 33 residues that assume a beta-hairpin helix-loop-helix fold. Mutagenesis and kinetic experiments (Phi-value analysis of the folding transition state) have shown that the tumor suppressor p16(INK4a), a four-repeat protein, unfolds sequentially starting from the two N-terminal repeats. Here, the flexibility of p16(INK4a) at room temperature and its unfolding mechanism at high temperature have been investigated by multiple molecular dynamics runs in explicit water for a total simulation time of 0.65 micros. The transition state ensemble (TSE) of p16(INK4a) was identified by monitoring both the deviation from the experimental Phi values and sudden conformational changes along the unfolding trajectories. Conformations in the TSE have a mainly unstructured second repeat whereas the other repeats are almost completely folded. A rigid-body displacement of the first repeat involving both a rotation and translation is observed in all molecular dynamics simulations at high temperature. The Trp(15), Pro(75), and Ala(76) side-chains are more buried in the TSE than the native state. The sequential unfolding starting at the second repeat is in agreement with the mutagenesis studies whereas the displacement of the first repeat and the presence of nonnative interactions at the TSE are simulation results which supplement the experimental data. Furthermore, the unfolding trajectories reveal the presence of two on-pathway intermediates with partial alpha-helical structure. Finally, on the basis of the available experimental and simulation results we suggest that in modular proteins the shift of the folding TSE toward the native structure upon reduction of the number of tandem repeats is consistent with the Hammond effect.     

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.     

Study of the Villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics

The folding mechanism of the Villin headpiece (HP36) is studied by means of a novel approach which entails an initial coarse-grained Monte Carlo (MC) scheme followed by all-atom molecular dynamics (MD) simulations in explicit solvent. The MC evolution occurs in a simplified free-energy landscape and allows an efficient selection of marginally-compact structures which are taken as viable initial conformations for the MD. The coarse-grained MC structural representation is connected to the one with atomic resolution through a "fine-graining" reconstruction algorithm. This two-stage strategy is used to select and follow the dynamics of seven different unrelated conformations of HP36. In a notable case the MD trajectory rapidly evolves towards the folded state, yielding a typical root-mean-square deviation (RMSD) of the core region of only 2.4 A from the closest NMR model (the typical RMSD over the whole structure being 4.0 A). The analysis of the various MC-MD trajectories provides valuable insight into the details of the folding and mis-folding mechanisms and particularly about the delicate influence of local and nonlocal interactions in steering the folding process.     

Parallel folding pathways in the SH3 domain protein

The transition-state ensemble (TSE) is the set of protein conformations with an equal probability to fold or unfold. Its characterization is crucial for an understanding of the folding process. We determined the TSE of the src-SH3 domain protein by using extensive molecular dynamics simulations of the Go model and computing the folding probability of a generated set of TSE candidate conformations. We found that the TSE possesses a well-defined hydrophobic core with variable enveloping structures resulting from the superposition of three parallel folding pathways. The most preferred pathway agrees with the experimentally determined TSE, while the two least preferred pathways differ significantly. The knowledge of the different pathways allows us to design the interactions between amino acids that guide the protein to fold through the least preferred pathway. This particular design is akin to a circular permutation of the protein. The finding motivates the hypothesis that the different experimentally observed TSEs in homologous proteins and circular permutants may represent potentially available pathways to the wild-type protein.     

Unfolding of hen egg lysozyme by molecular dynamics simulations at 300K: insight into the role of the interdomain interface

We present the results of two 1.2 ns molecular dynamics (MD) unfolding simulations on hen egg lysozyme in water at 300K, performed using a new procedure called PEDC (Path Exploration With Distance Constraints). This procedure allows exploration of low energy structures as a function of increasing RMSD from the native structure, and offers especially the possibility of extensive exploration of the conformational space during the initial unfolding stages. The two independent MD simulations gave similar chronology of unfolding events: disruption of the active site, kinking of helix C, partial unfolding of the three-stranded beta-sheet to a two-stranded sheet (during which the helices A, B, and D remain to a great extent native), and finally unfolding of the beta-domain and partial unfolding of the alpha-domain in which hydrophobic clusters persist. We show particularly that the loss of hydrophobic contacts between the beta-sheet turn residues Leu55 and Ile56 and the hydrobic patch of the alpha-domain destabilizes the beta-domain and leads to its unfolding, suggesting that the correct embedding of these residues in the alpha-beta interface may constitute the rate limiting step in folding. These results are in accord with experimental observations on the folding/unfolding behavior of hen egg lysozyme at room temperature. They would also explain the loss of stability and the tendency to aggregation observed for the mutant Leu55Thr, and the slow refolding kinetics observed in the analogous amyloidogenic variant of human lysozyme.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C^α chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.     

Chevron behavior and isostable enthalpic barriers in protein folding: successes and limitations of simple Gō-like modeling

It has been demonstrated that a "near-Levinthal" cooperative mechanism, whereby the common Gō interaction scheme is augmented by an extra favorability for the native state as a whole, can lead to apparent two-state folding/unfolding kinetics over a broad range of native stabilities in lattice models of proteins. Here such a mechanism is shown to be generalizable to a simplified continuum (off-lattice) Langevin dynamics model with a Calpha protein chain representation, with the resulting chevron plots exhibiting an extended quasilinear regime reminiscent of that of apparent two-state real proteins. Similarly high degrees of cooperativity are possible in Gō-like continuum models with rudimentary pairwise desolvation barriers as well. In these models, cooperativity increases with increasing desolvation barrier height, suggesting strongly that two-state-like folding/unfolding kinetics would be achievable when the pairwise desolvation barrier becomes sufficiently high. Besides cooperativity, another generic folding property of interest that has emerged from published experiments on several apparent two-state proteins is that their folding relaxation under constant native stability (isostability) conditions is essentially Arrhenius, entailing high intrinsic enthalpic folding barriers of approximately 17-30 kcal/mol. Based on a new analysis of published data on barnase, here we propose that a similar property should also apply to a certain class of non-two-state proteins that fold with chevron rollovers. However, several continuum Gō-like constructs considered here fail to predict any significant intrinsic enthalpic folding barrier under isostability conditions; thus the physical origin of such barriers in real proteins remains to be elucidated.     

Predicting Atomic Details of the Unfolding Pathway for YibK,a Knotted Protein from the SPOUT Superfamily

Abstract

Several protein structures have been reported to contain intricate knots of the polypeptide backbone but the mechanism of the (un)folding process of knotted proteins remains unknown. The members of the SPOUT superfamily of RNA methyltransferases are some of the most intensely studied systems for investigation of the knot formation and function. YibK (whose biochemical function remains unknown) is the representative protein of the SPOUT superfamily. This protein exhibits a deep trefoil knot at the C-terminus.

We conducted an extensive computational analysis of the unfolding process for the monomeric form of YibK. In order to predict the (un)folding pathway of YibK, we have calculated the order of secondary structure disassembly using UNFOLD, and performed thermal unfolding simulations using classical Molecular Dynamics (MD), as well as simulations employing reduced representation of the peptide chain using either MD with the UNRES method or the Monte Carlo (MC) unfolding with the REFINER method.

Results obtained from all methods used in this work are in qualitative agreement. We found that YibK unfolds through four intermediate states. The trefoil knot in YibK disappears at the end of the unfolding process, long after the protein loses its native topology. We observed that the C-terminus leaves the knotting loop folded into a hairpin-like structure, in agreement with the results of coarse-grained simulation reported earlier. We propose that the folding pathway of YibK corresponds to the reversed sequence of events observed in the unfolding pathway elucidated in this study. Thus, we predict that the knot formation is the slowest part of the YibK folding process.     

Phi-analysis at the experimental limits: mechanism of beta-hairpin formation

The 37-residue Formin-binding protein, FBP28, is a canonical three-stranded beta-sheet WW domain. Because of its small size, it is so insensitive to chemical denaturation that it is barely possible to determine accurately a denaturation curve, as the transition spans 0-7 M guanidinium hydrochloride (GdmCl). It is also only marginally stable, with a free energy of denaturation of just 2.3 kcal/mol at 10 degrees Celsius so only small changes in energy upon mutation can be tolerated. But these properties and relaxation times for folding of 25 micros-400 micros conspire to allow the rapid acquisition of accurate and reproducible kinetic data for Phi-analysis using classical temperature-jump methods. The transition state for folding is highly polarized with some regions having Phi-values of 0 and others 1, as readily seen in chevron plots, with Phi-values of 0 having the refolding arms overlaying and those of 1 the unfolding arms superimposable. Good agreement is seen with transition state structures identified from independent molecular dynamics (MD) simulations at 60, 75, and 100 degrees Celsius, which allows us to explore further the details of the folding and unfolding pathway of FBP28. The first beta-turn is near native-like in the transition state for folding (experimental) and unfolding (MD and experiment). The simulations show that there are transient contacts between the aromatic side-chains of the beta-strands in the denatured state and that these interactions provide the driving force for folding of the first beta-hairpin of this three-stranded sheet. Only after the backbone hydrogen bonds are formed between beta1 and beta2 does a hydrogen bond form to stabilize the intervening turn, or the first beta-turn.     

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.     

Mechanical unfolding of a beta-hairpin using molecular dynamics

Single-molecule mechanical unfolding experiments have the potential to provide insights into the details of protein folding pathways. To investigate the relationship between force-extension unfolding curves and microscopic events, we performed molecular dynamics simulations of the mechanical unfolding of the C-terminal hairpin of protein G. We have studied the dependence of the unfolding pathway on pulling speed, cantilever stiffness, and attachment points. Under conditions that generate low forces, the unfolding trajectory mimics the untethered, thermally accessible pathway previously proposed based on high-temperature studies. In this stepwise pathway, complete breakdown of backbone hydrogen bonds precedes dissociation of the hydrophobic cluster. Under more extreme conditions, the cluster and hydrogen bonds break simultaneously. Transitions between folding intermediates can be identified in our simulations as features of the calculated force-extension curves.     

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.     

Molecular dynamics simulations of N-terminal peptides from a nucleotide binding protein

Molecular dynamics (MD) simulations of N-terminal peptides from lactate dehydrogenase (LDH) with increasing length and individual secondary structure elements were used to study their stability in relation to folding. Ten simulations of 1–2 ns of different peptides in water starting from the coordinates of the crystal structure were performed. The stability of the peptides was compared qualitatively by analyzing the root mean square deviation (RMSD) from the crystal structure, radius of gyration, secondary and tertiary structure, and solvent accessible surface area. In agreement with earlier MD studies, relatively short (< 15 amino acids) peptides containing individual secondary structure elements were generally found to be unstable; the hydrophobic α₁-helix of the nucleotide binding fold displayed a significantly higher stability, however. Our simulations further showed that the first βαβ supersecondary unit of the characteristic dinucleotide binding fold (Rossmann fold) of LDH is somewhat more stable than other units of similar length and that the α₂-helix, which unfolds by itself, is stabilized by binding to this unit. This finding suggests that the first βαβ unit could function as an N-terminal folding nucleus, upon which the remainder of the polypeptide chain can be assembled. Indeed, simulations with longer units (βαβα and βαβαββ) showed that all structural elements of these units are rather stable. The outcome of our studies is in line with suggestions that folding of the N-terminal portion of LDH in vivo can be a cotranslational process that takes place during the ribosomal peptide synthesis.     

Protein folding and unfolding simulations: a new challenge for data mining

One of the unsolved paradigms in molecular biology is the protein folding problem. In recent years, with the identification of several diseases as protein folding disorders and with the explosion of genome information and the need for efficient ways to predict protein structure, protein folding became a central issue in molecular sciences research. Using molecular dynamics unfolding simulations of an amyloidogenic protein--transthyretin--as an example, we put forward a series of ideas on how simulations of this type may be used to infer rules and unfolding behavior in amyloidogenic proteins, and to extrapolate rules for protein folding in different structural classes of proteins. These, in turn, could help in the development of protein structure prediction methods. The need to analyse different proteins and to run multiple simulations creates a huge amount of data which has to be stored, managed, analyzed and shared (database and Grid technology; data mining). Once the data is captured, the next challenge is to find meaningful patterns (associations, correlations, clusters, rules, relationships) among molecular properties, or their relative importance at different stages of the folding or unfolding processes. This clearly puts new and interesting challenges to the bioinformatics community.