Comparison of Generalised Born/Surface Area with Periodic Boundary Simulations to Study Protein Unfolding

Simulations comparing the rapid unfolding behaviour of the model protein barnase under explicit and implicit solvent systems have been undertaken in order to validate a faster implicit solvent method for studying proteins which are kinetically stable in silico. A comparison is made between all-atom explicitly solvated simulations of barnase undertaken using Particle Mesh Ewald electrostatic interactions with all-atom implicit solvent simulations undertaken using the generalised born/surface area (GBSA) method with a long non-bonded cut-off. The two explicit solvent unfolding trajectories appear to explore slightly different pathways showing the importance of having statistically valid ensembles which are not accessible from a single trajectory. The 500?K GBSA trajectory is unsuitable for exploring intermediate structures on the unfolding pathway of barnase, as the protein almost immediately jumps to a predominately random coil conformation. However, dropping the temperature to 400?K gives rise to trajectories where the protein is unable to climb out of the energy well containing the first intermediate state, in a reasonable timescale. A similar pattern to the explicit solvent unfolding trajectories is seen in 450?K GBSA runs, with the intermediate states differing between trajectories. The development of computer simulation methods suitable for application to more kinetically stable proteins will offer insight into the atomic detail of the conformational changes associated with protein unfolding diseases.     

Unfolding pathways of goat alpha-lactalbumin as revealed in multiple alignment of molecular dynamics trajectories

Molecular dynamics simulations of protein unfolding were performed at an elevated temperature for the authentic and recombinant forms of goat alpha-lactalbumin. Despite very similar three-dimensional structures, the two forms have significantly different unfolding rates due to an extra N-terminal methionine in the recombinant protein. To identify subtle differences between the two forms in the highly stochastic kinetics of unfolding, we classified the unfolding trajectories using the multiple alignment method based on the analogy between the biological sequences and the molecular dynamics trajectories. A dendrogram derived from the multiple trajectory alignment revealed a clear difference in the unfolding pathways of the authentic and recombinant proteins, i.e. the former reached the transition state in an all-or-none manner while the latter unfolded less cooperatively. It was also found in the classification that the two forms of the protein shared a common transition state structure, which was in excellent agreement with the transition state structure observed experimentally in the Phi-value analysis.     

Computer simulations of protein folding by targeted molecular dynamics

We have performed 128 folding and 45 unfolding molecular dynamics runs of chymotrypsin inhibitor 2 (CI2) with an implicit solvation model for a total simulation time of 0.4 microseconds. Folding requires that the three-dimensional structure of the native state is known. It was simulated at 300 K by supplementing the force field with a harmonic restraint which acts on the root-mean-square deviation and allows to decrease the distance to the target conformation. High temperature and/or the harmonic restraint were used to induce unfolding. Of the 62 folding simulations started from random conformations, 31 reached the native structure, while the success rate was 83% for the 66 trajectories which began from conformations unfolded by high-temperature dynamics. A funnel-like energy landscape is observed for unfolding at 475 K, while the unfolding runs at 300 K and 375 K as well as most of the folding trajectories have an almost flat energy landscape for conformations with less than about 50% of native contacts formed. The sequence of events, i.e., secondary and tertiary structure formation, is similar in all folding and unfolding simulations, despite the diversity of the pathways. Previous unfolding simulations of CI2 performed with different force fields showed a similar sequence of events. These results suggest that the topology of the native state plays an important role in the folding process.     

Is protein unfolding the reverse of protein folding? A lattice simulation analysis.

Simulations and experiments that monitor protein unfolding under denaturing conditions are commonly employed to study the mechanism by which a protein folds to its native state in a physiological environment. Due to the differences in conditions and the complexity of the reaction, unfolding is not necessarily the reverse of folding. To assess the relevance of temperature initiated unfolding studies to the folding problem, we compare the folding and unfolding of a 125-residue protein model by Monte Carlo dynamics at two temperatures; the lower one corresponds to the range used in T -jump experiments and the higher one to the range used in unfolding simulations of all-atom models. The trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations. At the lower temperature, the system unfolds through a mandatory intermediate that corresponds to a local free energy minimum. At the higher temperature, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble most closely those that make up the "fast track" of folding. The transition state for unfolding at the lower temperature (above Tm) is determined and is found to be more structured than the transition state for folding below the melting temperature. This shift towards the native state is consistent with the Hammond postulate. The implications for unfolding simulations of higher resolution models and for unfolding experiments of proteins are discussed.     

Unfolding of the cold shock protein studied with biased molecular dynamics

The cold shock protein from Bacillus caldolyticus is a small beta-barrel protein that folds in a two-state mechanism. For the native protein and for several mutants, a wealth of experimental data are available on stability and folding, so that it is an optimal system to study this process. We compare data from unfolding simulations (trajectories of 5 and up to 12 ns) obtained with a bias potential at room temperature and from unbiased thermal unfolding simulations with experimental data. The unfolding patterns derived from the trajectories starting from different native-like conformations and subject to different unfolding conditions agree. The transition state found in the simulations of unfolding is close to the native structure in agreement with experiment. Moreover, a lower value of the free energy barrier of unfolding was found for the mutant R3E than for the mutant E46A and the native protein, as indicated by experimental data. The first unfolding event involves the three-stranded beta-sheet whose decomposition corresponds to the transition state. In contrast to conclusions drawn from experiments, we found that the two-stranded beta-strand forms the most stable substructure, which decomposes very late in the unfolding process. However, assuming that this structure forms very early in the folding process, our findings would not contradict the experiments but require a different interpretation of them.     

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.     

Study of multiple unfolding trajectories and unfolded states of the protein GB1 under the physical property space

Forty nine molecular dynamics simulations of unfolding trajectories of the segment B1 of streptococcal protein G (GB1) provide a direct demonstration of the diversity of unfolding pathway and give a statistically utmost unfolding pathway under the physical property space. Twelve physical properties of the protein were chosen to construct a 12-dimensional property space. Then the 12-dimensional property space was reduced to a 3-dimensional principle component property space. Under the property space, the multiple unfolding trajectories look like "trees", which have some common characters. The "root of the tree" corresponds to the native state, the "bole" homologizes the partially unfolded conformations, and the "crown" is in correspondence to the unfolded state. These unfolding trajectories can be divided into three types. The first one has the characters of straight "bole" and "crown" corresponding to a fast two-state unfolding pathway of GB1. The second one has the character of "the standstill in the middle tree bole", which may correspond to a three-state unfolding pathway. The third one has the character of "the circuitous bole" corresponding to a slow two-state unfolding pathway. The fast two-state unfolding pathway is a statistically utmost unfolding pathway or preferred pathway of GB1, which occupies 53% of 49 unfolding trajectories. In the property space all the unfolding trajectories construct a thermal unfolding pathway ensemble of GB1. The unfolding pathway ensemble resembles a funnel that is gradually emanative from the native state ensemble to the unfolded state ensemble. In the property space, the thermal unfolded state distribution looks like electronic cloud in quantum mechanics. The unfolded states of the independent unfolding simulation trajectories have substantial overlaps, indicating that the thermal unfolded states are confined by the physical property values, and the number of protein unfolded state are much less than that was believed before.     

A Comprehensive Multidimensional-Embedded, One-Dimensional Reaction Coordinate for Protein Unfolding/Folding

The goal of the Dynameomics project is to perform, store, and analyze molecular dynamics simulations of representative proteins, of all known globular folds, in their native state and along their unfolding pathways. To analyze unfolding simulations, the location of the protein along the unfolding reaction coordinate (RXN) must be determined. Properties such as the fraction of native contacts and radius of gyration are often used; however, there is an issue regarding degeneracy with these properties, as native and nonnative species can overlap. Here, we used 15 physical properties of the protein to construct a multidimensional-embedded, one-dimensional RXN coordinate that faithfully captures the complex nature of unfolding. The unfolding RXN coordinates for 188 proteins (1534 simulations and 22.9 μs in explicit water) were calculated. Native, transition, intermediate, and denatured states were readily identified with the use of this RXN coordinate. A global native ensemble based on the native-state properties of the 188 proteins was created. This ensemble was shown to be effective for calculating RXN coordinates for folds outside the initial 188 targets. These RXN coordinates enable, high-throughput assignment of conformational states, which represents an important step in comparing protein properties across fold space as well as characterizing the unfolding of individual proteins.     

On the roles of substrate binding and hinge unfolding in conformational changes of adenylate kinase

We characterized the conformational change of adenylate kinase (AK) between open and closed forms by conducting five all-atom molecular-dynamics simulations, each of 100 ns duration. Different initial structures and substrate binding configurations were used to probe the pathways of AK conformational change in explicit solvent, and no bias potential was applied. A complete closed-to-open and a partial open-to-closed transition were observed, demonstrating the direct impact of substrate-mediated interactions on shifting protein conformation. The sampled configurations suggest two possible pathways for connecting the open and closed structures of AK, affirming the prediction made based on available x-ray structures and earlier works of coarse-grained modeling. The trajectories of the all-atom molecular-dynamics simulations revealed the complexity of protein dynamics and the coupling between different domains during conformational change. Calculations of solvent density and density fluctuations surrounding AK did not show prominent variation during the transition between closed and open forms. Finally, we characterized the effects of local unfolding of an important hinge near Pro¹⁷⁷ on the closed-to-open transition of AK and identified a novel mechanism by which hinge unfolding modulates protein conformational change. The local unfolding of Pro¹⁷⁷ hinge induces alternative tertiary contacts that stabilize the closed structure and prevent the opening transition.     

Polymer principles of protein calorimetric two-state cooperativity

The experimental calorimetric two-state criterion requires the van't Hoff enthalpy DeltaH(vH) around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy DeltaH(cal) of the entire transition. We use an analytical model with experimental parameters from chymotrypsin inhibitor 2 to elucidate the relationship among several different van't Hoff enthalpies used in calorimetric analyses. Under reasonable assumptions, the implications of these DeltaH(vH)'s being approximately equal to DeltaH(cal) are equivalent: Enthalpic variations among denatured conformations in real proteins are much narrower than some previous lattice-model estimates, suggesting that the energy landscape theory "folding to glass transition temperature ratio" T(f) /T(g) may exceed 6.0 for real calorimetrically two-state proteins. Several popular three-dimensional lattice protein models, with different numbers of residue types in their alphabets, are found to fall short of the high experimental standard for being calorimetrically two-state. Some models postulate a multiple-conformation native state with substantial pre-denaturational energetic fluctuations well below the unfolding transition temperature, or predict a significant post-denaturational continuous conformational expansion of the denatured ensemble at temperatures well above the transition point, or both. These scenarios either disagree with experiments on protein size and dynamics, or are inconsistent with conventional interpretation of calorimetric data. However, when empirical linear baseline subtractions are employed, the resulting DeltaH(vH)/DeltaH(cal)'s for some models can be increased to values closer to unity, and baseline subtractions are found to correspond roughly to an operational definition of native-state conformational diversity. These results necessitate a re-assessment of theoretical models and experimental interpretations.     

Structure of an Unfolding Intermediate of an RRM Domain of ETR-3 Reveals Its Native-like Fold

Prevalence of one or more partially folded intermediates during protein unfolding with different secondary and ternary conformations has been identified as an integral character of protein unfolding. These transition-state species need to be characterized structurally for elucidation of their folding pathways. We have determined the three-dimensional structure of an intermediate state with increased conformational space sampling under urea-denaturing condition. The protein unfolds completely at 10 M urea but retains residual secondary structural propensities with restricted motion. Here, we describe the native state, observable intermediate state, and unfolded state for ETR-3 RRM-3, which has canonical RRM fold. These observations can shed more light on unfolding events for RRM-containing proteins.     

Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Formation of the folding nucleus of an SH3 domain investigated by loosely coupled molecular dynamics simulations

The experimentally well-established folding mechanism of the src-SH3 domain, and in particular the phi-value analysis of its transition state, represents a sort of testing table for computational investigations of protein folding. Here, parallel molecular dynamics simulations of the src-SH3 domain have been performed starting from denatured conformations. By rescuing and restarting only trajectories approaching the folding transition state, an ensemble of conformations was obtained with a completely structured central beta-sheet and a native-like packing of residues Ile-110, Ala-121, and Ile-132. An analysis of the trajectories shows that there are several pathways leading to the formation of the central beta-sheet whereas its two hairpins form in a different but consistent way.     

Dual energy landscape: the functional state of the β-barrel outer membrane protein G molds its unfolding energy landscape

We applied dynamic single-molecule force spectroscopy to quantify the parameters (free energy of activation and distance of the transition state from the folded state) characterizing the energy barriers in the unfolding energy landscape of the outer membrane protein G (OmpG) from Escherichia coli. The pH-dependent functional switching of OmpG directs the protein along different regions on the unfolding energy landscape. The two functional states of OmpG take the same unfolding pathway during the sequential unfolding of β-hairpins I-IV. After the initial unfolding events, the unfolding pathways diverge. In the open state, the unfolding of β-hairpin V in one step precedes the unfolding of β-hairpin VI. In the closed state, β-hairpin V and β-strand S11 with a part of extracellular loop L6 unfold cooperatively, and subsequently β-strand S12 unfolds with the remaining loop L6. These two unfolding pathways in the open and closed states join again in the last unfolding step of β-hairpin VII. Also, the conformational change from the open to the closed state witnesses a rigidified extracellular gating loop L6. Thus, a change in the conformational state of OmpG not only bifurcates its unfolding pathways but also tunes its mechanical properties for optimum function.     

Multiscale computational study of ligand binding pathways: Case of p38 MAP kinase and its inhibitors

Protein kinases are one of the most important drug targets in the past 10 years. Understanding the inhibitor association processes will profoundly impact new binder designs with preferred binding kinetics. However, after more than a decade of effort, a complete atomistic-level study of kinase inhibitor binding pathways is still lacking. As all kinases share a similar scaffold, we used p38 kinase as a model system to investigate the conformational dynamics and free energy transition of inhibitor binding toward kinases. Two major kinase conformations, Asp-Phe-Gly (DFG)-in and DFG-out, and three types of inhibitors, type I, II, and III, were thoroughly investigated in this work. We performed Brownian dynamics simulations and up to 340 μs Gaussian-accelerated molecular dynamics simulations to capture the inhibitor binding paths and a series of conformational transitions of the p38 kinase from its apo to inhibitor-bound form. Eighteen successful binding trajectories, including all types of inhibitors, are reported herein. Our simulations suggest a mechanism of inhibitor recruitment, a faster ligand association step to a pre-existing DFG-in/DFG-out p38 protein, followed by a slower molecular rearrangement step to adjust the protein-ligand conformation followed by a shift in the energy landscape to reach the final bound state. The ligand association processes also reflect the energetic favor of type I and type II/III inhibitor binding through ATP and allosteric channels, respectively. These different binding routes are directly responsible for the fast (type I binders) and slow (type II/III binders) kinetics of different types of p38 inhibitors. Our findings also echo the recent study of p38 inhibitor dissociation, implying that ligand unbinding could undergo a reverse path of binding, and both processes share similar metastates. This study deepens the understanding of molecular and energetic features of kinase inhibitor-binding processes and will inspire future drug development from a kinetic point of view.     

Simulations of human lysozyme: probing the conformations triggering amyloidosis

A natural mutant of human lysozyme, D67H, causes hereditary systemic nonneuropathic amyloidosis, which can be fatal. In this disease, insoluble beta-stranded fibrils (amyloids) are found in tissues stemming from the aggregation of partially folded intermediates of the mutant. In this study, we specifically compare the conformation and properties of the structures adopted from the induced unfolding, at elevated temperature, using molecular dynamics. To increase the sampling of the unfolding conformational landscape, three 5 ns trajectories are performed for each of the wild-type and mutant D67H proteins resulting in a total of 30 ns simulation. Our results show that the mutant unfolds slightly faster than the wild-type with both wild-type and mutant proteins losing most of their native secondary structure within the first 2 ns. They both develop random transient beta-strands across the whole polypeptide chain. Clustering analysis of all the conformations shows that a high population of the mutant protein conformations have a distorted beta-domain. This is consistent with experimental results suggesting that this region is pivotal in the formation of conformations prone to act as "seeds" for amyloid fiber formation.     

Abstracts: Albany 2007, The 15th Conversation

Abstract

Forty nine molecular dynamics simulations of unfolding trajectories of the segment B1 of streptococcal protein G (GB1) provide a direct demonstration of the diversity of unfolding pathway and give a statistically utmost unfolding pathway under the physical property space. Twelve physical properties of the protein were chosen to construct a 12-dimensional property space. Then the 12-dimentional property space was reduced to a 3-dimentional principle component property space. Under the property space, the multiple unfolding trajectories look like “trees”, which have some common characters. The “root of the tree” corresponds to the native state, the “bole” homologizes the partially unfolded conformations, and the “crown” is in correspondence to the unfolded state. These unfolding trajectories can be divided into three types. The first one has the characters of straight “bole” and “crown” corresponding to a fast two-state unfolding pathway of GB1. The second one has the character of “the standstill in the middle tree bole”, which may correspond to a three-state unfolding pathway. The third one has the character of “the circuitous bole” corresponding to a slow two-state unfolding pathway. The fast two-state unfolding pathway is a statistically utmost unfolding pathway or preferred pathway of GB1, which occupies 53% of 49 unfolding trajectories. In the property space all the unfolding trajectories construct a thermal unfolding pathway ensemble of GB1. The unfolding pathway ensemble resembles a funnel that is gradually emanative from the native state ensemble to the unfolded state ensemble. In the property space, the thermal unfolded state distribution looks like electronic cloud in quantum mechanics. The unfolded states of the independent unfolding simulation trajectories have substantial overlaps, indicating that the thermal unfolded states are confined by the physical property values, and the number of protein unfolded state are much less than that was believed before.     

Wild type, mutant protein unfolding and phase transition detected by single-nanopore recording

Understanding protein folding remains a challenge. A difficulty is to investigate experimentally all the conformations in the energy landscape. Only single molecule methods, fluorescence and force spectroscopy, allow observing individual molecules along their folding pathway. Here we observe that single-nanopore recording can be used as a new single molecule method to explore the unfolding transition and to examine the conformational space of native or variant proteins. We show that we can distinguish unfolded states from partially folded ones with the aerolysin pore. The unfolding transition curves of the destabilized variant are shifted toward the lower values of the denaturant agent compared to the wild type protein. The dynamics of the partially unfolded wild type protein follows a first-order transition. The denaturation curve obtained with the aerolysin pore is similar to that obtained with the α-hemolysin pore. The nanopore geometry or net charge does not influence the folding transition but changes the dynamics.