Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

Application of biasing‐potential replica‐exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target‐template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP‐REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP‐REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T‐REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP‐REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Conformational flexibility of N-glycans in solution studied by REMD simulations

Protein–glycan recognition regulates a wide range of biological and pathogenic processes. Conformational diversity of glycans in solution is apparently incompatible with specific binding to their receptor proteins. One possibility is that among the different conformational states of a glycan, only one conformer is utilized for specific binding to a protein. However, the labile nature of glycans makes characterizing their conformational states a challenging issue. All-atom molecular dynamics (MD) simulations provide the atomic details of glycan structures in solution, but fairly extensive sampling is required for simulating the transitions between rotameric states. This difficulty limits application of conventional MD simulations to small fragments like di- and tri-saccharides. Replica-exchange molecular dynamics (REMD) simulation, with extensive sampling of structures in solution, provides a valuable way to identify a family of glycan conformers. This article reviews recent REMD simulations of glycans carried out by us or other research groups and provides new insights into the conformational equilibria of N-glycans and their alteration by chemical modification. We also emphasize the importance of statistical averaging over the multiple conformers of glycans for comparing simulation results with experimental observables. The results support the concept of “conformer selection” in protein–glycan recognition.     

Characterization of the internal dynamics and conformational space of zinc-bound amyloid β peptides by replica-exchange molecular dynamics simulations

Amyloid β (Aβ) peptides and metal ions have been associated with the pathogenesis of Alzheimer’s disease. The conformational space of Aβ fragments of different length with and without binding of metal ions has been extensively investigated by replica-exchange molecular dynamics (REMD) simulation. However, only trajectories extracted at relatively low temperatures have been used for this analysis. The capability of REMD simulations to characterize the internal dynamics of such intrinsically disordered proteins (IDPs) as Aβ has been overlooked. In this work, we use an approach recently developed by Xue and Skrynnikov (J Am Chem Soc 133:14614–14628, 2011) to calculate NMR observables, including ¹⁵N relaxation rates and ¹⁵N–¹H nuclear Overhauser enhancement (NOE), from the high-temperature trajectory of REMD simulations for zinc-bound Aβ peptides. The time axis of the trajectory was rescaled to correct for the effect of the high temperature (408 K) compared with the experimental temperature (278 K). Near-quantitative agreement between simulated values and experimental results was obtained. When the structural properties and free-energy surfaces of zinc-bound Aβ_(1–40) and Aβ_(1–42) were compared at the physiological temperature 310 K it was found that zinc-bound Aβ_(1–42) was more rigid than Aβ_(1–40) at the C terminus, and its conformational transitions were also more preferred. The self-consistent results derived from trajectories at high and low temperatures demonstrate the capability of REMD simulations to capture the internal dynamics of IDPs.     

The investigation of the secondary structure propensities and free-energy landscapes of peptide ligands by replica exchange molecular dynamics simulations

The conformational states of two peptide sequences that bind to staphylococcal enterotoxin B are sampled by replica exchange molecular dynamic (REMD) simulations in explicit water. REMD simulations were treated with 52 replicas in the range of 280–501 K for both peptides. The conformational ensembles of both peptides are dominated by random coil, bend and turn structures with a small amount of helical structures for each temperature. In addition, while an insignificant presence of β-bridge structures were observed for both peptides, the β-sheet structure was observed only for peptide 3. The results obtained from simulations at 300 K are consistent with the experimental results obtained from circular dichroism spectroscopy. From the analysis of REMD results, we also calculated hydrophobic and hydrophilic solvent accessible surface areas for both peptides, and it was observed that the hydrophobic segments of the peptides tend to form bend or turn structures. Moreover, the free-energy landscapes of both peptides were obtained by principal component analysis to understand how the secondary structural properties change according to their complex space. From the free-energy analysis, we have found several minima for both peptides at decreased temperature. For these obvious minima of both peptides, it was observed that the random coil, bend and turn structures are still dominant and the helix, β-bridge or β-sheet structures can appear or disappear with respect to minima. On the other hand, when we compare the results of REMD with conventional MD simulations for these peptides, the configurations of peptide 3 might be trapped in energy minima during the conventional MD simulations. Hence, it can be said that the REMD simulations have provided a sufficiently high sampling efficiency.     

Structure and energy landscape of a photoswitchable peptide: a replica exchange molecular dynamics study

A replica exchange molecular dynamics (REMD) simulation of a bicyclic azobenzene peptide in explicit dimethyl sulfoxide solution is presented in order to characterize the conformational structures and energy landscape of a photoswitchable peptide. It is shown that an enhanced-sampling technique such as the REMD method is essential to obtain a converged conformational sampling of the peptide at room temperature. This is because conventional MD simulations of less than approximately 100-ns length are either trapped in local minima (at 295 K) or-if run at high temperature-do not resemble the room-temperature REMD results. Calculating various nuclear Overhauser effects (NOEs) and (3)J-couplings, a good overall agreement between the REMD simulations and the NMR experiments of Renner et al. (Biopolymers 2000;54:501-514) is found. In particular, the REMD study confirms the general picture drawn by Renner et al. that the trans-isomer of the azobenzene peptide exhibits a well-defined structure, while the cis-isomer is a conformational heterogeneous system; that is, the trans-isomer occurs in 2 well-defined conformers, while the cis-isomer represents an energetically frustrated system that leads to an ensemble of conformational structures. Employing a principal component analysis of the REMD data, the free energy landscape of the systems is studied at various temperatures. The implications for the folding and unfolding pathways of the system are discussed.     

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.     

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.     

Structural elucidation of type III group B Streptococcus capsular polysaccharide using molecular dynamics simulations: the role of sialic acid

The conformational properties of the capsular polysaccharide (CPS) from group B Streptococcus serotype III (GBS III) are derived from 50 ns explicitly solvated molecular dynamics simulations of a 25-residue fragment of the CPS. The results from the simulations are shown to be consistent with experimental NMR homo- and heteronuclear J-coupling and NOE data for both the sialylated native CPS and for the chemically desialylated polysaccharide. A helical structure is predicted with a diameter of 29.3 A and a pitch 89.5 A, in which the sialylated side chains are arrayed on the exterior surface of the helix. The results provide an explanation for the observation that CPS antigenicity varies with carbohydrate chain length up to approximately 4 pentasaccharide repeat units. The conformation of the immunodominant region is established and shown to be independent of the presence of sialic acid. The data provide an explanation for the observation that the specificity of the determinant, associated with the major population of antibodies raised upon immunization of rabbits with GBS III, is dependent on the presence of sialic acid. In the sialylated native CPS, the antibody response is largely directed against the immunodominant core of the helix. From simulations of the desialylated CPS, a model emerges which suggests that the minor population of antibodies, whose determinant is not sialic acid dependent, recognizes the same immunodominant region, but that in the disordered CPS this region is not presented in a regular repeating motif.     

Solution NMR and computer simulation studies of active site loop motion in triosephosphate isomerase

Solution NMR spin relaxation experiments and classical MD simulations are used to study the dynamics of triosephosphate isomerase (TIM) in complex with glycerol 3-phosphate (G3P). Three regions in TIM exhibit conformational transitions on the micros-ms time scale as detected by chemical exchange broadening effects in NMR spectroscopy: residue Lys 84 on helix C, located at the dimeric interface; active site loop 6; and helix G. The results indicate that the conformational exchange process affecting the residues of loop 6 is the correlated opening and closing of the loop. Distinct processes are responsible for the chemical exchange linebroadening observed in the other regions of TIM. MD simulations confirm that motions of individual residues within the active site loop are correlated and suggest that the chemical exchange processes observed for residues in helix G arise from transitions between 3(10)- and alpha-helical structures. The results of the joint NMR and MD study provide global insight into the role of conformational dynamic processes in the function of TIM.     

Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.     

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.     

Molecular dynamics simulations of Ac-3Aib-Cage-3Aib-NHMe

Solvents play a stabilising role with the more stable conformations obtained in polar solvents than in vacuo. We investigate to what extent the structural propensities of the pentacyclo-undecane (PCU) cage polypeptide chain of the type Ac-3Aib-Cage-3Aib-NHMe are influenced in implicit water and in explicit solvents: methanol (MEOH), dimethyl sulphoxide (DMSO) and TIP3P water. The sampling of the α-helical conformations of the PCU cage polypeptide was investigated using the in-house modified PARM94 force-field parameters. Analysis of 50 ns molecular dynamics (MD) simulations revealed a tendency of the PCU cage polypeptide to assume bent structures, especially in polar solvents. The choice of solvents was designed to relate the simulations to physiological conditions. The individual amino-isobutyric acid residues predominantly sampled the right-handed and left-handed 3₁₀-helical conformations, indicating that the helical conformations are preferred in all four environments (in vacuo, MEOH, water and DMSO). Additionally, the 100 ns replica exchange MD (REMD) simulations of the PCU cage polypeptide in implicit water revealed more conformational variety present than in explicit solvents, and is more consistent with previous theoretical studies on the PCU cage residue. The present theoretical results may help in rationalising experimental results on these PCU cage polypeptides, and definitely show the importance of a dynamical approach for a correct interpretation and prediction of the conformational behaviour of the PCU cage molecules in different environments.     

Conformational interconversion in compstatin probed with molecular dynamics simulations

Compstatin is a 13-residue cyclic peptide that has the potential to become a therapeutic agent against unregulated complement activation. In our effort to understand the structural and dynamic characteristics of compstatin that form the basis for rational and combinatorial optimization of structure and activity, we performed 1-ns molecular dynamics (MD) simulations. We used as input in the MD simulations the ensemble of 21 lowest energy NMR structures, the average minimized structure, and a global optimization structure. At the end of the MD simulations we identified five conformations, with populations ranging between 9% and 44%. These conformations are as follows: 1) coil with alphaR-alphaR beta-turn, as was the conformation of the initial ensemble of NMR structures; 2) beta-hairpin with epsilon-alphaR beta-turn; 3) beta-hairpin with alphaR-alphaR beta-turn; 4) beta-hairpin with alphaR-beta beta-turn; and 5) alpha-helical. Conformational switch was possible with small amplitude backbone motions of the order of 0.1-0.4 A and free energy barrier crossing of 2-11 kcal/mol. All of the 21 MD structures corresponding to the NMR ensemble possessed a beta-turn, with 14 structures retaining the alphaR-alphaR beta-turn type, but the average minimized structure and the global optimization structures were converted to alpha-helical conformations. Overall, the MD simulations have aided to gain insight into the conformational space sampled by compstatin and have provided a measure of conformational interconversion. The calculated conformers will be useful as structural and possibly dynamic templates for optimization in the design of compstatin using structure-activity relations (SAR) or dynamics-activity relations (DAR).     

Calculation of protein ionization equilibria with conformational sampling: pK(a) of a model leucine zipper, GCN4 and barnase.

The use of conformational ensembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dynamics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK(a) calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK(a) estimates computed from long multiple MD simulations and NMR ensembles. As model systems, a synthetic leucine zipper, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modified to investigate the effect of extensive global conformational sampling on the accuracy of pK(a) calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK(a) predictions was achieved by the use of multiple MD simulations. By using multiple trajectories the absolute error in pK(a) predictions for the model leucine zipper was reduced to as low as approximately 0.25 pK(a) units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK(a) calculations, are discussed.     

Conformational properties of a cyclic peptide bradykinin B2 receptor antagonist using experimental and theoretical methods.

The solution conformation of the cyclic peptide J324 (cyclo0,6-[Lys0,Glu6,D-Phe7]BK), an antagonist targeted at the bradykinin (BK) B2 receptor, has been investigated using experimental and theoretical methods. In order to gain insight into the structural requirements essential for BK antagonism, we carried out molecular dynamics (MD) simulations using simulated annealing as the sampling protocol. Following a free MD simulation we performed simulations using nuclear Overhauser enhancement (NOE) distance constraints determined by NMR experiments. The low-energy structures obtained were compared with each other, grouped into families and analyzed with respect to the presence of secondary structural elements in their backbone. We also introduced new ways of plotting structural data for a more comprehensive analysis of large conformational sets. Finally, the relationship between characteristic backbone conformations and the spatial arrangement of specific pharmacophore centers was investigated.     

Construction, MD Simulation, and Hydrodynamic Validation of an All-Atom Model of a Monoclonal IgG Antibody

At 150 kDa, antibodies of the IgG class are too large for their structure to be determined with current NMR methodologies. Because of hinge-region flexibility, it is difficult to obtain atomic-level structural information from the crystal, and questions regarding antibody structure and dynamics in solution remain unaddressed. Here we describe the construction of a model of a human IgG1 monoclonal antibody (trastuzumab) from the crystal structures of fragments. We use a combination of molecular-dynamics (MD) simulation, continuum hydrodynamics modeling, and experimental diffusion measurements to explore antibody behavior in aqueous solution. Hydrodynamic modeling provides a link between the atomic-level details of MD simulation and the size- and shape-dependent data provided by hydrodynamic measurements. Eight independent 40 ns MD trajectories were obtained with the AMBER program suite. The ensemble average of the computed transport properties over all of the MD trajectories agrees remarkably well with the value of the translational diffusion coefficient obtained with dynamic light scattering at 20°C and 27°C, and the intrinsic viscosity measured at 20°C. Therefore, our MD results likely represent a realistic sampling of the conformational space that an antibody explores in aqueous solution.     

PPM: a side-chain and backbone chemical shift predictor for the assessment of protein conformational ensembles

The combination of the wide availability of protein backbone and side-chain NMR chemical shifts with advances in understanding of their relationship to protein structure makes these parameters useful for the assessment of structural-dynamic protein models. A new chemical shift predictor (PPM) is introduced, which is solely based on physical?Cchemical contributions to the chemical shifts for both the protein backbone and methyl-bearing amino-acid side chains. To explicitly account for the effects of protein dynamics on chemical shifts, PPM was directly refined against 100?ns long molecular dynamics (MD) simulations of 35 proteins with known experimental NMR chemical shifts. It is found that the prediction of methyl-proton chemical shifts by PPM from MD ensembles is improved over other methods, while backbone C??, C??, C??, N, and H^N chemical shifts are predicted at an accuracy comparable to the latest generation of chemical shift prediction programs. PPM is particularly suitable for the rapid evaluation of large protein conformational ensembles on their consistency with experimental NMR data and the possible improvement of protein force fields from chemical shifts.     

Predicting Peptide Structures in Native Proteins from Physical Simulations of Fragments

It has long been proposed that much of the information encoding how a protein folds is contained locally in the peptide chain. Here we present a large-scale simulation study designed to examine the extent to which conformations of peptide fragments in water predict native conformations in proteins. We perform replica exchange molecular dynamics (REMD) simulations of 872 8-mer, 12-mer, and 16-mer peptide fragments from 13 proteins using the AMBER 96 force field and the OBC implicit solvent model. To analyze the simulations, we compute various contact-based metrics, such as contact probability, and then apply Bayesian classifier methods to infer which metastable contacts are likely to be native vs. non-native. We find that a simple measure, the observed contact probability, is largely more predictive of a peptide''s native structure in the protein than combinations of metrics or multi-body components. Our best classification model is a logistic regression model that can achieve up to 63% correct classifications for 8-mers, 71% for 12-mers, and 76% for 16-mers. We validate these results on fragments of a protein outside our training set. We conclude that local structure provides information to solve some but not all of the conformational search problem. These results help improve our understanding of folding mechanisms, and have implications for improving physics-based conformational sampling and structure prediction using all-atom molecular simulations.