2H-NMR study and molecular dynamics simulation of the location, alignment, and mobility of pyrene in POPC bilayers

The alignment of pyrene in a 1-palmitoyl-2-oleoyl-phosphatidylcholine bilayer was investigated using two different approaches, namely solid-state (2)H-NMR spectroscopy and molecular dynamics (MD) simulations. Quadrupolar splittings from (2)H-NMR spectra of deuterated pyrene-d(10) in an oriented lipid bilayer give information about the orientation of C-D bonds with respect to the membrane normal. From MD simulations, geometric information is accessible via trajectories. By defining molecular and bond order parameters, the data from MD trajectories and NMR spectra can be compared straightforwardly. To ensure that the results from both methods are comparable, parameters of the experimental and the simulation setup were chosen to be as similar as possible. From simulations, we saw that pyrene prefers a position inside the lipid membrane near the headgroups and has no tendency to diffuse from one monolayer of the membrane to the other. The results from simulation and NMR show that the normal of the molecular plane is aligned nearly perpendicular to the bilayer normal. The long axis of pyrene lies preferentially parallel to the bilayer normal within a range of +/-30 degrees . The results from the two different methods are remarkably consistent. The good agreement can be explained by the fact that the different kind of motions of a pyrene molecule are already averaged within a few nanoseconds, which is the timescale covered by the MD simulation.     

A short guide for molecular dynamics simulations of RNA systems

As a result of important methodological advances and of the rapid growth of experimental data, the number of molecular dynamics (MD) simulations related to RNA systems has significantly increased. However, such MD simulations are not straightforward and great care has to be exerted during the setup stage in order to choose the appropriate MD package, force fields and ionic conditions. Furthermore, the choice and a correct evaluation of the main characteristics of the starting structure are primordial for the generation of informative and reliable MD trajectories since experimental structures are not void of inaccuracies and errors. The aim of this review is to provide, through numerous examples, practical guidelines for the setup of MD simulations, the choice of ionic conditions and the detection and correction of experimental inaccuracies in order to start MD simulations of nucleic acid systems under the best auspices.     

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.     

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.     

Deducing hydration sites of a protein from molecular dynamics simulations

Invariant water molecules that are of structural or functional importance to proteins are detected from their presence in the same location in different crystal structures of the same protein or closely related proteins. In this study we have investigated the location of invariant water molecules from MD simulations of ribonuclease A, HIV1-protease and Hen egg white lysozyme. Snapshots of MD trajectories represent the structure of a dynamic protein molecule in a solvated environment as opposed to the static picture provided by crystallography. The MD results are compared to an analysis on crystal structures. A good correlation is observed between the two methods with more than half the hydration sites identified as invariant from crystal structures featuring as invariant in the MD simulations which include most of the functionally or structurally important residues. It is also seen that the propensities of occupying the various hydration sites on a protein for structures obtained from MD and crystallographic studies are different. In general MD simulations can be used to predict invariant hydration sites when there is a paucity of crystallographic data or to complement crystallographic results.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

Observation of an A-DNA to B-DNA transition in a nonhelical nucleic acid hairpin molecule using molecular dynamics.

One of the truly challenging problems for molecular dynamics (MD) simulations is demonstrating that the trajectories can sample not only in the vicinity of an experimentally determined structure, but also that the trajectories can find the correct experimental structure starting from some other structure. Frequently these transitions to the correct structure require that the simulations overcome energetic barriers to conformational change. Here we present unrestrained molecular dynamics simulations of the DNA analogs of the RNA 5'-GGACUUCGGUCC-3' hairpin tetraloop. In one simulation we have used deoxyuracil residues, and in the other we have used the native DNA deoxythymine residues. We demonstrate that, on a nanosecond time scale, MD is able to simulate the transitions of both of the A-DNA stems to B-DNA stems within the constraints imposed by the four-base loop that caps the helix. These results suggest that we are now in a position to use MD to address the nature of sequence-dependent structural effects in nonduplex DNA structures.     

Conformational sampling by NMR solution structures calculated with the program DIANA evaluated by comparison with long-time molecular dynamics calculations in explicit water

The NMR solution structure of bovine pancreatic trypsin inhibitor (BPTI) obtained by distance geometry calculations with the program DIANA is compared with groups of conformers generated by molecular dynamics (MD) simulations in explicit water at ambient temperature and pressure. The MD simulations started from a single conformer and were free or restrained either by the experimental NOE distance restraints or by time-averaged restraints; the groups of conformers were collected either in 10 ps intervals during 200 ps periods of simulation, or in 50 ps intervals during a 1 ns period of simulation. Overall, these comparisons show that the standard protein structure determination protocol with the program DIANA provides a picture of the protein structure that is in agreement with MD simulations using “realistic” potential functions over a nanosecond timescale. For well-constrained molecular regions there is a trend in the free MD simulation of duration 1 ns that the sampling of the conformation space is slightly increased relative to the DIANA calculations. In contrast, for surface-exposed side-chains that are less extensively constrained by the NMR data, the DIANA conformers tend to sample larger regions of conformational space than conformers selected from any of the MD trajectories. Additional insights into the behavior of surface side-chains come from comparison of the MD runs of 200 ps or 1 ns duration. In this time range the sampling of conformation space by the protein surface depends strongly on the length of the simulation, which indicates that significant side-chain transitions occur on the nanosecond timescale and that much longer simulations will be needed to obtain statistically significant data on side-chain dynamics.     

Reduced point charge models of proteins: assessment based on molecular dynamics simulations

A reduced point charge distribution is used to model Ubiquitin and two complexes, Vps27 UIM-1–Ubiquitin and Barnase–Barstar. It is designed from local extrema in charge density distributions obtained from the Poisson equation applied to smoothed molecular electrostatic potentials. A variant distribution is built by locating point charges on atoms. Various charge fitting conditions are selected, i.e. from either electrostatic Amber99 (Assisted Model Building with Energy Refinement) Coulomb potential or forces, considering reference grid points located within various distances from the protein atoms, with or without separate treatment of main and side chain charges. The program GROMACS (Groningen Machine for Chemical Simulations) is used to generate Amber99SB molecular dynamics (MD) trajectories of the solvated proteins modelled using the various reduced point charge models (RPCMs) so obtained. Point charges that are not located on atoms are considered as virtual sites. Some RPCMs lead to stable MD trajectories. They, however, involve a partial loss in the protein secondary structure and lead to a less-structured solute solvation shell. The model built by fitting charges on Coulomb forces calculated at grid points ranging between 1.4 and 2.0 times the van der Waals radius of the atoms, with a separate treatment of main chain and side chain charges, appears to best approximate all-atom MD trajectories.     

Principal component and normal mode analysis of proteins; a quantitative comparison using the GroEL subunit

Principal component analysis (PCA) and normal mode analysis (NMA) have emerged as two invaluable tools for studying conformational changes in proteins. To compare these approaches for studying protein dynamics, we have used a subunit of the GroEL chaperone, whose dynamics is well characterized. We first show that both PCA on trajectories from molecular dynamics (MD) simulations and NMA reveal a general dynamical behavior in agreement with what has previously been described for GroEL. We thus compare the reproducibility of PCA on independent MD runs and subsequently investigate the influence of the length of the MD simulations. We show that there is a relatively poor one-to-one correspondence between eigenvectors obtained from two independent runs and conclude that caution should be taken when analyzing principal components individually. We also observe that increasing the simulation length does not improve the agreement with the experimental structural difference. In fact, relatively short MD simulations are sufficient for this purpose. We observe a rapid convergence of the eigenvectors (after ca. 6 ns). Although there is not always a clear one-to-one correspondence, there is a qualitatively good agreement between the movements described by the first five modes obtained with the three different approaches; PCA, all-atoms NMA, and coarse-grained NMA. It is particularly interesting to relate this to the computational cost of the three methods. The results we obtain on the GroEL subunit contribute to the generalization of robust and reproducible strategies for the study of protein dynamics, using either NMA or PCA of trajectories from MD simulations.     

Quantification and visualization of molecular surface flexibility

Two new methods for the quantification and visualization of the flexibility of molecular surfaces are presented. Both methods rely on results of molecular dynamics (MD) simulations. Whereas method I is based on a simple but fast grid-counting algorithm, method II uses a mapping function that allows for a sharp and clear visualization of atomic RMS fluctuations on a molecular surface. To demonstrate the scope of the methods, MD simulations of two proteins, PTI and ubiquitin, were performed. The flexibility data are mapped onto the molecular surfaces of the proteins and visualized using texture mapping technology available on modern workstations.     

Headgroup Conformations of Phospholipids from Molecular Dynamics Simulation: Sampling Challenges and Comparison to Experiment

The preferred conformations of the glycerol region of a phospholipid have been explored using replica exchange molecular dynamics (MD) simulations and compared with the results of standard MD approaches and with experiment. We found that due to isomerization rates in key torsions that are slow on the timescale of atomistic MD simulations, standard MD is not able to produce accurate equilibrium conformer distributions from reasonable trajectory lengths (e.g., on the 100 ns) timescale. Replica exchange MD, however, results in quite efficient sampling due to the rapid increase in isomerization rate with temperature. The equilibrium distributions obtained from replica exchange MD have been compared with the results of experimental nuclear magnetic resonance observations. This comparison suggests that the sampling approach demonstrated here is a valuable tool that can be used in evaluating force fields for molecular simulation of lipids.     

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.     

MoDEL (Molecular Dynamics Extended Library): a database of atomistic molecular dynamics trajectories

More than 1700 trajectories of proteins representative of monomeric soluble structures in the protein data bank (PDB) have been obtained by means of state-of-the-art atomistic molecular dynamics simulations in near-physiological conditions. The trajectories and analyses are stored in a large data warehouse, which can be queried for dynamic information on proteins, including interactions. Here, we describe the project and the structure and contents of our database, and provide examples of how it can be used to describe the global flexibility properties of proteins. Basic analyses and trajectories stripped of solvent molecules at a reduced resolution level are available from our web server.     

Effect of charge redistribution on the binding of DNA nucleotide to carbon nanotube in molecular dynamics

All-atom molecular dynamics (MD) simulations are performed to study the binding of DNA nucleotides with two carbon nanotubes (CNTs) with similar diameters but different chiralities. Two schemes for assigning partial atomic charges (PACs) are adopted: (I) using PACs obtained from isolated DNA nucleotide and CNT optimised in vacuum, and (II) using PACs obtained from optimising nucleotide-CNT hybrid in solution. The former approach is what most MD simulations have used in the study of DNA-CNT hybrids, while in the latter approach, a redistribution of the PACs has occurred upon the hybridisation. Our results show that the charge redistribution has a profound effect on the dynamics of binding. In particular, PACs obtained from (II) lead to more stable binding structures in the MD simulations. The findings suggest that care should be taken in simulating DNA-CNT interactions using the classical force field approach.     

Essential spaces defined by NMR structure ensembles and molecular dynamics simulation show significant overlap

Large concerted motions of proteins which span its “essential space,” are an important component of protein dynamics. We investigate to what extent structure ensembles generated with standard structure calculation techniques such as simulated annealing can capture these motions by comparing them to long-time molecular dynamics (MD) trajectories. The motions are analyzed by principal component analysis and compared using inner products of eigenvectors of the respective covariance matrices. Two very different systems are studied, the β-spectrin PH domain and the single-stranded DNA binding protein (ssDBP) from the filamentous phage Pf3. A comparison of the ensembles from NMR and MD shows significant overlap of the essential spaces, which in the case of ssDBP is extraordinarily high. The influence of variations in the specifications of distance restraints is investigated. We also study the influence of the selection criterion for the final structure ensemble on the definition of mobility. The results suggest a modified criterion that improves conformational sampling in terms of amplitudes of correlated motion. Proteins 31:370–382, 1998. © 1998 Wiley-Liss, Inc.     

Conformational space search of Neuromedin C using replica exchange molecular dynamics and molecular dynamics

The present study involves the utilization of replica exchange molecular dynamics (REMD) methodology to explore the conformational space of Neuromedin C (NMC) using implicit (REMD^implicit) and explicit (REMD^explicit) water models. Comparison of the structures obtained from these simulations indicate that REMD^explicit trajectory display a greater tendency to induce β‐turns and bent structures as compared to those obtained from the REMD^implicit simulation. Moreover, two additional MD trajectories performed using Langevin (MD^Lang) and Berendsen (MD^Berend) algorithms under generalized born (GB) solvent conditions were also suitably competent to sample similar kinds of conformations, although the extent of beta turns was low compared to those observed in REMD^explicit simulation. Finally, the comparison of results obtained from all the trajectories and those derived from the NMR studies of Ni(II) complex of NMC indicates that the REMD under explicit conditions is more efficient in sampling the conformations, and show good agreement with the experimental results. Copyright © 2010 European Peptide Society and John Wiley & Sons, Ltd.     

Unfolding stabilities of two structurally similar proteins as probed by temperature-induced and force-induced molecular dynamics simulations

Unfolding stabilities of two homologous proteins, cardiotoxin III and short-neurotoxin (SNTX) belonging to three-finger toxin (TFT) superfamily, have been probed by means of molecular dynamics (MD) simulations. Combined analysis of data obtained from steered MD and all-atom MD simulations at various temperatures in near physiological conditions on the proteins suggested that overall structural stabilities of the two proteins were different from each other and the MD results are consistent with experimental data of the proteins reported in the literature. Rationalization for the differential structural stabilities of the structurally similar proteins has been chiefly attributed to the differences in the structural contacts between C- and N-termini regions in their three-dimensional structures, and the findings endorse the ‘CN network’ hypothesis proposed to qualitatively analyse the thermodynamic stabilities of proteins belonging to TFT superfamily of snake venoms. Moreover, the ‘CN network’ hypothesis has been revisited and the present study suggested that ‘CN network’ should be accounted in terms of ‘structural contacts’ and ‘structural strengths’ in order to precisely describe order of structural stabilities of TFTs.     

Ranking ligand binding affinities with avidin: a molecular dynamics-based interaction energy study.

The binding of 14 biotin analogues to avidin is examined to evaluate the viability of calculating binding free energy based on molecular dynamics (MD) trajectories. Two approaches were investigated in this work. The first one uses the linear interaction energy approximation, while the other approach utilizes the interaction free energy. The results obtained from these two methods were found to correlate well with the experimental binding free energy data for 10 out of 14 ligands. For the other four ligands, both methods overestimate their binding strength by more than 7 kcal/mol. Free energy calculations using the thermodynamic integration method are employed to understand this overestimation. The effect of protein flexibility on binding free energy calculation and the effect of charged or neutral ligands on the calculated results are discussed. MD simulations are shown to be able to provide insight into the interactions occurring in the active site and the origins of variations in binding free energy.     

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.