Going beyond Clustering in MD Trajectory Analysis: An Application to Villin Headpiece Folding

Recent advances in computing technology have enabled microsecond long all-atom molecular dynamics (MD) simulations of biological systems. Methods that can distill the salient features of such large trajectories are now urgently needed. Conventional clustering methods used to analyze MD trajectories suffer from various setbacks, namely (i) they are not data driven, (ii) they are unstable to noise and changes in cut-off parameters such as cluster radius and cluster number, and (iii) they do not reduce the dimensionality of the trajectories, and hence are unsuitable for finding collective coordinates. We advocate the application of principal component analysis (PCA) and a non-metric multidimensional scaling (nMDS) method to reduce MD trajectories and overcome the drawbacks of clustering. To illustrate the superiority of nMDS over other methods in reducing data and reproducing salient features, we analyze three complete villin headpiece folding trajectories. Our analysis suggests that the folding process of the villin headpiece is structurally heterogeneous.     

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.     

Principal component and clustering analysis on molecular dynamics data of the ribosomal L11·23S subdomain

With improvements in computer speed and algorithm efficiency, MD simulations are sampling larger amounts of molecular and biomolecular conformations. Being able to qualitatively and quantitatively sift these conformations into meaningful groups is a difficult and important task, especially when considering the structure-activity paradigm. Here we present a study that combines two popular techniques, principal component (PC) analysis and clustering, for revealing major conformational changes that occur in molecular dynamics (MD) simulations. Specifically, we explored how clustering different PC subspaces effects the resulting clusters versus clustering the complete trajectory data. As a case example, we used the trajectory data from an explicitly solvated simulation of a bacteria’s L11·23S ribosomal subdomain, which is a target of thiopeptide antibiotics. Clustering was performed, using K-means and average-linkage algorithms, on data involving the first two to the first five PC subspace dimensions. For the average-linkage algorithm we found that data-point membership, cluster shape, and cluster size depended on the selected PC subspace data. In contrast, K-means provided very consistent results regardless of the selected subspace. Since we present results on a single model system, generalization concerning the clustering of different PC subspaces of other molecular systems is currently premature. However, our hope is that this study illustrates a) the complexities in selecting the appropriate clustering algorithm, b) the complexities in interpreting and validating their results, and c) by combining PC analysis with subsequent clustering valuable dynamic and conformational information can be obtained.     

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.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

Multiple loop conformations of peptides predicted by molecular dynamics simulations are compatible with nuclear magnetic resonance

The affinity and selectivity of protein-protein interactions can be fine-tuned by varying the size, flexibility, and amino acid composition of involved surface loops. As a model for such surface loops, we study the conformational landscape of an octapeptide, whose flexibility is chemically steered by a covalent ring closure integrating an azobenzene dye into and by a disulfide bridge additionally constraining the peptide backbone. Because the covalently integrated azobenzene dyes can be switched by light between a bent cis state and an elongated trans state, six cyclic peptide models of strongly different flexibilities are obtained. The conformational states of these peptide models are sampled by NMR and by unconstrained molecular dynamics (MD) simulations. Prototypical conformations and the free-energy landscapes in the high-dimensional space spanned by the phi/psi angles at the peptide backbone are obtained by clustering techniques from the MD trajectories. Multiple open-loop conformations are shown to be predicted by MD particularly in the very flexible cases and are shown to comply with the NMR data despite the fact that such open-loop conformations are missing in the refined NMR structures.     

A structure-based simulation approach for electron paramagnetic resonance spectra using molecular and stochastic dynamics simulations

Electron paramagnetic resonance (EPR) spectroscopy using site-directed spin-labeling is an appropriate technique to analyze the structure and dynamics of flexible protein regions as well as protein-protein interactions under native conditions. The analysis of a set of protein mutants with consecutive spin-label positions leads to the identification of secondary and tertiary structure elements. In the first place, continuous-wave EPR spectra reflect the motional freedom of the spin-label specifically linked to a desired site within the protein. EPR spectra calculations based on molecular dynamics (MD) and stochastic dynamics simulations facilitate verification or refinement of predicted computer-aided models of local protein conformations. The presented spectra simulation algorithm implies a specialized in vacuo MD simulation at 600 K with additional restrictions to sample the entire accessible space of the bound spin-label without large temporal effort. It is shown that the distribution of spin-label orientations obtained from such MD simulations at 600 K agrees well with the extrapolated motion behavior during a long timescale MD at 300 K with explicit water. The following potential-dependent stochastic dynamics simulation combines the MD data about the site-specific orientation probabilities of the spin-label with a realistic rotational diffusion coefficient yielding a set of trajectories, each more than 700 ns long, essential to calculate the EPR spectrum. Analyses of a structural model of the loop between helices E and F of bacteriorhodopsin are illustrated to demonstrate the applicability and potentials of the reported simulation approach. Furthermore, effects on the motional freedom of bound spin-labels induced by solubilization of bacteriorhodopsin with Triton X-100 are examined.     

The Mechanism by which 146-N-Glycan Affects the Active Site of Neuraminidase

One of the most conserved glycosylation sites of neuraminidase (NA) is 146-N-glycan. This site is adjacent to the 150-cavity of NA, which is found within the active site and thought to be a target for rational drug development against the antiviral resistance of influenza. Here, through a total of 2.4 μs molecular dynamics (MD) simulations, we demonstrated that 146-N-glycan can stabilize the conformation of the 150-loop that controls the volume of the 150-cavity. Moreover, with 146-N-glycan, our simulation result was more consistent with crystal structures of NAs than simulations conducted without glycans. Cluster analysis of the MD trajectories showed that 146-N-glycan adopted three distinct conformations: monomer-bridged, dimer-bridged and standing. Of these conformations, the dimer-bridged 146-N-glycan was the most stable one and contributed to stabilization of the 150-loop conformation. Furthermore, our simulation revealed that various standing conformations of 146-N-glycan could block the entrance of the binding pocket. This result was consistent with experimental data and explained the relatively low activity of inhibitors with flexible substituents toward the 150-cavity. Together, our results lead us to hypothesize that rigid and hydrophobic substituents could serve as better inhibitors targeting the 150-cavity.     

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.     

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.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.     

Virtual screening of a natural compound library at orthosteric and allosteric binding sites of the neurotensin receptor

Abstract

Molecular dynamics (MD) simulation using the AMBER force field has been performed on the neurotensin (NT) receptor, a class A type G-protein-coupled receptor in its activated conformation co-crystallized with the non-peptide agonists. For structure-based hit molecule identification via natural chemical compound library, orthosteric sites on NT receptor have been mapped by docking using AutoDock4.0 and Vina with the known agonists and antagonists SR48692, SR142948, ML301 and ML314 of the receptor. Furthermore, clustering analysis on the MD trajectories by SIMULAID has been performed to filter receptor conformations for the allosteric binders from the Otava natural compound library. Comparative mappings of contrasting binding region patterns have been done between the crystal structure orthosteric sites as well as the binding regions in the SIMULAID-based cluster center conformations from MD trajectories with the FTmap server using the small organic molecule fragments as the probes. The distinct binding region in the cluster-based conformations in the extracellular region of the receptor has been identified for targeted docking by Otava natural chemical compound library using AutoDock4.0 and Vina docking suites to obtain putative allosteric binders. A group of compounds from the Otava library has been identified as showing high free energy in both AutoDock4.0 and Vina docking suites. Biophysical assessments on the natural compound computational hit molecules will be done to identify lead structures from the hit molecules.

Communicated by Ramaswamy H. Sarma     

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.     

Domain motions in bacteriophage T4 lysozyme: A comparison between molecular dynamics and crystallographic data

A comparison of a series of extended molecular dynamics (MD) simulations of bacteriophage T4 lysozyme in solvent with X-ray data is presented. Essential dynamics analyses were used to derive collective fluctuations from both the simulated trajectories and a distribution of crystallographic conformations. In both cases the main collective fluctuations describe domain motions. The protein consists of an N- and C-terminal domain connected by a long helix. The analysis of the distribution of crystallographic conformations reveals that the N-terminal helix rotates together with either of these two domains. The main domain fluctuation describes a closure mode of the two domains in which the N-terminal helix rotates concertedly with the C-terminal domain, while the domain fluctuation with second largest amplitude corresponds to a twisting mode of the two domains, with the N-terminal helix rotating concertedly with the N-terminal domain. For the closure mode, the difference in hinge-bending angle between the most open and most closed X-ray structure along this mode is 49 degrees. In the MD simulation that shows the largest fluctuation along this mode, a rotation of 45 degrees was observed. Although the twisting mode has much less freedom than the closure mode in the distribution of crystallographic conformations, experimental results suggest that it might be functionally important. Interestingly, the twisting mode is sampled more extensively in all MD simulations than it is in the distribution of X-ray conformations. Proteins 31:116–127, 1998. © 1998 Wiley-Liss, Inc.     

Induced‐fit or preexisting equilibrium dynamics? Lessons from protein crystallography and MD simulations on acetylcholinesterase and implications for structure‐based drug design

Crystal structures of acetylcholinesterase complexed with ligands are compared with side-chain conformations accessed by native acetylcholinesterase in molecular dynamics (MD) simulations. Several crystallographic conformations of a key residue in a specific binding site are accessed in a simulation of native acetylcholinesterase, although not seen in rotomer plots. Conformational changes upon ligand binding thus involve preexisting equilibrium dynamics. Consequently, rational drug design could benefit significantly from conformations monitored by MD simulations of native targets.     

Comparison of multiple molecular dynamics trajectories calculated for the drug-resistant HIV-1 integrase T66I/M154I catalytic domain

HIV-1 integrase (IN) is an essential enzyme for the viral replication and an interesting target for the design of new pharmaceuticals for multidrug therapy of AIDS. Single and multiple mutations of IN at residues T66, S153, or M154 confer degrees of resistance to several inhibitors that prevent the enzyme from performing its normal strand transfer activity. Four different conformations of IN were chosen from a prior molecular dynamics (MD) simulation on the modeled IN T66I/M154I catalytic core domain as starting points for additional MD studies. The aim of this article is to understand the dynamic features that may play roles in the catalytic activity of the double mutant enzyme in the absence of any inhibitor. Moreover, we want to verify the influence of using different starting points on the MD trajectories and associated dynamical properties. By comparison of the trajectories obtained from these MD simulations we have demonstrated that the starting point does not affect the conformational space explored by this protein and that the time of the simulation is long enough to achieve convergence for this system.     

Accessible conformations of melanin-concentrating hormone: a molecular dynamics approach

Molecular dynamics simulations have been used to search for the accessible conformations of the melanin-concentrating hormone (MCH). The studies have been performed on native MCH and two of its peptide fragments, a cyclic MCH(5-14) fragment and a linear MCH(5-14) fragment. An analysis of the molecular dynamics trajectories of the three peptides indicates that two regions of the peptide have characteristic conformational properties that may be important for the biological activity. One is a region around Gly8, which is conformationally mobile, and the other is around Pro13, which shows unusual rigidity. The molecular dynamics simulation results are discussed in terms of backbone structural features like beta turns, side-chain interactions, and orientations of the disulfide bridge. The results of this analysis are used to suggest new analogues that will modify the conformational features of the peptide and further define the conformational requirements for activity. Finally, the results are related to nmr studies of the peptide and reveal agreements between the experimental nuclear Overhauser effect constraints and some of the accessible conformations obtained from the simulation.     

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.     

A comparison between elastic network interpolation and MD simulation of 16S ribosomal RNA

In this paper a coarse-grained method called elastic network interpolation (ENI) is used to generate feasible transition pathways between two given conformations of the core central domain of 16S Ribosomal RNA (16S rRNA). The two given conformations are the extremes generated by a molecular dynamics (MD) simulation, which differ from each other by 10A in root-mean-square deviation (RMSD). It takes only several hours to build an ENI pathway on a 1.5GHz Pentium with 512 MB memory, while the MD takes several weeks on high-performance multi-processor servers such as the SGI ORIGIN 2000/2100. It is shown that multiple ENI pathways capture the essential anharmonic motions of millions of timesteps in a particular MD simulation. A coarse-grained normal mode analysis (NMA) is performed on each intermediate ENI conformation, and the lowest 1% of the normal modes (representing about 40 degrees of freedom (DOF)) are used to parameterize fluctuations. This combined ENI/NMA method captures all intermediate conformations in the MD run with 1.5A RMSD on average. In addition, if we restrict attention to the time interval of the MD run between the two extreme conformations, the RMSD between the closest ENI/NMA pathway and the MD results is about 1A. These results may serve as a paradigm for reduced-DOF dynamic simulations of large biological macromolecules as well as a method for the reduced-parameter interpretation of massive amounts of MD data.