Application of time series analysis on molecular dynamics simulations of proteins: a study of different conformational spaces by principal component analysis

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.     

vmdICE: a plug-in for rapid evaluation of molecular dynamics simulations using VMD

Molecular dynamics (MD) is a powerful in silico method to investigate the interactions between biomolecules. It solves Newton's equations of motion for atoms over a specified period of time and yields a trajectory file, containing the different spatial arrangements of atoms during the simulation. The movements and energies of each single atom are recorded. For evaluating of these simulation trajectories with regard to biomedical implications, several methods are available. Three well-known ones are the root mean square deviation (RMSD), the root mean square fluctuation (RMSF) and solvent accessible surface area (SASA). Herein, we present a novel plug-in for the software "visual molecular dynamics" (VMD) that allows an interactive 3D representation of RMSD, RMSF, and SASA, directly on the molecule. On the one hand, our plug-in is easy to handle for inexperienced users, and on the other hand, it provides a fast and flexible graphical impression of the spatial dynamics of a system for experts in the field.     

MDAnalysis: A toolkit for the analysis of molecular dynamics simulations

MDAnalysis is an object‐oriented library for structural and temporal analysis of molecular dynamics (MD) simulation trajectories and individual protein structures. It is written in the Python language with some performance‐critical code in C. It uses the powerful NumPy package to expose trajectory data as fast and efficient NumPy arrays. It has been tested on systems of millions of particles. Many common file formats of simulation packages including CHARMM, Gromacs, Amber, and NAMD and the Protein Data Bank format can be read and written. Atoms can be selected with a syntax similar to CHARMM's powerful selection commands. MDAnalysis enables both novice and experienced programmers to rapidly write their own analytical tools and access data stored in trajectories in an easily accessible manner that facilitates interactive explorative analysis. MDAnalysis has been tested on and works for most Unix‐based platforms such as Linux and Mac OS X. It is freely available under the GNU General Public License from http://mdanalysis.googlecode.com . © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

FAMUSAMM: An algorithm for rapid evaluation of electrostatic interactions in molecular dynamics simulations

Within molecular dynamics simulations of protein–solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-adapted multipole method (SAMM) [C. Niedermeier and P. Tavan, J. Chem. Phys., 101 , 734 (1994)] with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-adapted multipole method (FAMUSAMM) scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that the applied approximations do not seriously affect structural or dynamical properties of the simulated systems. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1729–1749, 1997     

nMoldyn: a program package for a neutron scattering oriented analysis of molecular dynamics simulations

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191-214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high-level language, Python, and of modern object-oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean-square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies.     

Alamethicin channels in a membrane: molecular dynamics simulations

Alamethicin (Alm) is a 20 residue peptide which forms a kinked alpha-helix in membrane and membrane-mimetic environments. Ion channels formed by intramembraneous aggregates of Alm are thought to be formed by bundles of approximately parallel Alm helices surrounding a central bilayer pore. Different channel conductance levels correspond to different numbers of helices per bundle, ranging from N = 5 to N > 8. Calculation of the predicted pKA values of the ring of Glu18 sidechains at the C-terminal mouth of the pore suggests that at neutral pH most or all of these sidechains will remain protonated. Nanosecond molecular dynamics (MD) simulations of N = 5, 6, 7 and 8 bundles of Alm helices in a POPC bilayer have been run, corresponding to a total simulation time of 4 ns. These simulations explore the stability and conformational dynamics of these helix bundle channels when embedded in a full phospholipid bilayer in an aqueous environment. The structural and dynamic properties of water in these model channels are examined. As in earlier in vacuo simulations (J. Breed, R. Sankararamakrishnan, I. D. Kerr and M. S. P. Sansom, Biophys. J., 1996, 70, 1643) the dipole moments of water molecules within the pores are aligned antiparallel to the helix dipoles. This helps to contribute to the stability of the helix bundles.     

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.     

Spin-labeled alkylphospholipids in a dipalmitoylphosphatidylcholine bilayer: molecular dynamics simulations

Molecular dynamics simulation has been performed to investigate the structural properties of perifosine and its synthetic spin-labeled alkylphospholipid analogues. The conformations adopted by these compounds in water and in a dipalmitoylphosphatidylcholine bilayer as a function of the presence and position of the N-oxyl-4',4'-dimethyloxazolidine ring (doxyl group) have been investigated by all-atom molecular dynamics. No predominant conformation was observed in water, but the molecules adopt specific orientations and conformations in the lipid bilayer. As is expected, alkyl chains tend to insert into the hydrophobic core, while charged groups stay at the lipid-water interface. A doxyl group in the middle of the alkyl chain moves up to the interface region, thus preventing adoption of the extended conformation. Compounds with a doxyl group close to the polar head group adopt conformations similar to that of unlabeled perifosine within the first nanoseconds of simulation. When the doxyl group is at the end of alkyl chain, the spin-labeled molecule needs more time to reach equilibrium. These results indicate a considerable effect of the doxyl position within the alkyl chain on its localization in the lipid bilayer and can be extended further to other similar spin probes used in the electron paramagnetic resonance spectroscopy of biological membranes.     

Newly developed ab initio fitted potentials for molecular dynamics simulations of n-pentane in the zeolite silicalite-1

Ab initio fitted potentials representing n-pentane/n-pentane and n-pentane/silicalite-1 interactions were newly developed at the second-order Møller-Plesset perturbation (MP2) level with the 6-31G* basis set. Characteristics of the functions were illustrated in comparison with available force field models. They were, then, applied for the molecular dynamics simulation of n-pentane in silicalite-1. The diffusion coefficients are in satisfactory agreement with the results of PFG-NMR experiments. The effect of the box size was also examined. It was found that the components of the diffusion tensor are very sensitive to this parameter. The structure of the n-pentane in the silicalite-1 pore was analyzed in terms of radial distribution functions. The first peak at 4.1 Å indicates the optimal diffusion route of the n-pentane along the central line of the channel of the silicalite-1.     

Bond detectors for molecular dynamics simulations,Part I: Hydrogen bonds

Charge sensitivity analysis in AMBER force‐field resolution has been used in quest for detectors of hydrogen bonds (HBs). The process of HB formation was investigated on ab initio classical trajectories (B3LYP/6‐31G*) of different nucleobase pairs. Several charge sensitivities, namely: electronegativity, hardness, Fukui function (FF), and polarization matrix, were analyzed. The global and constrained equilibria were considered. It was demonstrated that FF indices and polarization matrix elements are good detectors of HB formation. © 2013 Wiley Periodicals, Inc.     

A nonadditive methanol force field: bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model

We study the bulk and interfacial properties of methanol via molecular dynamics simulations using a CHARMM (Chemistry at HARvard Molecular Mechanics) fluctuating charge force field. We discuss the parametrization of the electrostatic model as part of the ongoing CHARMM development for polarizable protein force fields. The bulk liquid properties are in agreement with available experimental data and competitive with existing fixed-charge and polarizable force fields. The liquid density and vaporization enthalpy are determined to be 0.809 g/cm3 and 8.9 kcal/mol compared to the experimental values of 0.787 g/cm3 and 8.94 kcal/mol, respectively. The liquid structure as indicated by radial distribution functions is in keeping with the most recent neutron diffraction results; the force field shows a slightly more ordered liquid, necessarily arising from the enhanced condensed phase electrostatics (as evidenced by an induced liquid phase dipole moment of 0.7 D), although the average coordination with two neighboring molecules is consistent with the experimental diffraction study as well as with recent density functional molecular dynamics calculations. The predicted surface tension of 19.66+/-1.03 dyn/cm is slightly lower than the experimental value of 22.6 dyn/cm, but still competitive with classical force fields. The interface demonstrates the preferential molecular orientation of molecules as observed via nonlinear optical spectroscopic methods. Finally, via canonical molecular dynamics simulations, we assess the model's ability to reproduce the vapor-liquid equilibrium from 298 to 423 K, the simulation data then used to obtain estimates of the model's critical temperature and density. The model predicts a critical temperature of 470.1 K and critical density of 0.312 g/cm3 compared to the experimental values of 512.65 K and 0.279 g/cm3, respectively. The model underestimates the critical temperature by 8% and overestimates the critical density by 10%, and in this sense is roughly equivalent to the underlying fixed-charge CHARMM22 force field.     

Advantages of a Lowe-Andersen thermostat in molecular dynamics simulations

The Lowe-Andersen thermostat is a momentum conserving and Galilean invariant analog of the Andersen thermostat. Like the Andersen thermostat it has the advantage of being local. We show that by using a minimal thermostat interaction radius in a molecular dynamics simulation, it perturbs the system dynamics to a far lesser extent than the Andersen method. This alleviates a well known drawback of the Andersen thermostat by allowing high thermostatting rates without the penalty of significantly suppressed diffusion in the system.     

Thermal analysis of interpenetrating polymer networks through molecular dynamics simulations: a comparison with experiments

Journal of Thermal Analysis and Calorimetry - In this work, we verified the synthesis of a novel sequential interpenetrating polymer network, composed of poly(2-hexyl-ethylacrylate) and...     

Effects of ionic strength on SAXS data for proteins revealed by molecular dynamics simulations

The combination of small-angle X-ray solution scattering (SAXS) experiments and molecular dynamics (MD) simulations is now becoming a powerful tool to study protein conformations in solution at an atomic resolution. In this study, we investigated effects of ionic strength on SAXS data theoretically by using MD simulations of hen egg white lysozyme at various NaCl concentrations from 0 to 1 M. The calculated SAXS excess intensities showed a significant dependence on ion concentration, which originates from the different solvent density distributions in the presence and absence of ions. The addition of ions induced a slow convergence of the SAXS data, and a ～20 ns simulation is required to obtain convergence of the SAXS data with the presence of ions whereas only a 0.2 ns simulation is sufficient in the absence of ions. To circumvent the problem of the slow convergence in the presence of ions, we developed a novel method that reproduces the SAXS excess intensities with the presence of ions from short MD trajectories in pure water. By applying this method to SAXS data for the open and closed forms of transferrin at 1 M ion concentration, the correct form could be identified by simply using short MD simulations of the protein in pure water for 0.2 ns.     

Enhanced sampling molecular dynamics simulations correctly predict the diverse activities of a series of stiff-stilbene G-quadruplex DNA ligands

Ligands with the capability to bind G-quadruplexes (G4s) specifically, and to control G4 structure and behaviour, offer great potential in the development of novel therapies, technologies and functional materials. Most known ligands bind to a pre-formed topology, but G4s are highly dynamic and a small number of ligands have been discovered that influence these folding equilibria. Such ligands may be useful as probes to understand the dynamic nature of G4 in vivo, or to exploit the polymorphism of G4 in the development of molecular devices. To date, these fascinating molecules have been discovered serendipitously. There is a need for tools to predict such effects to drive ligand design and development, and for molecular-level understanding of ligand binding mechanisms and associated topological perturbation of G4 structures. Here we study the G4 binding mechanisms of a family of stiff-stilbene G4 ligands to human telomeric DNA using molecular dynamics (MD) and enhanced sampling (metadynamics) MD simulations. The simulations predict a variety of binding mechanisms and effects on G4 structure for the different ligands in the series. In parallel, we characterize the binding of the ligands to the G4 target experimentally using NMR and CD spectroscopy. The results show good agreement between the simulated and experimentally observed binding modes, binding affinities and ligand-induced perturbation of the G4 structure. The simulations correctly predict ligands that perturb G4 topology. Metadynamics simulations are shown to be a powerful tool to aid development of molecules to influence G4 structure, both in interpreting experiments and to help in the design of these chemotypes.

Enhanced sampling molecular dynamics simulations and solution-phase experiments come together to demonstrate the diverse effects of G4-interactive small molecules.     

Time series analysis of ion dynamics in glassy ionic conductors obtained by a molecular dynamics simulation

We present several characteristics of ionic motion in glassy ionic conductors brought out by time series analysis of molecular dynamics (MD) simulation data. Time series analysis of data obtained by MD simulation can provide crucial information to describe, understand and predict the dynamics in many systems. The data have been treated by the singular spectrum analysis (SSA), which is a method to extract information from noisy short time series and thus provide insight into the unknown or partially unknown dynamics of the underlying system that generated the time series. Phase-space plot reconstructed using the principal components of SSA exhibited complex but clear structures, suggesting the deterministic nature of the dynamics.     

Conformational analysis of a tetrasaccharide based on NMR spectroscopy and molecular dynamics simulations

The conformational preference of the human milk oligosaccharide lacto-N-neotetraose, beta-d-Galp-(1 --> 4)-beta-d-GlcpNAc-(1 --> 3)-beta-d-Galp-(1 --> 4)-d-Glcp, has been analyzed using (1)H,(1)H T-ROESY and (1)H,(13)C trans-glycosidic J coupling experiments in isotropic solution and (1)H,(13)C residual dipolar couplings (RDCs) obtained in lyotropic liquid crystalline media. Molecular dynamics simulations of the tetrasaccharide with explicit water as the solvent revealed that two conformational states are significantly populated at the psi glycosidic torsion angle, defined by C(anomeric)-O-C-H, of the (1 --> 3)-linkage. Calculation of order parameters, related to the molecular shape, were based on the inertia tensor and fitting of experimental RDCs to different conformational states showed that psi(+) > 0 degrees is the major and psi(-) < 0 degrees is the minor conformation in solution, in complete agreement with a two-state analysis based on the T-ROESY data. Attention was also given to the effect of salt (200 mM NaCl) in the anisotropic medium, which was a ternary mixture of n-octyl-penta(ethylene glycol), n-octanol, and D(2)O.     

nMoldyn 3: Using task farming for a parallel spectroscopy‐oriented analysis of molecular dynamics simulations

We present a new version of the program package nMoldyn, which has been originally developed for a neutron‐scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in‐depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed‐memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods. © 2012 Wiley Periodicals, Inc.     

MBO(N)D: A multibody method for long‐time molecular dynamics simulations

A modeling approach that can significantly speed up the dynamics simulation of large molecular systems is presented herein. A multigranular modeling approach, whereby different parts of the molecule are modeled at different levels of detail, is enabled by substructuring. Substructuring the molecular system is accomplished by collecting groups of atoms into rigid or flexible bodies. Body flexibility is modeled by a truncated set of body‐based modes. This approach allows for the elimination of the high‐frequency harmonic motion while capturing the low‐frequency anharmonic motion of interest. This results in the use of larger integration step sizes, substantially reducing the computational time required for a given dynamic simulation. The method also includes the use of a multiple time scale (MTS) integration scheme. Speed increases of 5‐ to 30‐fold over atomistic simulations have been realized in various applications of the method. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 159–184, 2000     

HTMoL: full-stack solution for remote access,visualization, and analysis of molecular dynamics trajectory data

Research on biology has seen significant advances with the use of molecular dynamics (MD) simulations. The MD methodology enables explanation and discovery of molecular mechanisms in a wide range of natural processes and biological systems. The need to readily share the ever-increasing amount of MD data has been hindered by the lack of specialized bioinformatic tools. The difficulty lies in the efficient management of the data, i.e., in sending and processing 3D information for its visualization. In this work, we present HTMoL, a plug-in-free, secure GPU-accelerated web application specifically designed to stream and visualize MD trajectory data on a web browser. Now, individual research labs can publish MD data on the Internet, or use HTMoL to profoundly improve scientific reports by including supplemental MD data in a journal publication. HTMoL can also be used as a visualization interface to access MD trajectories generated on a high-performance computer center directly. Furthermore, the HTMoL architecture can be leveraged with educational efforts to improve learning in the fields of biology, chemistry, and physics.