Characterizing rare-event property distributions via replicate molecular dynamics simulations of proteins

As computational resources increase, molecular dynamics simulations of biomolecules are becoming an increasingly informative complement to experimental studies. In particular, it has now become feasible to use multiple initial molecular configurations to generate an ensemble of replicate production-run simulations that allows for more complete characterization of rare events such as ligand-receptor unbinding. However, there are currently no explicit guidelines for selecting an ensemble of initial configurations for replicate simulations. Here, we use clustering analysis and steered molecular dynamics simulations to demonstrate that the configurational changes accessible in molecular dynamics simulations of biomolecules do not necessarily correlate with observed rare-event properties. This informs selection of a representative set of initial configurations. We also employ statistical analysis to identify the minimum number of replicate simulations required to sufficiently sample a given biomolecular property distribution. Together, these results suggest a general procedure for generating an ensemble of replicate simulations that will maximize accurate characterization of rare-event property distributions in biomolecules.     

Solvation Effects on the Conformational Behaviour of Gellan and Calcium Ion Binding to Gellan Double Helices

The contribution of the presence of solvent to the conformations adopted by disaccharide fragments within the repeat unit of gellan have been studied by molecular modelling techniques. Initial conformational energy searches, using a dielectric continuum to represent the solvent, provided starting geometries for a series of molecular dynamics simulations. The solution behaviour from these simulations was subsequently compared to fibre diffraction data of the potassium gellan salt. The present calculations indicate considerable flexibility of the glycosidic linkages, and this is discussed in relation to its effect on gel formation. One of the fragments was solvated with explicit water molecules. These calculations showed the same conformational behaviour as those simulations conducted in implicit solvent.Finally, a series of molecular dynamics (MD) simulations were performed to study the calcium binding to gellan. The results from this clearly showed a well defined binding site for this ion.Abbreviations MM molecular mechanics - MD molecular dynamics     

Data mining of molecular dynamics trajectories of nucleic acids

Analysis, storage, and transfer of molecular dynamic trajectories are becoming the bottleneck of computer simulations. In this paper we discuss different approaches for data mining and data processing of huge trajectory files generated from molecular dynamic simulations of nucleic acids.     

High-Performance Drug Discovery: Computational Screening by Combining Docking and Molecular Dynamics Simulations

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, this method is not completely reliable and therefore unsatisfactory. In this study, we used massive molecular dynamics simulations of protein-ligand conformations obtained by molecular docking in order to improve the enrichment performance of molecular docking. Our screening approach employed the molecular mechanics/Poisson-Boltzmann and surface area method to estimate the binding free energies. For the top-ranking 1,000 compounds obtained by docking to a target protein, approximately 6,000 molecular dynamics simulations were performed using multiple docking poses in about a week. As a result, the enrichment performance of the top 100 compounds by our approach was improved by 1.6–4.0 times that of the enrichment performance of molecular dockings. This result indicates that the application of molecular dynamics simulations to virtual screening for lead discovery is both effective and practical. However, further optimization of the computational protocols is required for screening various target proteins.     

Computation of elastic constants of solids using molecular simulation: comparison of constant volume and constant pressure ensemble methods

We compute the elastic stiffness tensor of fcc argon at 60 K and 1 bar using molecular simulation tools. Three different methods are investigated: explicit deformations of the simulation box, strain fluctuations at constant pressure and stress fluctuations at constant volume. Statistical ensemble sampling is done using molecular dynamics and Monte Carlo simulations. We observe a good agreement between the different methods and sampling algorithms excepted with molecular dynamics simulations in the (NpT) ensemble. There, we notice a strong dependence of the computed elastic constants with the barostat parameter, whereas molecular dynamics simulations in the (NVT) ensemble are not affected by the thermostat parameter.     

Molecular properties of a bent-core nematic liquid crystal A131 by multi-level theory simulations

ABSTRACT

Multi-level theory simulations have been performed to model a number of important molecular properties of a bent-core nematic liquid crystal (LC) A131. These important properties include molecular conformations, molecular Raman spectra, differential polarisability ratios, molecular crystals packing, atomic LC structures, order parameters, and Raman depolarisation spectra. The simulations contain four theory levels, involving molecular quantum chemistry, molecular crystal packing, super cell density functional based tight binding optimisation, and super cell molecular dynamics calculations. To heat initial optimised super cell structures, molecular dynamics simulations reveal phase transitions to uniaxial and biaxial nematic phases from molecular crystals. LC atomic structures result in direct calculations on order parameters, which can be further applied to computations on Raman depolarisation spectra with differential polarisability ratios, obtained in the molecular quantum chemistry theory level. The good agreement of simulated Raman depolarisation spectra with the experiment provides a detailed analysis on the unusually low values of experimental uniaxial order parameters.     

Overview of simulation studies on the enzymatic activity and conformational dynamics of the GTPase Ras

Over the last 40 years, we have learnt a great deal about the Ras onco-proteins. These intracellular molecular switches are essential for the function of a variety of physiological processes, including signal transduction cascades responsible for cell growth and proliferation. Molecular simulations and free energy calculations have played an essential role in elucidating the conformational dynamics and energetics underlying the GTP hydrolysis reaction catalysed by Ras. Here we present an overview of the main lessons from molecular simulations on the GTPase reaction and conformational dynamics of this important anti-cancer drug target. In the first part, we summarise insights from quantum mechanical and combined quantum mechanical/molecular mechanical simulations as well as other free energy methods and highlight consensus viewpoints as well as remaining controversies. The second part provides a very brief overview of new insights emerging from large-scale molecular dynamics simulations. We conclude with a perspective regarding future studies of Ras where computational approaches will likely play an active role.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Molecular simulations of protein dynamics: new windows on mechanisms in biology

Recent advances in computer hardware and software have led to the development of increasingly successful molecular simulations of protein structural dynamics that are intrinsic to biological processes. These simulations have resulted in models that increasingly agree with experimental observations, suggest new experiments and provide insights into biological mechanisms. Used in combination with data obtained with sophisticated experimental techniques, simulations are helping us to understand biological complexity at the atomic and molecular levels and are giving promising insights into the genetic, thermodynamic and functional/mechanistic behaviour of biological processes. Here, we highlight some examples of such approaches that illustrate the current state and potential of the field of molecular simulation.     

Molecular Dynamics Simulations of Proteins in Water Without the Truncation of Long-range Coulomb Interactions

A new program package (COSMOS90) for molecular dynamics simulations was developed to simulate large molecular systems consisting of more than tens of thousands of atoms without the truncation of long-range coulomb interactions. This program package was based on a new approximation scheme (PPPC) for calculating efficiently the coulomb interactions without sacrificing accuracy. In this approximation scheme, the group of charges at a long distance from each atom was represented by a total charge and total dipole moment of the group. In order to assess the accuracy of PPPC and the ability of COSMOS90, molecular dynamics simulations were carried out for a large system consisting of 16108 atoms (human lysozyme in water) for 50 ps using this program package. The coulomb energy per solute atom was calculated with only five percent of the error found in the 10 Å cut-off approximation (about 0.9 kcal/mol versus 18 kcal/mol, respectively). The molecular dynamics simulations using COSMOS90 require no more CPU time than the simulations based on the 10 Å cut-off approximation of the conventional programs for macromolecular simulations.     

Weight average approaches for predicting dynamical properties of biomolecules

Recent advances in atomistic molecular dynamics (MD) simulations of biomolecules allow us to explore their conformational spaces widely, observing large-scale conformational fluctuations or transitions between distinct structures. To reproduce or refine experimental data using MD simulations, structure ensembles, which are characterized by multiple structures and their statistical weights on the rugged free-energy landscapes, are often used. Here, we summarize weight average approaches for various experimental measurements. Weight average approaches are now applied to hybrid quantum mechanics/molecular mechanics MD simulations to predict fast vibrational motions in a protein with a high accuracy for better understanding of molecular functions from atomic structures.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

Investigating lipid composition effects on the mechanosensitive channel of large conductance (MscL) using molecular dynamics simulations

Previous experimental work has shown that the functional properties of the mechanosensitive channel of large conductance (MscL) are affected by variations in lipid composition. Here, we utilize molecular dynamics simulations of Mycobacterium tuberculosis MscL to investigate such lipid composition effects on a molecular level. In particular, two sets of simulations were performed. In the first, trajectories using lipids with different headgroups (phosphatidylcholine and phosphatidylethanolamine) were compared. Protein-lipid interactions were clearly altered by the headgroup changes, leading to conformational differences in the C-terminal region of M. tuberculosis MscL. In the second set of simulations, lipid tails were gradually shortened, thinning the membrane over a molecular dynamics trajectory. These simulations showed evidence of hydrophobic matching between MscL and the lipid membrane, as previously proposed. For all simulations, protein-lipid interaction energies in the second transmembrane region were correlated to mutagenic data, emphasizing the importance of lipid interactions for proper MscL function.     

Data Mining of Molecular Dynamics Trajectories of Nucleic Acids

Abstract

Analysis, storage, and transfer of molecular dynamic trajectories are becoming the bottleneck of computer simulations. In this paper we discuss different approaches for data mining and data processing of huge trajectory files generated from molecular dynamic simulations of nucleic acids.     

Comparison of molecular dynamics simulation methods for amyloid β(1-42) monomers containing D-aspartic acid residues for predicting retention times in chromatography

Molecular dynamics simulations of amyloid β(1-42) containing D-aspartic acid residues were performed using several continuous solvent models to investigate the usefulness of simulation methods for D-amino acid-containing proteins and peptides. Normal molecular dynamics simulations and replica exchange molecular dynamics simulations, which are one of the generalized-ensemble algorithms, were performed. Because the β-structure contents of amyloid β(1-42) peptides obtained by replica exchange molecular dynamics simulations with Onufriev-Bashford-Case generalized Born implicit solvent were qualitatively consistent with experimental data, replica exchange molecular dynamics rather than other methods appeared to be more reasonable for calculations of amyloid β(1-42) containing D-aspartic acid residues. Computational results revealed that peptides with stereoinversion of Asp23 tend to form β-sheet structures by themselves, in contrast to the wild-type peptides that form β-sheet structures only after aggregation. These results are expected to be useful for computational investigations of proteins and peptides such as prediction of retention time of peptides and proteins containing D-aspartic acid residues.     

Ten-microsecond molecular dynamics simulation of a fast-folding WW domain

All-atom molecular dynamics (MD) simulations of protein folding allow analysis of the folding process at an unprecedented level of detail. Unfortunately, such simulations have not yet reached their full potential both due to difficulties in sufficiently sampling the microsecond timescales needed for folding, and because the force field used may yield neither the correct dynamical sequence of events nor the folded structure. The ongoing study of protein folding through computational methods thus requires both improvements in the performance of molecular dynamics programs to make longer timescales accessible, and testing of force fields in the context of folding simulations. We report a ten-microsecond simulation of an incipient downhill-folding WW domain mutant along with measurement of a molecular time and activated folding time of 1.5 microseconds and 13.3 microseconds, respectively. The protein simulated in explicit solvent exhibits several metastable states with incorrect topology and does not assume the native state during the present simulations.     

Advances in biomolecular simulations: methodology and recent applications

Molecular dynamics simulations are widely used today to tackle problems in biochemistry and molecular biology. In the 25 years since the first simulation of a protein computers have become faster by many orders of magnitude, algorithms and force fields have been improved, and simulations can now be applied to very large systems, such as protein-nucleic acid complexes and multimeric proteins in aqueous solution. In this review we give a general background about molecular dynamics simulations, and then focus on some recent technical advances, with applications to biologically relevant problems.     

The consistency of large concerted motions in proteins in molecular dynamics simulations.

A detailed investigation is presented into the effect of limited sampling time and small changes in the force field on molecular dynamics simulations of a protein. Thirteen independent simulations of the B1 IgG-binding domain of streptococcal protein G were performed, with small changes in the simulation parameters in each simulation. Parameters studied included temperature, bond constraints, cut-off radius for electrostatic interactions, and initial placement of hydrogen atoms. The essential dynamics technique was used to reveal dynamic differences between the simulations. Similar essential dynamics properties were found for all simulations, indicating that the large concerted motions found in the simulations are not particularly sensitive to small changes in the force field. A thorough investigation into the stability of the essential dynamics properties as derived from a molecular dynamics simulation of a few hundred picoseconds is provided. Although the definition of the essential modes of motion has not fully converged in these short simulations, the subspace in which these modes are confined is found to be reproducible.     

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.     

Non-Ewald methods: theory and applications to molecular systems

Several non-Ewald methods for calculating electrostatic interactions have recently been developed, such as the Wolf method, the reaction field method, the pre-averaging method, and the zero-dipole summation method, for molecular dynamics simulations of various physical systems, including biomolecular systems. We review the theories of these approaches and their potential applications to molecular simulations, and discuss their relationships.