Isobaric and Isothermal Molecular Dynamics Simulations of Diatomic Systems

Abstract

Isobaric molecular dynamics simulations were carried out for diatomic systems using different algorithms available in the literature. Two-centered Lennard-Jones potentials with and without quadrupolar interactions were used. Thermodynamic properties obtained from the isobaric algorithms compared very well with those of an equivalent simulation in the microcanonical ensemble; however, some differences were observed when similar comparisons were carried out for dynamic properties. More specifically, the constant pressure constraint affects the translational dynamics of the system because of the non-negligible differences between the momenta and the instantaneous velocities of the molecules.

Furthermore, the following studies were carried out using isobaric MD simulations: 1. Low temperature spontaneous FCC-orthorhombic (and vice versa) transition of a diatomic system with quadrupolar interactions as a function of the molecular bond length. 2. Effect of quadrupolar interaction on isobaric melting of a model diatomic system. 3. Effect of pressure on melting properties of a model diatomic system with quadrupolar interactions.     

Motional timescale predictions by molecular dynamics simulations: Case study using proline and hydroxyproline sidechain dynamics

We propose a new approach for force field optimizations which aims at reproducing dynamics characteristics using biomolecular MD simulations, in addition to improved prediction of motionally averaged structural properties available from experiment. As the source of experimental data for dynamics fittings, we use ¹³C NMR spin‐lattice relaxation times T₁ of backbone and sidechain carbons, which allow to determine correlation times of both overall molecular and intramolecular motions. For structural fittings, we use motionally averaged experimental values of NMR J couplings. The proline residue and its derivative 4‐hydroxyproline with relatively simple cyclic structure and sidechain dynamics were chosen for the assessment of the new approach in this work. Initially, grid search and simplexed MD simulations identified large number of parameter sets which fit equally well experimental J couplings. Using the Arrhenius‐type relationship between the force constant and the correlation time, the available MD data for a series of parameter sets were analyzed to predict the value of the force constant that best reproduces experimental timescale of the sidechain dynamics. Verification of the new force‐field (termed as AMBER99SB‐ILDNP) against NMR J couplings and correlation times showed consistent and significant improvements compared to the original force field in reproducing both structural and dynamics properties. The results suggest that matching experimental timescales of motions together with motionally averaged characteristics is the valid approach for force field parameter optimization. Such a comprehensive approach is not restricted to cyclic residues and can be extended to other amino acid residues, as well as to the backbone. Proteins 2014; 82:195–215. © 2013 Wiley Periodicals, Inc.     

Biomembrane simulations of 12 lipid types using the general amber force field in a tensionless ensemble

The AMBER family of force fields is one of the most commonly used alternatives to describe proteins and drug-like molecules in molecular dynamics simulations. However, the absence of a specific set of parameters for lipids has been limiting the widespread application of this force field in biomembrane simulations, including membrane protein simulations and drug-membrane simulations. Here, we report the systematic parameterization of 12 common lipid types consistent with the General Amber Force Field (GAFF), with charge-parameters determined with RESP at the HF/6–31G(d) level of theory, to be consistent with AMBER. The accuracy of the scheme was evaluated by comparing predicted and experimental values for structural lipid properties in MD simulations in an NPT ensemble with explicit solvent in 100:100 bilayer systems. Globally, a consistent agreement with experimental reference data on membrane structures was achieved for some lipid types when using the typical MD conditions normally employed when handling membrane proteins and drug-membrane simulations (a tensionless NPT ensemble, 310?K), without the application of any of the constraints often used in other biomembrane simulations (such as the surface tension and the total simulation box area). The present set of parameters and the universal approach used in the parameterization of all the lipid types described here, as well as the consistency with the AMBER force field family, together with the tensionless NPT ensemble used, opens the door to systematic studies combining lipid components with small drug-like molecules or membrane proteins and show the potential of GAFF in dealing with biomembranes.     

Toward a predictive understanding of slow methyl group dynamics in proteins

The development of the most recent generation of molecular mechanics force fields promises an increasingly predictive understanding of the protein dynamics-function relationship. Based on extensive validation against various types of experimental data, the AMBER force field ff99SB was benchmarked in recent years as a favorable force field for protein simulations. Recent improvements of the side chain and backbone potentials, made by different groups, led to the ff99SB-ILDN and ff99SBnmr1 force fields, respectively. The combination of these potentials into a unified force field, termed ff99SBnmr1-ILDN, was used in this study to perform a microsecond time scale molecular dynamics simulation of free ubiquitin in explicit solvent for validation against an extensive set of experimental NMR methyl group residual dipolar couplings. Our results show a high level of consistency between the experimental data and the values predicted from the molecular dynamics trajectory reflecting a systematically improved performance of ff99SBnmr1-ILDN over the original ff99SB force field. Moreover, the unconstrained ff99SBnmr1-ILDN MD ensemble achieves a similar level of agreement as the recently introduced EROS ensemble, which was constructed based on a large body of NMR data as constraints, including the methyl residual dipolar couplings. This suggests that ff99SBnmr1-ILDN provides a high-quality representation of the motions of methyl-bearing protein side chains, which are sensitive probes of protein-protein and protein-ligand interactions.     

Parameterization of aromatic azido groups: application as photoaffinity probes in molecular dynamics studies

The accuracy of molecular dynamics (MD) simulations is limited by the availability of parameters for the molecular system of interest. In most force fields, parameters of common chemical groups are already present. With the development of novel small organic molecules as probes to study biological systems, more chemical groups require parameterization. An azide group is often used in studies of biological systems but computational studies are still impeded by the lack of parameters. In this paper, we present a set of molecular mechanics (MM) parameters for aromatic and aliphatic azido groups, and their application in MD simulations of a photoaffinity probe currently used in our laboratory for mapping binding modes available in the active site of histone deacetylases. The parameters were developed for the generalized Amber force field (GAFF) using density functional theory (DFT) calculations at B3LYP 6-311G(d) level. The parameters were validated by geometry optimization and MD simulations.     

Computer simulations of the flexibility of a series of synthetic cyclic peptide analogues

The flexibility of a series of cyclic peptides derived from the epitope of a snake toxin is investigated using computer simulation techniques. Molecular dynamics (MD) simulations and vibrational analyses are performed on chemically constrained peptides modeled on the parent protein loop. In the 50 ps MD simulations, large variations in the atomic fluctuations are seen between the peptides, and can be related to the nature of the chemical constraints present in the molecules. Normal mode analyses are performed on energy-minimized configurations derived from the dynamics trajectories. The atomic fluctuations calculated from the normal modes are about 30% of those of the molecular dynamics for the more flexible peptides and 70% for the more constrained molecules. The calculated differences in flexibility between the molecules are much less significant in the harmonic approximation. © 1993 John Wiley & Sons, Inc.     

Internal mobility of the ologonucleotide duplexes d(TCGCG)2 and d(CGCGCG)2 in aqueous solution from molecular dynamics simulations

Summary In this paper we present longitudinal relaxation times, order parameters and effective correlation times for the base and sugar carbons in both strands of the oligonucleotide duplexes d(TCGCG)₂ and d(CGCGCG)₂, as calculated from 400 ps molecular dynamics trajectories in aqueous solution. The model-free approach (Lipari and Szabo, 1982) was used to determine the amplitudes and time scales of the internal motion. Comparisons were made with NMR relaxation measurements (Borer et al., 1994). The order parameters could acceptably be reproduced, and the effective correlation times were found to be lower than the experimental estimates. Reasonable T₁ relaxation times were obtained in comparison with experiment for the nonterminal nucleosides. The T₁ relaxation times were found to depend mainly on the order parameters and overall rotational correlation time.Abbreviations MD molecular dynamics - CSA chemical shift anisotropy To whom correspondence should be addressed.     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Constructing RNA dynamical ensembles by combining MD and motionally decoupled NMR RDCs: new insights into RNA dynamics and adaptive ligand recognition

We describe a strategy for constructing atomic resolution dynamical ensembles of RNA molecules, spanning up to millisecond timescales, that combines molecular dynamics (MD) simulations with NMR residual dipolar couplings (RDC) measured in elongated RNA. The ensembles are generated via a Monte Carlo procedure by selecting snap-shot from an MD trajectory that reproduce experimentally measured RDCs. Using this approach, we construct ensembles for two variants of the transactivation response element (TAR) containing three (HIV-1) and two (HIV-2) nucleotide bulges. The HIV-1 TAR ensemble reveals significant mobility in bulge residues C24 and U25 and to a lesser extent U23 and neighboring helical residue A22 that give rise to large amplitude spatially correlated twisting and bending helical motions. Omission of bulge residue C24 in HIV-2 TAR leads to a significant reduction in both the local mobility in and around the bulge and amplitude of inter-helical bending motions. In contrast, twisting motions of the helices remain comparable in amplitude to HIV-1 TAR and spatial correlations between them increase significantly. Comparison of the HIV-1 TAR dynamical ensemble and ligand bound TAR conformations reveals that several features of the binding pocket and global conformation are dynamically preformed, providing support for adaptive recognition via a ‘conformational selection’ type mechanism.     

Interpretation of H-NMR Experiments on the Orientation of the Transmembrane Helix WALP23 by Computer Simulations

Orientation, dynamics, and packing of transmembrane helical peptides are important determinants of membrane protein structure, dynamics, and function. Because it is difficult to investigate these aspects by studying real membrane proteins, model transmembrane helical peptides are widely used. NMR experiments provide information on both orientation and dynamics of peptides, but they require that motional models be interpreted. Different motional models yield different interpretations of quadrupolar splittings (QS) in terms of helix orientation and dynamics. Here, we use coarse-grained (CG) molecular dynamics (MD) simulations to investigate the behavior of a well-known model transmembrane peptide, WALP23, under different hydrophobic matching/mismatching conditions. We compare experimental ²H-NMR QS (directly measured in experiments), as well as helix tilt angle and azimuthal rotation (not directly measured), with CG MD simulation results. For QS, the agreement is significantly better than previously obtained with atomistic simulations, indicating that equilibrium sampling is more important than atomistic details for reproducing experimental QS. Calculations of helix orientation confirm that the interpretation of QS depends on the motional model used. Our simulations suggest that WALP23 can form dimers, which are more stable in an antiparallel arrangement. The origin of the preference for the antiparallel orientation lies not only in electrostatic interactions but also in better surface complementarity. In most cases, a mixture of monomers and antiparallel dimers provides better agreement with NMR data compared to the monomer and the parallel dimer. CG MD simulations allow predictions of helix orientation and dynamics and interpretation of QS data without requiring any assumption about the motional model.     

High-resolution NMR structure of an RNA model system: the 14-mer cUUCGg tetraloop hairpin RNA

We present a high-resolution nuclear magnetic resonance (NMR) solution structure of a 14-mer RNA hairpin capped by cUUCGg tetraloop. This short and very stable RNA presents an important model system for the study of RNA structure and dynamics using NMR spectroscopy, molecular dynamics (MD) simulations and RNA force-field development. The extraordinary high precision of the structure (root mean square deviation of 0.3 Å) could be achieved by measuring and incorporating all currently accessible NMR parameters, including distances derived from nuclear Overhauser effect (NOE) intensities, torsion-angle dependent homonuclear and heteronuclear scalar coupling constants, projection-angle-dependent cross-correlated relaxation rates and residual dipolar couplings. The structure calculations were performed with the program CNS using the ARIA setup and protocols. The structure quality was further improved by a final refinement in explicit water using OPLS force field parameters for non-bonded interactions and charges. In addition, the 2′-hydroxyl groups have been assigned and their conformation has been analyzed based on NOE contacts. The structure currently defines a benchmark for the precision and accuracy amenable to RNA structure determination by NMR spectroscopy. Here, we discuss the impact of various NMR restraints on structure quality and discuss in detail the dynamics of this system as previously determined.     

Glycan flexibility: insights into nanosecond dynamics from a microsecond molecular dynamics simulation explaining an unusual nuclear Overhauser effect

An atomistic all-atom molecular dynamics simulation of the trisaccharide β-d-ManpNAc-(1→4)[α-d-Glcp-(1→3)]-α-l-Rhap-OMe with explicit solvent molecules has been carried out. The trisaccharide represents a model for the branching region of the O-chain polysaccharide of a strain from Aeromonas salmonicida. The extensive MD simulations having a 1-μs duration revealed a conformational dynamics process on the nanosecond time scale, that is, a ‘time window’ not extensively investigated for carbohydrates to date. The results obtained from the MD simulation underscore the predictive power of molecular simulations in studies of biomolecular systems and also explain an unusual nuclear Overhauser effect originating from conformational exchange.     

NMR and modelling studies of disaccharide conformation

Long-range heteronuclear coupling constants were measured across the glycosidic linkages for a series of eight alpha- or beta-linked disaccharides in aqueous solution. Multiple 13C site-selective excitation experiments using 1H decoupling in conjunction with pulsed field gradient-enhanced spectroscopy were used to determine 3J(C,H) values. These were subsequently compared with the respective couplings calculated, using a Karplus relationship, from molecular dynamics simulations with the explicit inclusion of water.     

Structural Dynamics and Conformational Equilibria of SERCA Regulatory Proteins in Membranes by Solid-State NMR Restrained Simulations

Solid-state NMR spectroscopy is emerging as a powerful approach to determine structure, topology, and conformational dynamics of membrane proteins at the atomic level. Conformational dynamics are often inferred and quantified from the motional averaging of the NMR parameters. However, the nature of these motions is difficult to envision based only on spectroscopic data. Here, we utilized restrained molecular dynamics simulations to probe the structural dynamics, topology and conformational transitions of regulatory membrane proteins of the calcium ATPase SERCA, namely sarcolipin and phospholamban, in explicit lipid bilayers. Specifically, we employed oriented solid-state NMR data, such as dipolar couplings and chemical shift anisotropy measured in lipid bicelles, to refine the conformational ensemble of these proteins in lipid membranes. The samplings accurately reproduced the orientations of transmembrane helices and showed a significant degree of convergence with all of the NMR parameters. Unlike the unrestrained simulations, the resulting sarcolipin structures are in agreement with distances and angles for hydrogen bonds in ideal helices. In the case of phospholamban, the restrained ensemble sampled the conformational interconversion between T (helical) and R (unfolded) states for the cytoplasmic region that could not be observed using standard structural refinements with the same experimental data set. This study underscores the importance of implementing NMR data in molecular dynamics protocols to better describe the conformational landscapes of membrane proteins embedded in realistic lipid membranes.     

Conformational investigation of a cyclic enterobacterial common antigen employing NMR spectroscopy and molecular dynamics simulations

The three-dimensional structure of a cyclic enterobacterial common antigen (ECA) having four trisaccharide repeating units has been investigated by NMR spectroscopy and molecular dynamics simulations. Three different NMR parameters were determined: (a) (1)H,(1)H cross-relaxation rates from NOE experiments were used for determination of proton-proton distances; (b) trans-glycosidic (3)J(C,H) scalar coupling constants analyzed via a Karplus-type relationship provided information on torsion angles; and (c) (1)H,(13)C one-bond dipolar couplings obtained in a dilute liquid-crystalline medium were interpreted in terms of the orientational order and molecular conformations. The molecular dynamics simulations of the dodecasaccharide were performed with explicit water and counterions, which are important factors that strongly influence molecular conformation. Subsequently, the results from computer simulation were used to generate a three-dimensional structure of the cyclic ECA which is consistent with the experimental NMR parameters.     

Structural Dynamics and Conformational Equilibria of SERCA Regulatory Proteins in Membranes by Solid-State NMR Restrained Simulations

Solid-state NMR spectroscopy is emerging as a powerful approach to determine structure, topology, and conformational dynamics of membrane proteins at the atomic level. Conformational dynamics are often inferred and quantified from the motional averaging of the NMR parameters. However, the nature of these motions is difficult to envision based only on spectroscopic data. Here, we utilized restrained molecular dynamics simulations to probe the structural dynamics, topology and conformational transitions of regulatory membrane proteins of the calcium ATPase SERCA, namely sarcolipin and phospholamban, in explicit lipid bilayers. Specifically, we employed oriented solid-state NMR data, such as dipolar couplings and chemical shift anisotropy measured in lipid bicelles, to refine the conformational ensemble of these proteins in lipid membranes. The samplings accurately reproduced the orientations of transmembrane helices and showed a significant degree of convergence with all of the NMR parameters. Unlike the unrestrained simulations, the resulting sarcolipin structures are in agreement with distances and angles for hydrogen bonds in ideal helices. In the case of phospholamban, the restrained ensemble sampled the conformational interconversion between T (helical) and R (unfolded) states for the cytoplasmic region that could not be observed using standard structural refinements with the same experimental data set. This study underscores the importance of implementing NMR data in molecular dynamics protocols to better describe the conformational landscapes of membrane proteins embedded in realistic lipid membranes.     

A molecular dynamics simulation study of polyamine– and sodium–DNA. Interplay between polyamine binding and DNA structure

Four different molecular dynamics (MD) simulations have been performed for infinitely long ordered DNA molecules with different counterions, namely the two natural polyamines spermidine(3+) (Spd³⁺) and putrescine(2+) (Put²⁺), the synthetic polyamine diaminopropane(2+) (DAP²⁺), and the simple monovalent cation Na⁺. All systems comprised a periodical hexagonal cell with three identical DNA decamers, 15 water molecules per nucleotide, and counterions balancing the DNA charge. The simulation setup mimics the DNA state in oriented DNA fibers, previously studied using NMR and other experimental methods. In this paper the interplay between polyamine binding and local DNA structure is analyzed by investigating how and if the minor groove width of DNA depends on the presence and dynamics of the counterions. The results of the MD simulations reveal principal differences in the polyamine–DNA interactions between the natural [spermine(4+), Spd³⁺, Put²⁺] and the synthetic (DAP²⁺) polyamines.Abbreviations DAP diaminopropane - DDD Drew–Dickerson dodecamer - MD molecular dynamics - Put putrescine - RDF radial distribution function - Spd spermidine - Spm spermine     

DRF90: a polarizable force field

The direct reaction field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) molecular dynamics (MD) simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as MD simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.