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.     

Examination of nanoflow in rectangular slits

This paper presents simulations of 3D nanoscale flow in rectangular channel with molecular dynamics simulation method. Rectangular cross section is a frequently encountered geometric shape for nanoscale flow problems. For a given cross sectional height h, we change the width w of the rectangular cross section and analyze the influence of w/h on the flow characteristics. The distributions of density, temperature, boundary slip and flow velocity inside the rectangular cross section are investigated in detail. Liquid argon material and Lennard-Jones potential are used in the simulations. The simulation results are also compared with Navier–Stokes solutions for rectangular channel flows.     

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

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

On the Atomic Velocities in Molecular and Langevin Dynamics Simulations of Soft-Sphere Systems

Abstract

Time dependent probability distributions of the changes of direction of atomic velocities are considered in order to examine in detail the shape of the trajectories obtained through molecular simulations. We have analysed the atomic motions obtained from molecular dynamics simulations of soft-sphere systems at three very different states, i.e. a dilute fluid, a liquid at high density, and a solid. The methodology has also been used to check the reliability of the velocity evolution obtained when it is assumed that a single particle obeys the generalized Langevin equation and the effect of the other particles is represented by friction and random forces.     

Simulated annealing coupled replica exchange molecular dynamics—An efficient conformational sampling method

Molecular dynamics simulated annealing (SA-MD) simulations are frequently used for refinement and optimization of peptide and protein structures. Depending on the simulation conditions and simulation length SA-MD simulations can be trapped in locally stable conformations far from the global optimum. As an alternative replica exchange molecular dynamics (RexMD) simulations can be used which allow exchanges between high and low simulation temperatures at all stages of the simulation. A significant drawback of RexMD simulations is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A combined SA-MD and RexMD approach termed SA-RexMD is suggested that employs a small number of replicas (4) and starts initially with a set of high simulation temperatures followed by gradual cooling of the set of temperatures until a target temperature has been reached. The protocol has been applied for the folding of several peptide systems and for the refinement of protein model structures. In all the cases, the SA-RexMD method turned out to be significantly more efficient in reaching low energy structures and also structures close to experiment compared to continuous MD simulations at the target temperature and to SA-MD simulations at the same computational demand. The approach is well suited for applications in structure refinement and for systematic force field improvement.     

On the Approximation of Solvent Effects on the Conformation and Dynamics of Cyclosporin A by Stochastic Dynamics Simulation Techniques

Abstract

The molecular simulation technique of stochastic dynamics (SD) is tested by application to the immunosuppressive drug cyclosporin A (CPA). Two stochastic dynamics simulations are performed, one (SD_CCl4 ) with atomic friction coefficients proportional to the viscosity of the nonpolar solvent CCl₄, and one (SD_H2O) with atomic friction coefficients corresponding to an aqueous solution. The atomic friction coefficients are also taken proportional to an approximate expression for the atomic accessible surface area. The properties of both stochastic dynamics simulations are compared to those of two full molecular dynamics (MD) simulations of cyclosporin A, one in a box with 591 CCl₄ molecules, and one in a box with 632 H₂O molecules.

The properties of cyclosporin A as found in the molecular dynamics simulation in CCl₄ are well reproduced by the SD_CCl4 simulation. This indicates that the neglect of a mean force reresenting the average solvent effects on the solute is justified in the case of nonpolar solvents. For polar solvents, like water, this mean force may not be neglected. The SD_H2O simulation of cyclosporin A clearly fails to reproduce the amount of hydrogen bonding found in the molecular dynamics stimulation of cyclosporin A in water.

A comparison with a molecular dynamics simulation of cyclosporin A in vacuo shows that both the SD_CCl4 and the SD_H2O simulation come closer to the properties of the molecular dynamics simulations in CCl₄ and in H₂O than a molecular dynamics simulation in vacuo.     

Molecular dynamics simulation of thread break-up and formation of droplets in nanoejection system

This study investigated nanojet processes by a non-equilibrium molecular dynamics simulation. The phenomena of liquid thread break-up and droplet formation were simulated by compressing liquid propane molecules with various compressing velocities. Properties' distributions show that, at the nanoscale, density and pressure were neither uniform nor continuous during the ejection process. Shear heating phenomena were found in the contact area of the nozzle channel. A linear relationship between the length of liquid threads and the compressing velocity was also found in this study. The results from different trials using various compressing velocities show that higher compressing velocities in nanojet processes result in longer liquid thread lengths and liquid molecules with higher energy levels. Therefore, the ejection process is more unstable, resulting in an increase in the number of evaporating molecules and satellite droplets. Results that illustrate various features are presented to aid in the comprehension of the nanojet processes.     

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.     

Molecular Dynamics Investigation of Bond Ordering of Unsaturated Lipids in Monolayers

Molecular dynamics simulations of three model lipid monolayers of 2,3-diacyl-D-glycerolipids, that contained stearoyl (18:0) in the position 3 and oleoyl (18:9cis), linoleoyl (18:26cis), or linolenoyl (18:33cis) in the position 2, have been carried out. The simulation systems consisted of 24 lipid molecules arranged in a rectangular simulation cell, with periodic boundary conditions in the surface plane. 1 nanosecond simulations were performed at T = 295 K. C-C and C-H bond order parameter profiles and the bond orientation distributions about the monolayer normal have been calculated. The relation of the distributions to the order parameters was analyzed in terms of maxima and widths of the distributions. The cis double bond order parameter is found to be higher than those of adjacent single C-C bonds. The widths of the two distributions of C-H bonds of the cis double bond segment in di- and triunsaturated molecules are much smaller than that obtained for methylene group located between the double bonds. The bond orientation distribution function widths depend on both the segment location in the chain and the segment chemical structure.     

Molecular dynamics simulations of concentrated aqueous electrolyte solutions

Transport properties of concentrated electrolytes have been analysed using classical molecular dynamics simulations with the algorithms and parameters typical of simulations describing complex electrokinetic phenomena. The electrical conductivity and transport numbers of electrolytes containing monovalent (KCl), divalent (MgCl₂), a mixture of both (KCl+MgCl₂) and trivalent (LaCl₃) cations have been obtained from simulations of the electrolytes in electric fields of different magnitude. The results obtained for different simulation parameters have been discussed and compared with experimental measurements of our own and from the literature. The electroosmotic flow of water molecules induced by the ionic current in different cases has been calculated and interpreted with the help of the hydration properties extracted from the simulations.     

Hydrogen-bond dynamics of water in presence of an amphiphile,tetramethylurea: signature of confinement-induced effects

Various experimental and simulation studies have suggested that the presence of amphiphilic molecules in aqueous solutions substantially perturbs the tetrahedral hydrogen-bond (H-bond) network of neat liquid water. Such structural perturbation is expected to impact H-bond lifetime of liquid water. Tetramethylurea (TMU) is an example of an amphiphile because it possesses both hydrophobic and hydrophilic moieties. Molecular dynamics simulations of (water+TMU) binary mixtures at various compositions have been performed in order to investigate the microscopic mechanism through which the amphiphiles influence the H-bond dynamics of liquid water at room temperature. Present simulations indicate lengthening of both water–water H-bond lifetime and H-bond structural relaxation time upon addition of TMU in aqueous solution. At the highest TMU mole fraction studied, H-bond lifetime and structural relaxation time are, respectively, ～4 and ～8 times longer than those in neat water. This is comparable with the slowing down of H-bond dynamics for water molecules confined in cyclodextrin cavities. Simulated relaxation profiles are multi-exponential in character at all mixture compositions, and simulated radial distribution functions suggest enhanced water–water and water–TMU interactions upon addition of TMU. No evidence for complete encapsulation of TMU by water H-bond network has been found.     

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

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

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.     

Systolic Loop Methods for Molecular Dynamics Simulation,Generalised for Macromolecules

Abstract

Systolic loop programs have been shown to be very efficient for molecular dynamics simulations of liquid systems on distributed memory parallel computers. The original methods address the case where the number of molecules simulated exceeds the number of processors used. Simulations of large flexible molecules often do not meet this condition, requiring the three- and four-body terms used to model chemical bonds within a molecule to be distributed over several processors. This paper discusses how the systolic loop methods may be generalised to accommodate such systems, and describes the implementation of a computer program for simulation of protein dynamics. Performance figures are given for this program running typical simulations on a Meiko Computing Surface using different number of processors.     

A molecular dynamics simulation of hexagonal solid platinum nanowires

Experimental evidence of the existence of multi-wall platinum (Pt) nanowires (NWs) has been reported. In this paper, we investigated structural formation of Pt NWs using the classical molecular dynamics (MD) simulation method. The simulations began from initial configurations with random distributions of atomic positions. The initial configuration was minimised by the steepest descent method, and assigned a temperature of 601?K with a random distribution of atomic velocities. Then simulated annealing was applied such that the temperature of the system was reduced gradually to 1?K and a stable NW structure was obtained. Types of hexagonal solid Pt NWs featuring different structures than those of previously reported NWs were found. Details of structural characteristics and mechanical properties of these Pt NWs are presented.     

Effects of interfaces on aggregates of peptides derived from pancreatic islet amyloid polypeptide

Recent experimental studies indicate that oligomeric complexes of misfolded proteins and peptides are the primary agents of cytotoxicity in amyloid-related diseases. Given the prevalence of mixed-polarity interfaces in physiological environments, an understanding of the mechanisms of interactions between amorphous (pre-fibrillar) aggregates and surfaces is important for completing our knowledge of the behaviour of peptide aggregation phenomena. We have employed fully solvated molecular dynamics simulations to study the morphology, interactions and peptide conformations of disordered aggregates of the amyloidogenic NFGAIL (derived from human islet amyloid polypeptide) and non-amyloidogenic AGAIL peptides upon adsorption to vapour–water, decane–water, bilayer and solid–water interfaces. All of the interfaces studied promote elongation and surface-spreading of both peptide aggregates, with the liquid–liquid interface being particularly efficient at altering the gross morphology of disordered aggregates. NFGAIL aggregates are more effective at disrupting lipid bilayers compared to AGAIL. Additionally, the interfaces studied cause greater changes in peptide conformations within the NFGAIL aggregates compared to AGAIL. We propose that simulations may elucidate the capability of interfaces to effect changes in the behaviour of disordered peptide aggregates, which may also serve to provide measures of the intrinsic fibrillogenicity of a given peptide sequence.     

Interchain hydrophobic clustering promotes rigidity in HIV-1 protease flap dynamics: new insights from Molecular Dynamics

The dynamics of HIV-1 protease (HIV-pr), a drug target for HIV infection, has been studied extensively by both computational and experimental methods. The flap dynamics of HIV-pr is considered to be more important for better ligand binding and enzymatic actions. Moreover, it has been demonstrated that the drug-induced mutations can change the flap dynamics of HIV-pr affecting the binding affinity of the ligands. Therefore, detailed understanding of flap dynamics is essential for designing better inhibitors. Previous computational investigations observed significant variation in the flap opening in nanosecond time scale indicating that the dynamics is highly sensitive to the simulation protocols. To understand the sensitivity of the flap dynamics on the force field and simulation protocol, molecular dynamics simulations of HIV-pr have been performed with two different AMBER force fields, ff99 and ff02. Two different trajectories (20?ns each) were obtained using the ff99 and ff02 force field. The results showed polarizable force field (ff02) make the flap tighter than the nonpolarizable force field (ff99). Some polar interactions and hydrogen bonds involving flap residues were found to be stronger with ff02 force field. The formation of interchain hydrophobic cluster (between flap tip of one chain and active site wall of another chain) was found to be dominant in the semi-open structures obtained from the simulations irrespective of the force field. It is proposed that an inhibitor, which will promote this interchain hydrophobic clustering, may make the flaps more rigid, and presumably the effect of mutation would be small on ligand binding.