Integrating experimental data with molecular simulations to investigate RNA structural dynamics

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule Förster resonance energy transfer, or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field.     

Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.     

Backbone conformational flexibility of the lipid modified membrane anchor of the human N-Ras protein investigated by solid-state NMR and molecular dynamics simulation

The lipid modified human N-Ras protein, implicated in human cancer development, is of particular interest due to its membrane anchor that determines the activity and subcellular location of the protein. Previous solid-state NMR investigations indicated that this membrane anchor is highly dynamic, which may be indicative of backbone conformational flexibility. This article aims to address if a dynamic exchange between three structural models exist that had been determined previously. We applied a combination of solid-state nuclear magnetic resonance (NMR) methods and replica exchange molecular dynamics (MD) simulations using a Ras peptide that represents the terminal seven amino acids of the human N-Ras protein. Analysis of correlations between the conformations of individual amino acids revealed that Cys 181 and Met 182 undergo collective conformational exchange. Two major structures constituting about 60% of all conformations could be identified. The two conformations found in the simulation are in rapid exchange, which gives rise to low backbone order parameters and nuclear spin relaxation as measured by experimental NMR methods. These parameters were also determined from two 300 ns conventional MD simulations, providing very good agreement with the experimental data.     

Molecular dynamics simulation of hen egg white lysozyme: a test of the GROMOS96 force field against nuclear magnetic resonance data

Biomolecular force fields for use in molecular dynamics (MD) simulations of proteins, DNA, or membranes are generally parametrized against ab initio quantum-chemical and experimental data for small molecules. The application of a force field in a simulation of a biomolecular system, such as a protein in solution, may then serve as a test of the quality and transferability of the force field. Here, we compare various properties obtained from two MD simulations of the protein hen egg white lysozyme (HEWL) in aqueous solution using the latest version, GROMOS96, of the GROMOS force field and an earlier version, GROMOS87+, with data derived from nuclear magnetic resonance (NMR) experiments: NOE atom-atom distance bounds, (3)J(HNalpha)-coupling constants, and backbone and side-chain order parameters. The convergence of these quantities over a 2-ns period is considered, and converged values are compared to experimental ones. The GROMOS96 simulation shows better agreement with the NMR data and also with the X-ray crystal structure of HEWL than the GROMOS87+ simulation, which was based on an earlier version of the GROMOS force field.     

Conformation and dynamics of the three-helix bundle UBA domain of p62 from experiment and simulation

The ubiquitin associated domain of p62 is a small three-helix bundle of approximately 50 residues that mediates the recognition of polyubiquitin chains and ubiquitylated substrates. The solution structure of a 52 residue construct containing this domain has been characterized using heteronuclear nuclear magnetic resonance (NMR) methods. The resulting ensemble of NMR-derived structures was used in molecular dynamics (MD) simulations to investigate the equilibrium conformation and dynamics of this domain. NOE and (15)N relaxation data have been used to validate the structural ensemble produced by the MD simulations and show a good correlation for residues in regions of secondary structure. A similar approach was taken using an ensemble of structures from the MD simulations to calculate electronic circular dichroism (CD) and IR spectra from first principles with an encouraging correlation with the experimental CD and IR data.     

Ab initio 3-D structure prediction of an artificially designed three-alpha-helix bundle via all-atom molecular dynamics simulations

The rate at which knowledge about genomic sequences and their protein products is produced is increasing much faster than the rate of 3-dimensional protein structure determination by experimental methods, such as X-ray diffraction and nuclear magnetic resonance. One of the major challenges in structural bioinformatics is the conversion of genomic sequences into useful information, such as characterization of protein structure and function. Using molecular dynamics (MD) simulations, we predicted the 3-dimensional structure of an artificially designed three- alpha -helix bundle, called A3, from a fully extended initial conformation, based on its amino acid sequence. The MD protocol enabled us to obtain the secondary, in 1.0 ns, as well as the supersecondary and tertiary structures, in 4.0-10.0 ns, of A3, much faster than previously described for a similar protein system. The structure obtained at the end of the 10.0-ns MD simulation was topologically a three-alpha-helix bundle.     

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.     

Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular Dynamics

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.     

Incoherent neutron scattering of copper azurin: a comparison with molecular dynamics simulation results

The low-frequency dynamics of copper azurin has been studied at different temperatures for a dry and deuterium hydrated sample by incoherent neutron scattering and the experimental results have been compared with molecular dynamics (MD) simulations carried out in the same temperature range. Experimental Debye-Waller factors are consistent with a dynamical transition at approximately 200 K which appears partially suppressed in the dry sample. Inelastic and quasielastic scattering indicate that hydration water modulates both vibrational and diffusive motions. The low-temperature experimental dynamical structure factor of the hydrated protein shows an excess of inelastic scattering peaking at about 3 meV and whose position is slightly shifted downwards in the dry sample. Such an excess is reminiscent of the “boson peak” observed in glass-like materials. This vibrational peak is quite well reproduced by MD simulations, although at a lower energy. The experimental quasielastic scattering of the two samples at 300 K shows a two-step relaxation behaviour with similar characteristic times, while the corresponding intensities differ only by a scale factor. Also, MD simulations confirm the two-step diffusive trend, but the slow process seems to be characterized by a decay faster than the experimental one. Comparison with incoherent neutron scattering studies carried out on proteins having different structure indicates that globular proteins display common elastic, quasielastic and inelastic features, with an almost similar hydration dependence, irrespective of their secondary and tertiary structure. Received: 12 October 1998 / Revised version: 19 February 1999 / Accepted: 1 March 1999     

Headgroup Conformations of Phospholipids from Molecular Dynamics Simulation: Sampling Challenges and Comparison to Experiment

The preferred conformations of the glycerol region of a phospholipid have been explored using replica exchange molecular dynamics (MD) simulations and compared with the results of standard MD approaches and with experiment. We found that due to isomerization rates in key torsions that are slow on the timescale of atomistic MD simulations, standard MD is not able to produce accurate equilibrium conformer distributions from reasonable trajectory lengths (e.g., on the 100 ns) timescale. Replica exchange MD, however, results in quite efficient sampling due to the rapid increase in isomerization rate with temperature. The equilibrium distributions obtained from replica exchange MD have been compared with the results of experimental nuclear magnetic resonance observations. This comparison suggests that the sampling approach demonstrated here is a valuable tool that can be used in evaluating force fields for molecular simulation of lipids.     

Molecular simulation of dioleoylphosphatidylcholine lipid bilayers at differing levels of hydration.

The structure and dynamics of the lipid and water components of dioleoylphosphatidylcholine bilayers at various levels of hydration were studied using molecular dynamics (MD) simulations. Equilibration of these systems proceeded by use of a hybrid MD and configurational-bias Monte Carlo technique using one atmosphere of pressure normal to the membrane and a set point for the lateral area derived from experimental Bragg spacings, combined with experimentally derived specific volumes for each of the system components. Membrane surface tensions were observed to be of the order of tens of dyn/cm. The transbilayer molecular fragment peak positions at low hydration were found to agree with experimental neutron and x-ray scattering profiles and previously published simulations. For hydration levels of 5.4, 11.4, and 16 waters/lipid, molecular fragment distributions and order parameters for the headgroup, lipid chains, and water were quantified. Spin-lattice relaxation rates and lateral self-diffusion coefficients of water agreed well with results from experimental nuclear magnetic resonance studies. Relaxation rates of the choline segments and chemical shift anisotropies for the phosphate and carbonyls were computed. Headgroup orientation, as measured by the P-N vector, showed enhanced alignment with the membrane surface at low hydration. The sign of the membrane dipole potential reversed at low hydration, with the membrane interior negative relative to the interlamellar region. Calculation of the number of water molecules in the headgroup hydration shell, as a function of hydration level, supports the hypothesis that the break point in the curve of Bragg spacing versus hydration level near 12 waters/lipid, observed experimentally by Hristova and White (1988. Biophys. J. 74:2419-2433), marks the completion of the first hydration shell.     

Molecular dynamics simulation of proteins under high pressure: Structure,function and thermodynamics

BackgroundMolecular dynamics (MD) simulation is well-recognized as a powerful tool to investigate protein structure, function, and thermodynamics. MD simulation is also used to investigate high pressure effects on proteins. For conducting better MD simulation under high pressure, the main issues to be addressed are: (i) protein force fields and water models were originally developed to reproduce experimental properties obtained at ambient pressure; and (ii) the timescale to observe the pressure effect is often much longer than that of conventional MD simulations.Scope of reviewFirst, we describe recent developments in MD simulation methodologies for studying the high-pressure structure and dynamics of protein molecules. These developments include force fields for proteins and water molecules, and enhanced simulation techniques. Then, we summarize recent studies of MD simulations of proteins in water under high pressure.Major conclusionsRecent MD simulations of proteins in solution under pressure have reproduced various phenomena identified by experiments using high pressure, such as hydration, water penetration, conformational change, helix stabilization, and molecular stiffening.General significanceMD simulations demonstrate differences in the properties of proteins and water molecules between ambient and high-pressure conditions. Comparing the results obtained by MD calculations with those obtained experimentally could reveal the mechanism by which biological molecular machines work well in collaboration with water molecules.     

Neutron frequency windows and the protein dynamical transition

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, , that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations---an "equilibrium" model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a "frequency window" model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.     

Low-temperature molecular dynamics simulations of horse heart cytochrome c and comparison with inelastic neutron scattering data

Molecular dynamics (MD) simulation combined with inelastic neutron scattering can provide information about the thermal dynamics of proteins, especially the low-frequency vibrational modes responsible for large movement of some parts of protein molecules. We performed several 30-ns MD simulations of cytochrome c (Cyt c) in a water box for temperatures ranging from 110 to 300 K and compared the results with those from experimental inelastic neutron scattering. The low-frequency vibrational modes were obtained via dynamic structure factors, S(Q, ω), obtained both from inelastic neutron scattering experiments and calculated from MD simulations for Cyt c in the same range of temperatures. The well known thermal transition in structural movements of Cyt c is clearly seen in MD simulations; it is, however, confined to unstructured fragments of loops Ω₁ and Ω₂; movement of structured loop Ω₃ and both helical ends of the protein is resistant to thermal disturbance. Calculated and experimental S(Q, ω) plots are in qualitative agreement for low temperatures whereas above 200 K a boson peak vanishes from the calculated plots. This may be a result of loss of crystal structure by the protein–water system compared with the protein crystal.     

The role of protein–solvent hydrogen bond dynamics in the structural relaxation of a protein in glycerol versus water

We used MD simulations to investigate the dependence of the dynamics of a soluble protein, RNase A, on temperature and solvent environment. Consistent with neutron scattering data, the simulations predict that the protein undergoes a dynamical transition in both glycerol and aqueous solutions that is absent in the dry protein. The temperature of the transition is higher, while the rate of increase with temperature of the amplitudes of motion on the 100 ps timescale is lower, in glycerol versus water. Analysis of the dynamics of hydrogen bonds revealed that the protein dynamical transition is connected to the relaxation of the protein-solvent hydrogen bond network, which, in turn, is associated with solvent translational diffusion. Thus, it appears that the role of solvent dynamics in affecting the protein dynamical transition is qualitatively similar in water and glycerol.     

Asymmetric stability among the transmembrane helices of lactose permease

Combining structure determinations from nuclear magnetic resonance (NMR) data and molecular dynamics simulations (MD) under the same environmental conditions revealed a startling asymmetry in the intrinsic conformational stability of secondary structure in the transmembrane domain of lactose permease (LacY). Eleven fragments, corresponding to transmembrane segments (TMs) of LacY, were synthesized, and their secondary structure in solution was determined by NMR. Eight of the TMs contained significant regions of helical structure. MD simulations, both in DMSO and in a DMPC bilayer, showed sites of local stability of helical structure in these TMs, punctuated by regions of conformational instability, in substantial agreement with the NMR data. Mapping the stable regions onto the crystal structure of LacY reveals a marked asymmetry, contrasting with the pseudosymmetry in the static structure: the secondary structure in the C-terminal half is more stable than in the N-terminal half. The relative stability of secondary structure is likely exploited in the transport mechanism of LacY. Residues supporting proton conduction are in more stable regions of secondary structure, while residues key to substrate binding are found in considerably unstable regions of secondary structure.