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.     

Simulation vs. reality: a comparison of in silico distance predictions with DEER and FRET measurements

Site specific incorporation of molecular probes such as fluorescent- and nitroxide spin-labels into biomolecules, and subsequent analysis by F?rster resonance energy transfer (FRET) and double electron-electron resonance (DEER) can elucidate the distance and distance-changes between the probes. However, the probes have an intrinsic conformational flexibility due to the linker by which they are conjugated to the biomolecule. This property minimizes the influence of the label side chain on the structure of the target molecule, but complicates the direct correlation of the experimental inter-label distances with the macromolecular structure or changes thereof. Simulation methods that account for the conformational flexibility and orientation of the probe(s) can be helpful in overcoming this problem. We performed distance measurements using FRET and DEER and explored different simulation techniques to predict inter-label distances using the Rpo4/7 stalk module of the M. jannaschii RNA polymerase. This is a suitable model system because it is rigid and a high-resolution X-ray structure is available. The conformations of the fluorescent labels and nitroxide spin labels on Rpo4/7 were modeled using in vacuo molecular dynamics simulations (MD) and a stochastic Monte Carlo sampling approach. For the nitroxide probes we also performed MD simulations with explicit water and carried out a rotamer library analysis. Our results show that the Monte Carlo simulations are in better agreement with experiments than the MD simulations and the rotamer library approach results in plausible distance predictions. Because the latter is the least computationally demanding of the methods we have explored, and is readily available to many researchers, it prevails as the method of choice for the interpretation of DEER distance distributions.     

Improved side‐chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side‐chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha‐helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side‐chain torsion potentials of these residues to match new, high‐level quantum‐mechanical calculations. Finally, we used microsecond‐timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side‐chain conformations. The new force field, which we have termed Amber ff99SB‐ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Flexibility of cold- and heat-adapted subtilisin-like serine proteinases evaluated with fluorescence quenching and molecular dynamics

The subtilisin-like serine proteinases, VPR, from a psychrotrophic Vibrio species and aqualysin I (AQUI) from the thermophile Thermus aquaticus, are structural homologues, but differ significantly with respect to stability and catalytic properties. It has been postulated that the higher catalytic activity of cold adapted enzymes when compared to homologues from thermophiles, reflects their higher molecular flexibility. To assess a potential difference in molecular flexibility between the two homologous proteinases, we have measured their Trp fluorescence quenching by acrylamide at different temperatures. We also investigated protein dynamics of VPR and AQUI at an atomic level by molecular dynamics simulations. VPR contains four Trp residues, three of which are at corresponding sites in the structure of AQUI. To aid in the comparison, a Tyr at the fourth corresponding site in AQUI was mutated to Trp (Y191W). A lower quenching effect of acrylamide on the intrinsic fluorescence of the thermophilic AQUI_Y191W was observed at all temperatures measured (10–55 °C), suggesting that it possesses a more rigid structure than VPR. The MD analysis (Cα rmsf profiles) showed that even though VPR and AQUI have similar flexibility profiles, the cold adapted VPR displays higher flexibility in most regions of the protein structure. Some of these regions contain or are in proximity to some of the Trp residues (Trp6, Trp114 and Trp208) in the proteins. Thus, we observe an overall agreement between the fluorescence quenching data and the flexibility profiles obtained from the MD simulations to different flexibilities of specific regions in the proteins.     

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.     

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.     

Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamics simulation and a Poisson‐Boltzmann approach

The ion atmosphere created by monovalent (Na⁺) or divalent (Mg²⁺) cations surrounding a B‐form DNA duplex were examined using atomistic molecular dynamics (MD) simulations and the nonlinear Poisson‐Boltzmann (PB) equation. The ion distributions predicted by the two methods were compared using plots of radial and two‐dimensional cation concentrations and by calculating the total number of cations and net solution charge surrounding the DNA. Na⁺ ion distributions near the DNA were more diffuse in PB calculations than in corresponding MD simulations, with PB calculations predicting lower concentrations near DNA groove sites and phosphate groups and a higher concentration in the region between these locations. Other than this difference, the Na⁺ distributions generated by the two methods largely agreed, as both predicted similar locations of high Na⁺ concentration and nearly identical values of the number of cations and the net solution charge at all distances from the DNA. In contrast, there was greater disagreement between the two methods for Mg²⁺ cation concentration profiles, as both the locations and magnitudes of peaks in Mg²⁺ concentration were different. Despite experimental and simulation observations that Mg²⁺ typically maintains its first solvation shell when interacting with nucleic acids, modeling Mg²⁺ as an unsolvated ion during PB calculations improved the agreement of the Mg²⁺ ion atmosphere predicted by the two methods and allowed for values of the number of bound ions and net solution charge surrounding the DNA from PB calculations that approached the values observed in MD simulations. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 834–848, 2014.     

Introducing a novel method based on the imperialistic competitive algorithm to determine fluorine intermolecular potential from ab initio calculations and calculation of some properties via MD simulations

In this work, the possibility of obtaining an accurate site-site potential model suitable for use in molecular dynamics (MD) simulations of fluorine from ab initio calculations has been explored. The exploration was made on ab initio calculations. To reduce the ab initio pair potentials into a site-site potential, a higher significance was assigned to the configuration which is more stable. For this purpose, the imperialistic competitive algorithm (ICA) was implemented as a powerful optimisation tool. The calculated second virial coefficients were compared to the experimental values to test the quality of the presented intermolecular potential. The relative error for the calculated second virial coefficient ranged from 0.1 to 5.6%. MD simulations were used to evaluate the ability of the proposed intermolecular potential function. The relative error for the MD simulations ranged from 0.5 to 5.2%. The results are in good agreement with experimental data.     

Comparative mechanical unfolding studies of spectrin domains R15, R16 and R17

Spectrins belong to repetitive three-helix bundle proteins that have vital functions in multicellular organisms and are of potential value in nanotechnology. To reveal the unique physical features of repeat proteins we have studied the structural and mechanical properties of three repeats of chicken brain α-spectrin (R15, R16 and R17) at the atomic level under stretching at constant velocities (0.01, 0.05 and 0.1?Å·ps^?1) and constant forces (700 and 900?pN) using molecular dynamics (MD) simulations at T?=?300?K. 114 independent MD simulations were performed and their analysis has been done. Despite structural similarity of these domains we have found that R15 is less mechanically stable than R16, which is less stable than R17. This result is in agreement with the thermal unfolding rates. Moreover, we have observed the relationship between mechanical stability, flexibility of the domains and the number of aromatic residues involved in aromatic clusters.     

The solvation of bromide anion in acetonitrile: a structural study based on the combination of theoretical calculations and X-ray absorption spectroscopy

This work studies the solvation of bromide in acetonitrile by combining quantum mechanics, computer simulations and X-ray absorption near edge structure (XANES) spectroscopy. Three different sets of interaction potentials were tested, one of them derived from literature and the other two are simple modifications of the previous one to include specificities of the bromide–acetonitrile interactions. Results for microsolvation of bromide were obtained by quantum mechanical optimization and classical minimization of small clusters [Br(ACN) _n ]^?  (n = 9, 20). Analysis of molecular dynamics (MD) simulations has provided structural, dynamic and energetic aspects of the solvation phenomenon. The theoretical computation of Br K-edge XANES spectrum in solution using the structural information obtained from the different simulations has allowed the comparison among the three different potentials, as well as the examination of the main structural and dynamic factors determining the shape of the experimental spectrum.     

Consequences of Sequential Ca2+ Occupancy for the Structure and Dynamics of CalbindinD9K: Computational Simulations and Comparison to Experimental Determinations in Solution

Abstract

Molecular dynamics (MD) simulations of the structures of calbindin_D9K (CAB) with different occupancies of the two Ca²⁺ binding sites were carried out to gain insight into structural and energetic consequences of sequential Ca²⁺ binding. The aim of the study is to identify effects of Ca-binding site occupancy that relate to the properties and functions of Ca-binding proteins containing EF-hand motifs. Two different models of solvation were employed, one defined by a linear, distance dependent dielectric permittivity (ε = r) and inclusion only of the 36 crystallographically observed water molecules, and the other with the protein immersed in a 9Å shell of explicit waters and ε = 1. Experimental results from x-ray crystallography, and insights from NMR and from measurements of hydrogen exchange rates in these systems served as tests and guides for assessing the quality, validity and mechanistic interpretation of the results from the computational study. The results of the MD simulations agree very well with earlier experimental observations that the structure of calbindin_D9k is rather insensitive to removal of Ca²⁺, and indicate that this insensitivity is not dependent on the order in which the ions are removed. The calculated values of the electrostatic potentials at the Ca²⁺ binding sites are very similar, in agreement with the small differences in the measured microscopic binding constants. Details of the dynamic mechanisms of molecular flexibility revealed by the MD simulations are also in good agreement with experimental findings, including the local properties identified from comparisons of hydrogen exchange rates in various parts of the structures of sequentially occupied forms of CAB. Estimation of the changes in configurational entropy from the rms fluctuations in the structures of CAB at various levels of Ca²⁺ occupancy in the EF-hands, supports earlier suggestions relating the dynamic properties of the protein to the observed cooperativity in the binding of Ca²⁺. The computational approaches and the results of the MD simulations are evaluated in relation to the study of effects of Ca²⁺ occupancy in calmodulin and troponin C where ion binding determines function and is known to trigger significant changes in structural and dynamic properties.     

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.     

Conformational landscapes of membrane proteins delineated by enhanced sampling molecular dynamics simulations

The expansion of computational power, better parameterization of force fields, and the development of novel algorithms to enhance the sampling of the free energy landscapes of proteins have allowed molecular dynamics (MD) simulations to become an indispensable tool to understand the function of biomolecules. The temporal and spatial resolution of MD simulations allows for the study of a vast number of processes of interest. Here, we review the computational efforts to uncover the conformational free energy landscapes of a subset of membrane proteins: ion channels, transporters and G-protein coupled receptors. We focus on the various enhanced sampling techniques used to study these questions, how the conclusions come together to build a coherent picture, and the relationship between simulation outcomes and experimental observables.     

Conformational ensemble of an intrinsically flexible loop in mitochondrial import protein Tim21 studied by modeling and molecular dynamics simulations

BackgroundTim21, a subunit of a highly dynamic translocase of the inner mitochondrial membrane (TIM23) complex, translocates proteins by interacting with subunits in the translocase of the outer membrane (TOM) complex and Tim23 channel in the TIM23 complex. A loop segment in Tim21, which is in close proximity of the binding site of Tim23, has different conformations in X-ray, NMR and new crystal contact-free space (CCFS) structures. MD simulations can provide information on the structure and dynamics of the loop in solution.MethodsThe conformational ensemble of the loop was characterized using loop modeling and molecular dynamics (MD) simulations.ResultsMD simulations confirmed mobility of the loop. Multidimensional scaling and clustering were used to characterize the dynamic conformational ensemble of the loop. Free energy landscape showed that the CCFS crystal structure occupied a low energy region as compared to the conventional X-ray crystal structure. Analysis of crystal packing indicates that the CCFS provides larger conformational space for the motions of the loop.ConclusionsOur work reported the conformational ensemble of the loop in solution, which is in agreement with the structure obtained from CCFS approach. The combination of the experimental techniques and computational methods is beneficial for studying highly flexible regions of proteins.General significanceComputational methods, such as loop modeling and MD simulations, have proved to be useful for studying conformational flexibility of proteins. These methods in integration with experimental techniques such as CCFS has the potential to transform the studies on flexible regions of proteins.     

A molecular dynamics approach for the generation of complete protein structures from limited coordinate data

Generation of full protein coordinates from limited information, e.g., the Cα coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5–0.7 Å, and all-atom RMS values of 1.5–1.9 Å). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available. © 1994 John Wiley & Sons, Inc.     

Molecular dynamics simulations of palmitoyloleoylphosphatidylglycerol bilayers

Phosphatidylglycerol (PG) is one of the important components of biological membranes, but there is a paucity of experimental data to test the accuracy of molecular dynamics (MD) simulations. This work consists of testing the accuracy of the CHARMM36 (C36) lipid force field on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG) lipid bilayers. MD simulations of POPG lipid bilayers are compared to recently available X-ray and neutron scattering and deuterium NMR measurements. Overall, the C36 lipid force field accurately represents the X-ray and neutron form factors, bilayer and hydrocarbon thicknesses and chain deuterium order parameters. The surface area per lipid from MD simulations with C36 (67.7 ± 0.2 Å²) is in excellent agreement with the experimentally determined value of 66.0 ± 1.3 Å². C36 outperforms the lipid force field developed by Berger et al. [15] and suggests that past studies with this force field may result in lateral areas that are too small. Moreover, our studies give some insight into the structural model used in experiments and suggest that the functional form for the head group may not be Gaussian-like. Based on our simulations, the POPG lipid in the C36 lipid force field is well parameterised and can be used for other PG lipids and membrane models with mixed lipids.     

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.