Banding 2of NMR‐derived methyl order parameters: Implications for protein dynamics

Our understanding of protein folding, stability, and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site‐resolved insight into protein motion. It has been observed that methyl‐group motion tends to cluster into three “classes” when expressed in terms of the popular Lipari‐Szabo model‐free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O² and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function. Proteins 2014; 82:2106–2117. © 2014 Wiley Periodicals, Inc.     

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.     

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.     

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.     

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.     

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.     

NMR (13)C-relaxation study of base and sugar dynamics in GCAA RNA hairpin tetraloop

Intramolecular dynamics of a 14-mer RNA hairpin including GCAA tetraloop was investigated by (13)C NMR relaxation. R(1) and R(1rho) relaxation rates were measured for all protonated base carbons as well as for C1' carbons of ribose sugars at several magnetic field strengths. The data has been interpreted in the framework of modelfree analysis [G. Lipari and A. Szabo. J Am Chem Soc 104, 4546-4559 (1982); G. Lipari and A. Szabo. J Am Chem Soc 104, 4559-4570 (1982)] characterizing the internal dynamics of the molecule by order parameters and correlation times for fast motions on picosecond to nanosecond time scale and by contributions of the chemical exchange. The fast dynamics reveals a rather rigid stem and a significantly more flexible loop. The cytosine and the last adenine bases in the loop as well as all the loop sugars exhibit a significant contribution of conformational equilibrium on microsecond to millisecond time scale. The high R(1rho) values detected on both base and sugar moieties of the loop indicate coordinated motions in this region. A semiquantitative analysis of the conformational equilibrium suggests the exchange rates on the order of 10(4) s(-1). The results are in general agreement with dynamics studies of GAAA loops by NMR relaxation and fluorescent spectroscopy and support the data on the GCAA loop dynamics obtained by MD simulations.     

Internal dynamics of d(CGCAAATTTGCG)2: a comparison of NMR relaxation measurements with a molecular dynamics simulation

We report the analysis of a 250 ps molecular dynamics simulation of the dodecamer d(CGCAAATTT-GCG)₂ immersed in a rectangular box of 3469 water molecules with 22 Na⁺ counterions. The internal dynamics of the molecule were investigated by studying the relevant autocorrelation functions related to the ¹³C-NMR relaxation parameters of the C1′-H1′ bonds of the sugar rings. The calculated effective correlation times τ _e (∼13 ps) and the order parameter S² (∼0.82) of the Lipari and Szabo formalism (Lipari and Szabo 1982a, b) are in satisfactory agreement with those determined previously by NMR (Gaudin et al. 1995, 1996). ¹H-¹H NOE buildups have also been measured experimentally and agree with those computed from the simulation. These results validate the simulation, and a more detailed analysis of the internal dynamics of the dodecamer was undertaken. Analysis of the distributions and of the autocorrelation functions of the glycosidic angle flucuations χ shows that the rotational motion of the sugar rings about their glycosidic bond conforms to a restricted diffusion mechanism. The amplitude of the motions and the diffusion constant are 20° and 17.10⁹ rad²s^–1 respectively. These values are in good agreement with ¹³C NMR data. Furthermore the simulation allows us to rule out another model also consistent with the experiment, consisting of a two-state jump between a syn and an anti conformation. Received: 19 November 1996 / Accepted: 17 March 1997     

Fast internal main-chain dynamics of human ubiquitin.

The fast internal dynamics of human ubiquitin have been studied by the analysis of 15N relaxation of backbone amide nitrogens. The amide 15N resonances have been assigned by use of heteronuclear multiple-quantum spectroscopy. Spin lattice relaxation times at 60.8 and 30.4 MHz and the steady-state nuclear Overhauser effect at 60.8 MHz have been determined for 67 amide 15N sites in the protein using two-dimensional spectroscopy. These data have been analyzed in terms of the model free treatment of Lipari and Szabo [Lipari, G., & Szabo, A. (1982) J. Am. Chem. Soc. 104, 4546-4559]. The global motion of the protein is shown to be isotropic and is characterized by a correlation time of 4.1 ns rad-1. The generalized order parameters (S2) of backbone amide N-H vectors in the globular region of the protein range from 0.5 to 0.95. No apparent correlation between secondary structure and generalized order parameters is observed. There is, however, a strong correlation between the magnitude of the generalized order parameters of a given N-H vector and the presence of hydrogen bonding of the amide hydrogen or its peptide bond associated carbonyl. Using a chemical shift tensor breadth of 160 ppm, the N-H vectors of peptide linkages participating in one or more hydrogen bonds to the main chain show an average generalized order parameter of 0.80 (SD 0.06), while those amide NH of peptide linkages free of hydrogen-bonding interactions with the main chain show an average order parameter of 0.69 (SD 0.06).(ABSTRACT TRUNCATED AT 250 WORDS)     

Backbone dynamics of ribonuclease T1 and its complex with 2′GMP studied by two-dimensional heteronuclear NMR spectroscopy

Summary The backbone dynamics of free ribonuclease T1 and its complex with the competitive inhibitor 2GMP have been studied by ¹⁵N longitudinal and transverse relaxation experiments, combined with {¹H, ¹⁵H} NOE measurements. The intensity decay of individual amide cross peaks in a series of (¹H, ¹⁵N)-HSQC spectra with appropriate relaxation periods (Kay, L.E. et al. (1989) Biochemistry, 28, 8972–8979; Kay, L.E. et al. (1992) J. Magn. Reson., 97, 359–375) was fitted to a single exponential by using a simplex algorithm in order to obtain ¹⁵N T₁ and T₂ relaxation times. These experimentally obtained values were analysed in terms of the model-free approach introduced by Lipari and Szabo (Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc., 104, 4546–4559; 4559–4570). The microdyramical parameters accessible by this approach clearly indicate a correlation between the structural flexibility and the tertiary structure of ribonuclease T1, as well as restricted mobility of certain regions of the protein backbone upon binding of the inhibitor. The results obtained by NMR are compared to X-ray crystallographic data and to observations made in molecular dynamics simulations.     

Lipid Configurations from Molecular Dynamics Simulations

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na⁺ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the ³¹P chemical shift anisotropy and ¹⁴N and CD₃ NMR quadrupole splittings.     

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.     

Main chain and side chain dynamics of oxidized flavodoxin from Cyanobacterium anabaena.

Oxidized flavodoxin from Cyanobacterium anabaena PCC 7119 is used as a model system to investigate the fast internal dynamics of a flavin-bearing protein. Virtually complete backbone and side chain resonance NMR assignments of an oxidized flavodoxin point mutant (C55A) have been determined. Backbone and side chain dynamics in flavodoxin (C55A) were investigated using (15)N amide and deuterium methyl NMR relaxation methods. The squared generalized order parameters (S(NH)(2)) for backbone amide N-H bonds are found to be uniformly high ( approximately 0.923 over 109 residues in regular secondary structure), indicating considerable restriction of motion in the backbone of the protein. In contrast, methyl-bearing side chains are considerably heterogeneous in their amplitude of motion, as indicated by obtained symmetry axis squared generalized order parameters (S(axis)(2)). However, in comparison to nonprosthetic group-bearing proteins studied with these NMR relaxation methods, the side chains of oxidized flavodoxin are unusually rigid.     

NMR investigations of interactions between anesthetics and lipid bilayers

Interactions between anesthetics (lidocaine and short chain alcohols) and lipid membranes formed by dimyristoylphosphatidylcholine (DMPC) were studied using NMR spectroscopy. The orientational order of lidocaine was investigated using deuterium NMR on a selectively labelled compound whereas segmental ordering in the lipids was probed by two-dimensional ¹H-¹³C separated local field experiments under magic-angle spinning conditions. In addition, trajectories generated in molecular dynamics (MD) computer simulations were used for interpretation of the experimental results. Separate simulations were carried out with charged and uncharged lidocaine molecules. Reasonable agreement between experimental dipolar interactions and the calculated counterparts was observed. Our results clearly show that charged lidocaine affects significantly the lipid headgroup. In particular the ordering of the lipids is increased accompanied by drastic changes in the orientation of the P-N vector in the choline group.     

Validation of the GROMOS force-field parameter set 45A3 against nuclear magnetic resonance data of hen egg lysozyme

The quality of molecular dynamics (MD) simulations of proteins depends critically on the biomolecular force field that is used. Such force fields are defined by force-field parameter sets, which are generally determined and improved through calibration of properties of small molecules against experimental or theoretical data. By application to large molecules such as proteins, a new force-field parameter set can be validated. We report two 3.5 ns molecular dynamics simulations of hen egg white lysozyme in water applying the widely used GROMOS force-field parameter set 43A1 and a new set 45A3. The two MD ensembles are evaluated against NMR spectroscopic data NOE atom–atom distance bounds, ³J_NH and ³J coupling constants, and ¹5N relaxation data. It is shown that the two sets reproduce structural properties about equally well. The 45A3 ensemble fulfills the atom–atom distance bounds derived from NMR spectroscopy slightly less well than the 43A1 ensemble, with most of the NOE distance violations in both ensembles involving residues located in loops or flexible regions of the protein. Convergence patterns are very similar in both simulations atom-positional root-mean-square differences (RMSD) with respect to the X-ray and NMR model structures and NOE inter-proton distances converge within 1.0–1.5 ns while backbone ³J_HN-coupling constants and ¹H– ¹5N order parameters take slightly longer, 1.0–2.0 ns. As expected, side-chain ³J-coupling constants and ¹H– ¹5N order parameters do not reach full convergence for all residues in the time period simulated. This is particularly noticeable for side chains which display rare structural transitions. When comparing each simulation trajectory with an older and a newer set of experimental NOE data on lysozyme, it is found that the newer, larger, set of experimental data agrees as well with each of the simulations. In other words, the experimental data converged towards the theoretical result.     

On the similarity of properties in solution or in the crystalline state: A molecular dynamics study of hen lysozyme

As protein crystals generally possess a high water content, it is assumed that the behaviour of a protein in solution and in crystal environment is very similar. This assumption can be investigated by molecular dynamics (MD) simulation of proteins in the different environments. Two 2ns simulations of hen egg white lysozyme (HEWL) in crystal and solution environment are compared to one another and to experimental data derived from both X-ray and NMR experiments, such as crystallographic B-factors, NOE atom–atom distance bounds, ³J_{H N}-coupling constants, and ¹H-¹⁵N bond vector order parameters. Both MD simulations give very similar results. The crystal simulation reproduces X-ray and NMR data slightly better than the solution simulation.     

Evaluating amber force fields using computed NMR chemical shifts

NMR chemical shifts can be computed from molecular dynamics (MD) simulations using a template matching approach and a library of conformers containing chemical shifts generated from ab initio quantum calculations. This approach has potential utility for evaluating the force fields that underlie these simulations. Imperfections in force fields generate flawed atomic coordinates. Chemical shifts obtained from flawed coordinates have errors that can be traced back to these imperfections. We use this approach to evaluate a series of AMBER force fields that have been refined over the course of two decades (ff94, ff96, ff99SB, ff14SB, ff14ipq, and ff15ipq). For each force field a series of MD simulations are carried out for eight model proteins. The calculated chemical shifts for the ¹H, ¹⁵N, and ¹³C^a atoms are compared with experimental values. Initial evaluations are based on root mean squared (RMS) errors at the protein level. These results are further refined based on secondary structure and the types of atoms involved in nonbonded interactions. The best chemical shift for identifying force field differences is the shift associated with peptide protons. Examination of the model proteins on a residue by residue basis reveals that force field performance is highly dependent on residue position. Examination of the time course of nonbonded interactions at these sites provides explanations for chemical shift differences at the atomic coordinate level. Results show that the newer ff14ipq and ff15ipq force fields developed with the implicitly polarized charge method perform better than the older force fields.     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.