Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

Diffraction-based density restraints for membrane and membrane-peptide molecular dynamics simulations

We have recently shown that current molecular dynamics (MD) atomic force fields are not yet able to produce lipid bilayer structures that agree with experimentally-determined structures within experimental errors. Because of the many advantages offered by experimentally validated simulations, we have developed a novel restraint method for membrane MD simulations that uses experimental diffraction data. The restraints, introduced into the MD force field, act upon specified groups of atoms to restrain their mean positions and widths to values determined experimentally. The method was first tested using a simple liquid argon system, and then applied to a neat dioleoylphosphatidylcholine (DOPC) bilayer at 66% relative humidity and to the same bilayer containing the peptide melittin. Application of experiment-based restraints to the transbilayer double-bond and water distributions of neat DOPC bilayers led to distributions that agreed with the experimental values. Based upon the experimental structure, the restraints improved the simulated structure in some regions while introducing larger differences in others, as might be expected from imperfect force fields. For the DOPC-melittin system, the experimental transbilayer distribution of melittin was used as a restraint. The addition of the peptide caused perturbations of the simulated bilayer structure, but which were larger than observed experimentally. The melittin distribution of the simulation could be fit accurately to a Gaussian with parameters close to the observed ones, indicating that the restraints can be used to produce an ensemble of membrane-bound peptide conformations that are consistent with experiments. Such ensembles pave the way for understanding peptide-bilayer interactions at the atomic level.     

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16–31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 ϕ torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular α-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured ³J(H_N-H_Cα)-coupling constants, indicating that different conformers of GCN4p16–31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and ³J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and ³J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16–31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16–31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.     

Restrained molecular dynamics of solvated duplex DNA using the particle mesh Ewald method

Restrained and unrestrained aqueous solution molecular dynamics simulations applying the particle mesh Ewald (PME) method to DNA duplex structures previously determined via in vacuo restrained molecular dynamics with NMR-derived restraints are reported. Without experimental restraints, the DNA decamer, d(CATTTGCATC)d(GATGCAAATG) and trisdecamer, d(AGCTTGCCTTGAG)d(CTCAAGGCAAGCT), structures are stable on the nanosecond time scale and adopt conformations in the B-DNA family. These free DNA simulations exhibit behavior characteristic of PME simulations previously performed on DNA sequences, including a low helical twist, frequent sugar pucker transitions, BI- BII(–) transitions and coupled crankshaft (–) motion. Refinement protocols similar to the original in vacuo restrained molecular dynamics (RMD) refinements but in aqueous solution using the Cornell et al. force field [Cornell et al. (1995) J. Am. Chem. Soc., 117, 5179–5197] and a particle mesh Ewald treatment produce structures which fit the restraints very well and are very similar to the original in vacuo NMR structure, except for a significant difference in the average helical twist. Figures of merit for the average structure found in the RMD PME decamer simulations in solution are equivalent to the original in vacuo NMR structure while the figures of merit for the free MD simulations are significantly higher. The free MD simulations with the PME method, however, lead to some sequence-dependent structural features in common with the NMR structures, unlike free MD calculations with earlier force fields and protocols. There is some suggestion that the improved handling of electrostatics by PME improves long-range structural aspects which are not well defined by the short-range nature of NMR restraints.     

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.     

Are time-averaged restraints necessary for nuclear magnetic resonance refinement? A model study for DNA.

A recently suggested method for refinement of structural data obtained from two-dimensional nuclear magnetic resonance experiments using molecular dynamics (MD) is explored. In this method, the time-averaged values of the appropriate internal co-ordinates of the molecule, calculated from the MD trajectory, are driven by restraints towards the experimental target values. This contrasts with most refinement procedures currently in use, where restraints are applied based on the instantaneous values of the appropriate co-ordinates. Both refinement methods are applied to the EcoRI restriction site DNA hexamer d(GAATTC)2, using target nuclear Overhauser enhancement distances derived from a one nanosecond unrestrained MD simulation of this structure. The resulting refined structures are compared to the results of the unrestrained MD trajectory, which serves as our "experimental" data. We show that although both methods can yield an average structure with the correct gross morphology, the new method allows both a much more realistic picture of inherent flexibility, and reproduces fine conformational detail better, such as sequence dependency. We also analyze the very long MD trajectory generated here (longer than any previously reported for a DNA oligomer), and find that significantly shorter simulations, typical of those frequently performed, may not yield acceptably reliable values for certain structural parameters.     

Can molecular dynamics simulations provide high‐resolution refinement of protein structure?

Recent advances in efficient and accurate treatment of solvent with the generalized Born approximation (GB) have made it possible to substantially refine the protein structures generated by various prediction tools through detailed molecular dynamics simulations. As demonstrated in a recent CASPR experiment, improvement can be quite reliably achieved when the initial models are sufficiently close to the native basin (e.g., 3-4 A C(alpha) RMSD). A key element to effective refinement is to incorporate reliable structural information into the simulation protocol. Without intimate knowledge of the target and prediction protocol used to generate the initial structural models, it can be assumed that the regular secondary structure elements (helices and strands) and overall fold topology are largely correct to start with, such that the protocol limits itself to the scope of refinement and focuses the sampling in vicinity of the initial structure. The secondary structures can be enforced by dihedral restraints and the topology through structural contacts, implemented as either multiple pair-wise C(alpha) distance restraints or a single sidechain distance matrix restraint. The restraints are weakly imposed with flat-bottom potentials to allow sufficient flexibility for structural rearrangement. Refinement is further facilitated by enhanced sampling of advanced techniques such as the replica exchange method (REX). In general, for single domain proteins of small to medium sizes, 3-5 nanoseconds of REX/GB refinement simulations appear to be sufficient for reasonable convergence. Clustering of the resulting structural ensembles can yield refined models over 1.0 A closer to the native structure in C(alpha) RMSD. Substantial improvement of sidechain contacts and rotamer states can also be achieved in most cases. Additional improvement is possible with longer sampling and knowledge of the robust structural features in the initial models for a given prediction protocol. Nevertheless, limitations still exist in sampling as well as force field accuracy, manifested as difficulty in refinement of long and flexible loops.     

Parametrisation of time-averaged distance restraints in MD simulations

Summary Time-averaged restraints in molecular dynamics simulations offer a means to account for the averaging that is implicit in NMR spectroscopic data. We present a systematic investigation of the parameters which characterise time-averaged distance restraints. Using previously published data for a small protein, chymotrypsin inhibitor 2, we identify conditions which can lead to undesirable heating or which grossly distort the dynamics of the system.Abbreviations NOE nuclear Overhauser effect - MD molecular dynamics - CI-2 chymotrypsin inhibitor 2     

The new program OPAL for molecular dynamics simulations and energy refinements of biological macromolecules

Summary A new program for molecular dynamics (MD) simulation and energy refinement of biological macromolecules, OPAL, is introduced. Combined with the supporting program TRAJEC for the analysis of MD trajectories, OPAL affords high efficiency and flexibility for work with diferent force fields, and offers a user-friendly interface and extensive trajectory analysis capabilities. Salient features are computational speeds of up to 1.5 GFlops on vector supercomputers such as the NEC SX-3, ellipsoidal boundaries to reduce the system size for studies in explicit solvents, and natural treatment of the hydrostatic pressure. Practical applications of OPAL are illustrated with MD simulations of pure water, energy minimization of the NMR structure of the mixed disulfide of a mutant E. coli glutaredoxin with glutathione in different solvent models, and MD simulations of a small protein, pheromone Er-2, using either instantaneous or time-averaged NMR restraints, or no restraints.Abbreviations D diffusion constant in cm²/s - Er-2 pheromone 2 from Euplotes raikovi - GFlop one billion floating point operations per second - Grx(C14S)-SG mixed disulfide between a mutant E. coli glutaredoxin, with Cys¹⁴ replaced by Ser, and glutathione - MD molecular dynamics - NOE nuclear Overhauser enhancement - rmsd root-mean-square deviation - density in g/cm³     

Refinement of the solution structure of the ribonucleotide 5'r(GCAUGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary hexamer 5'r(GCAUGC)2 is investigated by means of nuclear magnetic resonance spectroscopy and restrained molecular dynamics. The proton resonances are assigned in a sequential manner, and a set of 110 approximate interproton distance restraints are derived from the two-dimensional nuclear Overhauser enhancement spectra. These distances are used as the basis of a structure refinement by restrained molecular dynamics in which the experimental restraints are incorporated into the total energy function of the system in the form of effective potentials. Eight restrained molecular dynamics simulations are carried out, four starting from a structure with regular A-type geometry and four from one with regular B-type geometry. The atomic root mean square (rms) difference between the initial structures is 3.2 A. In the case of all eight simulations, convergence is achieved both globally and locally to a set of very similar A-type structures with an average atomic rms difference between them of 0.8 +/- 0.2 A. Further, the atomic rms differences between the restrained dynamics structures obtained by starting out from the same initial structures but with different random number seeds for the assignment of the initial velocities are the same as those between the restrained dynamics structures starting out from the two different initial structures. These results suggest that the restrained dynamics structures represent good approximations of the solution structure. The converged structures exhibit clear sequence-dependent variation in some of the helical parameters, in particular helix twist, roll, slide, and propellor twist.(ABSTRACT TRUNCATED AT 250 WORDS)     

Major groove width variations in RNA structures determined by NMR and impact of <Superscript>13</Superscript>C residual chemical shift anisotropy and <Superscript>1</Superscript>H–<Superscript>13</Superscript>C residual dipolar coupling on refinement

Ribonucleic acid structure determination by NMR spectroscopy relies primarily on local structural restraints provided by ¹H– ¹H NOEs and J-couplings. When employed loosely, these restraints are broadly compatible with A- and B-like helical geometries and give rise to calculated structures that are highly sensitive to the force fields employed during refinement. A survey of recently reported NMR structures reveals significant variations in helical parameters, particularly the major groove width. Although helical parameters observed in high-resolution X-ray crystal structures of isolated A-form RNA helices are sensitive to crystal packing effects, variations among the published X-ray structures are significantly smaller than those observed in NMR structures. Here we show that restraints derived from aromatic ¹H– ¹³C residual dipolar couplings (RDCs) and residual chemical shift anisotropies (RCSAs) can overcome NMR restraint and force field deficiencies and afford structures with helical properties similar to those observed in high-resolution X-ray structures.     

Solution structure of neurotoxin I from the sea anemone Stichodactyla helianthus. A nuclear magnetic resonance, distance geometry, and restrained molecular dynamics study

The three-dimensional structure of the sea anemone polypeptide Stichodactyla helianthus neurotoxin I in aqueous solution has been determined using distance geometry and restrained molecular dynamics simulations based on NMR data acquired at 500 MHz. A set of 470 nuclear Overhauser enhancement values was measured, of which 216 were used as distance restraints in the structure determination along with 15 dihedral angles derived from coupling constants. After restrained molecular dynamics refinement, the eight structures that best fit the input data form a closely related family. They describe a structure that consists of a core of twisted, four-stranded, antiparallel beta-sheet encompassing residues 1-3, 19-24, 29-34, and 40-47, joined by three loops, two of which are well defined by the NMR data. The third loop, encompassing residues 7-16, is poorly defined by the data and is assumed to undergo conformational averaging in solution. Pairwise root mean square displacement values for the backbone heavy atoms of the eight best structures are 1.3 +/- 0.2A when the poorly defined loop is excluded and 3.6 +/- 1.0A for all backbone atoms. Refinement using restrained molecular dynamics improved the quality of the structures generated by distance geometry calculations with respect to the number of nuclear Overhauser enhancements violated, the size of the total distance violations and the total potential energies of the structures. The family of structures for S. heliathus neurotoxin I is compared with structures of related sea anemone proteins that also bind to the voltage-gated sodium channel.     

Analysis of the relative contributions of the nuclear Overhauser interproton distance restraints and the empirical energy function in the calculation of oligonucleotide structures using restrained molecular dynamics

The relative contributions of the interproton distance restraints derived from nuclear Overhauser enhancement measurements and of the empirical energy function in the determination of oligonucleotide structures by restrained molecular dynamics are investigated. The calculations are based on 102 intraresidue and 126 interresidue interproton distance restraints derived from short mixing time two-dimensional nuclear Overhauser enhancement data on the dodecamer 5'd(CGCGPATTCGCG)2 [Clore, G.M., Oschkinat, H., McLaughlin, L.W., Benseler, F., Scalfi Happ, C., Happ, E., & Gronenborn, A.M. (1988) Biochemistry 27, 4185-4197]. Eight interproton distance restraint lists were made up with errors ranging from -0.1/+0.2 to -1.2/+1.3 A for r less than 2.5 A and from -0.2/+0.3 to -1.3/+1.4 A for r greater than or equal to 2.5 A. These restraints were incorporated into the total energy function of the system in the form of square-well potentials with force constants set sufficiently high to ensure that the deviations between calculated distances and experimental restraints were very small (average interproton distance rms deviation of less than 0.06 A). For each data set, six calculations were carried out, three starting from classical A-DNA and three from classical B-DNA. The results show that structural changes occurring during the course of restrained molecular dynamics and the degree of structural convergence are determined by the interproton distance restraints. All the structures display similar small deviations from idealized geometry and have the same values for the nonbonding energy terms comprising van der Waals, electrostatic, and hydrogen-bonding components. Thus, the function of the empirical energy function is to maintain near perfect stereochemistry and nonbonded interactions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Practical applications of time-averaged restrained molecular dynamics to ligand-receptor systems: FK506 bound to the Q50R,A95H,K98I triple mutant of FKBP-13

Summary The ability of time-averaged restrained molecular dynamics (TARMD) to escape local low-energy conformations and explore conformational space is compared with conventional simulated-annealing methods. Practical suggestions are offered for performing TARMD calculations with ligand-receptor systems, and are illustrated for the complex of the immunosuppressant FK506 bound to Q50R,A95H,K98I triple mutant FKBP-13. The structure of ¹³C-labeled FK506 bound to triple-mutant FKBP-13 was determined using a set of 87 NOE distance restraints derived from HSQC-NOESY experiments. TARMD was found to be superior to conventional simulated-annealing methods, and produced structures that were conformationally similar to FK506 bound to wild-type FKBP-12. The individual and combined effects of varying the NOE restraint force constant, using an explicit model for the protein binding pocket, and starting the calculations from different ligand conformations were explored in detail.Abbreviations DG distance geometry - dmFKBP-12 double-mutant (R42K,H87V) FKBP-12 - FKBP-12 FK506-binding protein (12 kDa) - FKBP-13 FK506-binding protein (13 kDa) - HSQC heteronuclear single-quantum coherence - K_NOE force constant (penalty) for NOE-derived distance restraints - MD molecular dynamics - NOE nuclear Overhauser effect - SA simulated annealing - TARMD molecular dynamics with time-averaged restraints - tmFKBP-13 triple-mutant (Q50R,A95H,K98I) FKBP-13 - wtFKBP-12 wild-type FKBP-12     

Calculating three-dimensional molecular structure from atom-atom distance information: cyclosporin A

In recent years methods for deriving spatial molecular structure from atom-atom distance information have gained in importance due to the emergence of two-dimensional nuclear magnetic resonance (n.m.r) techniques, which make it possible to obtain such distance information for polypeptides, small proteins, sugars, and DNA fragments in solution. Distance geometry (DG) and restrained molecular dynamics (MD) refinement are applied to a cyclic polypeptide, the immunosuppressive drug cyclosporin A, and the results are compared. Two different procedures, DG followed by restrained MD, and straightforward restrained MD starting from the X-ray structure, both lead to a unique conformation that satisfies the 58 experimentally determined distance constraints. The results nicely show the relative merits of DG and restrained MD techniques for determining spatial molecular structure from distance information.     

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.     

Crystallographic Refinement and Structure-Factor Time-Averaging by Molecular Dynamics in the Absence of a Physical Force Field

Abstract

The application of Molecular-Dynamics simulation in protein-crystallographic structure refinement has become common practice. In this paper, structure optimizations are described where the driving force is derived only from the crystallographic data and not from any physical potential energy function. Under this extreme condition ab initio structure refinement and the application of structure-factor time averaging was investigated using a small 9 atom test system. Success in ab initio refinement, where the starting atomic positions are randomly distributed, depends on the resolution of the crystallographic data used in the optimization. The presence of high resolution data introduces false minima in the X-ray energy profile, enhancing the search problem significantly. On the same system, we also tested the method of time-averaged crystallographically restrained Molecular Dynamics, again in the absence of a physical force field. In this method, the diffraction data is modelled by an ensemble of structures instead of one single structure. In comparison to conventional single-structure refinement, more reflections were required to determine a correct atomic distribution. A time-averaging simulation at 0.2 nm resolution (40 reflections) yielded an incorrect distribution, although a low R-factor was obtained. Simulations at 0.1 nm resolution (248 reflections) gave both low R-factors, 3 to 4%, and correct atomic distributions. The scale factor between the observed and time-averaged calculated structure factor amplitudes appeared to be unstable, when optimized during a time-averaging simulation. Tests of time-averaged restrained simulations with noise added to the observed structure-factor amplitudes, indicated that noise is modelled when no information in the form of constraints or restraints is available to distinguish it from real data.