Biomolecular structure refinement using the GROMOS simulation software

For the understanding of cellular processes the molecular structure of biomolecules has to be accurately determined. Initial models can be significantly improved by structure refinement techniques. Here, we present the refinement methods and analysis techniques implemented in the GROMOS software for biomolecular simulation. The methodology and some implementation details of the computation of NMR NOE data, ³ J-couplings and residual dipolar couplings, X-ray scattering intensities from crystals and solutions and neutron scattering intensities used in GROMOS is described and refinement strategies and concepts are discussed using example applications. The GROMOS software allows structure refinement combining different types of experimental data with different types of restraining functions, while using a variety of methods to enhance conformational searching and sampling and the thermodynamically calibrated GROMOS force field for biomolecular simulation.     

Relaxation matrix refinement of the solution structure of squash trypsin inhibitor

The structure of the small squash trypsin inhibitor CMTI-I is refined by directly minimizing the difference between the observed two-dimensional nuclear Overhauser enhancement (NOE) intensities and those calculated by the full relaxation matrix approach. To achieve this, a term proportional to this difference was added to the potential energy function of the molecular dynamics program X-PLOR. Derivatives with respect to atomic co-ordinates are calculated analytically. Spin diffusion effects are thus accounted for fully during the refinement. Initial structures for the refinement were those determined recently by solution nuclear magnetic resonance using the isolated two-spin approximation to derive distance range estimates. The fits to the nuclear magnetic resonance data improve significantly with only small shifts in the refined structures during a few cycles of conjugate gradient minimization. However, larger changes (approximately 1 A) in the conformation occur during simulated annealing, which is accompanied by a further reduction of the difference between experimental and calculated two-dimensional NOE intensities. The refined structures are closer to the X-ray structure of the inhibitor complexed with trypsin than the initial structures. The root-mean-square difference for backbone atoms between the initial structures and the X-ray structure is 0.96 A, and that between the refined structures and the X-ray structure 0.61 A.     

A new constraint potential for the structure refinement of biomolecules in solution using experimental nuclear overhauser effect intensity

A new constraint potential is proposed for the refinement of the three-dimensional structure of biomolecules in solution from nmr data. It is based on the nuclear Overhauser effect (NOE) intensity calculations, taking into account the spin diffusion phenomenon. For restrained energy minimization or molecular dynamics techniques, a constraint potential term expressed as a function of the negative inverse of the sixth power of the NOE intensities (NOE^?1/6) is added to the classical potential energy function. The properties of this new NOE constraint potential are discussed and compared to those of a harmonic NOE intensity potential. The method integrated in the molecular modeling program GROMOS is tested on the regular α-helical structure of a decaglycylpeptide.     

Homonuclear three-dimensional NOE-NOE nuclear magnetic resonance/spectra for structure determination of proteins in solution.

The solution structures of two proteins (CMTI-I, a trypsin inhibitor from Cucurbita maxima, and hisactophilin, an actin binding protein of 118 amino acids) have been determined based on the NOE data derived solely from the homonuclear 3D NOE-NOE magnetic resonance spectroscopy. Two different approaches for extraction of the structural information from the 3D NOE-NOE experiment were tested. One approach was based on the transformation of the 3D intensities into distance constraints. In the second, and more robust approach, the 3D NOE intensities were used directly in structure calculations, without the need to transform them into distance constraints. A new 2D potential function representing the 3D NOE-NOE intensity was developed and used in the simulated annealing protocol. For CMTI-I, a comparison between structures determined with the 3D NOE-NOE method and various 2D NOE approaches was carried out. The 3D data set allowed better definition of the structures than was previously possible with the 2D NOE procedures that used the isolated two-spin approximation to derive distance information.     

Solution structure of phage lambda half-operator DNA by use of NMR, restrained molecular dynamics, and NOE-based refinement

The structure of a DNA decamer comprising the left half of the OR3 operator from bacteriophage lambda is determined in solution by using nuclear magnetic resonance spectroscopy and restrained molecular mechanics calculations. Nuclear magnetic resonance assignments for nonexchangeable protons are obtained by two-dimensional correlated and nuclear Overhauser effect (NOE) spectroscopies. Exchangeable proton resonances are assigned by one-dimensional NOE experiments. Coupling constant measurements from one- and two-dimensional experiments are used to determine approximate dihedral angles within the deoxyribose ring. Distances between protons are estimated by extrapolating distances derived from the time-dependent NOE intensities to initial mixing times. The sets of dihedral angles and distances form a basis for structure determination by restrained molecular dynamics. Separate runs start from classical A and from B DNA and converge to essentially identical structures (atomic root mean square difference of 0.8 A). The structures are improved by NOE-based refinement in which observed NOE intensities are compared to those calculated by using a full matrix analysis procedure. Final NOE residual (R) factors were less than 0.19. The resultant structures are generally B type in character, but display local sequence-dependent variations in dihedral angles and in the spatial arrangement of adjacent base pairs. Although the entire structure exhibits a small bend, the central core of the half-operator, which comprises the sequence-specific recognition site for cro repressor, is straight.     

Structure of DNA hexamer sequence d-CGATCG by two-dimensional nuclear magnetic resonance spectroscopy and restrained molecular dynamics

Solution conformation of self-complementary DNA duplex d-CGATCG, containing 5' d-CpG 3' site for intercalation of anticancer drug, daunomycin and adriamycin, has been investigated by nuclear magnetic resonance (NMR) spectroscopy. Complete resonance assignments of all the protons (except some H5'/H5" protons) have been obtained following standard procedures based on double quantum filtered correlation spectroscopy (dQF COSY) and two-dimensional nuclear Overhauser effect (NOE) spectra. Analysis of sums of coupling constants in one-dimensional NMR spectra, cross peak patterns in dQF COSY spectra and inter proton distances shows that the DNA sequence assumes a conformation close to the B-DNA family. The deoxyribose sugar conformation is in dynamic equilibrium with predominantly S-type conformer and a minor N-type conformer with N<-->S equilibrium varying with temperature. At 325 K, the mole fraction of the N-conformer increases for some of the residues by approximately 9%. Using a total of 10 spin-spin coupling constants and 112 NOE intensities, structural refinement has been carried out using Restrained Molecular Dynamics (rMD) with different starting structures, potential functions and rMD protocols. It is observed that pseudorotation phase angle of deoxyribose sugar for A3 and T4 residues is approximately 180 degrees and approximately 120 degrees, respectively while all other residues are close to C2'endo-conformation. A large propeller twist (approximately -18 degrees) and smallest twist angle (approximately 31 degrees) at A3pT4 step, in the middle of the sequence, a wider (12 A) and shallower (3.0 A) major groove with glycosidic bond rotation as high anti at both the ends of hexanucleotide are observed. The structure shows base-sequence dependent variations and hence strong local structural heterogeneity, which may have implications in ligand binding.     

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.     

Time- and ensemble-averaged direct NOE restraints

Summary NMR data are collected as time- and ensemble-averaged quantities. Yet, in commonly used methods for structure determination of biomolecules, structures are required to satisfy simultaneously a large number of constrainsts. Recently, however, methods have been developed that allow a better fit of the experimental data by the use of time- or ensemble-averaged restraints. Thus far, these methods have been applied to structure refinement using distance and J-coupling restraints. In this paper, time and ensemble averaging is extended to the direct refinement with experimental NOE data. The implementation of time- and ensemble-averaged NOE restraints in DINOSAUR is described and illustrated with experimental NMR data for crambin, a 46-residue protein. Structure refinement with both time- and ensemble-averaged NOE restraints results in lower R-factors, indicating a better fit of the experimental NOE data.     

Complete relaxation matrix refinement of NMR structures of proteins using analytically calculated dihedral angle derivatives of NOE intensities

Summary A new method for refining three-dimensional (3D) NMR structures of proteins is described, which takes account of the complete relaxation pathways. Derivatives of the NOE intensities with respect to the dihedral angles are analytically calculated, and efficiently evaluated with the use of a filter technique for identifying the dominant terms of these derivatives. This new method was implemented in the distance geometry program DIANA. As an initial test, we refined 30 rigid distorted helical structures, using a simulated data set of NOE distance constraints for a rigid standard -helix. The final root-mean-square deviations of the refined structures relative to the standard helix were less than 0.1 Å, and the R-factors dropped from values between 7% and 32% to values of less than 0.5% in all cases, which compares favorably with the results from distance geometry calculations. In particular, because spin diffusion was not explicitly considered in the evaluation of exact¹H–¹H distances corresponding to the simulated NOE intensities, a group of nearly identical distance geometry structures was obtained which had about 0.5 Å root-mean-square deviation from the standard -helix. Further test calculations using an experimental NOE data set recorded for the protein trypsin inhibitor K showed that the complete relaxation matrix refinement procedure in the DIANA program is functional also with systems of practical interest.Abbreviations RMSD root-mean-square deviation - NOE nuclear Overhauser enhancement - NOESY 2-dimensional nuclear Overhauser enhancement spectroscopy - CPU central processing unit     

An estimate of spin diffusion in a spin subset: Application to iterative distance calculation from 3D 15N NOESY-HMQC

Summary A method for quantification of distances between amide hydrogens using only the 3D NOESY-HMQC experiment recorded on a ¹⁵N-labelled protein is presented. This method is based on an approximate expression of the NOE intensities between amide hydrogens obtained from continuum modelling of the non-amide spins; this expression is used in a distance calculation algorithm. The algorithm has been named CROWD, standing for Continuum approximation of Relaxati On path Ways between Dilute spins. This approximation as well as the CROWD algorithm are tested on a simulated case; the CROWD algorithm is then applied to experimental data, measured on a fragment of bacteriorhodopsin.     

On the calculation of 3 J αβ-coupling constants for side chains in proteins

Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or (3) J-coupling constants on the other. The standardly used relation connecting (3) J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and (3) J (αβ)-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between (3) J (αβ)-couplings and the corresponding χ(1)-angle in proteins.     

The determination of the conformational properties of nucleic acids in solution from NMR data

A program, NUCFIT, has been written for simulating the effects of conformational averaging on nuclear Overhauser enhancement (NOE) intensities for the spin systems found in nucleic acids. Arbitrary structures can be generated, and the NOE time courses can be calculated for truncated one-dimensional NOEs, two-dimensional NOE and rotating frame NOE spectroscopy (NOESY and ROESY) experiments. Both isotropic and anisotropic molecular rotation can be treated, using Woessner's formalism (J. Chem. Phys. (1962) 37, 647-654). The effects of slow conformational averaging are simulated by taking population-weighted means of the conformations present. Rapid motions are allowed for by using order parameters which can be supplied by the user, or calculated for specific motional models using the formalism of Tropp (J. Chem. Phys. (1980) 72, 6035-6043). NOE time courses have been simulated for a wide variety of conformations and used to determine the quality of structure determinations using NMR data for nucleic acids. The program also allows grid-searching with least-squares fitting of structures to experimental data, including the effects of spin-diffusion, conformational averaging and rapid internal motions. The effects of variation of intra and internucleotide conformational parameters on NOE intensities has been systematically explored. It is found that (i) the conformation of nucleotides is well determined by realistic NOE data sets, (ii) some of the helical parameters, particularly the base pair roll, are poorly determined even for extensive, noise-free data sets, (iii) conformational averaging of the sugars by pseudorotation has at most second-order influence on the determination of other parameters and (iv) averaging about the glycosidic torsion bond also has, in most cases, an insignificant effect on the determination of the conformation of nucleotides.     

Conformational analysis of a segment in bacterioopsin by two-dimensional (1)H-NMR spectroscopy]

The spatial structure of a synthetic peptide, an analogue of the membrane spanning segment B (residues 34-65) of bacterioopsin from Halobacterium halobium, has been refined. Backbone torsion angles were derived from intensities of short-range interproton NOEs. These, together with a complete set of the NOEs integral intensities formed the basis for the three-dimensional structure refinement by the energy minimization with consideration of NOE penalty functions. Analysis indicates the right-handed alpha-helical conformation of segment B extending from Asp-38 to Tyr-64 with a kink of the helical axis (27 degrees) at Pro-50. The most stable region with an average root-mean-square deviation of 0.43 A between the backbone atoms includes residues 42-60 in six energy refined structures. The N-terminal part of segment B (residues 34-37) has no ordered conformation. The inferred structure is in close agreement with the electron cryomicroscopy structure of bacteriorhodopsin, differing from it in conformations of most of the side chains.     

A computationally efficient method for evaluating the gradient of 2D NOESY intensities

Summary A computationally efficient method for calculating the derivative of NOE intensities with respect to any parameter is presented. This method is based on an integral expression representing the gradient. We will derive this expression from first principles using standard perturbation expansion techniques, and show it to be equivalent to an analytical expression [Yip, P. and Case, D.A. (1989) J. Magn. Reson., 83, 643] Implementation of this method in a refinement scheme (NOE-MD) is also briefly mentioned.     

Knowledge-based versus experimentally acquired distance and angle constraints for NMR structure refinement

Nuclear Overhauser effects (NOE) distance constraints and torsion angle constraints are major conformational constraints for nuclear magnetic resonance (NMR) structure refinement. In particular, the number of NOE constraints has been considered as an important determinant for the quality of NMR structures. Of course, the availability of torsion angle constraints is also critical for the formation of correct local conformations. In our recent work, we have shown how a set of knowledge-based short-range distance constraints can also be utilized for NMR structure refinement, as a complementary set of conformational constraints to the NOE and torsion angle constraints. In this paper, we show the results from a series of structure refinement experiments by using different types of conformational constraints--NOE, torsion angle, or knowledge-based constraints--or their combinations, and make a quantitative assessment on how the experimentally acquired constraints contribute to the quality of structural models and whether or not they can be combined with or substituted by the knowledge-based constraints. We have carried out the experiments on a small set of NMR structures. Our preliminary calculations have revealed that the torsion angle constraints contribute substantially to the quality of the structures, but require to be combined with the NOE constraints to be fully effective. The knowledge-based constraints can be functionally as crucial as the torsion angle constraints, although they are statistical constraints after all and are not meant to be able to replace the latter.     

Transient versus steady state NOE in paramagnetic molecules Cu2Co2SOD as an example

Truncated, steady state and transient NOE experiments have been performed on bovine Cu2Co2 superoxide dismutase. The effectiveness of the different NOE experiments in the general case of paramagnetic macromolecules is discussed. It is concluded that steady state NOEs give superior results. The validity of the two spins approximation is discussed, and NOE values for a fully coupled set of nuclei have been calculated. Transient NOE experiments, when properly performed, confirm the previous assignment of the hyperfine shifted signals in Cu2Co2SOD based on steady state NOE measurements [(1989) Inorg. Chem. 28, 4650] and eliminate any further reason for controversy on an important issue as the assignment of the 1H NMR signals of protons of metal-coordinated imidazoles.     

Solution conformation of purine-pyrimidine DNA octamers using nuclear magnetic resonance, restrained molecular dynamics and NOE-based refinement

The solution structures of two alternating purine-pyrimidine octamers, [d(G-T-A-C-G-T-A-C)]2 and the reverse sequence [d(C-A-T-G-C-A-T-G)]2, are investigated by using nuclear magnetic resonance spectroscopy and restrained molecular dynamics calculations. Chemical shift assignments are obtained for non-exchangeable protons by a combination of two-dimensional correlation and nuclear Overhauser enhancement (NOE) spectroscopy experiments. Distances between protons are estimated by extrapolating distances derived from time-dependent NOE measurements to zero mixing time. Approximate dihedral angles are determined within the deoxyribose ring from coupling constants observed in one and two-dimensional spectra. Sets of distance and dihedral determinations for each of the duplexes form the bases for structure determination. Molecular dynamics is then used to generate structures that satisfy the experimental restraints incorporated as effective potentials into the total energy. Separate runs start from classical A and B-form DNA and converge to essentially identical structures. To circumvent the problems of spin diffusion and differential motion associated with distance measurements within molecules, models are improved by NOE-based refinement in which observed NOE intensities are compared to those calculated using a full matrix analysis procedure. The refined structures generally have the global features of B-type DNA. Some, but not all, variations in dihedral angles and in the spatial relationships of adjacent base-pairs are observed to be in synchrony with the alternating purine-pyrimidine sequence.     

Protein NMR Structures Refined without NOE Data

The refinement of low-quality structures is an important challenge in protein structure prediction. Many studies have been conducted on protein structure refinement; the refinement of structures derived from NMR spectroscopy has been especially intensively studied. In this study, we generated flat-bottom distance potential instead of NOE data because NOE data have ambiguity and uncertainty. The potential was derived from distance information from given structures and prevented structural dislocation during the refinement process. A simulated annealing protocol was used to minimize the potential energy of the structure. The protocol was tested on 134 NMR structures in the Protein Data Bank (PDB) that also have X-ray structures. Among them, 50 structures were used as a training set to find the optimal “width” parameter in the flat-bottom distance potential functions. In the validation set (the other 84 structures), most of the 12 quality assessment scores of the refined structures were significantly improved (total score increased from 1.215 to 2.044). Moreover, the secondary structure similarity of the refined structure was improved over that of the original structure. Finally, we demonstrate that the combination of two energy potentials, statistical torsion angle potential (STAP) and the flat-bottom distance potential, can drive the refinement of NMR structures.     

High-resolution NMR structure of an RNA model system: the 14-mer cUUCGg tetraloop hairpin RNA

We present a high-resolution nuclear magnetic resonance (NMR) solution structure of a 14-mer RNA hairpin capped by cUUCGg tetraloop. This short and very stable RNA presents an important model system for the study of RNA structure and dynamics using NMR spectroscopy, molecular dynamics (MD) simulations and RNA force-field development. The extraordinary high precision of the structure (root mean square deviation of 0.3 Å) could be achieved by measuring and incorporating all currently accessible NMR parameters, including distances derived from nuclear Overhauser effect (NOE) intensities, torsion-angle dependent homonuclear and heteronuclear scalar coupling constants, projection-angle-dependent cross-correlated relaxation rates and residual dipolar couplings. The structure calculations were performed with the program CNS using the ARIA setup and protocols. The structure quality was further improved by a final refinement in explicit water using OPLS force field parameters for non-bonded interactions and charges. In addition, the 2′-hydroxyl groups have been assigned and their conformation has been analyzed based on NOE contacts. The structure currently defines a benchmark for the precision and accuracy amenable to RNA structure determination by NMR spectroscopy. Here, we discuss the impact of various NMR restraints on structure quality and discuss in detail the dynamics of this system as previously determined.