Vibrational modes of A-DNA,B-DNA,and A-RNA backbones: An application of a green-function refinement procedure

Normal vibrational analysis was carried out for DNA molecules in both A and B conformations as well as for A-RNA. A simplified backbone model was examined and expanded to include the backbone phosphate-group and the ribose ring. We applied the new force-constant refinement procedure discussed in the preceeding paper [Van Zandt, L. L., Lu, K.-C. & Prohofsky, E. W. (1977) Biopolymers, 16 , 2481–90] to fit some observed frequencies in the Raman spectra for all three nucleic acids with the same set of force constants. The results indicate that the observed frequency shift can be attributed to the conformational change solely. We ignored the second-order differences in force constants for the different geometries. The agreement between the observed and calculated frequencies derived from the final refined set of force constants is good and apparently justifies this assumption. Two modes previously assigned to the symmetric diester O-P-O stretch and the symmetric dioxy O‥P‥O stretch are actually fitted. They are mainly backbone phosphate-group modes. The refined ribose-ring force-constants were transferred to the calculation of the vibrational spectrum of tetrahydrofuran. The overall agreement is again good. We discuss these calculations and the resulting normal modes. We also discuss the application of the Green-function refinement scheme and several strategies adopted to bias the convergence of the procedure.     

Refinement of protein structures in explicit solvent

We present a CPU efficient protocol for refinement of protein structures in a thin layer of explicit solvent and energy parameters with completely revised dihedral angle terms. Our approach is suitable for protein structures determined by theoretical (e.g., homology modeling or threading) or experimental methods (e.g., NMR). In contrast to other recently proposed refinement protocols, we put a strong emphasis on consistency with widely accepted covalent parameters and computational efficiency. We illustrate the method for NMR structure calculations of three proteins: interleukin-4, ubiquitin, and crambin. We show a comparison of their structure ensembles before and after refinement in water with and without a force field energy term for the dihedral angles; crambin was also refined in DMSO. Our results demonstrate the significant improvement of structure quality by a short refinement in a thin layer of solvent. Further, they show that a dihedral angle energy term in the force field is beneficial for structure calculation and refinement. We discuss the optimal weight for the energy constant for the backbone angle omega and include an extensive discussion of meaning and relevance of the calculated validation criteria, in particular root mean square Z scores for covalent parameters such as bond lengths.     

On using time-averaging restraints in molecular dynamics simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulations to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, 3J coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. To account for the averaging of experimentally derived quantities inherent in the experimental techniques, time-averaging restraining methods may be used. In the case of structure refinement using 3J coupling constants from NMR experiments, time-averaging methods previously proposed can suffer from large artificially induced structural fluctuations. A modified time-averaged restraining potential energy function is proposed which overcomes this problem. The different possible approaches are compared using stochastic dynamics simulations of antamanide, a cyclic peptide of ten residues.     

NMR investigations of protein-carbohydrate interactions binding studies and refined three-dimensional solution structure of the complex between the B domain of wheat germ agglutinin and N,N', N"-triacetylchitotriose.

The specific interaction of the isolated B domain of wheat germ agglutinin (WGA-B) with N,N',N"-triacetylchitotriose has been analyzed by 1H-NMR spectroscopy. The association constants for the binding of WGA-B to this trisaccharide have been determined from both 1H-NMR titration experiments and microcalorimetry methods. Entropy and enthalpy of binding have been obtained. The driving force for the binding process is provided by a negative DeltaH which is partially compensated by negative DeltaS. These negative signs indicate that hydrogen bonding and van der Waals forces are the major interactions stabilizing the complex. NOESY NMR experiments in water solution provided 327 protein proton-proton distance constraints. All the experimental constraints were used in a refinement protocol including restrained molecular dynamics in order to determine the refined solution conformation of this protein/carbohydrate complex. With regard to the NMR structure of the free protein, no important changes in the protein NOEs were observed, indicating that carbohydrate-induced conformational changes are small. The average backbone rmsd of the 35 refined structures was 1.05 A, while the heavy atom rmsd was 2.10 A. Focusing on the bound ligand, two different orientations of the trisaccharide within WGA-B binding site are possible. It can be deduced that both hydrogen bonds and van der Waals contacts confer stability to both complexes. A comparison of the three-dimensional structure of WGA-B in solution to that reported in the solid state and to those deduced for hevein and pseudohevein in solution has also been performed.     

Crystallographic structure refinement of Chromatium high potential iron protein at two Angstroms resolution.

The structure of Chromatium high potential iron protein (HiPIP) has been refined by semiautomatic Fo-Fc (observed minus calculated structure amplitude Fourier methods to a convential R index, R=sum of the absolute value of Fo-Fc divided by the sum of Fo, of 24.7% for a model in which bond distances and angles are constrained to standard values. Bond length and angle constraints were applied only intermittenly during the computations. At a late stage of the refinement, atomic parameters for only the Fe4S4 cluster plus the 4 associated cystein S-gamma atoms were adjusted by least squares methods and kept fixed during the rest of the refinement. The refined model consists of 625 of the 632 nonhydrogen atoms in the protein plus 75 water molecules. Seven side chain atoms could not be located in the final electron density map. A computer program rather than visual inspection was used wherever possible in the refinement: for locating water molecules, for removing water molecules that too closely approach other atoms, for deleting atoms that lay in regions of low electron density, and for evaluating the progress of refinement. Fo-Fc Fourier refinement is sufficiently economical to be applied routinely in protein crystal structure determinations. The complete HiPIP refinement required approximately 12 hours of CDC 3600 computer time and cost less than $3000 starting from a "trial structure," based upon multipe isomorphoous replacement phases, which gave an R of 43%...     

Structural refinement of protein segments containing secondary structure elements: Local sampling, knowledge-based potentials, and clustering

In this article, we present an iterative, modular optimization (IMO) protocol for the local structure refinement of protein segments containing secondary structure elements (SSEs). The protocol is based on three modules: a torsion-space local sampling algorithm, a knowledge-based potential, and a conformational clustering algorithm. Alternative methods are tested for each module in the protocol. For each segment, random initial conformations were constructed by perturbing the native dihedral angles of loops (and SSEs) of the segment to be refined while keeping the protein body fixed. Two refinement procedures based on molecular mechanics force fields - using either energy minimization or molecular dynamics - were also tested but were found to be less successful than the IMO protocol. We found that DFIRE is a particularly effective knowledge-based potential and that clustering algorithms that are biased by the DFIRE energies improve the overall results. Results were further improved by adding an energy minimization step to the conformations generated with the IMO procedure, suggesting that hybrid strategies that combine both knowledge-based and physical effective energy functions may prove to be particularly effective in future applications.     

The effects of rigid motions on elastic network model force constants

Elastic network models provide an efficient way to quickly calculate protein global dynamics from experimentally determined structures. The model's single parameter, its force constant, determines the physical extent of equilibrium fluctuations. The values of force constants can be calculated by fitting to experimental data, but the results depend on the type of experimental data used. Here, we investigate the differences between calculated values of force constants and data from NMR and X-ray structures. We find that X-ray B factors carry the signature of rigid-body motions, to the extent that B factors can be almost entirely accounted for by rigid motions alone. When fitting to more refined anisotropic temperature factors, the contributions of rigid motions are significantly reduced, indicating that the large contribution of rigid motions to B factors is a result of over-fitting. No correlation is found between force constants fit to NMR data and those fit to X-ray data, possibly due to the inability of NMR data to accurately capture protein dynamics.     

Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.     

A simple spectral-driven procedure for the refinement of DNA structures by NMR spectroscopy.

We have developed a simple and quantitative procedure (SPEDREF) for the refinement of DNA structures using experimental two-dimensional nuclear Overhauser effect (2D NOE) data. The procedure calculates the simulated 2D NOE spectrum using the full matrix relaxation method on the basis of a molecular model. The volume of all NOE peaks is measured and compared between the experimental and the calculated spectra. The difference of the experimental and simulated volumes is minimized by a conjugated gradient procedure to adjust the interproton distances in the model. An agreement factor (analogous to the crystallographic R-factor) is used to monitor the progress of the refinement. The procedure is an The agreement is considered to be complete when several parameters, including the R-factor, the energy associated with the molecule, the local conformation (as judged by the sugar pseudorotation), and the global conformation (as judged by the helical x-displacement), are refined to their respective convergence. With the B-DNA structure of d(CGATCG) as an example, we show that DNA structure may be refined to produce calculated NOE spectra that are in excellent agreement with the experimental 2D NOE spectra. This is judged to be effective by the low R-factor of approximately 15%. Moreover, we demonstrate that not only are NOE data very powerful in providing details of the local structure but, with appropriate weighting of the NOE constraints, the global structure of the DNA double helix can also be determined, even when starting with a grossly different model. The reliability and limitations of a DNA structure as determined by NMR spectroscopy are discussed.     

Coarse Grained Normal Mode Analysis vs. Refined Gaussian Network Model for Protein Residue-Level Structural Fluctuations

We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C _α , C, N, and C _β are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.     

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.     

GENFOLD: a genetic algorithm for folding protein structures using NMR restraints.

We report the development and validation of the program GENFOLD, a genetic algorithm that calculates protein structures using restraints obtained from NMR, such as distances derived from nuclear Overhauser effects, and dihedral angles derived from coupling constants. The program has been tested on three proteins: the POU domain (a small three-helix DNA-binding protein), bovine pancreatic trypsin inhibitor (BPTI), and the starch-binding domain from Aspergillus niger glucoamylase I, a 108-residue beta-sheet protein. Structures were calculated for each protein using published NMR restraints. In addition, structures were calculated for BPTI using artificial restraints generated from a high-resolution crystal structure. In all cases the fittest calculated structures were close to the target structure, and could be refined to structures indistinguishable from the target structures by means of a low-temperature simulated annealing refinement. The effectiveness of the program is similar to that of distance geometry and simulated annealing methods, and it is capable of using a very wide range of restraints as input. It can thus be readily extended to the calculation of structures of large proteins, for which few NOE restraints may be available.     

Refinement of F-Actin Model against Fiber Diffraction Data by Long-Range Normal Modes

The atomic model of F-actin was refined against fiber diffraction data using long-range normal modes as adjustable parameters to account for the collective long-range filamentous deformations. To determine the effect of long-range deformations on the refinement, each of the four domains of G-actin was treated as a rigid body. It was found that among all modes, the bending modes make the most significant contributions to the improvement of the refinement. Inclusion of only 7–9 bending modes as adjustable parameters yielded a lowest R-factor of 6.3%. These results demonstrate that employing normal modes as refinement parameters has the advantage of using a small number of adjustable parameters to achieve a good fitting efficiency. Such a refinement procedure may therefore prevent the refinement from overfitting the structural model. More importantly, the results of this study demonstrate that, for any fiber diffraction data, a substantial amount of refinement error is due to long-range deformations, especially the bending, of the filaments. The effects of these intrinsic deformations cannot be easily compensated for by adjusting local structural parameters, and must be properly accounted for in the refinement to achieve improved fit of refined models with experimental diffraction data.     

FireDock: fast interaction refinement in molecular docking

Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.     

Refinement of an enzyme complex with inhibitor bound at partial occupancy. Hen egg-white lysozyme and tri-N-acetylchitotriose at 1.75 A resolution.

The structure of the tri-N-acetylchitotriose inhibitor complex of hen egg-white lysozyme has been refined at 1.75 A resolution, using data collected from a complex crystal with ligand bound at less than full occupancy. To determine the exact value of the inhibitor occupancy, a model comprising unliganded and sugar-bound protein molecules was generated and refined against the 1.75 A data, using a modified version of the Hendrickson & Konnert least-squares procedure. The crystallographic R-factor for the model was found to fall to a minimum at 55% bound sugar. Conventional refinement assuming unit occupancy was found to yield incorrect thermal and positional parameters. Application of the same refinement procedures to an earlier 2.0 A data set, collected independently on different complex crystals by Blake et al. gave less consistent results than the 1.75 A refinement. From an analysis of the high resolution structure a detailed picture of the protein-carbohydrate interactions in the non-productive complex has emerged, together with the conformation and mobility changes that accompany ligand binding. The specificity of interaction between the protein and inhibitor, bound in subsites A to C of the active site, is seen to be generated primarily by an extensive network of hydrogen bonds, both to the protein itself and to bound solvent molecules. The latter also play an important role in maintaining the structural integrity of the active site cleft in the apo-protein.     

NMR investigations of protein-carbohydrate interactions: refined three- dimensional structure of the complex between hevein and methyl beta- chitobioside

The specific interaction of hevein with GlcNAc-containing oligosaccharides has been analyzed by1H-NMR spectroscopy. The association constants for the binding of hevein to a variety of ligands have been estimated from1H-NMR titration experiments. The association constants increase in the order GlcNAc-alpha(1-->6)-Man < GlcNAc < benzyl-beta-GlcNAc < p-nitrophenyl-beta-GlcNAc < chitobiose < p- nitrophenyl-beta-chitobioside < methyl-beta-chitobioside < chitotriose. Entropy and enthalpy of binding for different complexes have been obtained from van't Hoff analysis. The driving force for the binding process is provided by a negative DeltaH0which is partially compensated by negative DeltaS0. These negative signs indicate that hydrogen bonding and van der Waals forces are the major interactions stabilizing the complex. NOESY NMR experiments in water solution provided 475 accurate protein proton-proton distance constraints after employing the MARDIGRAS program. In addition, 15 unambiguous protein/carbohydrate NOEs were detected. All the experimental constraints were used in a refinement protocol including restrained molecular dynamics in order to determine the highly refined solution conformation of this protein- carbohydrate complex. With regard to the NMR structure of the free protein, no important changes in the protein nOe's were observed, indicating that carbohydrate-induced conformational changes are small. The average backbone rmsd of the 20 refined structures was 0.055 nm, while the heavy atom rmsd was 0.116 nm. It can be deduced that both hydrogen bonds and van der Waals contacts confer stability to the complex. A comparison of the three-dimensional structure of hevein in solution to those reported for wheat germ agglutinin (WGA) and hevein itself in the solid state has also been performed. The polypeptide conformation has also been compared to the NMR-derived structure of a smaller antifungical peptide, Ac-AMP2.      

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.     

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.