Determining local conformational variations in DNA. Nuclear magnetic resonance structures of the DNA duplexes d(CGCCTAATCG) and d(CGTCACGCGC) generated using back-calculation of the nuclear Overhauser effect spectra, a distance geometry algorithm and constrained molecular dynamics

Two-dimensional nuclear magnetic resonance (n.m.r.) spectroscopy and a variety of computational techniques have been used to generate three-dimensional structures of the two DNA duplexes d(CGCCTAATCG) and d(CGTCACGCGC). The central six base-pairs in these two decamers contain all ten dinucleotide pairs in DNA and thus, represent a model system for investigating how the local structure of DNA varies with base sequence. Resonance assignments were made for the non-exchangeable base protons and most of the C-1'-C-4' sugar protons in both decamers. Three-dimensional structures were generated using a distance geometry algorithm and these initial structures were refined by optimizing the fit of back-calculated spectra against the experimental two-dimensional nuclear Overhauser effect (NOE) spectra. This back-calculation procedure consists of calculating NOE cross relaxation rates for a given structure by solution of the Bloch equations, and directly accounts for spin diffusion effects. Use of this refinement procedure eliminates some assumptions that have been invoked when generating structures of DNA oligomers from n.m.r. data. Constrained energy minimization and constrained quenched molecular dynamics calculation were also performed on both decamers to help generate energetically favorable structures consistent with the experimental data. Analysis of the local conformational parameters of helical twist, helical rise, propeller twist, displacement and the alpha, beta, gamma, epison and zeta backbone torsion angles in these structures shows that these parameters span a large range of values relative to the X-ray data of nucleic acids. However, the glycosidic and pseudorotation angles are quite well defined in these structures. The implications that these results have for determination of local structural variations of DNA in solution, such as those predicted by Callidine's rules, are discussed. Our results differ significantly from some previous studies on determining local conformations of nucleic acids and comparisons with these studies are made.     

1H-NMR stereospecific assignments by conformational data-base searches

A search procedure is described for making stereospecific assignments at prochiral centers in proteins on the basis of nuclear Overhauser enhancement and coupling constant data derived from nmr experiments. A data base comprising torsion angles, associated 1H-1H coupling constants and interproton distances is searched by a computer algorithm for sets of values that match the experimental data within specified error limits. Two different data bases are used. The first is a crystallographic data base derived from 34 well-refined crystal structures; the second is a systematic data base derived from conformations of a short peptide fragment with idealized geometry by systematically varying the phi, psi, and chi 1 torsion angles. Both approaches are tested for beta-methylene groups with model data obtained from 20 crystal structures. The results for the two methods are similar though not identical, so that a combination of the two methods appears to be useful. With an appropriate choice of error estimates, around 80% of the beta-methylene groups could be assigned in the test calculations. In addition, results with experimental nmr data indicate that a similar percentage of stereospecific assignments can be made in practical situations.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.     

A 1:2 crystalline complex of ApA:proflavine: a model for binding to single-stranded regions in RNA.

The structure of a 1"2 complex of adenylyl-(3',5')-adenosine phosphate and proflavine hemisulfate has been determined using the methods of x-ray crystallography. Since the ApA does not form a mini double helix, it may serve as a model for the interaction of planar molecules with single stranded nucleic acids. The dinucleotide adopts an extended conformation with the adenines in adjacent molecules forming base pairs. A most unusual feature of the molecule is that it does not obey the "rigid nucleotide" concept although none of the torsion angles occur in energetically unfavourable regions. This is most probably due to the strong interactions between the proflavine and the oligonucleotide.     

Computation of DNA backbone conformations

We present an algorithm for the computation of 2'-deoxyribose-phosphodiester backbone conformations that are stereochemically compatible with a given arrangement of nucleic acid bases in a DNA structure. The algorithm involves the sequential computation of 2'-deoxyribose and phosphodiester conformers (collectively referred to as a backbone 'segment'), beginning at the 5'-end of a DNA strand. Computation of the possible segment conformations is achieved by the initial creation of a fragment library, with each fragment representing a set of bond lengths, bond angles and torsion angles. Following exhaustive searching of sugar conformations, each segment conformation is reduced to a single vector, defined by a specific distance, angle and torsion angle, that allows calculation of the O(1)' position. A given 'allowed' conformation of a backbone segment is determined based on its compatibility with the base positions and with the position of the preceding backbone segment. Initial computation of allowable segment conformations of a strand is followed by the determination of continuous backbone solutions for the strand, beginning at the 3'-end. The algorithm is also able to detect repeating segment conformations that arise in structures containing geometrically repeating dinucleotide steps. To illustrate the utility and properties of the algorithm, we have applied it to a series of experimental DNA structures. Regardless of the conformational complexity of these structures, we are able to compute backbone conformations for each structure. Hence, the algorithm, which is currently implemented within a new computer program NASDAC (Nucleic Acids: Structure, Dynamics and Conformation), should have generally applicability to the computation of DNA structures.     

Stereochemistry of nucleic acids and polynucleotides. VI. Minimum energy conformations of dimethyl phosphate

As part of a study on the conformation of polynucleotides and nucleic acids the preferred conformations of the model conpound dimethyl phosphate are worked out using potential energy functions. In calculating the total potential energy associated with the conformation, nonbonded, torsional, and electrostatic terms have been considered. The variation of the total conformational energy is represented as a function of two torsion angles ? and ψ which are the rotations about the two phosphoester bonds. The most stable conformations are found to be the gauche–gauche conformations about these bonds. The conformations observed for phosphodiesters in the solid state and in the proposed structures of polynucleotides and nucleic acids cluster around the minimum. Also, regions of minimum energy correspond well with the typical allowed regions of a representative dinucleotide.     

Efficient search on energy minima for structure prediction of nucleic acid motifs

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during conformational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

HYPER: A hierarchical algorithm for automatic determination of protein dihedral-angle constraints and stereospecific CβH2 resonance assignments from NMR data

A new computer program, HYPER, has been developed for automated analysis of protein dihedral angle values and CH₂ stereospecific assignments from NMR data. HYPER uses a hierarchical grid-search algorithm to determine allowed values of , , and ₁ dihedral angles and CH₂ stereospecific assignments based on a set of NMR-derived distance and/or scalar-coupling constraints. Dihedral-angle constraints are valuable for restricting conformational space and improving convergence in three-dimensional structure calculations. HYPER computes the set of , , and ₁dihedral angles and CH₂ stereospecific assignments that are consistent with up to nine intraresidue and sequential distance bounds, two pairs of relative distance bounds, thirteen homo- and heteronuclear scalar coupling bounds, and two pairs of relative scalar coupling constant bounds. The program is designed to be very flexible, and provides for simple user modification of Karplus equations and standard polypeptide geometries, allowing it to accommodate recent and future improved calibrations of Karplus curves. The C code has been optimized to execute rapidly (0.3–1.5 CPU-sec residue^–1 using a 5° grid) on Silicon Graphics R8000, R10000 and Intel Pentium CPUs, making it useful for interactive evaluation of inconsistent experimental constraints. The HYPER program has been tested for internal consistency and reliability using both simulated and real protein NMR data sets.     

Unique helical conformation of the fourth cytoplasmic loop of the CB1 cannabinoid receptor in a negatively charged environment

The proximal portion of the C-terminus of the CB(1) cannabinoid receptor is a primary determinant for G-protein activation. A 17 residue proximal C-terminal peptide (rodent CB1 401-417), the intracellular loop 4 (IL4) peptide, mimicked the receptor's G-protein activation domain. Because of the importance of the cationic amino acids to G-protein activation, the three-dimensional structure of the IL4 peptide in a negatively charged sodium dodecyl sulfate (SDS) micellar environment has been studied by two-dimensional proton nuclear magnetic resonance (2D (1)H NMR) spectroscopy and distance geometry calculations. Unambiguous proton NMR assignments were carried out with the aid of correlation spectroscopy (DQF-COSY and TOCSY) and nuclear Overhauser effect spectroscopy (NOESY and ROESY) experiments. The distance constraints were used in torsion angle dynamics algorithm for NMR applications (DYANA) to generate a family of structures which were refined using restrained energy minimization and dynamics. In water, the IL4 peptide prefers an extended conformation, whereas in SDS micelles, 3(10)-helical conformation is induced. The predominance of 3(10)-helical domain structure in SDS represents a unique difference compared with structure in alternative environments, which can significantly impact global electrostatic surface potential on the cytoplasmic surface of the CB(1) receptor and might influence the signal to the G-proteins.     

Efficient Search on Energy Minima for Structure Prediction of Nucleic Acid Motifs

Abstract

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during con-formational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Torsional relaxation for biopolymers.

We describe a method for making natural, physical movements in a chained polymer by sequentially adjusting a few neighboring torsion angles in the polymer backbone. In addition to being very fast and easy to implement, the method is also very general. It applies equally well to proteins and nucleic acids. This method is then used to design a local refinement procedure. We test the refinement procedure on the minimization of a simple energy function for proteins. The energy function has a simplified potential for hydrophobic interaction, a hydrogen-bond term, and a term for van der Waals interaction. There is considerable current interest in such simple energy functions for protein folding. When applied to refine structures found by a global search method, the refinement is able to produce large reduction in the hydrogen-bond term and the van der Waal term of the energy. We conclude that the method is particularly effective in finding good "packing" of residues in an initially compact conformation.     

Conformational studies of nucleic acids: III. Empirical multiple correlation functions for nucleic acid torsion angles

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, alpha (O3'-P-O5'-C5'), delta (C5'-C4'-C3'-O3') and epsilon (C4'-C3'-O3'-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, alpha, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

Distance geometry and related methods for protein structure determination from NMR data

Computational tools have been developed in the last few years, to allow a direct determination of protein structures from NMR data. Numerical calculations with simulated and experimental NMR constraints for distances and torsional angles show that data sets available with present NMR techniques carry enough information to determine reliably the global fold of a small protein. The maximum size of a protein for which the direct method can be applied is not limited by the computational tools but rather by the resolution of the two-dimensional spectra. A general estimate of the maximum size would be a molecular weight of about 10,000 (Markley et al. 1984), but parts of larger proteins might be accessible with the method. Effort for improvement of the NMR structures should be concentrated more on the local conformation rather than the global features. The r.m.s. D values for variations of the polypeptide backbone fold are on the order of 1.5-2 A for several of the studied proteins, indicating that the global structure is well determined by the present NMR data and their interpretation. The local structures are sometimes rather poor, with standard deviations for the backbone torsion angles of about 50 degrees. Possible improvements would be stereospecific resonance assignments of individual methylene protons and individual assignments of the methyl groups of the branched side-chains. Accurate estimates of the short-range NOE distance constraints by calibrating the distance constraints, including segmental flexibility effects, and combined use of distance geometry, energy minimization and molecular dynamics calculations, are further tools for improving the structures.     

Conformational Studies of Nucleic Acids: III. Empirical Multiple Correlation Functions for Nucleic Acid Torsion Angles

Abstract

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, α (03′-P-05′-C5′), δ (C5′-C4′-C3′-03′) and ε (C4′-C3′-03′-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, α, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

NAExplor: A Software Tool for Managing and Analyzing Nucleic Acid Structure Files

NAExplor is a software tool for converting coordinates files between the software packages AMBER, CHARMM, and XPLOR. In addition, it manages the conversion of NMR-derived distance restraints information from the MARDIGRAS program into the appropriate file formats used for input in AMBER, CHARMM, and XPLOR. Analyses of H-H distances in nucleic acid structures and calculations of torsion angles for nucleic acid backbone and riboses are also possible.     

PSEUDYANA for NMR structure calculation of paramagnetic metalloproteins using torsion angle molecular dynamics

The program DYANA, for calculation of solution structures of biomolecules with an algorithm based on simulated annealing by torsion angle dynamics, has been supplemented with a new routine, PSEUDYANA, that enables efficient use of pseudocontact shifts as additional constraints in structure calculations of paramagnetic metalloproteins. PSEUDYANA can determine the location of the metal ion inside the protein frame and allows to define a single tensor of magnetic susceptibility from a family of conformers. As an illustration, a PSEUDYANA structure calculation is provided for a metal-undecapeptide complex, where simulated pseudocontact shifts but no NOE restraints are used as conformational constraints.     

A stereochemical model for phospholipids. II: Conformational analysis and molecular packing of phosphatidylethanolamine (PE)

A partition energy method procedure was applied to select the energetically favoured conformations of phosphatidylethanolamine (PE) as polar constituents of phospholipid molecules. The result indicated a large degree of freedom for the two torsion angles of the ester bond of the phosphate and a gauche, gauche star conformation for the ethane bond.A packing process of the molecule was carried out through a potential energy calculation by considering the conformers selected above, using previously published procedure and conventions. All the arrangements which possess the best packing energy values were characterised by an orientation of the PN dipolar segment parallel to the lattice plain. Rotation of the internal torsion angles and rotation in the eulerian space of the molecule produced differences in the charged groups that interact. An additional minimum was present in the energy packing process of those conformers which have the first torsion angle of the phosphate in a trans conformation. This minimum, which corresponds to an orientation of the molecule orthogonal to the lattice plane, requires a complete neutralisation of the point charges on the system.The results of the calculation underline the importance of changes in the behaviour of the polar group of the phospholipids in the packing process.     

The influence of stereospecific assignments on the determination of three-dimensional structures of proteins by nuclear magnetic resonance spectroscopy. Application to the sea anemone protein BDS-I

The influence of the stereospecific assignments of beta-methylene protons and the classification of chi 1 torsion angles on the definition of the three-dimensional structures of proteins determined from NMR data is investigated using the sea anemone protein BDS-I (43 residues) as a model system. Two sets of structures are computed. The first set comprises 42 converged structures (denoted STEREO structures) calculated on the basis of the complete list of restraints derived from the NMR data, consisting of 489 interproton and 24 hydrogen bonding distance restraints, supplemented by 23 phi backbone and 21 chi 1 side chain torsion angle restraints. The second set comprises 31 converged structures (denoted NOSTEREO structures) calculated from a reduced data set in which those restraints arising from stereospecific assignments, and the corresponding chi 1 torsion angle restraints, are explicitly omitted. The results show that the inclusion of the stereospecific restraints leads to a significant improvement in the definition of the structure of BDS-I, both with respect to the backbone and the detailed arrangement of the side chains. Average atomic rms differences between the individual structures and the mean structures for the backbone atoms are 0.67 +/- 0.12 A and 0.93 +/- 0.16 A for the STEREO and NOSTEREO structures, respectively; the corresponding values for all atoms are 0.90 +/- 0.17 A and 1.17 +/- 0.17 A, respectively. In addition, while the overall fold remains unchanged, there is a small but significant atomic displacement between the two sets of structures.     

Statistical analysis of RNA backbone

Local conformation is an important determinant of RNA catalysis and binding. The analysis of RNA conformation is particularly difficult due to the large number of degrees of freedom (torsion angles) per residue. Proteins, by comparison, have many fewer degrees of freedom per residue. In this work, we use and extend classical tools from statistics and signal processing to search for clusters in RNA conformational space. Results are reported both for scalar analysis, where each torsion angle is separately studied, and for vectorial analysis, where several angles are simultaneously clustered. Adapting techniques from vector quantization and clustering to the RNA structure, we find torsion angle clusters and RNA conformational motifs. We validate the technique using well-known conformational motifs, showing that the simultaneous study of the total torsion angle space leads to results consistent with known motifs reported in the literature and also to the finding of new ones.