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  • 1
    Electronic Resource
    Electronic Resource
    Force field based conformational analysis of RNA structural motifs: GNRA tetraloops and their pyrimidine relatives (1999)
    Springer
    European biophysics journal 28 (1999), S. 564-573 
    Details
    ISSN: 1432-1017
    Keywords: Key words RNA structural motifs ; GNRA tetraloops ; Conformational search ; Solvent effects ; Electrostatic continuum model ; AbbreviationsMC-SYM Macromolecular conformations by symbolic programming ; JUMNA Junction minimization of nucleic acids ; AMBER Assisted model building with energy refinement ; RF Reaction field ; FIESTA Field integrated electrostatic approach ; FD Finite difference ; sc Synclinal ; ac Anticlinal ; ap Antiperiplanar ; ED Electrostatic damping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract The protocol of conformational analysis applied here to ribonucleotide oligomers combines conformational search in the space of torsion angles and energy minimization using the AMBER4.1 force field with a continuum treatment of electrostatic solute-solvent interactions. RNA fragments with 5′-GGGCGNNAGCCU-3′ sequences commonly fold into hairpins with four-membered loops. The combinatorial search for acceptable conformations using the MC-SYM program was restricted to loop nucleotides and yielded roughly 1500 structures being compatible with a double-stranded stem. After energy minimization by the JUMNA program (without applying any experimental constraints), these structures converged into an ensemble of 74 different conformers including 26 structures which contained the sheared G-A base pair observed in experimental studies of GNRA tetraloops. Energetic analysis shows that inclusion of solvent electrostatic effects is critically important for the selection of conformers that agree with experimentally determined structures. The continuum model accounts for solvent polarization by means of the electrostatic reaction field. In the case of GNRA loop sequences, the contributions of the reaction field shift relative stabilities towards conformations showing most of the structural features derived from NMR studies. The agreement of computed conformations with the experimental structures of GAAA, GCAA, and GAGA tetraloops suggests that the continuum treatment of the solvent represents a definitive improvement over methods using simple damping models in electrostatic energy calculations. Application of the procedure described here to the evaluation of the relative stabilities of conformers resulting from searching the conformational space of RNA structural motifs provides some progress in (non-homology based) RNA 3D-structure prediction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002490050238
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  • 2
    Electronic Resource
    Electronic Resource
    A numerical method for the solution of the one-dimensional Schrödinger equation (1974)
    Springer
    Theoretical chemistry accounts 33 (1974), S. 29-41 
    Details
    ISSN: 1432-2234
    Keywords: Numerical solution of the Schrödinger equation ; Schrödinger equation, numerical solution of ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A numerical method for the calculation of bound states in a one-dimensional potential is suggested, the application of which is very simple and economic. The wavefunctions as well as the potential are approximated by Lagrange interpolation polynomials of the order 2N. The application of the variational principle yields a (2N−1)th order eigenvalue problem of the symmetric matrix H derived from the universal matrices' T and V (l) (l = 0,1,..., N) and (2N + 1) discrete potential values of the actual problem by means of simple matrix algebra. The accuracy of the obtained energies and wavefunctions depends on the parameter N. The proposed method has been applied to different types of potentials. Using polynomials of the order twenty (N=10), generally the results are quite satisfactory for the states of quantum numbers n≦4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527623
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  • 3
    Electronic Resource
    Electronic Resource
    Describing protein structure: A general algorithm yielding complete helicoidal parameters and a unique overall axis (1989)
    New York, NY : Wiley-Blackwell
    Proteins: Structure, Function, and Genetics 6 (1989), S. 46-60 
    Details
    ISSN: 0887-3585
    Keywords: macromolecular conformation ; protein folding ; helical axis ; secondary structure ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: We present a general and mathematically rigorous algorithm which allows the helicoidal structure of a protein to be calculated starting from the atomic coordinated of its peptide backbone. This algorithm yields a unique curved axis which quantifies the folding of the backbone and a full set of helicoidal parameters describing the location of each peptide unit. The parameters obtained form a complete and independent set and can therefore be used for analyzing, comparing, or reconstructing protein backbone geometry. This algorithm has been implemented in a computer program named P-Curve. Several examples of its possible applications are discussed.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prot.340060105
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  • 4
    Electronic Resource
    Electronic Resource
    Conformational and helicoidal analysis of the molecular dynamics of proteins: “Curves,” dials and windows for a 50 psec dynamic trajectory of BPTIEditors note: The authors submitted an entire data set, and agreed to publish in this article only the first panel in each of Figures 9 through 12. The entire data set in these figures is available from David Beveridge or Richard Lavery upon request. (1990)
    New York, NY : Wiley-Blackwell
    Proteins: Structure, Function, and Genetics 8 (1990), S. 179-193 
    Details
    ISSN: 0887-3585
    Keywords: protein conformation ; helicoidal parameters ; molecular dynamics ; bovine pancreatic trypsin inhibitor ; simulation ; protein-protein interactions ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method “Curves,” developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels (“dials”) for each torsional parameter and “windows” on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2° structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prot.340080208
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  • 5
    Electronic Resource
    Electronic Resource
    Molecular structure-biological activity relationships on the basis of quantum-chemical calculations (1979)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 16 (1979), S. 467-484 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Detailed quantum-chemical calculations by means of semiempirical all-valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560160306
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  • 6
    Electronic Resource
    Electronic Resource
    The structure of the left-handed antiparallel amylose double helix: Theoretical studies (1993)
    New York : Wiley-Blackwell
    Biopolymers 33 (1993), S. 363-375 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The atomic coordinates from the crystal structure of a hexasaccharide complex accommodating a zigzag polyiodide [ W. Hinrichs, G. Büttner, M. Steifa, Ch. Betzel, V. Zabel, B. Pfannemüller, and W. Saenger (1987) Science Vol. 238, pp. 205-208; W. Hinrichs and W. Saenger (1990) Journal of the American Chemical Society, Vol. 112, pp. 2789-2796 ] served to construct an antiparallel-stranded amylose double helix with a 5 Å wide central cavity. Using our methodology for the energetic optimization of polymer structures in the internal/ helical variable space [ H. Sklenar, R. Lavery, and B. Pullman (1986) Journal of Biomolecular Structure Dynamics, Vol. 3, pp. 967-987, 989-1014; 1015-1031], we have calculated a theoretical counterpart of this idealized double helix by constraining the helical twist and rise to their experimental values (-45° and 2.33 Å, respectively). Applying the same constraints to the parallel-stranded duplex, this also leads to a low-energy structure with wide central cavity. It is considered as an alternative model to accommodate iodine as observed in the starch-iodine complex.Release of the helical constraints leads to left-handed antiparallel- and parallel-stranded double helices, respectively, with narrow central cavities. Both structures have very similar helix parameters and correspond, in their main characteristics, to the experimentally derived parallel-stranded structure of amylose in starch (6 residues per turn and a pitch height of about 21 Å). The intramolecular energy calculated for the optimized antiparallel-stranded amylose double helix is comparable to that of the parallel-stranded structure. This result raises the question why parallel-stranded amylose seems to be favored in nature. © 1993 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360330305
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