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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Biochemistry 33 (1994), S. 13164-13171 
    ISSN: 1520-4995
    Source: ACS Legacy Archives
    Topics: Biology , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of organic chemistry 44 (1979), S. 4594-4597 
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 481-492 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two general methods for calculating the reaction field generated by a set of off-center point multipoles in a spherical cavity are presented. The methods are a generalization of Kirkwood's original theory for an arbitrary charge distribution. A polytensor formulation, similar to that previously developed for direct multipole interactions, serves to organize the computation and allows straightforward extension to higher derivatives of reaction field energy and gradients of the potential. The computation is reduced to calculation of the Cartesian derivatives of biaxial harmonics. Recursive and explicit formulas are given for the calculation. As an example, the incorporation of reaction field effects in computation of induced dipole moments is discussed. The second procedure, the central multipole method, scales linearly in calculation time with the size of the system. Methods to obtain derivatives analytically based on this method are also described. Our developments allow use of reaction field energy terms with atomic multipole-based empirical potential energy functions. Both methods show particular promise for use in simulation of heterogeneous systems, such as biopolymers, where the remainder of the cavity can be filled explicitly with solvent. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature America Inc.
    Nature structural biology 6 (1999), S. 50-55 
    ISSN: 1072-8368
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Medicine
    Notes: [Auszug] Potential smoothing, a deterministic analog of stochastic simulated annealing, is a powerful paradigm for the solution of conformational search problems that require extensive sampling, and should be a useful tool in computational approaches to structure prediction and refinement. A novel ...
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature America Inc.
    Nature structural biology 6 (1999), S. 199-199 
    ISSN: 1072-8368
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Medicine
    Notes: [Auszug] Nature Struct. Biol. 6, 50– 55 (1999). Tables 1 and 2 were inadvertently omitted from the text of the paper. They are printed below in full. We regret this error and any confusion it may have ...
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 8 (1987), S. 1016-1024 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N2)) and computer time of O(N3). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N1.5) and CPU time of less than O(N2) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10-6 kcal/mol/Å per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 402-409 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A numerical method for calculating the volume of a macromolecule and its first and second derivatives as a function of atomic coordinates is presented. For N atoms, the method requires about 0.3 N ln(N) seconds of CPU time on a VAX-8800 to evaluate the volume and derivatives. As a test case, the method was used to evaluate a pressure-volume energy term in energy minimizations of the protein lysozyme at 1000 atm (1 atm = 1.013 × 105 Pa). R.m.s. gradients of 10-4 kcal/mol/Å were obtained at convergence. The calculated structures exhibited pressure-induced changes which were qualitatively similar to the changes observed in the 1000 atm structure determined by X-ray crystallography.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 548-573 
    ISSN: 0192-8651
    Keywords: surface loops ; structure prediction ; global energy minimization ; energy functions ; hydration free energy ; atomic multipoles ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A protein energy surface is constructed. Validation is through applications of global energy minimization to surface loops of protein crystal structures. For 9 of 10 predictions, the native backbone conformation is identified correctly. Electrostatic energy is modeled as a pairwise sum of interactions between anisotropic atomic charge densities. Model repulsion energy has a softness similar to that seen in ab initio data. Intrinsic torsional energy is modeled as a sum over pairs of adjacent torsion angles of 2-dimensional Fourier series. Hydrophobic energy is that of a hydration shell model. The remainder of hydration free energy is obtained as the energetic effect of a continuous dielectric medium. Parameters are adjusted to reproduce the following data: a complete set of ab initio energy surfaces, meaning one for each pair of adjacent torsion angles of each blocked amino acid; experimental crystal structures and sublimation energies for nine model compounds; ab initio energies over 1014 conformations of 15 small-molecule dimers; and experimental hydration free energies for 48 model compounds. All ab initio data is at the Hartree-Fock/6-31G* level.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 548-573, 1998
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 791-816 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The (φ, ψ) energy surface of blocked alanine (N-acetyl-N′-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters - in the form of partial charges, atomic multipoles, or generalized atomic densities - were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) accurate representation of electrostatic interaction energies of types 1 - 2 and 1 - 3. This result suggests an electrostatic origin for at least part of the error between standard model and ab initio energy surfaces. Given the range of functional forms that is used by the current generation of protein potential functions, these errors cannot be corrected by compensating for errors in other energy components. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Proteins: Structure, Function, and Genetics 33 (1998), S. 204-217 
    ISSN: 0887-3585
    Keywords: rotamer libraries ; energy minimization ; self consistent mean-field theory ; torsion space ; modeling ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The ab initio folding problem can be divided into two sequential tasks of approximately equal computational complexity: the generation of native-like backbone folds and the positioning of side chains upon these backbones. The prediction of side-chain conformation in this context is challenging, because at best only the near-native global fold of the protein is known. To test the effect of displacements in the protein backbones on side-chain prediction for folds generated ab initio, sets of near-native backbones (≤ 4 Å Cα RMS error) for four small proteins were generated by two methods. The steric environment surrounding each residue was probed by placing the side chains in the native conformation on each of these decoys, followed by torsion-space optimization to remove steric clashes on a rigid backbone. We observe that on average 40% of the χ1 angles were displaced by 40° or more, effectively setting the limits in accuracy for side-chain modeling under these conditions. Three different algorithms were subsequently used for prediction of side-chain conformation. The average prediction accuracy for the three methods was remarkably similar: 49% to 51% of the χ1 angles were predicted correctly overall (33% to 36% of the χ1+2 angles). Interestingly, when the inter-side-chain interactions were disregarded, the mean accuracy increased. A consensus approach is described, in which side-chain conformations are defined based on the most frequently predicted χ angles for a given method upon each set of near-native backbones. We find that consensus modeling, which de facto includes backbone flexibility, improves side-chain prediction: χ1 accuracy improved to 51-54% (36-42% of χ1+2). Implications of a consensus method for ab initio protein structure prediction are discussed. Proteins 33:204-217, 1998. © 1998 Wiley-Liss, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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