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  • 1
    Electronic Resource
    Electronic Resource
    An efficient, differentiable hydration potential for peptides and proteins (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 17 (1996), S. 1549-1558 
    Details
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An approximate method for calculating the exposed volume of the hydration shell (VHS) about an atom, the Reduced Radius Independent Gaussian Sphere (RRIGS) approximation, is presented. A key ingredient in this method is the use of reduced van der Waals radii so that the error of including only double overlap terms (and omitting multiple overlap terms) in calculating the VHS is balanced by a reduction in the magnitude of the double overlap terms. Also, the double overlap is modeled with a gaussian function. The RRIGS approximate calculation of the VHS is shown to be very accurate (the rms deviation of the VHS of each atom in avian pancreatic polypeptide and bovine pancreatic trypsin inhibitor was 14.0 and 15.8 Å3, respectively, out of a range of values between 0 and 600 Å3). The RRIGS approximation is used to develop a potential function to represent the free energy of solvation for proteins. The pairwise gaussian form of the potential enables it to be incorporated into a gaussian representation of ECEPP (Empirical Conformational Energy Program for Peptides) for use in the Diffusion Equation Method (DEM) of global optimization. Inclusion of the effects of hydration by means of this potential is shown to require less than twice the computational time needed for computing the ECEPP conformational potential energy alone; this makes inclusion of solvent computationally feasible. Furthermore, this gaussian hydration potential function and its derivatives are continuous, so that it may be readily minimized. The combined potential of ECEPP/3 plus hydration is shown to require fewer energy evaluations per local minimization than ECEPP/3 alone for two small peptides. © 1996 by John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.6
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  • 2
    Electronic Resource
    Electronic Resource
    A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 569-583 
    Details
    ISSN: 0192-8651
    Keywords: fast multigrid boundary element method ; macromolecular electrostatic calculations ; poisson equation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A fast multigrid boundary element (MBE) method for solving the Poisson equation for macromolecular electrostatic calculations in a solvent is developed. To convert the integral equation of the BE method into a numerical linear equation of low dimensions, the MBE method uses an adaptive tesselation of the molecular surface by BEs with nonregular size. The size of the BEs increases in three successive levels as the uniformity of the electrostatic field on the molecular surface increases. The MBE method provides a high degree of consistency, good accuracy, and stability when the sizes of the BEs are varied. The computational complexity of the unrestricted MBE method scales as O(Nat), where Nat is the number of atoms in the macromolecule. The MBE method is ideally suited for parallel computations and for an integrated algorithm for calculations of solvation free energy and free energy of ionization, which are coupled with the conformation of a solute molecule. The current version of the 3-level MBE method is used to calculate the free energy of transfer from a vacuum to an aqueous solution and the free energy of the equilibrium state of ionization of a 17-residue peptide in a given conformation at a given pH in ∼ 400 s of CPU time on one node of the IBM SP2 supercomputer. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 569-583, 1997
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New optimization method for conformational energy calculations on polypeptides: Conformational space annealing (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 1222-1232 
    Details
    ISSN: 0192-8651
    Keywords: optimization method ; global minimum-energy conformations ; polypeptides ; conformational space annealing ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A new optimization method is presented to search for the global minimum-energy conformations of polypeptides. The method combines essential aspects of the build-up procedure and the genetic algorithm, and it introduces the important concept of “conformational space annealing.” Instead of considering a single conformation, attention is focused on a population of conformations while new conformations are obtained by modifying a “seed conformation.” The annealing is carried out by introducing a distance cutoff, Dcut, which is defined in the conformational space; Dcut effectively divides the whole conformational space of local minima into subdivisions. The value of Dcut is set to a large number at the beginning of the algorithm to cover the whole conformational space, and annealing is achieved by slowly reducing it. Many distinct local minima designed to be distributed as far apart as possible in conformational space are investigated simultaneously. Therefore, the new method finds not only the global minimum-energy conformation but also many other distinct local minima as by-products. The method is tested on Met-enkephalin, a 24-dihedral angle problem. For all 100 independent runs, the accepted global minimum-energy conformation was obtained after about 2600 minimizations on average. © 1997 John Wiley & Sons, Inc.   J Comput Chem 18: 1222-1232
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 17 (1996), S. 1453-1480 
    Details
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ1 dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ1 dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.6
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  • 5
    Electronic Resource
    Electronic Resource
    An assessment of the accuracy of the RRIGS hydration potential: Comparison to solutions of the Poisson-Boltzmann equation (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 1072-1078 
    Details
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A rapid, pairwise hydration potential, the reduced radius independent Gaussian sphere (RRIGS) approximation, has been presented recently. Because experimental values of the conformational dependence of the hydration free energy are unavailable, this hydration potential is testable by comparison to a presumably more accurate (yet more computationally intensive) model. One such method is the electrostatic hydration approach, which models the protein as a collection of point charges in a low-dielectric medium and the solvent as a high-dielectric continuum. The electrostatic free energy can be determined by solving the Poisson-Boltzmann equation, which is carried out with the program DelPhi. The total free energy of hydration is calculated by adding a free energy of cavity formation term to this electrostatic term. Comparison is made for many conformations of two proteins, bovine pancreatic trypsin inhibitor (BPTI) and the carboxy-terminal fragment of the L7/L12 ribosomal protein (CTF). Thirty-nine near-native structures of BPTI, previously generated by Ripoll and coworkers, and 150 conformations of CTF, generated by a threading algorithm to cover a wide range of conformational space, were used in these comparisons. It is shown that, for the neutral forms of these proteins, the RRIGS hydration potential correlates very well with the electrostatic model hydration free energy, although the correlation is better for the CTF conformations than for the near-native BPTI conformations. For charged forms, the correlation is much poorer. These results serve as evidence that solvent-exposure models of hydration, which leave out cooperative effects between different groups, may be appropriate for modeling neutral or slightly charged species, because these cooperative effects are likely to be small. However, for highly charged species where cooperative effects are surely large, such an approach will be less accurate. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1072-1078, 1997
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    B-spline method for energy minimization in grid-based molecular mechanics calculations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 71-85 
    Details
    ISSN: 0192-8651
    Keywords: molecular docking ; protein folding ; grid approximation ; trilinear interpolation ; potential energy ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A method is described for molecular mechanics calculations based on a cubic B-spline approximation of the potential energy. This method is useful when parts of the system are allowed to remain fixed in position so that a potential energy grid can be precalculated and used to approximate the interaction energy between parts of a molecule or between molecules. We adapted and modified the conventional B-spline method to provide an approximation of the Empirical Conformational Energy Program for Peptides (ECEPP) potential energy function. The advantage of the B-spline method over simpler approximations is that the resulting B-spline function is C2 continuous, which allows minimization of the potential energy by any local minimization algorithm. The standard B-spline method provides a good approximation of the electrostatic energy; but in order to reproduce the Lennard-Jones and hydrogen-bonding functional forms accurately, it was necessary to modify the standard B-spline method. This modification of the B-spline method can also be used to improve the accuracy of trilinear interpolation for simulations that do not require continuous derivatives. As an example, we apply the B-spline method to rigid-body docking energy calculations using the ECEPP potential energy function. Energies are calculated for the complex of Phe-Pro-Arg with thrombin. For this system, we compare the performance of the B-spline method to that of the standard pairwise summation in terms of speed, accuracy, and overhead costs for a variety of grid spacings. In our rigid-body docking calculations, the B-spline method provided an accurate approximation of the total energy of the system, and it resulted in an 180-fold reduction in the time required for a single energy and gradient calculation for this system.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 71-85, 1998
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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