Journal of Computational Chemistry

doi: 10.1002/jcc.540160301pmid: N/A

Llamas‐Saiz, Antonio L.; Foces‐Foces, Concepción; Mó, Otilia; Yáñez, Manuel; Elguero, Eric; Elguero, José

doi: 10.1002/jcc.540160302pmid: N/A

Ab initio calculations on the structure of pyrazole have been carried out at different levels of accuracy. At the Hartree‐Fock (HF) level, the performance of several basis sets, namely 3‐21G, 6‐31G, 6‐31G**, and 6–311G** was investigated. The influence of electron correlation effects also was studied by carrying out geometry optimizations at the MP2, MP4, and QCISD levels. The performance of a density functional method also was evaluated. We have also investigated the possible influence of the frozen core approximation on the final optimized geometry. Three different statistical analyses were considered in determining which geometry is closest to the experimental microwave geometry—namely Paul Curtin's diagrams, cluster analysis, and multidimensional scaling. From these analyses, we conclude that there is no asymptotic approach to the experimental geometry by increasing the quality of the theoretical model, although, as expected, the more reliable structures are those obtained at the MP2, MP4, and QCISD levels, as well as those obtained by the B3LYP density functional method. We have also found that the values of the rotational constants are a tight criterion to define the quality of a molecular geometry. © 1995 by John Wiley & Sons, Inc.

Eisenhaber, Frank; Lijnzaad, Philip; Argos, Patrick; Sander, Chris; Scharf, Michael

doi: 10.1002/jcc.540160303pmid: N/A

The double cubic lattice method (DCLM) is an accurate and rapid approach for computing numerically molecular surface areas (such as the solvent accessible or van der Waals surface) and the volume and compactness of molecular assemblies and for generating dot surfaces. The algorithm has no special memory requirements and can be easily implemented. The computation speed is extremely high, making interactive calculation of surfaces, volumes, and dot surfaces for systems of 1000 and more atoms possible on single‐processor workstations. The algorithm can be easily parallelized. The DCLM is an algorithmic variant of the approach proposed by Shrake and Rupley (J. Mol. Biol., 79, 351–371, 1973). However, the application of two cubic lattices—one for grouping neighboring atomic centers and the other for grouping neighboring surface dots of an atom—results in a drastic reduction of central processing unit (CPU) time consumption by avoiding redundant distance checks. This is most noticeable for compact conformations. For instance, the calculation of the solvent accessible surface area of the crystal conformation of bovine pancreatic trypsin inhibitor (entry 4PTI of the Brookhaven Protein Data Bank, 362‐point sphere for all 454 nonhydrogen atoms) takes less than 1 second (on a single R3000 processor of an SGI 4D/480, about 5 MFLOP). The DCLM does not depend on the spherical point distribution applied. The quality of unit sphere tesselations is discussed. We propose new ways of subdivision based on the icosahedron and dodecahedron, which achieve constantly low ratios of longest to shortest arcs over the whole frequency range. The DCLM is the method of choice, especially for large molecular complexes and high point densities. Its speed has been compared to the fastest techniques known to the authors, and it was found to be superior, especially when also taking into account the small memory requirement and the flexibility of the algorithm. The program text may be obtained on request. © 1995 by John Wiley & Sons, Inc.

Lipkowitz, Kenny B.; Peterson, Michael A.

doi: 10.1002/jcc.540160304pmid: N/A

The concept of moment statistics for evaluating conformations of molecules derived from molecular dynamics simulations is presented. A comparison of the rigidity of tetralin with benzene and cyclohexane, the effect of “tooth thickness” in geared systems, the fluctional motion of a linear alkane, and the differences between dynamical motions of hydrogen‐bonded systems in gas versus solution phases were studied. The strengths and weaknesses of implementing moment statistics as a tool for data reduction are described. © 1995 by John Wiley & Sons, Inc.

Koča, Jaroslav; Pérez, Serge; Imberty, Anne

doi: 10.1002/jcc.540160305pmid: N/A

The potential energy hypersurfaces (PES) of several carbohydrate molecules were studied with a new algorithm for conformational searches, CICADA (Channels in Conformational Space Analyzed by Driver Approach) interfaced with the molecular mechanics program MM3(92). The method requires (1) one or a few low‐energy conformations as starting points; and (2) designation of the torsion angles important for understanding the conformational behavior of the molecule. The PES is explored by driving separately each selected torsion angle (in both directions) with a concomitant full‐geometry optimization at each increment (except for the driven angle). When a minimum has been detected, the molecule is freely optimized, and the minima so detected are then stored if not encountered previously. The new minima serve as starting structures for further explorations. The results from CICADA permit prediction of relative and absolute flexibility and conformational softness for both the entire molecule as well as for individual group rotations and local minima. The carbohydrates analyzed were Me‐α‐D‐glucopyranoside, β‐D‐GlcNAc(1‐2)α‐D‐Man, and α‐D‐GalNAc(1‐3)(α‐L‐Fuc(1‐2))Gal‐O‐Me. All the low‐energy conformers along with the transition states and flexibilities features were characterized. CICADA found all minima and low‐energy conversion pathways for the disaccharide that were found by a traditional grid search. In contrast to the grid search method, CICADA concentrates mostly on the exploration of the low‐energy regions of the PES, thereby saving a significant amount of computational time. The performance of the method opens new routes for exploring conformational space of larger molecules, such as oligosaccharides. © 1995 by John Wiley & Sons, Inc.

Severance, Daniel L.; Essex, Jonathan W.; Jorgensen, William L.

doi: 10.1002/jcc.540160306pmid: N/A

A modified derivation of the free energy perturbation (FEP) equation leads to a more general interpretation of the procedures for generating the geometry of a perturbed molecule from the reference one in FEP simulations of flexible systems. Using this form of the equation, it is possible to implement a wide variety of procedures which heretofore would have been considered impossible. A new method, generalized alteration of structure and parameters (GASP), has been implemented in the BOSS program and has been found to be more efficient for perturbations of harmonic degrees of freedom than the commonly adopted procedure. Additionally, an extreme example for which the new procedure proves less satisfactory is presented, and a more efficient method which is also derived from the new form of the FEP equation is devised and tested. It is concluded that the key to a convergent FEP method is efficient sampling of low‐energy configurations of the perturbed state; the new form of the equation suggests ways of generating such configurations. © 1995 by John Wiley & Sons, Inc.

Sunada, Shinji; Go, Nobuhiro

doi: 10.1002/jcc.540160307pmid: N/A

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time‐dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second‐order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first‐order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second‐order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second‐order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.

Holst, Michael J.; Saied, Faisal

doi: 10.1002/jcc.540160308pmid: N/A

We present a robust and efficient numerical method for solution of the nonlinear Poisson‐Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact‐Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. © 1995 by John Wiley & Sons, Inc.

Zhang, Mei‐Qing; Skeel, Robert D.

doi: 10.1002/jcc.540160309pmid: N/A

In this article we observe that generally symplectic integrators conserve angular momentum exactly, whereas nonsymplectic integrators do not. We show that this observation extends to multiple timesteps and to constrained dynamics. Both of these devices are important for efficient molecular dynamics simulations. © 1995 by John Wiley & Sons, Inc.

Svensson, Bo; Jönsson, Bo

doi: 10.1002/jcc.540160310pmid: N/A

We present an efficient technique for Monte Carlo simulation of electrostatic free energy changes in biomolecular systems. It is a development of a recent method for the study of the influence of electrostatic interactions on the ion binding properties and redox potentials of biomolecules. The electrolyte solution is described by the primitive model, in which ions are treated as hard charged spheres and the solvent is replaced by a structureless continuum. The protein is kept fixed in the center of a spherical simulation cell, and the dielectric constant has the solvent value throughout the cell. By a multiparticle perturbation approach, it is possible to obtain a number of free energy changes within one simulation only. The usefulness of the method is illustrated with a study of the copper binding electron‐transport protein azurin (from Alcaligenes denitrificans). The change in acidity of the histidine residues upon changing the redox state of the copper ion is calculated. The theoretical predictions agree well with available experiments. © 1995 by John Wiley & Sons, Inc.