Smooth Molecular Surface Research Articles

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

In this paper, an efficient solver for the polarizable continuum model in quantum chemistry is developed which takes the solvent excluded surface (the smooth molecular surface) as the solute–solvent boundary. This model requires to solve a generalized Poisson (GP) equation defined in [Formula: see text] with a space-dependent dielectric permittivity function. First, the original GP-equation is transformed into a system of two coupled equations defined in a bounded domain. Then, this domain is decomposed into overlapping balls and the Schwarz domain decomposition method is used. This method involves a direct Laplace solver and an efficient GP-solver to solve the local sub-equations in balls. For each solver, the spherical harmonics are used as basis functions in the angular direction of the spherical coordinate system. A series of numerical experiments are presented to test the performance of this method.

SIMS: computation of a smooth invariant molecular surface

SIMS, a new method of calculating a smooth invariant molecular dot surface, is presented. The SIMS method generates the smooth molecular surface by rolling two probe spheres. A solvent probe sphere is rolled over the molecule and produces a Richards-Connolly molecular surface (MS), which envelops the solvent-excluded volume of the molecule. In deep crevices, Connolly's method of calculating the MS has two deficiencies. First, it produces self-intersecting parts of the molecular surface, which must be removed to obtain the correct MS. Second, the correct MS is not smooth, i.e., the direction of the normal vector of the MS is not continuous, and some points of the MS are singular. We present an exact method for removing self-intersecting parts and smoothing the singular regions of the MS. The singular MS is smoothed by rolling a smoothing probe sphere over the inward side of the singular MS. The MS in the vicinity of singularities is replaced with the reentrant surface of the smoothing probe sphere. The smoothing method does not disturb the topology of a singular MS, and the smooth MS is a better approximation of the dielectric border between high dielectric solvent and the low dielectric molecular interior. The SIMS method generates a smooth molecular dot surface, which has a quasi-uniform dot distribution in two orthogonal directions on the molecular surface, which is invariant with molecular rotation and stable under changes in the molecular conformation, and which can be used in a variety of implicit methods of modeling solvent effects. The SIMS program is faster than the Connolly MS program, and in a matter of seconds generates a smooth dot MS of a 200-residue protein. The program is available from the authors on request (see http:@femto.med.unc.edu/SIMS).

SMART: a solvent-accessible triangulated surface generator for molecular graphics and boundary element applications.

An algorithm is presented for generating a representation of the solvent-accessible molecular surface as a smooth triangulated manifold. The algorithm, called SMART (SMooth moleculAR surface Triangulator), divides the contact and reentrant portions of the solvent-accessible molecular surface into curvilinear three-sided elements. In contrast to the author's earlier implementation of this general approach [Zauhar, R.J. and Morgan, R.S., J. Comput. Chem., 11 (1990) 603], the SMART algorithm defines elements directly on the appropriate geometric surface types (rather than using interpolation over cubic elements), and has special features to handle highly distorted regions which often appear in deep crevices and internal cavities. While the method is designed for use with boundary element techniques in continuum electrostatics, it can also be applied to the accurate computation of molecular surface areas and volumes, and the generation of shaded surfaces for display with interactive computer graphics.

The molecular surface package

The Molecular Surface Package is a reimplementation, in C, of a set of earlier FORTRAN programs for computing analytical molecular surfaces, areas, volumes, polyhedral molecular surfaces, and surface curvatures. The software does not do interactive molecular graphics, but it will produce pixel maps of smooth molecular surfaces. The polyhedral molecular surfaces are suited to display on graphics systems with real-time rendering of polyhedra.

A fast algorithm for generating smooth molecular dot surface representations

The smooth molecular surface originally described by Richards and later implemented by Connolly in his MS program has become an important visualization technique in the field of molecular modeling. We describe here a new algorithm, called USURF, which approximates the MS dot surface, but with a twofold to sixfold enhancement of speed. The algorithm has been incorporated into our interactive modeling system, Mosaic, and is also available as a stand-alone program.