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Abstract:Recent new interest in modelling the protein-solvent interactions by continuum methods lead to several improvements for calculating the solvent accessible surface area and its derivative [1]. One of the most efficient analytical method is a parametric approach based on the Gauss-Bonnet theorem. This approach has been implemented as molecular surface routine PARAREA [2] in the energy minimization and Monte Carlo simulation package FANTOM [3]. In this study we demonstrate that this approach can be further enhanced by avoiding the calculation of a relatively large number of potential intersection points in the Gauss-Bonnet path. PARAREA finds them by a straightforward test of all atom pairs in the neighbor list of each atom. Numerical tests showed that this part of the routine consumes a significant portion of the execution time. The new surface routine GETAREA efficiently finds the solvent exposed vertices of the Gauss-Bonnet path by calculating the intersection of half-spaces (IHS). These half-spaces are defined by the planes of two-sphere intersection. Geometric inversion conveniently transforms intersection planes into a set points in dual space. Convex hull of these points corresponds to the desired IHS [4]. Finally, the vertices of Gauss-Bonnet path are found by intersecting edges of IHS with the central atom sphere. Additionally, the list of neighbor atoms is obtained with the aid of a cubic lattice algorithm, as opposed to direct search in PARAREA. Numerical tests with several conformations of the peptide Met-enkephalin and the medium-size protein tendamistat show the correctness of the area and gradient calculation. The CPU time spent in GETAREA has been significantly reduced by factors of 0.4 (Met-enkephalin) and 0.6 (tendamistat) as compared to PARAREA. With the improved performance of the method we are currently performing search for low energy conformations of peptides in solution and apply the improved version of FANTOM in studies of protein folding.
References
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