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J Comput Chem. 2002 Jan 15;23(1):128-37.

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects.

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Research Center E. Piaggio, University of Pisa, Italy.


This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571(3) can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.


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