this paper is concerned, have been derived in several ways. Levitt (1976) generated potentials of mean force by averaging energies over all relative orientations of pairs of side-chains. More recently these kinds of energy functions have been derived as potentials of mean force from the ever-growing database of known protein structures (see the references in Sippl, 1995). Huang et al. (1995) have devised a potential which does not explicitly use the database of known structures; they use only a simple classification of different residues as hydrophobic or hydrophilic, reminiscent of the theoretical energy models of Dill et al. (reviewed by Dill et al., 1995; Yue & Dill, 1995). Maiorov & Crippen (1992) generated a potential function by an optimization procedure which sought to maximize the difference in energy between correct and incorrect protein conformations.

Protein structure prediction has remained elusive because it requires an energy function that can distinguish the correct conformation from the astronomically large number of possibilities (see

The rational approach to pharmaceutical drug design begins with an investigation of the relationship between chemical structure and biological activity. Information gained from this analysis is used to aid the design of new, or improved, drugs. Primary considerations during this investigation are the geometric and chemical characteristics of the molecules.

The motion of a biomolecule greatly depends on the engulfing solution, which is mostly water. Instead of representing individual water molecules, it is desirable to develop implicit solvent models that nevertheless accurately represent the contribution of the solvent interaction to the motion. In such models, hydrophobicity is expressed as a weighted sum of atomic surface areas. The derivatives of these weighted areas contribute to the force that drives the motion. In this paper we give formulas for the weighted and unweighted area derivatives of a molecule modeled as a space-filling diagram made up of balls in motion. Other than the radii and the centers of the balls, the formulas are given in terms of the sizes of circular arcs of the boundary and edges of the power diagram. We also give inclusion–exclusion formulas for these sizes.

We present an adaptive grid based algorithm to compute a family of relevant molecular surfaces. Molecular interfaces are important in simulations and visualization involving biomolecules. The Richards surface has traditionally been used as a good approximation to the surface, and defined as the surface formed by the inner facing part of a solvent probe atom rolling along the van der Waals surface of the molecule. Computing and representing this surface has traditionally involved complex geometrical data structures like alpha shapes. Adaptive and uniform trilinear grids are commonly used in various simulations involving interactions of molecules or computation of electrostatics and other energy terms. We make use of this grid directly to compute the Molecular Surface and properties like area, volume, curvatures, surface atoms and other surfaces. We compare geometrical and biochemical properties with other methods as a validation. 1 Molecular Surface Definitions Explicit surface definitions as the interface between the solvent and proteins have been given since 1970s. Since it is easier to handle implicitly defined models mathematically, different implicit approximations to these surfaces have been developed. 1.1 van der Waals and Lee Richards Surface Definitions The most common model for molecules is as a collection of atoms represented by spheres, with radii equal to their van der Waals radii. The surface of the set of spheres is known as the van der Waals surface. Lee and Richards introduced the concept

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