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Publications [#243379] of Robert Bryant
search www.ams.org.Papers Published
 with Bryant, R; Edelsbrunner, H; Koehl, P; Levitt, M, The area derivative of a spacefilling diagram,
Discrete & Computational Geometry, vol. 32 no. 3
(January, 2004),
pp. 293308, Springer Nature (ISSN: 01795376.) [MR2005k:92077], [doi]
(last updated on 2019/09/23)
Abstract: 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 spacefilling 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 inclusionexclusion formulas for these sizes.


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