Discrete & Computational Geometry

, Volume 32, Issue 3, pp 293–308 | Cite as

The Area Derivative of a Space-Filling Diagram

  • Robert BryantEmail author
  • Herbert EdelsbrunnerEmail author
  • Patrice KoehlEmail author
  • Michael LevittEmail author


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.


Water Molecule Solvent Model Atomic Surface Solvent Interaction Individual Water 
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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics, Duke University, Durham, NC 27708USA
  2. 2.Department of Computer Science, Duke University, Durham, NC 27708USA
  3. 3.Department of Structural Biology, Stanford University, CA 94305USA

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