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Issue No. 06 - November/December (2011 vol. 8)
ISSN: 1545-5963
pp: 1458-1467
Wenqi Zhao , University of Texas at Austin, Austin
Guoliang Xu , Chinese Academy of Sciences, Beijing
Chandrajit Bajaj , University of Texas at Austin, Austin
In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the Protein data bank (PDB). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F, which is nearly C^1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation.
Polynomial splines, molecular surfaces, prismatic scaffolds, Bernstein-Bezier basis, solvation energetics, error bounds, rate of convergence.

C. Bajaj, G. Xu and W. Zhao, "An Algebraic Spline Model of Molecular Surfaces for Energetic Computations," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. , pp. 1458-1467, 2011.
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