Commun. Comput. Phys., 6 (2009), pp. 777-792. |
Model the Solvent-Excluded Surface of 3D Protein Molecular Structures Using Geometric PDE-Based Level-Set Method Qing Pan ^{1}, Xue-Cheng Tai ^{2*} 1 College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China.2 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore; and Department of Mathematics, University of Bergen, Norway. Received 26 March 2008; Accepted (in revised version) 21 January 2009 Available online 5 March 2009 Abstract This paper presents an approach to model the solvent-excluded surface (SES) of 3D protein molecular structures using the geometric PDE-based level-set method. The level-set method embeds the shape of 3D molecular objects as an isosurface or level set corresponding to some isovalue of a scattered dense scalar field, which is saved as a discretely-sampled, rectilinear grid, i.e., a volumetric grid. Our level-set model is described as a class of tri-cubic tensor product B-spline implicit surface with control point values that are the signed distance function. The geometric PDE is evolved in the discrete volume. The geometric PDE we use is the mean curvature specified flow, which coincides with the definition of the SES and is geometrically intrinsic. The technique of speeding up is achieved by use of the narrow band strategy incorporated with a good initial approximate construction for the SES. We get a very desirable approximate surface for the SES. AMS subject classifications: 65D07, 65D10, 65D17, 65D18 Key words: Solvent-excluded surface, implicit surface, mean curvature specified flow, level-set method. *Corresponding author. Email: panqing@lsec.cc.ac.cn (Q. Pan), Tai@mi.uib.no (X.-C. Tai) |