This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, multi-scale volumetric synthetic electron density maps are constructed from parsed atomic location data of biomolecules in the PDB, using Gaussian isotropic kernels. An appropriate parameter selection is made for constructing an error bounded implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the molecular surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flows are used to improve the mesh quality. Some of our generated meshes have been successfully used in finite element simulations.
1. Implicit solvation models.
(a) Implicit solvation models of Thermus Thermophilus small Ribosome 30S (1J5E) crystal subunit for various Gaussian kernel parameters. The pink color shows 16S rRNA and the remaining colors are proteins.
(b) Implicit solvation models of Haloarcula Marismortui large Ribosome 50S (1JJ2) crystal subunit. The light yellow and the pink color show 5S and 23S rRNA respectively, the remaining colors are proteins.
(c) Implicit solvation models of mAChE for various parameters. mAChE has a cavity as shown in (a). Cavity vanishes in (d) and (e). (a), (b), (c) and (f) show multi-scale models and cavities.
2. Surface Smoothing.
(a) Comparison of mAChE (9308 vertices, 18612 triangles) before and after surface smoothing. (a) - original; (b) - after smoothing.
(b) Comparison of Ribosome 30S (13428 vertices, 26852 triangles) before and after surface smoothing. Left - original; Right - after smoothing.
3. Interior/Exterior Tetrahedral Meshes.
(a) Monomeric mAChE. From left to right: sigma = 2 (65147 vertices, 323442 tetra) and (121670 vertices, 656823 tetra), C = -0.262346 (103680 vertices, 509597 tetra) and (138967 vertices, 707284 tetra). The color shows potential (leftmost) or residues (the right two).
(b) Tetrameric mAChE, sigma = 2. The left two pictures show the 1st crystal structure 1C2O (133078 vertices, 670950 tetra), and the right two pictures show the 2nd one 1C2B, (106463 vertices, 551074 tetra). Cavities are shown in red boxes.
(c) Ribosome 30S, low resolution, C = -0.03125. From left to right: (33612 vertices, 163327 tetra), (37613 vertices, 186496 tetra) and (40255 vertices, 201724 tetra). The pink color shows 16S rRNA and other colors show proteins.
(d) Ribosome 50S, residual level, C = -0.0625. From left to right: (230025 vertices, 1141575 tetra), (234902 vertices, 1162568 tetra), (260858 vertices, 1315112 tetra). The light yellow/pink color show 5S/23S rRNA, other colors show proteins.