Advances in biomolecular surface meshing and its applications to mathematical modeling

Abstract

In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and simulation. Recently, with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation, providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure. In this review, we summarize recent works on this issue. First, various definitions of molecular surfaces and corresponding meshing methods are introduced. Second, our recent meshing tool, TMSmesh, and its performances are presented. Finally, we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM). molecular surface meshing, manifold mesh, mathematical modeling, TMSmeshCitation: Chen M X, Lu B Z. Advances in biomolecular surface meshing and its applications to mathematical modeling. Chin Sci Bull, 2013Bull, , 58: 1843Bull, -1849 10.1007/s11434-013-5829-8One main goal of computational structural biology/chemistry is to understand the functions and mechanisms of biomolecular systems and their relations to molecular structures with a wide range of computational approaches. To achieve this, proper and correct representation of the interface between biomolecule and solvent, molecular surface, is a primary task. In the field of implicit solvent modeling and continuum modeling, the molecular surface is used to model the dielectric interface which is the transition from the low-dielectric solute region to the high-dielectric solvent region. It is also important and useful in materials science and surface science [1]. Meshing molecular surface is a prerequisite for using boundary element method (BEM) and finite element method (FEM) in the implicit solvent models, and it is a more demanding task than for the only purposes of visualization and/or geometry analyses of molecular structure. So far, due to the highly complex and irregular shape of the molecular surface, *Corresponding author (email: bzlu@lsec.cc.ac.cn) efficient meshing of molecular surface for large real biomolecule with high quality remains a challenging problem. Actually, it was historically a great impediment to use BEM/FEM in continuum modeling of large molecular systems.The main purpose of this paper is to review the various definitions and meshing methods for molecular surface, including our recent work, and introduce their applications in implicit solvent modeling and simulation. Following this introduction section, in Section 1, various definitions of molecular surfaces and corresponding meshing methods are introduced. In Section 2, our recent algorithm and software, TMSmesh, are focused. We also made comparisons with some other methods. In Section 3, a closely related topic, volume me...

Molecular Surface Remeshing with Local Region Refinement

“…Molecular surfaces have various definitions based on their molecular structure. In a recent study [ 11 ], Chen and Lu summarized molecular surfaces, including van der Waals (VDW) surfaces, solvent accessible surfaces (SASs), solvent excluded surfaces (SESs), molecular skin surfaces, minimal molecular surfaces, and Gaussian surfaces. In this section, we briefly review the existing methods in molecular surface meshing.…”

“…In this section, we briefly review the existing methods in molecular surface meshing. We recommend books [ 12 ] and review articles [ 11 , 13 , 14 ] for detailed studies. Alliez et al [ 13 ] reviewed surface remeshing techniques generally used in computer graphics and geometry processing applications.…”

“…Alliez et al [ 13 ] reviewed surface remeshing techniques generally used in computer graphics and geometry processing applications. Chen and Lu [ 11 ] conducted a review specific in molecular surface remeshing. Similarly, Bade et al [ 14 ] compared state-of-the-art methods of medical mesh smoothing.…”

Molecular Sparse Representation by a 3D Ellipsoid Radial Basis Function Neural Network via L1 Regularization

“…16 Due to high complexity and irregularity of the large size molecular models, new issues arise in simulations and other downstream applications. 17 Therefore, efficient representation of the molecular shape (as well as the "molecular surface" or "molecular volume") for large size biomolecules with high quality is an open challenge. 16 The molecular shape is defined in various ways.…”

Molecular Sparse Representation by 3D Ellipsoid Radial Basis Function Neural Networks via $L_1$ Regularization

“…And biomolecules geometric shape (especially molecular surface) is prerequisite for using boundary element method (BEM) and finite element method (FEM) in the implicit solvent models [28]. Considering the highly complex and irregular shape of a molecule, new challenges arise in simulations involving extremely large biomolecular [5] (e.g., viruses, biomolecular complexes etc.). And the efficient representation of the molecular shape (as well as the "molecular surface" or "molecular volume") for large real biomolecule with high quality remains a critical topic [28].…”