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 visualizati… Show more
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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 surface mesh generation is a prerequisite for using the boundary element method (BEM) and finite element method (FEM) in implicit-solvent modeling. Molecular surface meshes typically have small angles, redundant vertices, and low-quality elements. In the implicit-solvent modeling of biomolecular systems it is usually required to improve the mesh quality and eliminate low-quality elements. Existing methods often fail to efficiently remove low-quality elements, especially in complex molecular meshes. In this paper, we propose a mesh refinement method that smooths the meshes, eliminates invalid regions in a cut-and-fill strategy, and improves the minimal angle. We compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method showed satisfactory results in terms of the ratio of regular vertices and the preservation of area and volume.
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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 surface mesh generation is a prerequisite for using the boundary element method (BEM) and finite element method (FEM) in implicit-solvent modeling. Molecular surface meshes typically have small angles, redundant vertices, and low-quality elements. In the implicit-solvent modeling of biomolecular systems it is usually required to improve the mesh quality and eliminate low-quality elements. Existing methods often fail to efficiently remove low-quality elements, especially in complex molecular meshes. In this paper, we propose a mesh refinement method that smooths the meshes, eliminates invalid regions in a cut-and-fill strategy, and improves the minimal angle. We compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method showed satisfactory results in terms of the ratio of regular vertices and the preservation of area and volume.
“…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.…”
The
three-dimensional structures and shapes of biomolecules provide
essential information about their interactions and functions. Unfortunately,
the computational cost of biomolecular shape representation is an
active challenge which increases rapidly as the number of atoms increase.
Recent developments in sparse representation and deep learning have
shown significant improvements in terms of time and space. A sparse
representation of molecular shape is also useful in various other
applications, such as molecular structure alignment, docking, and
coarse-grained molecular modeling. We have developed an ellipsoid
radial basis function neural network (ERBFNN) and an algorithm for
sparsely representing molecular shape. To evaluate a sparse representation
model of molecular shape, the Gaussian density map of the molecule
is approximated using ERBFNN with a relatively small number of neurons.
The deep learning models were trained by optimizing a nonlinear loss
function with L1 regularization. Experimental results reveal that
our algorithm can represent the original molecular shape with a relatively
higher accuracy and fewer scale of ERBFNN. Our network in principle
is applicable to the multiresolution sparse representation of molecular
shape and coarse-grained molecular modeling. Executable files are
available at . The program was implemented in PyTorch and was run on Linux.
“…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].…”
In this paper, we have developed an ellipsoid radial basis function neural network (ERBFNN) and algorithm for sparse representing of a molecular shape. To evaluate a sparse representation of the molecular shape model, the Gaussian density map of molecule is approximated by ERBFNN with a relatively small number of neurons. The deep learning models were trained by optimizing a nonlinear loss function with L 1 regularization. Experimental results demonstrate that the original molecular shape is able to be represented with good accuracy by much fewer scale of ERBFNN by our algorithm. And our network in principle can be applied to multi-resolution sparse representation of molecular shape and coarse-grained molecular modeling.
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