Triangulated manifold meshing method preserving molecular surface topology

Chen, Minxin; Tu, Bin; Lu, Benzhuo

doi:10.1016/j.jmgm.2012.09.006

Cited by 39 publications

(49 citation statements)

References 31 publications

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“…To accelerate the calculations, the algorithms are implemented with the parallel adaptive finite element package PHG [65]. The molecular surface and volume meshes, that are necessary for FEM computation, are generated by TMSmesh [7,8] and Tetgen [57].…”

Section: Methodsmentioning

confidence: 99%

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al Phys. Rev. Lett. 1997, 79, 435-438; Kilic et al Phys. Rev. E 2007, 75, 021502; Lu and Zhou Biophys. J. 2011, 100, 2475-2485; Liu and Eisenberg J. Chem. Phys. 2014, 141, 22D532) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

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Section: Methodsmentioning

confidence: 99%

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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“…TMSmesh is a method for triangular meshing of the Gaussian surface [32,33]. The trace technique which is a generalization of predictor-corrector technique is used in TMSmesh to connect sampled surface points.…”

Section: A Robust Manifold Meshing Method: Tmsmeshmentioning

confidence: 99%

“…And manifoldness is one of the primary requirements of the surface mesh that can be used in FEM/BEM computations. In [32] and [33], the performance of TMSmesh is shown to be improved in the following aspects compared with MSMS. Firstly, TMSmesh is robust.…”

Section: A Robust Manifold Meshing Method: Tmsmeshmentioning

confidence: 99%

“…Also, it is found that TMSmesh has smoother convergent behaviors of areas and volumes of surface meshes than MSMS when the grid space tends to zero. Furthermore, as presented in [33], TMSmesh generates manifold meshes and preserved the topology of molecular surface. However, as to the aspect of computational efficiency, although the computational complexity is linear with respect to the number of atoms as showed in [32], the efficiency of TMSmesh still needs to be improved.…”

Section: A Robust Manifold Meshing Method: Tmsmeshmentioning

confidence: 99%

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Advances in biomolecular surface meshing and its applications to mathematical modeling

Chen

2013

Chin. Sci. Bull.

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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...

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“…The method essentially has four components: surface meshing, quality improvement, volume mesh generation and membrane mesh construction. The triangulated molecular surface can be generated by some surface mesh generator, such as TMSmesh [22,23], MSMS [24], NanoShaper [25], Molsurf [26,27], GAMer [28], EDTsurf [29] and so on. These softwares generate triangulated mesh based on different definitions of the molecular surface, including van der Waals surface, the solvent accessible surface [30], the solvent excluded surface [31], Gaussian surface [32] and the molecular skin surface [33].…”

Section: Introductionmentioning

confidence: 99%

Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

Liu

Bai

et al. 2015

Computational and Mathematical Biophysics

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We present a method of constructing the volume meshes of the membrane-channel protein system for finite element simulation of ion channels. The membrane channel system consists of the solvent region and the membrane-protein region. Our method focuses on labeling the tetrahedra in the solvent and membrane-protein regions and collecting the interface triangles between different regions. It contains two stages. Firstly, a volume mesh conforming the surface of the channel protein is generated by the surface and volume mesh generation tools: TMSmesh and TetGen. Then a walk-and-detect algorithm is used to identify the pore region to embed the membrane correctly. This method is shown to be robust because of its independence of the pore structure of the ion channels. In addition, we can also get the information of whether the ion channel is open or closed by the walk-and-detect algorithm. An on-line meshing procedure will be available at our website www.continuummodel.org.

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Triangulated manifold meshing method preserving molecular surface topology

Cited by 39 publications

References 31 publications

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

Advances in biomolecular surface meshing and its applications to mathematical modeling

Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

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