Membrane-Channel Protein System Mesh
Construction for Finite Element Simulations

Liu, Tiantian; Bai, Shiyang; Tu, Bin; Chen, Minxin; Lu, Benzhuo

doi:10.1515/mlbmb-2015-0008

Cited by 12 publications

(14 citation statements)

References 46 publications

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“…A universal sphere that is suitable for different ion channels is not available. In 2015, Liu et al [103] presented an algorithm to detect the inner triangulated surface of the pore to separate the membrane region and the pore region in tetrahedral mesh (Fig. 7).…”

Section: Resultsmentioning

confidence: 99%

Frontiers in biomolecular mesh generation and molecular visualization systems

Gui

Khan

Wang

et al. 2018

Vis. Comput. Ind. Biomed. Art

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With the development of biomolecular modeling and simulation, especially implicit solvent modeling, higher requirements are set for the stability, efficiency and mesh quality of molecular mesh generation software. In this review, we summarize the recent works in biomolecular mesh generation and molecular visualization. First, we introduce various definitions of molecular surface and corresponding meshing software. Second, as the mesh quality significantly influences biomolecular simulation, we investigate some remeshing methods in the fields of computer graphics and molecular modeling. Then, we show the application of biomolecular mesh in the boundary element method (BEM) and the finite element method (FEM). Finally, to conveniently visualize the numerical results based on the mesh, we present two types of molecular visualization systems.

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Section: Resultsmentioning

confidence: 99%

Frontiers in biomolecular mesh generation and molecular visualization systems

Gui

Khan

Wang

et al. 2018

Vis. Comput. Ind. Biomed. Art

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“…The addition of membranes increases the difficulty for the mesh construction. In this paper, we use a previously published method to generate meshes for implicit membrane solvation models containing membrane transport proteins [ 29 ]. The difficulty in the process of generating meshes for membrane protein system is to identify the elements inside a channel (see Figure 1 ).…”

Section: Methodsmentioning

confidence: 99%

“…The solvent region is labeled 1, the membrane channel protein is labeled 2 and the membrane is labeled 3. The solvent part between the white dotted lines is the channel region [ 29 ].…”

Section: Figurementioning

confidence: 99%

“… Volume mesh of gramicidin A (gA): ( a ) Wire-frame of volume mesh conforming to the boundary of a channel protein and membrane system; ( b ) the surface mesh of the membrane-protein region; and ( c ) the upper boundary surface of the membrane-protein region, in which the membrane is represented as a slab [ 29 ]. …”

Section: Figurementioning

confidence: 99%

“…This method is neither efficient nor practical because any change on the radius of each membrane channel protein needs to be made by hand. In our previous work, we applied a “walk-and-detect” algorithm to directly identify the channel and, therefore, to avoid limitation above [ 29 ]. In this paper, we further expanded the algorithm to handle the membrane channel protein with a tilt angle with respect to the z -axis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

Nan

Liu

et al. 2018

IJMS

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Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations.

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An improved Poisson‐Nernst‐Planck ion channel model and numerical studies on effects of boundary conditions, membrane charges, and bulk concentrations

Chao

Xie

2021

J Comput Chem

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In this paper, an improved Poisson‐Nernst‐Planck ion channel (PNPic) model is presented, along with its effective finite element solver and software package for an ion channel protein in a solution of multiple ionic species. Numerical studies are then done on the effects of boundary value conditions, membrane charges, and bulk concentrations on electrostatics and ionic concentrations for an ion channel protein, a gramicidin A (gA), and five different ionic solvents with up to four species. Numerical results indicate that the cation selectivity property of gA occurs within a central portion of ion channel pore, insensitively to any change of boundary value condition, membrane charge, or bulk concentration. Moreover, a numerical scheme for computing the electric currents induced by ion transports across membrane via an ion channel pore is presented and implemented as a part of the PNPic finite element package. It is then applied to the calculation of current–voltage curves, well validating the PNPic model and finite element package by electric current experimental data.

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Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

Cited by 12 publications

References 46 publications

Frontiers in biomolecular mesh generation and molecular visualization systems

Frontiers in biomolecular mesh generation and molecular visualization systems

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

An improved Poisson‐Nernst‐Planck ion channel model and numerical studies on effects of boundary conditions, membrane charges, and bulk concentrations

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