A parallel finite element simulator for ion transport through three‐dimensional ion channel systems

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Robert S.; Lu, Benzhuo

doi:10.1002/jcc.23329

Cited by 52 publications

(58 citation statements)

References 55 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…45 leads to a nonlinear weak form. Similar weak forms and the bilinear forms for FEM to solve the SMPNP have been presented explicitly in our former work [62,63]. To deal with the nonlinearity of the weak form of Eq.…”

Section: Methodsmentioning

confidence: 92%

“…To deal with the nonlinearity of the weak form of Eq. 45, we use Newton method to linearize the system as given in previous work [62,63]. Also, relaxation iteration is employed to obtain convergent simulation results for the coupled PDE systems.…”

Section: Methodsmentioning

confidence: 99%

“…which plays an essential role during biological processes, such as ionic flow across channel, protein modification or interaction with a protein or substrate molecule and cell signaling [38,62]. These shape information is hard to be captured in 1D case resulted from the symmetric boundary simplifications.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Methodsmentioning

confidence: 92%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…In our previous work [32], we have already shown that the mesh generated by TMSmesh can be successfully applied to BEM calculations with better convergence performance and lead to reasonable results. The volume tetrahedral mesh generated from the TMSmesh surface mesh by the tool chain described in this review also show good performance in the usage of FEM computations [38].…”

Section: Application Of Molecular Surface Mesh To Bem and Fem In Contmentioning

confidence: 88%

Advances in biomolecular surface meshing and its applications to mathematical modeling

Chen

2013

Chin. Sci. Bull.

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…A widely used continuum model for simulating ionic transport is based on the Poisson-Nernst-Planck (PNP) equation [9,12]. A number of numerical algorithms including finite difference [13,14], finite element [15][16][17][18][19], spectral element [20], and finite volume methods [21] have been utilized in the past two decades to solve the PNP equation. The finite element method has the advantage of handing complex geometries and curved boundaries.…”

Section: Introductionmentioning

confidence: 99%

Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

Liu

Bai

et al. 2015

Computational and Mathematical Biophysics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

A parallel finite element simulator for ion transport through three‐dimensional ion channel systems

Cited by 52 publications

References 55 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

Contact Info

Product

Resources

About