SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson‐Boltzmann equation

Xie, Yang; Ying, Jinyong; Xie, Dexuan

doi:10.1002/jcc.24703

Cited by 16 publications

(21 citation statements)

References 44 publications

(74 reference statements)

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“…We developed an effective finite element algorithm for solving our SMPBIC model, and programmed it as a software package based on the above submodel partitioning (eq. ()), our PBE and SMPBE program packages, the state‐of‐the‐art finite element library from the FEniCS project, and an ion channel membrane finite element mesh program package from . Using this software package and three ionic solvents with up to five ionic species, we simulated the ionic concentrations, electrostatic potential, and electrostatic solvation free energy based on a 3D human VDAC1 (hVDAC1) structure, which we downloaded from the Orientations of Proteins in Membranes (OPM) database https://opm.phar.umich.edu using the PDB identification number 2JK4.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In the currently used size‐modified Poisson–Boltzmann equation (SMPBE), the protein region D p is surrounded by the solvent region D s , as illustrated in Figure b, and there is no membrane region involved. In addition, an electrostatic potential function, u , of the electric field induced by the atomic charges of the protein and the ionic charges of the ionic solvent is governed by a Poisson equation in D p ,

- ɛ_{p} normalΔ u ((), r) = α \sum_{j = 1}^{n_{p}} z_{j} δ_{{boldr}_{j}}, boldr \in D_{p},

and a Poisson–Boltzmann equation in D s ,

ɛ_{s} normalΔ u ((), r) + β \frac{\sum_{i = 1}^{n} Z_{i} c_{i}^{b} e^{- Z_{i} u ((), r)}}{1 + γ \frac{{\overset{v}{true}}^{2}}{v_{0}} \sum_{i = 1}^{n} c_{i}^{b} e^{- Z_{i} u ((), r)}} = 0, boldr \in D_{s},

together with the following interface and boundary value conditions:

u ((), {bolds}^{-}) = u ((), {bolds}^{+}), ɛ_{s} \frac{\partial u ((), {bolds}^{+})}{\partial n_{p} ((), s)} = ɛ_{p} \frac{\partial u ((), {bolds}^{-})}{\partial n_{p} ((), s)}, bolds \in normalΓ, u ((), s) = g ((), s), bolds \in ∂Ω,

where n p is the unit...…”

Section: Methodsmentioning

confidence: 99%

“…In this section, we on our SMPBIC model into three submodels to overcome the solution singularity difficulties caused by the atomic charges from an ion channel molecular structure. Similar partitioning was done for a protein surrounded by an ionic solvent in References , but its construction becomes more difficult for the case of SMPBIC model since it involves more complicated geometries, more difficult interface conditions, and more difficult boundary value conditions. The three submodels of our SMPBIC model are referred to as models 1–3 for clarity.…”

Section: Methodsmentioning

confidence: 99%

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A size‐modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage‐dependent anion channel

2019

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We present a new size‐modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage‐dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.

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Section: Numerical Resultsmentioning

confidence: 99%

- ɛ_{p} normalΔ u ((), r) = α \sum_{j = 1}^{n_{p}} z_{j} δ_{{boldr}_{j}}, boldr \in D_{p},

and a Poisson–Boltzmann equation in D s ,

ɛ_{s} normalΔ u ((), r) + β \frac{\sum_{i = 1}^{n} Z_{i} c_{i}^{b} e^{- Z_{i} u ((), r)}}{1 + γ \frac{{\overset{v}{true}}^{2}}{v_{0}} \sum_{i = 1}^{n} c_{i}^{b} e^{- Z_{i} u ((), r)}} = 0, boldr \in D_{s},

together with the following interface and boundary value conditions:

u ((), {bolds}^{-}) = u ((), {bolds}^{+}), ɛ_{s} \frac{\partial u ((), {bolds}^{+})}{\partial n_{p} ((), s)} = ɛ_{p} \frac{\partial u ((), {bolds}^{-})}{\partial n_{p} ((), s)}, bolds \in normalΓ, u ((), s) = g ((), s), bolds \in ∂Ω,

where n p is the unit...…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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A size‐modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage‐dependent anion channel

2019

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“…The improved meshes can be applicable in AFMPB [ 37 ] and TetGen [ 38 ] directly. The volume mesh generated by TetGen can used in finite element method simulations, such as Ichannel [ 39 ], SMPBS [ 40 ], mFES [ 41 ] and so on.…”

Section: Resultsmentioning

confidence: 99%

Quality improvement of surface triangular mesh using a modified Laplacian smoothing approach avoiding intersection

et al. 2017

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We present a systematic procedure to improve the qualities of triangular molecular surface meshes and at the same time preserve the manifoldness. The procedure utilizes an algorithm to remove redundant points having three or four valences and another algorithm to smooth the mesh using a modified version of Laplacian method without causing intersecting triangles. This approach can be effectively applied to any manifold surface meshes with arbitrary complex geometry. In this paper, the tested meshes are biomolecular surface meshes exhibiting typically highly irregular geometry. The results show that the qualities of the surface meshes are greatly improved and the manifoldness of the surface meshes are preserved. Compared with the original meshes, these improved molecular surface meshes can be directly applied to boundary element simulations and generation of body-fitted volume meshes using Tetgen. The procedure has been incorporated into our triangular molecular surface mesh generator, TMSmesh 2.0. It can be also used as a standalone program and works together with any other surface triangular mesh generator to obtain qualified manifold mesh. The package is downloadable at https://doi.org/10.6084/m9.figshare.5346169.v1 and can be run online at http://www.xyzgate.com.

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“…We developed finite element iterative algorithms and software packages for solving nuNPF and uNPF based on our PBE 052610-3 and SMPBE program packages [13][14][15], and the state-of-theart finite element library from the FEniCS project [16]. In our algorithms, we constructed a Lagrange finite element function space M as a subspace of the usual Sobolev space H 1 (D s ) using a tetrahedral mesh of D s , and a finite element vector function space N 1 × N 2 .…”

Section: Numerical Solversmentioning

confidence: 99%

Nonlocal Poisson-Fermi double-layer models: Effects of nonuniform ion sizes on double-layer structure

Xie

Jiang

2018

Phys. Rev. E

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This paper reports a nonuniform ionic size nonlocal Poisson-Fermi double-layer model (nuNPF) and a uniform ionic size nonlocal Poisson-Fermi double-layer model (uNPF) for an electrolyte mixture of multiple ionic species, variable voltages on electrodes, and variable induced charges on boundary segments. The finite element solvers of nuNPF and uNPF are developed and applied to typical double-layer tests defined on a rectangular box, a hollow sphere, and a hollow rectangle with a charged post. Numerical results show that nuNPF can significantly improve the quality of the ionic concentrations and electric fields generated from uNPF, implying that the effect of nonuniform ion sizes is a key consideration in modeling the double-layer structure.

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SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson‐Boltzmann equation

Cited by 16 publications

References 44 publications

A size‐modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage‐dependent anion channel

A size‐modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage‐dependent anion channel

Quality improvement of surface triangular mesh using a modified Laplacian smoothing approach avoiding intersection

Nonlocal Poisson-Fermi double-layer models: Effects of nonuniform ion sizes on double-layer structure

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