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

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 extend...

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Detalles Bibliográficos
Autores principales: Ji, Nan, Liu, Tiantian, Xu, Jingjie, Shen, Longzhu Q., Lu, Benzhuo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5877556/
https://www.ncbi.nlm.nih.gov/pubmed/29495644
http://dx.doi.org/10.3390/ijms19030695
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author Ji, Nan
Liu, Tiantian
Xu, Jingjie
Shen, Longzhu Q.
Lu, Benzhuo
author_facet Ji, Nan
Liu, Tiantian
Xu, Jingjie
Shen, Longzhu Q.
Lu, Benzhuo
author_sort Ji, Nan
collection PubMed
description 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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spelling pubmed-58775562018-04-09 A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins Ji, Nan Liu, Tiantian Xu, Jingjie Shen, Longzhu Q. Lu, Benzhuo Int J Mol Sci Article 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. MDPI 2018-02-28 /pmc/articles/PMC5877556/ /pubmed/29495644 http://dx.doi.org/10.3390/ijms19030695 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Ji, Nan
Liu, Tiantian
Xu, Jingjie
Shen, Longzhu Q.
Lu, Benzhuo
A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title_full A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title_fullStr A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title_full_unstemmed A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title_short A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
title_sort finite element solution of lateral periodic poisson–boltzmann model for membrane channel proteins
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5877556/
https://www.ncbi.nlm.nih.gov/pubmed/29495644
http://dx.doi.org/10.3390/ijms19030695
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