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Advances in biomolecular surface meshing and its applications to mathematical modeling

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Chinese Science Bulletin 2013年第16期58卷 1843-1849页

作者： CHEN MinXin lu benzhuo Center for System Biology Department of Mathematics Soochow University State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

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).

关键词：数学建模分子表面应用啮合生物表面网格分子结构分子建模

An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

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Advances in Applied Mathematics and Mechanics 2013年第1期5卷 113-130页

作者： Ying Yang benzhuo lu Department of Computational Science and Mathematics Guilin University of Electronic TechnologyGuilin 541004GuangxiChina LSEC Institute of Computational Mathematics and Scientific/Engineering Computingthe National Center for Mathematics and Interdisciplinary SciencesAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which describe the electrodiffusion of ions in a solvated biomolecular *** this paper,some error bounds for a piecewise finite element approximation to this problem are *** numerical examples including biomolecular problems are shown to support our analysis.

关键词： Poisson-Nernst-Planck equations finite element method error bounds

A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

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Journal of Computational Mathematics 2019年第4期37卷 556-578页

作者： Ying Yang benzhuo lu Yan Xie School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing the National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.

关键词： Poisson-Nernst-Planck equations Two-grid finite element method Decoupling method Error analysis Gummel iteration

A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient

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Communications in Computational Physics 2012年第9期12卷 1148-1162页

作者： Beibei Huang Bin Tu benzhuo lu Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System SciencesAcademy of ScienceBeijing 100190P.R.China Departament d’Enginyeria Quíímica Universitat Rovirai VirgiliAvdels Päsos Catalans26 Tarragona 43007Spain

We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient,and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient *** some appropriate finite difference operators,we derive a second-order scheme for the solver,and then two suitable high-order compact schemes are also *** a cube containing N nodes,the solver requires O(N^(3/2)log^(2)N)arithmetic operations and O(NlogN)memory to store the necessary *** efficiency is illustrated with examples,and the numerical results are analysed.

关键词： Fast solver direct method discrete Laplace operator fast matrix inversion

A simulation method of combinding boundary element method with generalized Langevin dynamics

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Chinese Science Bulletin 2000年第24期45卷 2227-2231页

作者： CHEN Weizu lu benzhuo WANG Cunxin Center tor Biomedical Engineering Beijing Polytechnic UniversityBeijing 100022China School of Life Science University of Science and Technology of ChinaHefei 230026China

A new simulation approach to incorporate hydration force into generalized Langevin dynamics (GLD) is developed in this note. The hydration force determined by the boundary element method (BEM) is taken into account as the mean force terms of solvent including Coulombic interactions with the induced surface charge and the surface pressure of solvent. The exponential model is taken for the friction kernel. A simulation study has been performed on the cyclic undecapeptide cyclosporin A (CPA). The results obtained from the new method (GLDBEM) have been analyzed and compared with that obtained from the molecular dynamics (MD) simulation and the conventional stochastic dynamics (SD) simulation. We have found that the results obtained from GLDBEM show the obvious improvement over the SD simulation technique in the study of molecular structure and dynamic properties.

关键词： potential of mean force of solvent boundary element method friction memory function generalized Langevin dynamics.

Salt and pH-dependent properties of native and mutant insulin

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Chinese Science Bulletin 2002年第6期47卷 464-466页

作者： MA Xiaohui LI Chunhua lu benzhuo CHEN Weizu WANG Cunxin XU Xiaojie Center for Biomedical Engineering Beijing Polytechnic UniversityBeijing 100022China Department of Astronomy and Applied Physics University of Science and Technology of ChinaHeifei 230026China College of Chemistry&Molecular Engineering Peking UniversityBeijing 100871China

A fast and effective model for predicting the salt and pH dependent properties of protein complexes is presented. It is based on the formal charge parameter sets of ionizable groups and applied in conjunction with the finite difference Poisson-Boltzmann (FDPB) method to calculate the electrostatic interactions. All simulations were performed on the native 2Zn insulin and its fast-acting mutants such as B9D (B9Ser→Asp), B9E (B9Aer→Glu), B9EB10D (B9Ser→ Glu, B10His→Asp), and B10D (B10His→Asp). The salt and pH dependent properties of these dimers were analyzed from the aspect of electrostatic interaction, and the theoretical basis of the fast-acting behavior of these mutants was explained. It is found that the results agree well with experimental observations.

关键词： formal charge electrostatic interaction insulin Pois-son-Boltzmann equation.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

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Communications in Computational Physics 2013年第1期13卷 107-128页

作者： Bo Zhang benzhuo lu Xiaolin Cheng Jingfang Huang Nikos P.Pitsianis Xiaobai Sun JAndrew McCammon Department of Computer Science Duke UniversityNC 27708USA Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100910China Center for Molecular Biophysics Oak Ridge National LaboratoryTN 37831USA Department of Mathematics University of North CarolinaChapel HillNC 27599USA Department of Electrical and Computer Engineering Aristotle UniversityThessaloniki54124Greece Department of Chemistry&Biochemistry Center for Theoretical Biological PhysicsDepartment of PharmacologyHoward Hughes Medical InstituteUniversity of CaliforniaSan DiegoCA 92093USA

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann(AFMPB)*** introduce and discuss the following components in order:the Poisson-Boltzmann model,boundary integral equation reformulation,surface mesh generation,the nodepatch discretization approach,Krylov iterative methods,the new version of fast multipole methods(FMMs),and a dynamic prioritization technique for scheduling parallel *** each component,we also remark on feasible approaches for further improvements in efficiency,accuracy and applicability of the AFMPB solver to largescale long-time molecular dynamics *** potential of the solver is demonstrated with preliminary numerical results.

关键词： Biomolecular system electrostatics Poisson-Boltzmann equation fast multipole methods mesh generation directed acyclic graph dynamic prioritization parallelization

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生物分子模拟中的静电计算

计算物理 2015年第2期32卷 127-159页

作者：彭波李翰林卢本卓科学与工程计算国家重点实验室中国科学院数学与系统科学研究院北京100190

在分子尺度上对生物系统的研究主要通过模拟生物分子间的相互作用来完成.在众多的分子间相互作用中,静电相互作用及其重要,对它的定量计算是了解生物分子的溶剂化效应、生物分子折叠和酶催化作用等的一个中心课题.本综述着重介绍用于计... 详细信息

在分子尺度上对生物系统的研究主要通过模拟生物分子间的相互作用来完成.在众多的分子间相互作用中,静电相互作用及其重要,对它的定量计算是了解生物分子的溶剂化效应、生物分子折叠和酶催化作用等的一个中心课题.本综述着重介绍用于计算溶剂化效应的泊松-玻尔兹曼模型,包括模型的理论基础、发展历程、数值求解方法、及在分子生物学研究中的应用等.同时,也介绍泊松-玻尔兹曼模型的一种近似模型,广义玻恩模型.

关键词：泊松-玻尔兹曼方程广义玻恩模型溶剂化效应边界元有限元

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胰岛素六聚体在水溶液中的稳定性研究

化学学报 2002年第12期60卷 2129-2134页

作者：王维宴卢本卓陈慰祖王存新北京工业大学生物医学工程中心北京100022

用分子动力学(MD)模拟方法设计了两个模拟时间为 60 0ps的对比计算机模拟实验,研究了R6态的胰岛素六聚体在水溶液中的稳定性以及苯酚和锌离子对结构稳定性的影响.通过对MD模拟所得到的轨迹的分析发现,在维系胰岛素六聚体稳定性的因素中... 详细信息

用分子动力学(MD)模拟方法设计了两个模拟时间为 60 0ps的对比计算机模拟实验,研究了R6态的胰岛素六聚体在水溶液中的稳定性以及苯酚和锌离子对结构稳定性的影响.通过对MD模拟所得到的轨迹的分析发现,在维系胰岛素六聚体稳定性的因素中,静电相互作用和氢键起着主要的作用.对于包含锌离子和苯酚的体系,胰岛素六聚体的稳定性得到了增强;对不含锌离子和苯酚的体系,胰岛素六聚体的稳定性明显减弱,在这种情况下,胰岛素六聚体还表现出解聚的倾向.

关键词：水溶液胰岛素六聚体分子动力学模拟结构稳定性