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# 2022 ** SIAM Annual Meeting, Pittsburgh, July 11-15, 2022. "Molecular Biosciences: Modeling and Computation of Ion Channel Transport", https://www.siam.org/conferences/cm/conference/an22 Title： An inverse averaging finite element method for solving three-dimensional Poisson–Nernst– Planck equations in nanopore system simulations Qianru Zhang, Qin Wang, Linbo Zhang, and Benzhuo Lu Abstract： The Poisson–Nernst–Planck (PNP) model plays an important role in simulating nanopore and ion channel systems. In nanopore simulations, the large-size nanopore system and convection-domination Nernst–Planck (NP) equations will bring convergence difficulties and numerical instability problems. Therefore, we propose an improved finite element method (FEM) with an inverse averaging technique to solve the threedimensional PNP model, named inverse averaging FEM (IAFEM). At first, the Slotboom variables are introduced aiming at transforming non-symmetric NP equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then, these exponential coefficients are approximated with their harmonic averages, which are calculated with an inverse averaging technique on every edge of each tetrahedral element in the grid. Our scheme shows good convergence when simulating single or porous nanopore systems. In addition, it is still stable when the NP equations are convection domination. Our method can also guarantee the conservation of computed currents well, which is the advantage that many stabilization schemes do not possess. Our numerical experiments on benchmark problems verify the accuracy and robustness of our scheme. The numerical results also show that the method performs better than the standard FEM when dealing with convection-domination problems. A successful simulation combined with realistic chemical experiments is also presented to illustrate that the IAFEM is still effective for simulating three-dimensional interconnected nanopore systems, ion channel systems, and semiconductor devices. # 2021 - 第二届全国集成微系统建模与仿真学术交流会，2021年10月20-23日，南京 （集成微系统跨空间、跨时间尺度建模与仿真 分会主席） https://www.iccip.org.cn/ims_2021 分会组织，主席 题目和摘要 3D半导体器件及其电离辐射损伤效应中的多尺度问题与模拟方法 辐照损伤对半导体器件的性能有很大影响，对其研究在核能、航天等诸多领域具有重要意义。我们基于本所自研的并行自适应有限元平台PHG 研发了半导体器件及其电离损伤的三维数值仿真方法，开发了通用半导体器件漂移扩散模型的求解器模块、电离辐照损伤求解器模块、以及包含前、后处理和解法器的整个应用仿真软件系统3Ddevice。这里报告3D器件漂移扩散模型模拟中对于从纳米到微米尺度都具有数值稳定性的有限元方法，以及对电离辐照损伤效应模拟中的时间多尺度的数值计算方法研究。仿真系统应用到MIS、MOSFET和双极器件等模拟中，模拟了他们的常规电学特性，以及它们在电离辐照环境下的缺陷损伤效应及其对器件电学特性的影响。 - 第三届全国大数据与人工智能科学大会, 2021-7-09 ~2021-7-11, 成都 - Mathematics in Action (MiA2021): Modeling and analysis in molecular biology and electrophysiology 分子生物学及电生理学的数学建模及模拟 Suzhou & Kunshan, June 10-13, 2021 https://sites.duke.edu/dkucmcs/events/conferences/mbe2021/ Title: On numerical aspects of Poisson-Nernst-Planck system Abstract: The PNP is an electric-coupled covection-diffusion system. Some typical properties/performance for this PNP system need to be considered in numerical solution, such as accuracy, robustness, and some special structures of preserving positivity, energy dissipation, and flux conservation. In convection-dominated cases, the flux conservation seems a key factor influencing the overall performace of the numerical method. This talk reports our recent advances in FEM solution of the PNP-like systems. A PNP benchmark for numerical test, a stabilized FEM, an average FEM, and perfromance comparision are to be presented. The stability, accuracy, robustness (involving in cases of poor mesh quality), flux-conservation property are extensively tested in 3D simulations of geometrically complicated ion channels, nanopores, and semiconductor devices. - 2021 全国网格生成及应用研讨会 MEGAS， http://www.cars.org.cn/home/articleList?type=inform&aid=834 http://megas2021.cars.org.cn （5月28日至5月30日正式举行（27日报到，28日会前课程）） 2021年5月27 ~ 29日， 杭州 生物分子表面网格生成 卢本卓*，刘田田，桂升，白石阳，陈旻昕 摘要： 分子表面的网格化表示可为分子几何特征研究、化学信息学、可视化、分子隐式模型模拟、反应扩散、粗粒化等研究提供基础和工具。本报告介绍生物分子表面三角化研究的背景、流程和存在的问题，主要报告我们近年关于分子表面网格生成的工作，包括大分子表面稳定、高效、保拓扑结构的三角化方法及软件TMSmesh、表面网格优化方法、空间四面体网格生成、离子通道及膜体系的网格生成方法等，其中表面三角化分别研究了用表面求迹、多项式逼近等技巧来三角化分子的高斯表面。 - “科学与工业软件研讨会”（5月23日，北京大学） 题目： 电-扩散问题软件平台研发及其在分子/纳米孔/半导体器件模拟中的应用介绍 - 中国化学会第32届学术年会，广东省珠海市，2021年4月19-22日 https://www.chemsoc.org.cn/meeting/32nd/ 也可参加：第三十三分会：基础电化学 主席：魏子栋、任 斌； 第三十五分会：胶体与界面化学 主席：黄建滨、江 雷；第三十六分会： 多孔功能材料 主席：于吉红、刘中民；第四十六分会：纳米体系理论与模拟 主席：杨金龙、施兴华； 题目：设计和模拟具有高效能量转换效率的水凝胶纳米孔-膜系统 （29分会） 题目：3维离子通道及仿生膜离子输运的有限元模拟研究 （29分会，改） 摘要：介绍我们发展的用于模拟3D离子通道、仿生膜、及纳米孔的并行有限元方法及程序包，包括生物分子及复杂纳米孔的几何搭建、网格生成等工具。离子输运模型采用Poisson-Nersnt-Planck（PNP）模型，程序包实现大规模并行有限元计算。应用于钾离子、钙离子等通道蛋白的模拟，也与实验小组合作进行了多孔仿生膜盐差能量转换的仿真研究，研究了非对称膜、空间带电特性和三维互通结构等对导电性、离子选择性、进而对盐差能量转换效率的影响。 # 2020 - Workshop for Protein Complexes and Quantitative Proteomics: Theory, Computation and Experiment 蛋白质复合物和定量组学：理论、计算与实验，2020年11月14-15 日，中国人民大学 分子几何相关研究 - 中国仿真学会集成微系统建模与仿真专委会2020年工作会与学术交流会，2020-10-24，北京，（会议组织） 题目：集成微系统器件级建模与仿真 - Protein Electrostatics Conference 2020, June 22-25, 2020, Istituto Italiano di Tecnologia, Genova, Italy - 2020 Biophysical Society Annual Meeting, February 15-19, 2020, San Diego, US https://www.biophysics.org/2020meeting#/ - 2nd Edition of World Nanotechnology Conference， April 27-29, 2020，Crowne Plaza Hotel， Baltimore, MD 21201, USA https://worldnanotechnologyconference.com/ - Global Congress and Expo on Renewable and Sustainable Energies, July 16-17, Las Vegas, USA. - 11th Liquid Matter Conference, Prague, Czech Republic, July 20-24 2020, http://www.lmc2020.cz - 11th International Conference on Computational Methods,ICCM2020, Ho Chi Minh City, Vietnam, July 7th to 11th, 2020 http://www.sci-en-tech.com/ICCM2020/ # 2019 - Workshop on Computational and Applied Mathematics， Mathematics Center of BNU-UIC in the BNU Zhuhai Campus， December 14-17, 2019， 珠海 分子几何相关的若干研究及应用 先介绍我们近年关于分子几何表示的一些工作，主要有：大分子表面稳定高效的三角化方法及软件TMSmesh2，空间四面体网格生成，通道蛋白及膜体系的网格生成方法，以及分子及其表面的稀疏化表示。它们可为进一步的分子几何特征研究、可视化、隐式模型模拟、反应扩散、粗粒化等提供恰当的工具。后面介绍几个在实际生物问题中基于求解PDE的例子：分子静电、离子通道的导电性、及第三代基因测序的模拟等。 - 第十五届全国计算（机）化学学术会议，2019年11月14-17日，上海市 分子几何研究 - 2019年数值方法及应用研讨会，报到时间：11月1日,会议时间：11月2日 -11月4日,成都 - PNP方程数值算法研讨会，时间为10.23-10.25日，桂林 半导体模拟介绍 - International Multigrid Conference (IMG2019), August 11-16, 2019, Kunming,China Title: Adaptive grid in Modeling of Biomolecular Electrostatics and Diffusion using FEM/BEM Abstract： The Poisson-Boltzmann equation and Poisson-Nernst-Planck equations are two common models used in simulating molecular electrostatics and ion transport in ionic solution. Molecular interface problem, singular charge distribution, the nonlinear coupled system, and meshing are issues to be addressed in numerical solutions of these equations. We will present our works on fast boundary element methods for solution of the linear PB equation, and stable finite element methods for solution of the PNP equations. Case studies are performed on calculations of macromolecular electrostatics, current-voltage curve of ion channels/nanopores, etc. - The International Conference on 3D Imaging Technology, IC3DIT2019, Kunming, Yunnan, China, August 15-18, 2019 - 湖南访问的两个报告 （1） 同 ICCM会议 （2） （类 2015MBI，2015人大，重庆pBEMFEM） Title：Continuum modeling of molecular solvation and ion transport in channels Abstract：Continuum models are commonly used to combine with molecular model in order to bridge different scales and to take into account the average influence of solvent environment on molecular processes. I’ll talk about our recent advances in developing continuum models, numerical algorithms and software for simulating variety of phenomena involving electrostatics and diffusion processes at molecular and nano-scales. Macromolecular electrostatics and ion transport in ion channel/nanopores are our focused interests. The governing equations of these phenomena are the Poisson-Boltzmann/Poisson-Nernst-Planck equations and their improved forms. We have developed a set of computational methods and software tool chain in this field, including finite element/boundary element simulation packages, molecular meshing tools, visualization software and web-based service (under way). Case studies are applied to calculate such as macromolecular electrostatics, current-voltage curve of ion channels (physiological property) and nanopores (potentially used in gen sequencing, electric nano-devices et al.). - the 8th International Congress of Chinese Mathematicians of 2019, 第八届华人数学家大会, June 9 to June 14, 2019. Beijing. Title: Ion conductance in membrane-channel systems: models, meshing, computing, and applications Abstract: Ion channels are pore-forming membrane proteins, as life's nano-valves that allow ions to pass through the channel pore. Many ion channel proteins are specialized to select for only a particular ion species. The continuum electrodiffusion model can qualitatively capture some macroscopic properties of certain ion channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. However, the macroscopic models are often challenged by the requirements: model accuracy, treatment of complex geometry of the membrane-channel protein system, and robustness of numerical computing. I will talk about the Poisson-Nernst-Planck type of PDE models (and the corresponding energy variational forms), meshing method for molecular surface and membrane-protein system, numerical techniques and finite element implementation. A particular application example is the simulation study of a potassium channel. With incorporation of ion solvation effect, the model is capable of simulating selective permeation in potassium channel, in which the larger potassium ions can much more easily pass through the channel than the relatively smaller sodium ions, although both type of ion species carry a same positive unit charge. Another application example is gene sequencing in nanopore. - 生命和物理科学中的微分方程及应用研讨会，2019年5月9-12日，重庆 Title: Continuum modeling of selective permeation in ion channel/nanopore Abstract: Electrodiffusion describes diffusion processes of charged particles in their self-induced (and sometimes together with external) electric field. The phenomena widely exist in electrochemistry, biology, semiconductor, etc. I will talk about a typical continuum modeling approach in biological ion channel studies, which involves researches on a set of Poisson-Nernst-Planck type of PDE models, finite element calculations, and molecular surface/volume mesh generation. The model can qualitatively capture some macroscopic properties of certain ion channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. With incorporation of other effects ignored in the mean field PNP theory such as size-effect, and in particular the ion solvation effect, the model is capable of simulating selective permeation in such as potassium channels, in which the larger potassium ions can much more easily pass through the channel than the relatively smaller sodium ions, although both type of ion species carry a same positive unit charge. Ion current rectification in the potassium channel (KcsA) was observed in both PNP and BPNP models. The method is also applied to studies of nanopore conductance, gene sequencing in nanopore, and so on. In addition, the newly developed molecular meshing method will be discussed if time allowed. - 2018年年终总结会拟定于2019年1月17-18日召开。 # 2018年 - 强约束条件下集成微系统的基础科学技术问题， 2018年12月21日-22日（20日报到），地点：北京大学东莞光电研究院 - Computational and Mathematical Approaches for Bioinformatics and Biophysics, Dec.10 to 14 (check in on 9), 2018， Sanya Title: Continuum modeling of selective ion permeation in a channel/nanopore Abstract: The Poisson-Nernst-Planck (PNP) model describing electrodiffusion processes can qualitatively capture some macroscopic properties of certain ion channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. With incorporation of other effects ignored in the mean field PNP theory such as size-effect, and in partcular the ion solvation effect, it is capable of simulating selective permeation in such as potassium channels. Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. We incorporated Born solvation energy into the PNP model (BPNP) to account for ion hydration/dehydration effects when passing through the inhomogeneous dielectric channel environments. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K+ over Na+ in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I-V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K+ (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na+ (rectification ratio of ∼1/6). These phenomena can be properly explained by the electrostatic energy landscape of the permeative ion along the channel resulted from the BPNP model. In addition, some other related models and applications will also be discussed in this talk. - （会议委员会）首届中国分子生物拓扑会议, 河北师范大学数学与信息科学学院, 10.26-29, 石家庄 - 科学挑战专题集成微系统领域方向一交流讨论会， 10.24-25，北京 - 第一届全国集成微系统科学技术及其建模与仿真学术交流会会议通知（第一轮）， 暨科学挑战专题强约束集成微系统领域十三五中期进展学术交流会、中国仿真学会第一届集成微系统建模与仿真专业委员会第二次工作会议，拟于2018年7.6-7.7日在四川成都举行。 - 第十一届海峡两岸生物学启发的理论问题研讨会，2018年7月3日至7月7日， 台湾中兴大学&中央大学，惠蓀林場 - SIAM 2018 Annual Meeting， (http://www.siam.org/meetings/an18/), July 9-13, Portland, Oregon, US Title: Finite Element simulations of the solvation of Membrane Channel Proteins and the transport of solvated ions in a channel Abstract: A Finite Element solver is developed to study the Laterally Periodic Poisson-Boltzmann model for Membrane Channel Proteins. Studies shows taht all the factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic concentration, have individually considerable influence on the solvation energy of a channel protein. In addition, the ion's Born energy is incorporated into the PNP model (BPNP), which is shown to be able to successfully simulate the selective permeation of K+ in KcsA channel. - Mathematics in Action (MiA2018): Modeling and analysis in molecular biology and electrophysiology， Soochow University, June 16-18, 2018. http://www.math.ucsd.edu/~s4zhou/MBE2018/speakers.html Title: (online) Continuum modeling of selective ion permeation in potassium channel Abstract: The Poisson-Nernst-Planck (PNP) model describing electrodiffusion processes can qualitatively capture some macroscopic properties of certain ion channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. In this talk, (1) we will present a proper free energy form for self-consistent variational analysis for inhomogeneous charged system with general nonhomogeneoous boundary conditions. (2) As the continuum mean-field PNP model has no or underestimates the discrete ion effects, in particular the ion solvation effect, it is not applicable to selective permeation simulations. Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. This puzzle cannot be solved based on the traditional PNP model because it treats all ions as point charges and has no any ion size information, therefore cannot discriminate potassium from sodium ions. It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. We incorporated Born solvation energy into the PNP model to account for ion hydration/dehydration effects when passing through the inhomogeneous dielectric channel environments. A variational approach was adopted to derive a Born-energy-modified PNP (BPNP) model. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K+ over Na+ in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I -V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K+ (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na+ (rectification ratio of ∼1/6). These phenomena can be properly explained by the electrostatic energy landscape of the permeative ion along the channel resulted from the BPNP model. (3) We will also demonstrate that these simulations can be performed online on the website xyzgate.com. - Symposium of the International Association for Boundary Element Methods June 26-28, 2018 - Paris, France - 3rd PROTEIN ELECTROSTATICS meeting， Belgrade, June 25 - 28 2018. https://www.proteinelectrostatics.org/ - 中国化学会第 31 届学术年会，2018 年 5 月 5-8，杭州。 报告题目：在线计算化学II：钾离子通道选择性通透的连续模型与模拟 - 2018 年核工程力学分会学术交流会议拟于2018年，第三季度在成都召开 2018 年 03 月 01 日，提交论文摘要，300 字以内； 2018 年 04 月 01 日，通知作者论文是否录用； 2018 年 06 月 01 日，提交论文全文； 会议具体时间和地点另行通知。 4、联系人及联系方式 胡杰：0816-2485436 18780517278 范宣华：0816-2492041 投稿邮箱：401hujie@caep.cn 微信群：中国核学会核工程力学分会学术交流 - 10th Edition of International Conference on Structural Biology 2018, March 15-16, 2018, at "The city of Dreams "Barcelona, Spain. - Fast Algorithms for Generating Static and Dynamically Changing Point Configurations， (March 12 - 16, 2018) https://icerm.brown.edu/programs/sp-s18/w2/ ICERM，Brown University Title: Molecular surface meshing and applications in numerical simulation Abstract: Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Adaptive Partition and Piecewise Polynomial Approximation, Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. We developed a ray-casting and surface-tracing method for manifold triangular meshing for large Gaussian molecular surfaces. A new algorithm is recently developed to greatly improve the meshing efficiency and qualities. In the first step, a new adaptive partition and estimation algorithm is proposed to locate the cubes in which the surface are approximated by piece-wise trilinear surface with controllable precision. Then, the piecewise trilinear surface is divided into single valued pieces by tracing along the fold curves, which ensures that the generated surface meshes are manifolds. The mesh quality can be further improved using post-processing techniques. An alternative way is to combine the molecular surface mesh identification and volume mesh generation teogether during mesh refinement procedure when using FEM. Numerical test results show that TMSmesh 2.0 is capable of handling arbitrary sizes of molecules and achieves ten to hundreds of times speedup over the previous algorithm. In all of our extensively tested molecules, the resulted surface meshes are all manifolds and can be used in boundary element method (BEM) and finite element method (FEM) simulations. - 2018软物质与生物物理理论研讨会,2018年1月28日（星期日）至31日（28日报到，31日离会）,中国科学院理论物理研究所，北京 钾离子通道选择性输运的隐式模型及有限元模拟 - "高性能科学计算的基础算法与可计算建模”重大研究计划 年会，2018年1月11-13，广州 钾离子通道选择性输运的隐式模型及有限元模拟 - 计算数学所2017年年终总结会的时间定于2018年1月24日、25日（周三、四）两天，在数学院召开 #2017年 - 12月16日，在北京九所，仿真分会专委会成立大会及第一次学术交流会 - 2017年1月12-14日期间在广州召开“高性能科学计算的基础算法与可计算建模”重大研究计划2017年度学术交流会， - 2017复杂体系计算统计力学研讨会，12月1-4日（暂定），福州 - 强约束集成微系统物理与技术全国研讨会，电扩散反应过程的有限元模拟及其在生物化学材料等领域的应用, 2017.12.2, 厦门 - 第十四届全国计算（机）化学学术会议，在线计算化学I：分子静电计算与可视化，2017年11月17-21，南京大学 - 数值方法及其应用研讨会 暨《计算数学》和《数值计算与计算应用》两刊编委会会议时间: 2017年11月3-5日，南京师范大学 - COMSOL Conference 2017 Beijing (COMSOL用户年会)，“计算化学/生物中的一些隐式溶剂模型模拟方法”，2017年11月2-3号，北京 - 多组分漂移扩散模型及跨尺度半导体器件损伤模拟 研讨会，2017年10月19-22 日，成都 （会议主席） - International Conference on Theoretical and High Performance Computational Chemistry 2017”（ICT-HPCC17），（2017 年理论与高性能计算化学国际会议），2017 年10 月26~29 日，杭州 - 中国力学大会2017，MS079 边界元法与降维方法专题研讨会，“分子模拟中快速边界元计算静电方法进展”，2017.8.13-16，北京 - 边界元法与降维方法进展与应用研讨会，生物分子Poisson-Boltzmann静电作用的高效边界元计算及程序包AFMPB，2017年7月29日-8月1日，桂林 - 8th International Conference on Computational Methods （ICCM 2017）, Accelerating BEM in macromolecular electrostatics computing， 2017.7.25-29，Guilin, China - 第十一届全国计算数学年会, 离子通道模拟, 2017年7月21-23，西安
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