报告1：Geometric singular approach to Poisson-Nernst-Planck type models for ionic flows through membrane channels
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月25日（周六）上午9:00-11:30
讲座地点：B2-410
Abstract:In this talk, a brief description of ion channels and the background of Poisson-Nernst-Planck (PNP) models are provided. Focusing on the key structure of ion channels, a one-dimensional PNP model is derived, from which qualitative properties of ionic flows can be studied in great details. The main idea of Geometric Singular Perturbation Theory is introduced, which is the main tool to study the PNP system. As an example, the theory is applied to a simple case of Poisson-Nernst-Planck system with two ion species, one positively charged and one negatively charged. Finally, interesting research topics and some obtained results related to ion channel problems are discussed.
报告2:Steric effects on ionic flows viaPoisson-Nernst-Planck systems
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月25日（周六）下午3:00-5:30
讲座地点：B2-410
Abstract:In this work, we analyze a quasi-one-dimensional steady-state Poisson– Nernst–Planck-type model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. We consider two ion species, one positively charged and one negatively charged, and assume zero permanent charge. A local hard-sphere potential that depends pointwise on ion concentrations is included in the model to account for ion size effects on the ionic flow. The existence of solutions to the boundary value problem for small ion sizes is established. Treating the ion sizes as small parameters, we also derive approximations of both individual fluxes and the I-V (current-voltage) relation and identify some critical potentials or voltages for ion size effects. Under electroneutrality boundary conditions, each of these critical potentials separates the potential into two regions over which the ion size effects are qualitatively opposite to each other. Important scaling laws of I-V relations and critical potentials in boundary concentrations are obtained.
报告3:Qualitative properties of ionic flows via steady-state Poisson-Nernst-Planck systems. Part I: Small permanent charge effects on current-voltage relations.
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月26日（周日）上午9:00-11:30
讲座地点：B2-410
Abstract:We analyze a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through a membrane channel with nonzero but small permanent charge. The system involves three ion species, two positively charged with the same valences and one negatively charged. We treat the model as a boundary value problem of a singularly perturbed differential system. Under the framework of geometric singular perturbation theory, together with specific structures of this concrete model, the existence and local uniqueness of solutions to the boundary value problem is established. In particular, treating the permanent charge as small parameter, under electroneutrality conditions, we are able to derive an approximation of the I-V (current-voltage) relation, from which the effects on ionic flows from the small permanent charge are analyzed in great detail. Critical potentials are identified and their roles in characterizing permanent charge effects are carefully studied.
报告4:Qualitative properties of ionic flows via steady-state Poisson-Nernst-Planck systems. Part II: Competitions among cations.
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月26日（周日）下午3:00-11:30
讲座地点：B2-410
Abstract:In this work, our main focus is on the competitions between different cations (such as Na^+ and K^+) due to the effects from small permanent charge and its distributions. Nonlinear interplays among physical parameters involved in the system are almost completely characterized, which provides deep insights for future analytical and numerical studies, and even for experimental studies.
报告5:Boundary layer effects on ionic flows via classical Poisson-Nernst-Planck systems
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月27日（周一）上午9:00-11:30
讲座地点：B2-410
Abstract:A quasi-one-dimensional steady-state Poisson-Nernst-Planck model of three ion species, two positively charged with the same valences and one negatively charged, through a membrane channel is analyzed. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this concrete model. The existence and (local) uniqueness of solutions to the boundary value problem is established. In particular, an approximation of both the individual flux and the I-V (current-voltage) relation are derived explicitly from the zeroth order approximation solutions, from which the boundary layer effects on ionic flows are studied in great details.
报告6:Individual flux study via steady-state Poisson-Nernst-Planck systems: Effects from boundary conditions
报告人：张明吉 （美国新墨西哥矿业理工学院）
讲座时间：2019年5月27日（周一）下午3:00-5:30
讲座地点：B2-410
Abstract:We provide a detailed study for ionic flow through ion channels for the case with three ion species, two positively charged having the same valence and one negatively charged, and with zero permanent charge. Our focus is on the effects of boundary conditions on the ionic flow. Beyond the existence of solutions of the model problem, we are able to obtain explicit approximations of individual fluxes and the I-V relations, from which effects of boundary conditions on ionic flows are examined in a great detail. Critical potentials are identified and their roles in characterizing these effects are studied. Compared to ionic mixtures with two ion species, a number of new features for mixtures of three ion species arise. Numerical simulations are performed, and numerical results are consistent with our analytical ones.
报告7:Cubic-like features of current-voltage relations via classical Poisson-Nernst-Planck models.
讲座时间：2019年5月27日（周一）晚上7:00-9:30
讲座地点：B2-410
Abstract:A steady state Poisson-Nernst-Planck (PNP) system is studied both analytically and numerically with particular attention on I-V relations of ion channels. Assuming the dielectric constant ε is small, the PNP system can be viewed as a singularly perturbed system. Due to the special structures of the zeroth order inner and outer systems, one is able to derive more explicit expressions of higher order terms in asymptotic expansions. For the case of zero permanent charge, under the assumption of electro-neutrality at both ends of the channel, our result concerning the I-V relation for two oppositely charged ion species is that the third order correction is cubic in V, and, furthermore, up to the third order, the cubic I-V relation has three distinct real roots (except for a very degenerate case) which corresponds to the bi-stable structure in the FitzHugh-Nagumo simplification of the Hodgkin-Huxley model. Three numerical experiments are conducted to check the cubic-like feature of the I-V curve, study the boundary value effect on the I-V relation and investigate the permanent charge effect on the I-V curve, respectively.
报告人简介：
Mingji Zhang (张明吉)，副教授，博士生导师，目前就职于美国新墨西哥矿业理工学院。2013年毕业于美国堪萨斯大学，获理学博士学位；2013-2015年跟随著名数学家Peter W. Bates在密歇根州立大学做博士后研究。研究方向为非线性动力系统，微分方程及其应用，特别是在离子通道问题(Ion Channel Problem)和发展生物学(developmental biology)中的应用。研究的主要工具是在非线性动力系统不变流形理论上发展起来的几何奇异摄动理论。在研究离子通道问题中，特别是对离子流的动力学行为的研究，做出了重要贡献，得到同行专家学者的高度认可。已在《J. Differential Equations》，《J. Dynamics and Differential Equations》,《SIAM J. Applied Mathematics》,《SIAM J. Applied Dynamical Systems》，《Advances in Computational Mathematics》,《Communications in Mathematical Sciences》，《Nonlinear Analysis: TMA》,《Discrete and Continuous Dynamical Systems-A》，《J. Computational and Applied Mathematics》等国际著名期刊发表论文近30篇。美国《数学评论》评论员，SIAM J. Applied Mathematics, Discrete and Continuous Dynamical System-A, Int. J. System Science等近20 SCI杂志特邀审稿人。
