报告人：张明吉 副教授 （New Mexico Institute of Mining and Technology）
报告题目一：Geometric singular approach to Poisson-Nernst-Planck type models for ionic flows through membrane channels
报告摘要：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.
报告题目二：Selectivity of cations via Poisson-Nernst-Planck systems with local excess chemical potentials: Effects from finite ion sizes
报告摘要：We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel. We consider three ion species, two positively charged with the same valence and one negatively charged, and assume zero permanent charge. Bikerman's local hard-sphere potential is included in the model to account for finite ion size effects. Treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations (positively charged ion species) due to finite ion sizes, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between physical parameters, such as ion sizes, diffusion coefficients, boundary concentrations and boundary potentials. This is the novelty of our work. We believe this work will be useful for future numerical studies and stimulate further analytical studies of ionic flows concerning the selectivity of cations.
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 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 problems) 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。 在离子通道问题研究中， 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》，等国际顶级期刊发表论文20余篇。