Wang Yiwei, Zhang Lijun, Zhang Mingji
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA.
Membranes (Basel). 2023 Jan 19;13(2):131. doi: 10.3390/membranes13020131.
We focus on a quasi-one-dimensional Poisson-Nernst-Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in terms of I-V (current-voltage) relations with boundary layers due to the relaxation of neutral conditions on boundary concentrations. This is achieved by employing the regular perturbation analysis on the solutions established through geometric singular perturbation analysis. Rich dynamics are observed, particularly, the nonlinear interplays among different physical parameters are characterized. Critical potentials are identified, which play critical roles in the study of ionic flows and can be estimated experimentally. Numerical simulations are performed to further illustrate and provide more intuitive understandings of our analytical results.
我们关注一个准一维的泊松-能斯特-普朗克模型，该模型用于描述两种带相反电荷的离子物种通过离子通道的离子流，且带有少量永久电荷。特别值得关注的是，根据电流-电压（I-V）关系来研究离子流的动力学，其中考虑了由于边界浓度中性条件的松弛而产生的边界层。这是通过对通过几何奇异摄动分析建立的解进行正则摄动分析来实现的。观察到了丰富的动力学现象，特别是刻画了不同物理参数之间的非线性相互作用。确定了临界电位，其在离子流研究中起着关键作用，并且可以通过实验进行估计。进行了数值模拟，以进一步说明并为我们的分析结果提供更直观的理解。
