Effects on zero current ionic flow and reversal potential from two piecewise permanent charges in opposite signs

Through this work, we investigated a quasi-one-dimensional Poisson-Nernst-Planck (PNP) system containing two segments of permanent charges with opposite signs. Under a zero current condition, the internal dynamics of ionic flows inside of an open ion channel including two types of ion species, one cation and one anion, were the main focus of this work. The existence and local uniqueness solution was proved along the framework of geometric singular perturbation theory, combining with the concrete structure of this model. Furthermore, we obtained three governing equations during the construction of a connecting orbit, which played a fundamental role in subsequent investigations for the impact of permanent charges on zero current ionic flow and reversal potential. In particular, richer dynamical behaviors were demonstrated under the set-up of a multiple nonzero permanent charge distribution, which is also more realistic to the practical problem.