A Poisson-Nernst-Planck single ion channel model and its effective finite element solver

A single ion channel is a membrane protein with an ion selectivity filter that allows only a single species of ions (such as potassium ions) to pass through in the “open” state. Its selectivity filter also naturally separates a solvent domain into an intracellular domain and an extracellular domain. Such biological and geometrical characteristics of a single ion channel are novelly adopted in the construction of a new kind of dielectric continuum ion channel model, called the Poisson-Nernst-Planck single ion channel (PNPSIC) model, in this paper. An effective PNPSIC finite element solver is then developed and implemented as a software package workable for a single ion channel with a three-dimensional X-ray crystallographic molecular structure and a mixture of multiple ionic species. Numerical results for a potassium channel confirm the convergence and efficiency of the PNPSIC finite element solver and demonstrate the high performance of the software package. Moreover, the PNPSIC model is applied to the calculation of electric current and validated by biophysical experimental data. •Construct a PNP single ion channel (PNPSIC) model by single ion channel selectivity property.•Solve the PNPSIC model by an effective finite element iterative algorithm.•Develop a PNPSIC software for crystallographic molecular structures and multiple ionic species.•Demonstrate the high performance of the PNPSIC software for a potassium channel.•Validate the PNPSIC model by comparing predicted I-V curves with biophysical experimental data.