Solution of the Poisson-Nernst-Planck equations in the cell-substrate interface

Abstract

Electrogenic cells are able to generate electrical signals which can be measured by various invasive electrophysiological methods such as patch-clamp or sharp microelectrode recordings. Growing cells on the surfaces of e.g. metal microelectrodes or field-effect transistors allows the recording of an extracellular component of these signals. For an understanding of such extracellular signals it is mandatory to get detailed topographical as well as electrical information about the cell-sensor interface. In a first approximation, this interface can be described by a flat disk between cell membrane and sensor surface. For a correct description of the signals, the electrodiffusion of ions in this interface is modeled by using the stationary Poisson-Nernst-Planck equations. We solve the equations analytically, and derive expressions for the potential, the ionic charge densities, and the seal resistance. The results provide a method for determining the distance h between sensor surface and cell membrane. For human embryonic kidney cells, we receive h approximately 70 nm. Comparison with literature shows good agreement.