Introduction

In this chapter we continue our study of continuum models for engineered membranes. We construct mesoscopic models for the electrophysiological response platform (ERP). The ERP is a synthetic biological device built out of artificial membranes for measuring ion-channel dynamics and the electrophysiological response of cells grown on the surface of the engineered membrane. Recall that the ERP was synthesized in Chapter 3; our aim now is to model how the ERP works mathematically. The ERP can be used for drug screening and diagnosing diseases in which ion-channel functionality is disrupted (i.e., channelopathies). To estimate the electrophysiological response of cells and embedded ion channels requires that the electroporation dynamics of the tethered membrane be accounted for in the mesoscopic model of the ERP.

Motivation: Ion-Channel and Cellular Measurements

For measuring the electrophysiological response of individual ions or groups of ions, patch clamping is the gold standard. Patch clamping involves electrical measurements of the current-voltage response at different electrolyte concentrations. Patch clamping produces information-rich data which are widely used to study and validate ion-channel gating models. However, patch clamping is a labor-intensive process requiring a highly skilled experimenter to micromanipulate a glass pipette under a microscope to record data from one cell or membrane segment at a time.

Regarding measuring the electrophysiological response of cells, there are two classical methods. The first is to use substrate-integrated microelectrode arrays, and the second is to use sharp or patch microelectrodes that puncture the cell membrane [400]. A limitation of these invasive cell-measurement techniques is that, because they use sharp and patch microelectrodes, only a limited number of cells can be measured. Moreover, these techniques can cause the interior of the cell to leak into the electrolyte. Hence, these techniques can only measure the response of cells for short periods of time before they destroy the cell. Substrate-integrated microelectrode arrays provide a noninvasive method for measuring the electrophysiological response of cells; however, a major challenge when using these sensors is to ensure sufficient cell adhesion and coverage [46, 400]. An emerging technology to ensure cell adhesion is to use a metal electrode coated with a polycationic film onto which an adhesion protein, such as Glycocalyx or Fibronectin, is used to bind with the cell membrane [400].