The induced transmembrane potential and effective conductivity of cells in dense cell system

Abstract

Studying electric potential distribution on the cell membrane and electric conductivity gives us an insight into the effects of the electric field on cells and tissues. Since cells are always surrounded by other cells we studied how their interactions influence the induced transmembrane potential (TMP) and effective conductivity. We studied numerically and analytically the effect of cells arrangement for cases, where cells were organized into simple-cubic, body-centered cubic and face-centered cubic lattices. We show that in contrast to some reported results the phenomenological effective medium equations (EMT) can not be used to determine the local electric field and the induced transmembrane potential in dense systems, whereas the effective conductivity of biological cells in dense system can be analyzed with Maxwell or Bruggeman EMT equations. We also derive a zero order approximation for the induced TMP in dense suspension, where dominant factors which govern the change in the local field are the cell volume fraction and number of nearest neighbors. The presented analysis demonstrates that the local electric field and induced TMP in dense system have to be calculated numerically, whereas EMT equations are useful only for estimating effective (bulk) values of a certain physical property such as dielectric constant or conductivity.