Analytical description of transmembrane voltage induced by electric fields on spheroidal cells

被引:182
作者
Kotnik, T [1 ]
Miklavcic, D [1 ]
机构
[1] Univ Ljubljana, Fac Elect Engn, SI-1000 Ljubljana, Slovenia
关键词
D O I
10.1016/S0006-3495(00)76325-9
中图分类号
Q6 [生物物理学];
学科分类号
071011 ;
摘要
An analytical description of transmembrane voltage induced on spherical cells was determined in the 1950s, and the tools for numerical assessment of transmembrane voltage induced on spheroidal cells were developed in the 1970s. However, it has often been claimed that an analytical description is unattainable for spheroidal cells, while others have asserted that even if attainable, it does not befit the reality due to the nonuniform membrane thickness, which is unrealistic but inevitable in spheroidal geometry. In this paper we show that for all spheroidal cells, membrane thickness is irrelevant to the induced transmembrane voltage under the assumption of a nonconductive membrane, which was also applied in the derivation of Schwan's equation. We then derive the analytical description of transmembrane voltage induced on prolate and oblate spheroidal cells. The final result, which we cast from spheroidal into more familiar spherical coordinates, represents a generalization of Schwan's equation to all spheroidal cells (of which spherical cells are a special case). The obtained expression is easy to apply, and we give a simple example of such application. We conclude the study by analyzing the variation of induced transmembrane voltage as a spheroidal cell is stretched by the field, performing one study at a constant membrane surface area, and another at a constant cell volume.
引用
收藏
页码:670 / 679
页数:10
相关论文
共 17 条
[1]   GENERATION OF POTENTIAL DIFFERENCES ACROSS MEMBRANES OF ELLIPSOIDAL CELLS IN AN ALTERNATING ELECTRICAL FIELD [J].
BERNHARDT, J ;
PAULY, H .
BIOPHYSIK, 1973, 10 (01) :89-98
[2]   ELECTROMECHANICAL STRESSES PRODUCED IN THE PLASMA-MEMBRANES OF SUSPENDED CELLS BY APPLIED ELECTRIC-FIELDS [J].
BRYANT, G ;
WOLFE, J .
JOURNAL OF MEMBRANE BIOLOGY, 1987, 96 (02) :129-139
[3]   Separable systems of Stackel [J].
Eisenhart, LP .
ANNALS OF MATHEMATICS, 1934, 35 :284-305
[4]   A polarization model overcoming the geometric restrictions of the laplace solution for spheroidal cells: Obtaining new equations for field-induced forces and transmembrane potential [J].
Gimsa, J ;
Wachner, D .
BIOPHYSICAL JOURNAL, 1999, 77 (03) :1316-1326
[5]   CELLULAR MEMBRANE-POTENTIALS INDUCED BY ALTERNATING-FIELDS [J].
GROSSE, C ;
SCHWAN, HP .
BIOPHYSICAL JOURNAL, 1992, 63 (06) :1632-1642
[6]   Potential distribution for a spheroidal cell having a conductive membrane in an electric field [J].
Jerry, RA ;
Popel, AS ;
Brownell, WE .
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 1996, 43 (09) :970-972
[7]   STIMULATION OF SPHEROIDAL CELLS - ROLE OF CELL-SHAPE [J].
KLEE, M ;
PLONSEY, R .
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 1976, 23 (04) :347-354
[8]   FINITE-DIFFERENCE SOLUTION FOR BIOPOTENTIALS OF AXIALLY SYMMETRIC CELLS [J].
KLEE, M ;
PLONSEY, R .
BIOPHYSICAL JOURNAL, 1972, 12 (12) :1661-1675
[9]   Sensitivity of transmembrane voltage induced by applied electric fields - a theoretical analysis [J].
Kotnik, T ;
Bobanovic, F ;
Miklavcic, D .
BIOELECTROCHEMISTRY AND BIOENERGETICS, 1997, 43 (02) :285-291
[10]   Time course of transmembrane voltage induced by time-varying electric fields - a method for theoretical analysis and its application [J].
Kotnik, T ;
Miklavcic, D ;
Slivnik, T .
BIOELECTROCHEMISTRY AND BIOENERGETICS, 1998, 45 (01) :3-16