ISSN:
1432-1416
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Summary A derivation is given of the equation and boundary condition for determining the electric potential in a cell. The potential is calculated for all time, everywhere inside a spherical cell and in the external bathing medium for the case of a point source of current inside the cell turned on abruptly at t= 0. The problem is solved by the singular perturbation technique of matching a short-time (inner) and a long time (outer) asymptotic expansion. The model for the cell consists of a sphere of radius a with an internal medium of conductivity σi, surrounded by a membrane of thickness δ, conductivity σm and surface capacity C m bathed in an external medium of conductivity σ0, The solution is discussed for the physiologically interesting case of ɛ=σma/σi δ ≪1, when the effective internal resistance is small compared to the effective membrane resistance. In the most important physiological case, for times much longer than C m a/σi, simple analytic expressions are obtained for the inside potential, the outside potential and the transmembrane potential. The leading term in the expansion, the isopotential cell interior, is obtained for arbitrary finite-cell shape.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00277156
Permalink