ISSN:
1432-1416
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Summary The potential is calculated for all time, inside and outside a spherical cell for a point source of current inside the cell and a point sink located a finite distance outside the cell. The source and sink are step functions in time. An eigenfunction expansion is obtained, valid for arbitrary ɛ =σm a/σi δ, where σi and σm are the conductivities inside the cell and in the membrane, respectively, a is the cell radius and δ the membrane thickness. For small ɛ, the eigenfunction expansion is expanded in powers of ɛ. The time dependence of the potential contains transients with two widely differing time constants τ=Cm a/σi, where Cm is the membrane surface capacitance, and τm=τ/ɛ. Closed-form expressions are obtained for the two leading terms, for small ɛ, after the rapid transient is over. The remaining time dependence is only in the potential inside the cell, and is a simple exponential increase, independent of position within the cell. It is found that the transmembrane potential is insensitive to the location of the extracellular sink at long times, but not at short times. The dependence of the potential on location of source, sink, and observer is studied for long times after the quick transients are over. A uniqueness theorem is derived for the solution to Laplace's equation for the membrane boundary condition.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00817388
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