EIGENSLOPE METHOD FOR SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS AND THE SPECIAL CASE OF CYLINDRICAL CELLULAR STRUCTURES WITH SPATIAL GRADIENTS IN MEMBRANE CAPACITANCE - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 270

Fig. 4. Eect of C m non uniformity of 20% on passive voltage responses of a membrane
cylinder. Average C m over the cylinder was the same in all three models, but it decreased
exponentially with distance in the upper curve (from 1.1F at X = 0 to 0.9 at X = L =
1), was constant in the middle curve, and increased exponentially with distance in the
lower curve (from 0.9 F at X = 0 to 1.1 at X = L = 1). Other parameters: L = 1,
R m = 10 4 cm, I stim = G 1
for the electrical property of capacitance. The capacitance of the mem-
branes depends on the thickness of the membrane, the number of carbons
in the lipid chain that comprises the membrane, the electrical properties
of the non polar, electrically-insulating interior of the bilayer membrane
(dielectric constant), the location and density of non polar residues of the
proteins embedded in the membrane 19;37;38 , and the size and time course
of ion channel gating currents.
Studies in spinal neurons, brain neurons, cell migration, cardiac muscle
cells, egg fertilization, and others 39;40;41;42;43;44 have been in agreement that