Structure of Membranes - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 25

cellular exterior

g L

G n (t,V)

C m

E n

E n

I p

cellular interior

Fig. 2.5 A capacitor-resistor circuit representation of the cell membrane. This is a more detailed
form of the equivalent circuit representation presented earlier in this chapter

of [ 8 ]). The evidence for the capacitive currents and ionic currents to be parallel was
well-established in the study by Hodgkin et al. [ 8 ]. A major reservation, however, is
that the earlier equation takes no account of dielectric loss in the membrane. Since
the capacitive surge was found to be reasonably close to that calculated for a perfect
capacitor [ 8 ], it was then predicted that the mentioned dielectric condition inside
the membrane would not change the structure of the equation dramatically. So far
this has been found consistent with the data obtained using modern approaches that
include other constituents inside membranes.

The Potassium Conductance

Hodgkin and Huxley investigated the time dependence of ionic conductance both
theoretically and experimentally. In their experimental investigations they studied in
detail, for example, the case of potassium ion conduction. Based on their famous
1952 paper [ 12 ], it is clear that the rise of potassium conductance associated with
depolarization of a potential is followed by the fall of conductance associated with
repolarization of the resting potential. Here, the nonlinear rise (depolarizing effect)
of conductance g K is found to be mathematically very well-fitted by the function
(

4 while the fall is approximately by the function e − 4 t . These two different
4th-order mathematical forms explain nicely the marked inflection for the rise, with
a simple exponential for the fall for g K . A similar mathematical fit to experimental
data using other functional forms could also be possible, but might require other

e − t

1 − )