Structure of Membranes - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 21

capacitance of the corresponding membranes may vary. However, a typical value is
often found to be of the order of 1 cm 2 . Most importantly, it is worth men-

tioning that the cholesterol level, phospholipids and glycolipids, membrane proteins,
hydrocarbons, etc. all together are responsible for yielding a certain value of mem-
brane capacitance. Unlike animal cytoplasmic membranes, bacteria (prokaryotes)
do not generate cholesterol, which may account for a considerable effect on their
membranes' electrical properties, including their capacitance.
Understanding the capacitive effect of the membrane helps in analyzing the mem-
brane's electrical properties, through a model often referred to as the Electrical Cir-
cuit Model of the Cell Membrane .
Here, the membrane is considered as a capacitor in parallel with a resistor. The
(not necessarily Ohmic) resistance acts against the flow of ions across the membrane,
which is represented by ion current I ion . The capacitive current is given by C m d d t .
The capacitive current and the ion current together conserve the current flow between
the inside and outside of the membrane. Therefore,

. 0 µ F /

C m d V

d t +

I ion = 0 (2.14)

The analytical calculation of I ion is a long-standing challenge. The following GHK
current equation is one such expression for I ion across the membrane:

] out e − zFV

z 2 F 2
RT

V [

] in −[

D
L

N N

RT

I ion = (2.15)

e − zFV

−

1

RT

Here, D denotes Einstein's diffusion constant, L is the membrane thickness, and

[ ] out are the ion concentrations inside and outside the cell across the

membrane, respectively (see Fig. 2.4 ).

N ] in and [ N

2.3.4 Excitability and the State of the Membrane Potential

Neurons, muscle cells, etc., are collectively called excitable cells, since they use
their membrane potentials as signals. The operation of the nervous system, muscle
contraction, etc., depends on the generation and propagation of electrical signals,
and membrane potentials in these cases mainly serve this purpose. We have earlier
described in detail how the membrane potential can be regulated by controlling cer-
tain cellular processes, such as the control of the ionic current carrying ion channels
across membranes.
Electrical signaling in cells depends largely on the type of cell involved (see
e.g., [ 17 ]). To understand it better, the cells are grouped into two categories, namely,
non-excitable cells and excitable cells. Non-excitable cells maintain stable equilib-
rium potentials. If an externally applied current perturbs the membrane potential of a
non-excitable cell, the withdrawal of the current ensures that the potential returns to