Structure of Membranes - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 20

positive/negative species, and out / in stands for extracellular /intracellular regions,
respectively. For example, in a real cell, in which Na + ,K + and Cl − ions are the
major contributors to the membrane potential, the GHK equation can be written as

ln p K [

Cl − ] in

RT
F

K + ] out + Na + ] out +

p Na [ p Cl [

p K [

Cl − ] out

V m = (2.11)

Na + ] in +

K + ] in + p Na [ p Cl [

K + ] Na + ] Cl − ] Here, represent ion concentrations with subscripts out and in

standing for the region (outside and inside) of the cell. Further, p K , p Na and p Cl are
the relative membrane permeabilities of the ions K + ,Na + and Cl − , respectively. Nor-
mally, permeability values for ions are reported as relative permeabilities (unitless)
with p K having the reference value of one.

[ , [ and [

The Membrane as a Capacitor

A cell membrane separates charges on both sides of it. The inner core of a membrane
experiences a low dielectric state, while the outside experiences a high dielectric
state [ 20 ]. The membrane therefore generally acts as an insulator, with conducting
media on both sides.
Based on a simple electrostatic analysis, we know that the capacitance of an
object is defined as the amount of charge separated across it and creating a potential
difference between the two terminals. That is, if a potential V can hold a charge Q
across a capacitor, the capacitance C can be defined as

Q
V

C = (2.12)

A cell membrane structure suggests a model where a relatively low dielectric
medium is surrounded by two conducting media on both sides (intracellular and
extracellular regions). This makes a membrane equivalent to a leaky capacitor, since
ions are still allowed to flow through it.
To calculate the membrane capacitance, we need to use standard electrostatics with
Coulomb's law applied to an equivalent model structure for the membrane, which
produces a separation of two parallel conducting plates by an insulating medium.
Here, the membrane is comparable to an insulating medium. The capacitance of a
cell membrane can thus be defined as

κε 0
d

C m = (2.13)

Here, κ is the dielectric constant for the membrane's inner core, ε 0 is the per-
mittivity of free space, and d is the membrane thickness. A low dielectric medium
(inner layer) exists in between two conducting media (outside membrane). Depend-
ing on the variations in the values of κε 0
d

in various types of cells, the values of