Structure of Membranes - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 15

for cell membranes. This relates to the membrane's dielectric constant κ via the
following equation:

C
A =

κε 0
d

(2.5)

Nm 2 , giving a value of κ =

10 − 12 C 2 where ε 0 = 8 . 85 × / 10, which is greater than

κ =

3 for phospholipids above, resulting from the active presence of proteins. The
cellular membrane is much more permeable to potassium ions than sodium ions (the
intercellular fluid contains primarily sodium chloride) in the normal resting state,
which results in an outward flow of potassium ions, and the voltage inside the cell is
−

85 mV. This voltage is called the resting potential of the cell. If the cell is stimu-
lated by mechanical, chemical, or electrical means, sodium ions diffuse more readily
into the cell since the stimulus changes the permeability of the cellular membrane.
The inward diffusion of a small amount of sodium ions increases the interior volt-
age to

+

60 mV, which is known as the action potential of the cell. The membrane
again changes its permeability once the cell has achieved its action potential, and
potassium ions then readily diffuse outward so the cell returns to its resting potential.
Depending on the state of the cell, the interior voltage can therefore vary from its
resting potential of 60 mV. This results in a net

voltage change of 145 mV in the cell interior. The voltage difference between the
two sides of the membrane is fixed by the concentration difference. Having a salt
concentration difference across a membrane, and allowing only one kind of ion to
pass the membrane produces a voltage difference given by

− 85 mV to its action potential of +

ln c R
c L

k B T
e

V L − V R = (2.6)

which is called the Nernst potential. This is the basic mechanism whereby electrical
potential differences are generated inside organisms. Note that the Nernst potential
difference only depends on the concentration ratio.
The membrane potential, also known as the transmembrane potential, quantifies
the electrical potential difference between the interior and exterior of a cell. If the
potential of the region just outside the membrane is V o , and the potential of the region
just inside the cell near the membrane is V i , the membrane potential of the cell is
V i −

V o . Using the traditional definition of electrical potential, we can also define
the membrane potential to be the energy required to transfer a unit charge from the
exterior to the interior of a cell, crossing through the membrane. For example, if the
transferofa Q -coulomb charge from the exterior to the interior of a cell requires an
energy of W joules, the potential difference (and hence the membrane potential of
the cell) will be W Q volts.

Both cellular interior and exterior regions exist with electrical conditions rep-
resented by electrical potentials. The electrical potentials of both regions depend
mainly on the constituents comprising the regions. The fluids on both sides of the
mainly lipid membrane contain high concentrations of various ions—both cations
and anions. Among the cations, sodium (Na + ), potassium (K + ) and calcium (Ca 2 + )

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