The membrane potential is the voltage difference between the interior and exterior of a cell membrane. It arises from differences in ion concentrations across the membrane. Key ions that contribute to the membrane potential include sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl-). The resting membrane potential of most cells is approximately -70mV, due primarily to higher intracellular potassium concentration compared to extracellular. Movement of potassium and sodium ions through membrane channels works to maintain this voltage difference at equilibrium.

1. Christiane Riedinger – HOM1 1
What is membrane potential? What is its ionic basis?
Some definitions of physical quantities and cellular components:
Voltage
Symbol: U, V (=Energy/Charge)
Unit: [V] (=joules/Coulomb)
A force caused by a difference in electric charge between two areas/points (Potential
difference). The force makes electrons move or provides the potential for them to
move. Also: Potential difference.
Electric Potential
Symbol: Φ
Unit: [V]
The difference in electrical charge between two points in a circuit, expressed in Volts.
Also (Wikipedia): “The electrical potential energy at a point in space divided by the
charge associated with a static (time-invariant) electric field.”
Membrane potential
The (trans)membrane potential is the difference in electric potential across a cell
membrane, i.e. between the interior and exterior of a cell.
Capacitor
Symbol: C (=Q/V, Charge/Voltage)
Unit: [F] (Farads)
A capacitor is an electrical device that can store an electric charge. It consists of a pair
of conductors separated by a dielectric layer (insulating layer). The size of the
capacitance depends on the area of the conductors and the thickness of the insulating
layer.

2. Christiane Riedinger – HOM1 2
5. The Cell Membrane
(View across a cell membrane, taken from cybermedicine.com)
- consists of phospholipid bilayer with hydrophobic end pointing inwards (=towards
cytoplasm) and hydrophilic head pointing towards extracellular matrix +cytoplasm
- contains ion channel proteins to transport ions in and out of cell
- most important cellular ions: Na+, K+, Ca2+ and Cl-
- typical concentrations in mammalian cells
Ion Cell [mM] Blood [mM]
+
Na 12 145
K+ 139 4
2+
Ca <0.2µM 1.8
-
Cl 4 116
(From Mol. Cell. Biol., Lodish et al., 3rd edition, page 641)

3. Christiane Riedinger – HOM1 3
What is membrane potential?
The phospholipid membrane is a thin (~3.5nm) layer of non-conducting material
(biological capacitor!) that separates the intra- and extracellular space, i.e. two
compartments with different ion concentrations (see above table). Since the cell
membrane is permeable to certain types of ions, their movement through the
membrane channels creates a difference in electric potential between the intra- and
extra cellular matrix. Ion-migration across the membrane results in an uneven charge
distribution, or separation of charges, which can be measured as a potential
difference. The average membrane potential is approx. 70mV, i.e. the inside of the
cell is more negative compared to the outside.
If a membrane with different intra and extracellular ion concentrations and ion
channels that allow the ions to travel along their concentration gradient was left to its
own devices, then the ions would migrate until a maximum potential difference is
measured. This state represents an electrochemical equilibrium between the maximum
possible charge separation and the maximum reduction of the concentration gradient
for the given system. This state is described by the Nernst equation:
RT · ln [ion]outside = EnF
[ion]inside
R = molar gas constant = 8.313372 m2 kg s-2 K-1 mol-1
F = Faraday constant = 96 485.3415 s A / mol (C/mol)
(Magnitude of electric charge per mole of electrons)
n (or z) = valency of ion moved, if n neg then potential sign changes
E = equilibrium potential VOLTAGE [V]
What is the ionic basis of the membrane potential?
In order for a membrane potential to occur, there has to be a concentration difference
of the ions/charged particles across the membrane. Furthermore, the membrane has to
be permeable to ions/charged particles; otherwise no difference in electric potential
can be measured (according to Mol. Cell. Biol., Lodish et al., 3rd edition, page 642).
For the majority of cellular membranes in the human body, the resting membrane
potential is -70mV. This value is close to the potential of a membrane solely
permeable to K+ ions. Most biological membranes are mainly permeable to K+ ions,
and therefore the value of the resting potential is close, but not identical, since there is
also a small permeability to Na+ ions (1/100th). Furthermore, electrogenic pumps
(Na+/K+) also contribute to the resting potential. Finally, the concentration
differences of ions across the membrane influence the resting membrane potential.
As the resting membrane potential depends mainly on the migration of K+ and Na+
ions, it cannot be calculated using the Nernst equation (only one ion), but by using the
Goldman-Hodgkin-Katz equation:
E [V] = RT/F * ln (PK[K+]z + PNa[Na+]z)
PK[K+]m + PNa[Na+]m
P = relative permeability
z = outside, m = inside
if Cl- was incorporated then it would be inside / outside due to inverted sign:
log a/b = - log b/a, if you want to add different valencies: more complicated