The Structure of the Cell Membrane Resting Membrane Potential

The Structure of the Cell Membrane
Resting Membrane Potential
25.09.2012.

Phospholipids
The main component of the biological membranes.
Phospholipid = diglyceride (glycerine+fatty acid) + phosphate
group + organic molecule (e.g. choline).
„water soluble fat”
Polar – head
(hydrophilic)
Non-polar – tail
(hydrophobic)
phosphatidil - cholin

Irving Langmuir
1881 - 1957
American physico-chemist
1932 Nobel-price in chemistry
• 1917 – lipids form a monolayer on the
surface of the water
polar heads (hydrophilic) – oriented
toward the water
nonpolar tails (hydrophobic) – oriented
away from water
Irving Langmuir, "The Constitution and Fundamental Properties of Solids and Liquids. II," Journal of the American Chemical Society 39 (1917): 1848-1906.
water

Lipid bilayer
1925 – Evert Gorter & F. Grendel (University of Leiden, Holland)
• compared the surface area of the erythrocytes and the surface
area calculated from the lipid content of them.
• Gorter E, Grendel F. On Bimolecular Layers of Lipoids on the
Chromocytes of the Blood. J Exp Med. 1925 Mar 31;41(4):439-43.
Gortel, E. & Grendel, F. (1925) On bimolecular layers of lipoid on the chromocytes of the blood. J. Exp. Med. 41, 439–443.

Lipid bilayer
• twice as much lipid in the membrane of the red blood cells than
needed for a monolayer → lipid bilayer
Polar heads toward the
intra- and extracellular
space
EC
IC
Gortel, E. & Grendel, F. (1925) On bimolecular layers of lipoid on the chromocytes of the blood. J. Exp. Med. 41, 439–443.
Apolar tails in the
middle

• phospho-lipid bilayer
„Fluid mosaic” model
• 1972 - Singer and Nicholson „fluid mosaic” model
• Fluid – lateral movement of the
components („floating”)
• Mosaic – the mosaic-like
arrangement of the
macromolecules
http://www.molecularexpressions.com/cells/plasmamembrane/plasmamembrane.html
Singer SJ, Nicolson GL. The fluid mosaic model of the structure of cell membranes. Science. 1972 Feb 18;175(23):720-31.

Structure of the cell membrane
Flip-flop
rotation
Lateral diffusion
Phospholipide molecule (~40-60%)
Polar
(hydrophilic) head
Non-polar
(hydrophobic) tail
Protein molecule (~30-50%)
~ 5 nm

Functions of the membrane poteins
• Ion channels (Na + /K + ATPase)
• Transporters (Aquaporin-H 2O transport)
• Structural elements
• Intracellular connections (anchoring – cytoskeleton)
• Extracellular connection (gap junction: cell to cell
contact between cardiac cell)
• Signal transduction (action potential)
• Receptors (insulin receptor)

The main components of the
intra- and extracellular space
• water
• Ions
– Kations (K + , Na + , Ca 2+ )
– Anions (Cl - , H 2PO 4 − and HPO4 2− ions)
• proteins
– Mainly intracellular localisation
– Negatively charged polyvalent (having more than one
valence) macromolecules (pH! – isoelectric point)

Membrane potential
The electrical potential
difference (voltage)
across a cell's plasma
membrane.
U resting=-30_-100 mV
Microelectrode
0V
Intracellular space
Extracellular space

Ionic concentrations inside and
outside of a muscle cell
Na + : 120 mM
K + : 2.5 mM
Cl - : 120 mM
Na + : 20 mM
K + : 139 mM
Cl - : 3.8 mM

Forces controlling the movements
● Chemical potential:
of charged particles
The chemical potential of a thermodynamic system is the amount of energy (Joule)
by which the system would change if an additional particle were introduced
(number of the particles!).
Concentration gradient → diffusion: moving the particles from a high
concentration area to a low concentration area → diffusion potential.

Electrical potential
● Electric potential: work required by an
electric field to move electric charges
(expressed in volts and can be measured
by a voltmeter).
● Electrical gradients:
The sum of the “+” and “-” are not the same
at the different points in space.
An electric field creates a force that can
move the charged particles (the work of the
electric field) → moving charged particles =
electric current.
K + : 100 mM
Cl - : 100 mM
K + : 5 mM
Cl - : 5 mM

Forces controlling the movements
of charged particles
Electro-chemical potential
= the combination (sum) of the chemical and the electric
potential.

Bernstein’s potassium
hypothesis (1902)
Julius Bernstein (1839 - 1917) - German physiologist
1./ The cell membrane is selectively permeable to potassium
• Ca2+ sensitive potassium channels
• Inwardly rectifying potassium channels
• Voltage-gated potassium channels
• “Tandem pore domain potassium channel” – “leak channel” (K2p)
̶ 1952: Hodgkin and Huxley suggested the leakage of current
̶ etchum, KA; Joiner, WJ; Sellers, AJ; Kaczmarek, LK; Goldstein, SA. (1995) A
new family of outwardly rectifying potassium channel proteins with two pore
domains in tandem. Nature, 376 (6542): 690-5.
2./ The intracellular potassium cc. is high
3./ The extracellular potassium cc. is low
Bernstein,J.(1902).Untersuchungen zur Thermodynamik der bioelektrischen Strome. Pflugers Arch.ges. Physiol. 92, 521–562.

Bernstein’s potassium hypothesis
K + : 100 mM
Cl - : 100 mM
K + : 5 mM
Cl - : 5 mM

Bernstein’s potassium hypothesis
The side with
high
concentration of
positive ions
becomes the
negative side !!!! [Cl - ] [Cl - ]
electric gradient
(electrical potential)
[K + ] [K + ]
K + gradient (chemical potential)

How is it possible to quantify the
Bernstein’s hypothesis ?
(calculating the electrical potencial)

Walther Hermann Nernst
German physical chemist
(June 25, 1864 – November 18, 1941)
Calculating the electrical
potential at which there is no
longer a net flux (movement) of a
specific ion across a membrane.

chemical potential Wchem
= ⇒
NRT
X
ln
X
N = number of moles associated with the concentration gradient
R = gas constant
T = absolute temperature
X 1 / X 2 = concentration gradient
electrical potential ⇒ Welectr
=
NzFE
N = number of moles of the charged particles
z = valency (number of + or – charges (e.g. K + : monovalent))
F = Faraday’s number
E= strength of the electric field (V)
1
2

Equlibrium (resting) condition
NzFE =
NRT
Electrical potential Chemical potential
zFE =
E =
RT
RT
zF
ln
ln
X
X
X
X
X
ln
X
1
2
1
2
1
2

Equlibrium potential
Nernst equation: What membrane potential
(E) can compensate (balance) the
concentration gradient (X 1/X 2).
E =
RT
zF
X
ln
X
The inward and outward flows of the ions are balanced
(net current = zero → equilibrium = stable, balanced, or unchanging
system).
1
2

Nernst equation
E =
RT
zF
ln
X
− 58
E = log
mV
z
X
1
2
( C ) in
( C ) out

Ionic concentrations inside and
Na + : 120 mM
K + : 2.5 mM
Cl - : 120 mM
outside of a muscle cell
[K + ] ⇒ E mV = -58/1 log (139/2.5) = - 101.2 mV
[Na + ] ⇒ E mV = -58/1 log (20/120) = + 45.1 mV
[Cl - ] ⇒ E mV = -58/1 log (3.8/120) = + 86.9 mV
Na + : 20 mM
K + : 139 mM
Cl - : 3.8 mM
= 30.8 mV
E mV=-92mV

What happens if the cell
membrane is permeable to
more than one type of ion?

Frederick George Donnan
(1870-1956; Irish chemist)
Donnan equilibrium: characterising
the equlibrium situation when the
membrane is not permeable for some
ionic components.
- non-moving charged component (e.g.
intracellular proteins) → equlibrium
concentration difference
- more than one diffusible ion (K + , Cl - )

Donnan rule of equilibrium
• Diffusible ions: K + , Cl -
• In equlibrium the elektro-chemical potentials are equal.
RT
zF
[ Kin
]
[ K ]
ln = E =
out
[ in ]
[ K ]
K =
out
RT
zF
ln
[ Clout
]
[ Cl ]
in
[ Clout
]
[ Cl ]
[ K ][ Cl ] = [ K ][ Cl ]
in
in
The Donnan rule is valid only when the ions are passively distributed.!
The Gibbs–Donnan equilibrium is a phenomenon that contributes to the formation of
an electrical potential across a cell membrane.
out
out
in

What happens if the Donnan rule is
not obeyed?

Goldman-Hodgkin-Katz Constant
field equation (Goldman equation)
David E. Goldman (USA)
Alan Lloyd Hodgkin (England)
Bernard Katz (England).
To determine the potential across a cell's membrane taking into
account all of the ions with different permeabilities through the
membrane.

Goldman equation
The Goldman equation for M positive ionic species and A negative:
E
m
=
⎛
RT ⎜
ln⎜
F ⎜
⎝
∑
∑
[ ] + [ ]
+
M −
M P − A
[ ] [ ] ⎟ ⎟⎟
j
+
M −
M i + ∑ P − A
in j A j
j out ⎠
•E m = The membrane potential
•P ion = the permeability for that ion
•[ion] out = the extracellular concentration of that ion
•[ion] in = the intracellular concentration of that ion
•R = The ideal gas constant
•T = The temperature in kelvins
•F = Faraday's constant
N
i
N
i
P
P
M
M
+
i
+
i
i
out
A "Nernst-like" equation with terms for each permeant ion.
- All the ions are involved.
- Good agreement with the measured values (muscle cell: U measured=-92mV_U calc.=-89.2mV).
∑
j A j in
⎞

Goldman equation
The membrane potential is the result of a
„compromise” between the various equlibrium
potentials, each weighted by the membrane
permeability and absolute concentration of the
ions.

The end!