resting potential 2014

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14/11/2014
The Structure of the Cell
Membrane
Resting Membrane Potential
Structure of the cell membrane.
Resting membrane potential.
• The Nernst equation.
• Donnan potential.
• The Goldman-Hodgkin-Katz equation
11.11.2014.
Phospholipids
The main component of the biological membranes.
Phospholipid = diglyceride (glycerine+fatty acid) + phosphate
group + organic molecule (e.g. choline).
Polar – head
(hydrophilic)
Non-polar – tail
(hydrophobic)
⇒ „water soluble fat”
phosphatidil – choline
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Irving Langmuir
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
water
Irving Langmuir, "The Constitution and Fundamental Properties of Solids and Liquids. II," Journal of the American Chemical Society 39 (1917): 1848-1906.
Lipid bilayer
1925 – Evert Gorter & F. Grendel (University of Leiden, Holland)
• Compared the measured 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.
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Lipid bilayer
• twice as much lipid in the membrane of the red blood cells than
needed for a monolayer → lipid bilayer
EC
Polar heads toward the
intra- and extracellular
space
Apolar (hydrophobic)
tails in the middle
IC
Gortel, E. & Grendel, F. (1925) On bimolecular layers of lipoid on the chromocytes of the blood. J. Exp. Med. 41, 439–443.
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Gibbs free energy [Joule]
G = H - TS
A spontaneous process is accompanied by
a decrease in the Gibbs energy at constant
temperature and pressure.
At constant temperature and pressure the
change in the Gibbs energy is equal to the
maximum
non-expansion
work
accompanying a process.
Hydrophobic interaction
• hydrophobic = water-repelling; low affinity (solubility) for water
• Walter Kauzmann (American chemist) - Nonpolar molecules in polar
environment (solvents) are trying to minimize their contact with water
• 1”cage” formation → 2clustering
• Factors affecting the strength of hydrophobic interaction
– Temperature (T ↑ ⇒ Strength ↑)
– Number of carbons in the hydrophobic molecule (Length ↑ ⇒ Strength ↑)
– Number of “non single” bonds (e.g. double, triple bonds…) in the hydrophobic molecule
(shape) ( # “non single” bonds ↑ ⇒ Strength ↓)
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Thermodynamic changes
H2O
hydrophobic
molecule
H2O
+
hydrophobic
molecule
H2O
→
Cage formation
(no interaction between hydrophobic molecules)
∆H = small positive
∆S = large negative
∆G = positive
NON SPONTANEOUS PROCESS
H2O
hydrophobic
molecule
hydrophobic
molecule
Clustering
(forming hydrophobic interactions)
∆H = small positive
∆S = large positive
∆G = negative
SPONTANEOUS PROCESS
„Fluid mosaic” model
• 1972 - Singer and Nicholson „fluid mosaic” model
• phospho-lipid bilayer
• Fluid – lateral movement of the components („floating”)
• Mosaic – the
macromolecules
mosaic-like
arrangement
of
the
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.
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Structure of the cell membrane
Lateral diffusion
Phospholipide molecule (~40-60%)
Polar
(hydrophilic) head
Non-polar
(hydrophobic) tail
Flip-flop
~ 5 nm
rotation
Protein molecule (~30-50%)
Functions of the membrane poteins
Ion channels (Na+/K+ ATPase; K+ channel…)
Transporters (Aquaporin-H2O 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)
•
•
•
•
•
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The main components of the
intra- and extracellular space
• water
• Ions
– Kations (K+, Na+, Ca2+)
– Anions (Cl-, H2PO4− and HPO42− ions)
• proteins
– Mainly intracellular localisation
– Negatively charged polyvalent (having more than one
valence) macromolecules (pH! – isoelectric point)
Membrane potential
0V
-100 mV > Uresting < -30 mV
The electrical potential
difference (voltage)
across a cell's plasma
membrane.
Microelectrode
Intracellular space
Extracellular space
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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
of charged particles
Chemical potential energy:
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 through the
permeable membrane from a high concentration area to a low
concentration area → diffusion potential.
Energy: Capacity for doing work.
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Electric potential energy
•
•
the result of conservative Coulomb forces
associated with the configuration of a particular
set of point charges within a defined system
•
work required by an electric field to move
electric charges (Joule).
•
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
K+ : 100 mM
K+ : 5 mM
Cl- : 100 mM
Cl- : 5 mM
the charged particles (the work of the electric
field) → moving charged particles = electric
current.
Force controlling the movements of
ions through the cell membrane
Electro-chemical potential
= the combination (sum) of the chemical and the electric
potential energy.
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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
K+ : 5 mM
Cl- : 100 mM
Cl- : 5 mM
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Bernstein’s potassium hypothesis
The side with
high
concentration of
positive ions
becomes the
negative side !!!!
+
[K+]
[
Cl-]
[K+]
[Cl-]
K+ gradient (chemical potential)
electric gradient
(electrical potential)
How is it possible to quantify the
Bernstein’s hypothesis ?
(calculating the electrical potencial (value, number)
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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 energy ⇒ Wchem=NRTln
N = number of moles associated with the concentration gradient
R = gas constant
T = absolute temperature
X1 / X2 = concentration gradient
Electric potential energy ⇒ Welectr=NZFE
N = number of moles of the charged particles
z = valency (number of + or – charges (e.g. K+ : monovalent))
F = Faraday’s number (constant)
E = strength of the electric field = electric potential or electrostatic potential
= The work needed to move a unit electric charge from one point to another
against an electric field (Joule/Coulomb = Volt).
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Equlibrium (resting) condition
Electrical potential energy
NzFE = NRT ln
X1
Chemical potential energy
X2
zFE = RT ln
X1
X2
E=
RT X 1
ln
zF X 2
Equlibrium potential
Nernst equation: What membrane potential
(E) can compensate (balance) the
concentration gradient (X1/X2).
RT X 1
E=
ln
zF X 2
The inward and outward flows of the ions are balanced
(net current = zero → equilibrium = stable, balanced or unchanging
system).
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Nernst equation
E=
RT
ln
zF
EmV
X1
X2
(
− 58
Cin )
=
log
(Cout )
z
Ionic concentrations inside and
outside of a muscle cell
Na+ : 120 mM
Na+ : 20 mM
K+ : 2.5 mM
K+ : 139 mM
Cl- : 120 mM
Cl- : 3.8 mM
[K+] ⇒ EmV = -58/1 log (139/2.5) = - 101.2 mV
[Na+] ⇒ EmV = -58/1 log (20/120) = + 45.1 mV
[Cl-] ⇒ EmV = -58/1 log (3.8/120) = + 86.9 mV
= 30.8 mV
EmV=-92mV
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What happens if the cell
membrane is not permeable to
a charged component?
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 is different
- more than one diffusible ion (K+, Cl-)
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Donan equlibrium - at equlibrium
A
[K+]
B
Cl- concentration gradient
Cl- electrical gradient
[K+]
K+ electrical gradient
[Cl-]
[Pr -]
-
[Cl-]
K+ concentration gradient
+
Donnan rule of equilibrium
• Diffusible ions: K+, Cl• In equlibrium the elektro-chemical potentials are equal.
RT [K in ]
RT [Clout ]
ln
=E=
ln
zF [K out ]
zF [Clin ]
[K in ] [Clout ]
=
[K out ] [Clin ]
[K in ][Clin ] = [K out ][Clout ]
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.
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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.
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Goldman equation
The Goldman equation for M positive ionic species and A negative:
[ ] + ∑ P [A ]
[ ] + ∑ P [A ]
 N
+
 ∑ i PM i+ M i
ln 
Em =
N
F  ∑ i PM + M i+
i

RT
M
out
j
A −j
M
in
j
A −j
−
j in
−
j out





•Em = The membrane potential
•Pion = 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
A "Nernst-like" equation with terms for each permeant ion (permeability).
- All the ions are involved with different concentrations.
- Good agreement with the measured values (muscle cell: Umeasured=-92mV_Ucalc.=-89.2mV).
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.
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14/11/2014
The end!
19
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