The membrane
Resting Membrane Potential
and
Action Potential
Bódis Emőke
13 October 2011
The chemical composition of the cell
Lipid monolayer
Irving Langmuir:
- - American physico chemist
- - 1932 Nobel-prise in chemistry
- - 1917: lipids form a monolayer on the surface of the water
Lipid bilayer
Gortel and Grendel:
1925: there is twice as much lipid
in the membrane of blood cells
than needed
•
•
•
•
Water
Kations: K+, Na+, Ca2+
Anions: Cl-, H2PO4-, HPO42Protein-anions
–  Localise mainly intracellularly
–  for which membrane is impermeable
–  Isoelectric point
Resting Membrane Potential
Animation
http://www.youtube.com/watch?v=YP_P6bYvEjE&hd=1
1
Resting Membrane Potential
4 mEq/L
K+
Cl-
Resting Membrane Potential
142 mEq/L
Typical:
Na+
-30 - 90 mV
142 mEq/L
4 mEq/L
K+
Cl-
Na+
Outside
+++++++++++++++++++++++++++++++++++
Outside
+++++++++++++++++++++++++++++++++++
-------------------------------------
-------------------------------------
A-
K+
Cl-
Na+
A-
Inside
14 mEq/L
140 mEq/L
K+
Cl-
Na+
Inside
14 mEq/L
140 mEq/L
• If electrode is inserted into cardiac cell, will detect a
negative reading compared to outside of the cell of -80mV
The electric field strength: 70 mM/5 nm = 140 000 V/cm
Resting Membrane Potential
Resting Membrane Potential
142 mEq/L
4 mEq/L
K+
Cl-
142 mEq/L
4 mEq/L
Na+
K+
Outside
Cl-
Na+
Outside
A-
K+
Cl-
Na+
Inside
14 mEq/L
A-
140 mEq/L
K+
Cl-
Na+
Inside
14 mEq/L
140 mEq/L
•  Make cell membrane SELECTIVELY permeable to K+
•  K+ wants to move toward region of lower concentration
(CHEMICAL FORCE to move down concentration gradient)
Resting Membrane Potential
Resting Membrane Potential
142 mEq/L
4 mEq/L
K+
Cl-
142 mEq/L
4 mEq/L
Na+
K+
Outside
+++++++++++++++++++++++++++++++++++
Cl-
Na+
Outside
+++++++++++++++++++++++++++++++++++
-------------------------------------
A-
K+
Cl-
Na+
Inside
14 mEq/L
A-
K+
Cl-
Na+
Inside
14 mEq/L
140 mEq/L
140 mEq/L
•  Make cell membrane SELECTIVELY permeable to K+
•  As K+ leaves cell, negativity increases on the inside
of the cell membrane and electrostatically attracts K+.
This electrostatic force prevents K+ from leaving cell.
•  K+ wants to move toward region of lower concentration
(CHEMICAL FORCE to move down concentration gradient)
2
Resting Membrane Potential
Forces controlling the movements of
charged particles
142 mEq/L
4 mEq/L
Cl-
K+
Na+
Outside
+++++++++++++++++++++++++++++++++++
-------------------------------------
A-
Cl-
K+
Na+
Inside
14 mEq/L
140 mEq/L
Chemical driving force is
eventually balanced by
Electrical driving force so no
further net movement of K+
Nernst Equation
Chemical potential: (Willard Gibbs (1876) - American mathematical physicist)
The chemical potential of a thermodynamic system is the amount of energy 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 one → diffusion potential.
Electric potential: the difference in electrical charge between two points in a circuit
expressed in volts.
Electrical gradients: An electric field creates a force that can move the charged(+ or -)
particles (the work of the electric field) → electric current: moving charged particles.
Electro-chemical potential
The combination (sum) of the chemical and the electric potential. Related to the
average energy affecting the charged particle.
Nernst Equation
chemical potential ⇒ Wchem = NRT ln (X1/X2)
N = number of moles associated with the concentration gradient
R = gas constant
T = absolute temperature
X1 / X2 = concentration gradient
electic potential ⇒ Wel = NzF ΔE
N = number of moles of the charged particles
z = valency
F = Faraday’s number
∆E (= E1-E2 ) = strength of the electric field (V)
A little bit more about the Nernst Equation
Nernst Equation
X
NzFE = NRT ln 1
X2
zFE = RT ln
€
€
X1
X2
RT X1
E=
ln
zF X 2
The general form of the equation in your
textbook:
What is the meaning of Ex?
Ex is the potential at which the flux due to diffusion is equal and
opposite to the flux due to electrophoresis
What is EK for the cell we showed at the beginning?
€
3
In our cell why was the resting potential -80mV if EK = -100mV?
This cell is permeable to more than one ionic species at rest.
How can we quantify the contribution of multiple ionic species?
Goldman-Hodgkin-Katz Equation
To determine the potential across a cell's membrane taking
into account all of the ions with different permeabilities
through the membrane.
The Goldman Equation (or the GHK Equation)
Some important details:
• Derives from the Nernst equation and a few assumptions permeability of the given ion
inside and outside concentrations
• Uses permeabilities rather than conductances
• Cl- is flipped to account for a -1 valence
Goldman-Hodgkin-Katz Equation
If the membrane is not permeable for an ion:
Donnan-potential
Donnan equilibrium: characterising the equlibrium situation when
the membrane is not permeable for some ionic components.
 Unequal distribution of diffusible ions
between two ionic solutions
 separated by a membrane
 impermeable to at least one of the ionic
species present (e.g. proteins)
Good agreement with the measured value.
Donnan-potential
Donnan-potential
  A negative non-diffusing charge on one side of a membrane
potential gradient across the membrane from which ions will diffuse.
  The result will be an electrochemical equilibrium.
  The concentration (chemical potential) of ions will not necessarily be the same
inside and outside. Thus, as an electrical disequilibrium is maintained because of
diffusing charges.
In a Donnan equilibrium, the charge imbalance in the vicinity of a semi-permeable
membrane gives rise to an electric field, with a jump in the electrostatic potential
typically occurring over a length of less than a micrometer.
Similarly, if a colloidal suspension has a gradient of concentration (such as is
produced in sedimentation or centrifugation), then a macroscopic electric field is
generated by the charge imbalance appearing at the top and bottom of the sample
column.
4
Resting Membrane Potential
Resting Membrane Potential
142 mEq/L
4 mEq/L
K+
Cl-
142 mEq/L
4 mEq/L
Na+
K+
Cl-
Na+
Outside
+++++++++++++++++++++++++++++++++++
Outside
+++++++++++++++++++++++++++++++++++
-------------------------------------
-------------------------------------
A-
K+
Cl-
Na+
Inside
14 mEq/L
140 mEq/L
A-
K+
Cl-
Na+
Inside
14 mEq/L
140 mEq/L
•  There is a small, but finite, leakage of Na+ into cell
(depolarizing effect)
Resting Membrane Potential
•  Potassium is the major determinant of the
Resting Membrane Potential
•  Potassium and sodium ion channels allow
leakage of these ions across the cell membranes
Animation
http://bcs.whfreeman.com/thelifewire/content/chp44/4401s.swf
Na+, K+ - ATPase Pump
•  In the normal nerve fiber, the permeability of the
membrane to potassium is about 100 times as
great as to sodium
Na+, K+ - ATPase Pump
(Sodium Pump)
  a highly-conserved integral membrane protein
  is expressed in virtually all cells of higher organisms
  it is estimated that roughly 25% of all cytoplasmic ATP is hydrolyzed by sodium
pumps
  depending on cell type, there are between 800,000 and 30 million pumps on
the surface of cells
  several types of heart failure are associated with significant reductions in
myocardial concentration of Na+-K+-ATPase
5
Na+, K+ - ATPase Pump
(Sodium Pump)
Na+, K+ - ATPase Pump
142 mEq/L
4 mEq/L
extracellular
K+
  composed of two subunits
  alpha subunit (~113 kD): it binds ATP and
both sodium and potassium ions, and
contains the phosphorylation site
intracellular
  beta subunit (~35 kDa glycoprotein):
absolutely necessary for activity of the
complex
  several isoforms of both alpha and beta
subunits have been identified
Cl-
Na+
Outside
+++++++++++++++++++++++++++++++++++
-------------------------------------
A-
3 Na+
Cl-
K+
Na+
Inside
14 mEq/L
140 mEq/L
2
K+
Na+, K+- ATPase Pump
Jens Christian Skou
(danish)
1997: Nobel prize
Action Potential
K+
Action Potential
Cl- Na+
Outside
+++++++++++++++++++++++++++++++++++
------------------------------------Na+
AK+ Cl
Inside
Action Potential
Action Potential
Na+
Outside
+++++++++++++++++- - - - - - - ++++++++++++
- - - - - - - - - - - - - - - - - - +++++++- - - - - - - - - - - -
K+
Inside
Na+
Outside
+++++++++++++++++- - - - - - - ++++++++++++
- - - - - - - - - - - - - - - - - - +++++++- - - - - - - - - - - 3 Na+
+
Inside
K
2 K+
Na+, K+- ATPase Pump
6
Course of the Action Potential
•  The action potential begins with a partial depolarization (e.g.
from firing of another neuron ) [A].
•  When the excitation threshold is reached there is a sudden
large depolarization [B].
•  This is followed rapidly by repolarization [C] and a brief
hyperpolarization [D].
•  There is a refractory period immediately after the action
potential where no depolarization can occur [E]
+40"
Membrane
potential 0"
(mV)"
[C]"
[B]"
[A]"
[E]
[D]"
excitation threshold!
-70"
0"
1"
2"
3"
Time (msec)"
7