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Measuring Membrane Potential
amplifier
microelectrode
Reference
electrode
Tutorial
Membrane potentials
and ion channels
Resting potential
0 mV
cell
-80 mV
Bathing solution
time
Resting Membrane Potential
• How is it generated?
1. differential distribution of ions inside
and outside the cell
1. How does unequal concentration of ions
give rise to membrane potential ?
2. Selective Permeability of the
membrane to some ions
1
Equal concentrations of ions
Unequal concentrations of ions
0 volts Artificial ion selective
voltmeter
-
membrane (only K+, not Cl-)
I
Cl-
II
K+
0.01 M
KCL
+
Ion selective membrane
(only K+, not Cl-)
I
Cl-
K+
Cl-
K+
Cl-
II
0.1 M
KCL
0.01 M
KCL
Cl-
Cl-
K+
Initial
K+ ClCl-
K+
Cl-
New Equilibrium
Cl-
K+
Cl-
K+
Cl-
Cl-
K+
Cl-
K+
Cl-
K+
K+
CHEMICAL
Cl-
K+
Cl-
Cl-
K+
ClCl-
+K+
+
+ K+
+
Cl-
ClCl-
+
+K
+K
+
Cl-
CHEMICAL
Cl-
K+
K+
K+
No net movement
K+
K+
Cl-
K+
0.01 M
KCL
volts
ClCl-
K+
K+ concentration
gradient
Unequal concentrations of ions
• Initial diffusion of K+ down concentration
gradient from I to II
• This causes + charge to accumulate in II
because + and - charges are separated
– Remember that Cl- can’t cross the
membrane !
• Therefore II becomes positive relative to I
ELECTRICAL
2
Equilibrium Potential
•
As II becomes +, movement of K+ is repelled
•
•
Every K+ near the membrane has two
opposing forces acting on it:
•
1. Chemical gradient
2. Electrical gradient
•
These two forces exactly balance each
other
•
Called the electrochemical equilibrium
•
The electrical potential that develops is called
the equilibrium potential for the ion.
Electrical potential at which there is no
net movement of the ion
Note:
1. only a very small number of ions actually contribute
to the electrical potential
2. the overall concentrations of K and Cl in solution do
not change.
Nernst Equation
• To calculate the equilibrium potential of any ion
(eg. K, Na, Ca,) at any concentration
– we use the Nernst Equation:
Gas Constant
Ex =
Temp (°K)
Ion Concentration I
RT [ X ]I
ln
zF [ X ]II
Equilibrium Potential
of X ion (eg. K+) in Volts
Valence of
ion (-1, +1, +2)
Ion Concentration II
Faraday constant
3
Nernst Equation
• At 18°C, for a monovalent ion, and converting to
log10 ,the equation simplifies to:
0.058
[ X[ X
]I ] I
0.058
log[ X ]II
EXEx== z log
z
[ X ] II
• By convention electrical potential inside of cells
is expressed relative to the outside of the cell
Ex =
0.058
[ X ]outside
log
z
[ X ]inside
Example: K+
in
out
0.058
[X ]I
EK =
log
z
[ X ] II
0.1 M
KCL
0.02 M
KCL
EK =
0.058
[ X ]out
log
z
[ X ]in
EK = 0.058log
0.02
0.1
• Therefore,
– initial movement of K+ down concentration
gradient
– When electrical potential of -40 mV develops,
there will be no net movement of K+
– Thus K+ is in electrochemical equilibrium
= -0.040 Volts
= - 40 mV
4
What if there is more than
one permeable ion?
in
out
0.1 M KCl
0.02 M NaCl
K+
Na+
0.01 M KCl
0.2 M NaCl
Na+
K+
K+
K+
Na+
Na+
K+
Na+
K+
Na+
• To calculate the overall potential of
multiple ions
• use the Goldman Equation
• Considers the permeability of ions and
their concentrations
Permeable to K+ and Na+, but not Cl-
Goldman equation
•
Voltage
Vm = 0.058log
Goldman equation
PK[ K ]outside + PNa[ Na ]outside + PCl[Cl ]inside
PK[ K ]inside + PNa[ Na ]inside + PCl[Cl ]outside
Permeability
Example, typical mammalian cell:
1. Assume permeability for Na is 1/100 of permeability
for K, and permeability of Cl is 0
2. Assume [K]in= 140, [K]out=5
[Na]in =10, [Na]out=120
Vm = 0.058log
Ion concentration
1[5] + 0.01[120] + 0
1[140] + 0.01[10] + 0
Because Cl is negative
Vm = −78mV
5
What confers selective
permeability?
Goldman equation
• The resting membrane potential of most
cells is predicted by the Goldman equation
Ion channels
• At rest:
– Leakage channels
– Open at rest – allow K+ to flow out
along its concentration gradient
K+
– Voltage gated channels
Summary
1. At rest PK>>PNa, PCl, PCa
2. Therefore, at rest, the membrane
potential is close to EK
•
Whether ions will flow depends on
1. Permeability
2. Electrochemical driving force
3. In general, the membrane potential will
be dominated by the equilibrium (Nernst)
potential of the most permeable ion
6
• Scenario
– Cell at rest Vm = -90 mV
– EK = -90 mV
– ENa = +50 mV
• If a K+ channel opens no ions flow since Vm =
EK
• If a Na+ channel open, Na+ will flow into the cell
because Vm≠ ENa
– +’ve charge flows into cell – depolarizes it
– When Vm= ENa Na stops going into cell
7