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Today Review membrane potential What establishes the ion distributions? What confers selective permeability? Ionic basis of membrane potential
Next Lectures Action Potentials
• Membrane Potential– Inside of cell is negative compared to outside
– Depends on:– High concentration K+ inside– Selective permeability of membrane
What causes the different ion distributions in cells?
1. Passive distribution – Donnan equilibrium
2. Active Transport
Passive distribution – Donnan equilibrium
• The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions
III
K+
Cl-
III
[K+] = [K+]
[Cl-] = [Cl-]
Start Equilibrium
Donnan Equilibrium
• Mathematically expressed:
•Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane
[ ] [ ]
[ ] [ ]I II
II I
K Cl
K Cl
Passive Distribution• BUT, in real cells there are a large number of
negatively charged, impermeable molecules (proteins, nucleic acids, other ions)
• call them A-
III
K+
Cl-
Start
A- III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A-
Passive Distribution
III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A- [K+]I = [A-]I + [Cl-]I
[K+]II = [Cl-]II
If [A-]I is large, [K+]I must also be large
+’ve = -’ve+’ve = -’ve
space-charge neutrality
• The presence of impermeable negatively charged molecules requires more positively charged molecules inside the cell.
Donnan Equilibrium Example
A- = 100
K+ = 150
Cl- = 50
A- = 0
K+ = 150
Cl- = 150
III
Initial Concentrations
Are these ions in electrochemical equilibrium?No,EK
+ = 0 mVECl
- = -27 mV
150 150
150 50
X X
X X
Solve for X, 7500 + 200X + X2 = 22500 - 300X + X2
X=30
[ ] [ ]
[ ] [ ]I II
II I
K Cl
K Cl
Let X be the amount of K+ and Cl- thatmoves
A- = 100
K+ = 180
Cl- = 80
A- = 0
K+ = 120
Cl- = 120
III
Final Concentrations
Are these ions in electrochemical equilibrium?Yes,EK
+ = -10 mVECl
- = -10 mV
space-charge neutrality
What causes the different ion distributions in cells?
1. Passive distribution – Donnan equilibrium
2. Active Transport
Active Transport
• ATP-powered pumps– Proteins that are capable of pumping ions
from one side of the cell membrane to the other
– Use energy
Active Transport
• Na+ - K+ pump– 3 Na+ move out– 2 K+ move in– Hydrolyzes ATP
• Maintains the concentration gradient
Active Transport
• Na+ - K+ pump
outside
inside3 Na+
2 K+
Electrogenic• net loss of 1 positive charge from inside• Inside becomes more negative • contributes a few mV to resting potential
• Na+/K+ pump is required– Due to low permeability for Na+ to leak into
the cell– Without pump,
Gradual accumulation of +’ve charge insideEventually lose the membrane potential
Active ingredient in rodent poison, ouabain, poisons the Na/K pump
What causes the different ion distributions in cells?
1. Passive distribution – Donnan equilibrium
2. Active Transport
What confers selective permeability?
Ion channels
– Non-gated
– Leakage channels
– Open at rest – allow K+ to flow out
along its concentration gradientK+
Membrane Potential Summary
1. Selective permeability• Ion channel – K+ leak channel
2. Unequal distribution of ions• Passive distribution (Donnan)• Active transport – Na+/K+ pump
3. The equilibrium potential of each ion is described by the Nernst equation
4. The total membrane potential is described by the Goldman equation
K+ 140 5 -84 mV
Na+ 10 120 +63 mV
Cl- 4 110 -83 mV
Ca2+ 0.001 5 +107 mV
Outside (mM)
Equilibrium(Nernst) PotentialInside (mM)
Mammalian Cell
Is the resting membrane potential controlled by one ion, or several?
• Do an experiment– Measure membrane potential (Vm) of a cell– Change extracellular concentration of an ion
in the bathing solution
– If Vm really depends on Eion than Vm should change as Eion changes
Measuring Membrane Potential
cell
microelectrodeamplifier
0 mV
-80 mVtime
Resting potentialReferenceelectrode
Expt #1vary extracellular Na
Assume [Na]in = 10 mM1 -58 mV
5 -17
10 0
20 17
100 58
200 75
[Na]out
[ ]0.058log
[ ]
outNa
in
NaE
Na
prediction
1 52 10 20 50 100 200
External Na+ concentration (mM)
Mem
bra
ne P
ote
nti
al (
mV
)Prediction of ENa
From Nernst equation
-120
-100
-80
-60
-40
20
0
40
-20
Measured Vm
Expt #2vary extracellular K
• Assume intracellular [K] = 140 mM
1 -124mV
5 -84
10 -66
20 -49
100 -8
200 9
Extracell [K][ ]
0.058log[ ]
outK
in
KE
K
prediction
1 52 10 20 50 100 200
External K+ concentration (mM)
Mem
bra
ne P
ote
nti
al (
mV
)
Prediction of EK
From Nernst equation
Deviation at low [K+] due to slightpermeability of Na+
-120
-100
-80
-60
-40
-20
0
Measured Vm
• Therefore, the resting membrane potential (Vm) is very close to the equilibrium potential for K+ (EK)
Summary
1. At rest PK>>PNa, PCl, PCa
2. Therefore, at rest, the membrane potential is close to EK
3. In general, the membrane potential will be dominated by the equilibrium (Nernst) potential of the most permeable ion
Sample Question
K = 140Na = 10Cl = 30
K = 5Na = 145Cl = 110
At rest Vm of this typicalcell is -75 mV. What would Vm be if PNa >> Pk,PCl?
Answer: Calculate ENa using Nernst equation.Assume Vm ENa = +67 mV