# Lect4

```• Announcements
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
Start
I
Equilibrium
II
K+
Cl-
I
II
[K+] = [K+]
[Cl-] = [Cl-]
Donnan Equilibrium
• Mathematically expressed:

[ K ]I

[ K ] II


[ C l ] II

[C l ]I
•Another way of saying the number of positive charges
must equal the number of negative charges on each side
of the membrane
Passive Distribution
• BUT, in real cells there are a large number of
negatively charged, impermeable molecules
(proteins, nucleic acids, other ions)
• call them AStart
I
AK+
Cl-
Equilibrium
II
I
A[K+] > [K+]
[Cl-] < [Cl-]
II
Passive Distribution
Equilibrium
I
A-
II
[K+]
>
[Cl-]
< [Cl-]
+’ve = -’ve
[K+]
[K+]I = [A-]I + [Cl-]I
[K+]II = [Cl-]II
If [A-]I is large, [K+]I must
also be large
+’ve = -’ve
space-charge neutrality
• The presence of impermeable negatively
charged molecules requires more
positively charged molecules inside the
cell.
Donnan Equilibrium Example
Initial Concentrations
I
II
A- = 100
A- = 0
K+ = 150
K+ = 150
Cl- = 50
Cl- = 150
Are these ions in electrochemical equilibrium?
No,
EK+ = 0 mV
ECl- = -27 mV

[ K ]I



[ C l ] II

[ K ] II
[C l ]I
150  X
150  X
150  X

Let X be the amount
of K+ and Cl- that
moves
50  X
Solve for X, 7500 + 200X + X2 = 22500 - 300X + X2
X=30
Final Concentrations
I
II
A- = 100
A- = 0
K+ = 180
K+ = 120
Cl- = 80
Cl- = 120
space-charge neutrality
Are these ions in electrochemical equilibrium?
Yes,
EK+ = -10 mV
ECl- = -10 mV
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
2 K+
outside
inside
3 Na+
ATP
Active Transport
• Na+ - K+ pump
– 3 Na+ move out
– 2 K+ move in
– Hydrolyzes ATP
Active Transport
• Na+ - K+ pump
2 K+
outside
inside
3 Na+
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 inside
Eventually 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
K+
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
• Ionic basis of membrane potential
Mammalian Cell
Inside (mM)
Outside (mM)
Equilibrium
(Nernst)
Potential
K+
140
5
-84 mV
Na+
10
120
+63 mV
Cl-
4
110
-83 mV
Ca2+
0.001
5
+107 mV
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
amplifier
microelectrode
Reference
electrode
Resting potential
0 mV
cell
-80 mV
time
Expt #1
vary extracellular Na
[Na]out
Assume [Na]in = 10 mM
1
5
10
20
100
200
prediction
E N a  0.058 log
[ N a ]out
[ N a ]in
-58 mV
-17
0
17
58
75
40
Membrane Potential (mV)
20
0
-20
Prediction of ENa
From Nernst equation
-40
-60
-80
-100
-120
Measured Vm
1
2
5
10
20 50 100
200
External Na+ concentration (mM)
• Therefore,
– Conclude that Vm does not follow ENa
Expt #2
vary extracellular K
Extracell [K]
• Assume intracellular
[K] = 140 mM
1
5
10
20
100
200
prediction
E K  0.058 log
[ K ]out
[ K ]in
-124mV
-84
-66
-49
-8
9
Membrane Potential (mV)
Deviation at low [K+] due to slight
permeability of Na+
0
-20
Prediction of EK
From Nernst equation
-40
-60
-80
-100
-120
Measured Vm
1
2
5
10 20 50 100 200
External K+ concentration (mM)
• 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
At rest Vm of this typical
cell is -75 mV. What would
Vm be if PNa >> Pk,PCl?
K = 140
Na = 10
Cl = 30
K=5
Na = 145
Cl = 110
Calculate ENa using Nernst equation.
Assume Vm ENa = +67 mV
• The resting membrane potential is the
basis for all electrical signaling
• Next Lecture:
Action Potentials
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