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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

outside

inside3 Na+

2 K+

ATP ADP + Pi

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

• Ionic basis of membrane potential

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

• Therefore,– Conclude that Vm does not follow ENa

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

• The resting membrane potential is the basis for all electrical signaling

• Next Lecture:

Action Potentials