previous lecture: three determinants of resting potential major role for k + ions which is described...

Previous lecture: three determinants of resting potential

•Major role for K+ ions which is described by the Nernst equation•This describes a true equilibrium•Deviation from Nernst prediction due to Na+ permeability•Makes resting potential less negative•Described by Goldman-Hodgkin-Katz equation•Non-equilibrium: the cell would run down were it not for the Na+/K+ ATPase•The Na+/K+ ATPase pumps more Na+ out than K+ in: makes resting potential more negative

1

Notes on the Purves chapter

•The Purves chapter has a few differences from the lectures when it explains/uses the GHK equation.

•Basic story is the same (and the maths are equivalent) – but differences in detail can be confusing.

•Please see the separate PDF file (in the resting potential section) for detailed explanation of the differences.

2

How is the action potential generated?

•Early finding: the inside becomes more positive during action potential (AP)

•Bernstein postulated that membrane selectivity breaks down:membrane can let all ions through

•This would predict membrane potential near zeroat peak of AP (no selectivityno potential)(Try working out Em using the GHK equation with PK = PNa!)

3

First action potential ever recorded:squid giant axon(Hodgkin & Huxley 1939)

What really happens

4

What really happens

•“Overshoot”

•Membrane potential becomes positive at peak of AP

•The membrane is still selective... but not for K+

•It becomes selective for Na+ 5

How would a Na+-selective membrane behave?

•Let’s suppose only Na+ can move•More Na+ enters than leaves•Inside becomes positive

– +

6

•This reduces Na+ entry and increases efflux•Inside becomes still more positive

– +– +

How would a Na+-selective membrane behave?

7

•Equilibrium is reached•Membrane potential is positive

– +– +– +

+34 mV

•Na+ selectivity generates positive equilibrium potential

How would a Na+-selective membrane behave?

8

•Even if many ions are able to go through the membrane, there is one voltage where each individual ion will be at equilibrium (i.e. where influx = efflux)•This is the equilibrium potential for that ion•Can be predicted from the Nernst equation, exactly as if it were the only permeant ion•So:

Equilibrium potentials

i

oK ]K[

]K[ln

zF

RTE

i

oNa ]Na[

]Na[ln

zF

RTE

9

+ –+ –+ –

–85 mV–85 mV

Equilibrium potentialsIt doesn’t matter what the other ions are doing!

mV85mM90

mM3ln

]K[

]K[ln

i

oK

zF

RT

zF

RTE

10

+ –+ –+ –

–85 mV–85 mV

Equilibrium potentialsIt doesn’t matter what the other ions are doing!

mV85mM90

mM3ln

]K[

]K[ln

i

oK

zF

RT

zF

RTE

•Sodium movement would be unequal at EK

•That would change the resting potential of the cell•...but it doesn’t change the equilibrium potential for K+

•...EK is where influx and efflux of K+ are equal, regardless of what other ions are doing

11

+ –+ –+ –

–85 mV–85 mV

Equilibrium potentialsIt doesn’t matter what the other ions are doing!

mV85mM90

mM3ln

]K[

]K[ln

i

oK

zF

RT

zF

RTE

•Sodium movement would be unequal at EK

•That would change the resting potential of the cell•...but it doesn’t change the equilibrium potential for K+

•...EK is where influx and efflux of K+ are equal, regardless of what other ions are doing

•Resting potential (of the whole cell)•and equilibrium potential (of a single type of ion)•are not the same thing

12

+34 mV

Equilibrium potentialsIt doesn’t matter what the other ions are doing!

mV34mM30

17mM1ln

]Na[

]Na[ln

i

oNa

zF

RT

zF

RTE

13

Evidence for the involvement of Na+

•Na+ selectivity would explain the overshoot

•How could we test this?...by changing [Na+]o

•You did this in the MEMPOT lab – now for the real experiment

14

Testing the hypothesis

•Prediction: if we reduce [Na+]o, the overshoot should be reduced•Tested by Hodgkin & Katz (1949) in squid axon•Replaced sodium with sucrose or choline

15

•Results just described suggest that increased Na+ permeability (i.e. a lot of Na+ channels opening transiently) underlies the action potential

•Goldman-Hodgkin-Katz (GHK) equation can describe it:

Conclusions about the action potential

16

iNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

iNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

•Results just described suggest that increased Na+ permeability (i.e. a lot of Na+ channels opening transiently) underlies the action potential

•Goldman-Hodgkin-Katz (GHK) equation can describe it:

Conclusions about the action potential

•At rest: PK>>PNa

•so Em near to EK

17

iNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

•Results just described suggest that increased Na+ permeability (i.e. a lot of Na+ channels opening transiently) underlies the action potential

•Goldman-Hodgkin-Katz (GHK) equation can describe it:

Conclusions about the action potential

•During AP: PNa>>PK

•so Em near to ENa

18

•Results just described suggest that increased Na+ permeability (i.e. a lot of Na+ channels opening transiently) underlies the action potential

•Goldman-Hodgkin-Katz (GHK) equation can describe it:

Conclusions about the action potential

•At any time:•Em depends on balance between PNa and PK

iNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

19

Conclusions about the action potential•Permeabilities (or conductances) shown below•Increased permeability = ion channels opening•Na+ channels open then later K+ channels•Increased K+ permeability helps to end the AP

20

Defining some terms

•Depolarising, repolarising, hyperpolarising:all defined relative to resting potential•Overshoot: defined relative to zero

21

Phases of the AP

Depolarisation(“upstroke”)

Peak

Repolarisation

Hyperpolarising afterpotential

Overshoot

22

At rest: membrane permeable to K+,i.e. K+ channels are open

What ion channels are doing:The resting potential

23

What ion channels are doing:The action potential

Na+ channels open, Na+ enters: depolarisation

24

What ion channels are doing:After the action potential

Na+ channels close, Na+ entry stops, K+ efflux increased: repolarisation

25

Conduction of the action potential

Na+ Na+ Na+ Na+ Na+ Na+

26

Current through a single Na+ channel from a human axon

closed

open

–90 mV

-60 mVVoltage (Em)

Current

Depolarisation opens the channel:activation

It closes again spontaneously:inactivation

27

Positive feedback during AP

28

...like an explosion

29

Reading for today’s lecture:

Action potential•Purves et al chapter 2 (page 37 onwards)•Nicholls et al pages 26-31, 62-63, 91-93

•Kandel et al chapter 8

Next lecture: Axon types and functions; conduction in myelinated axons

Reading for next lecture:•Purves et al chapter 3 (page 49 onwards)•Purves et al chapter 9 (pages 189-194)

•Nicholls et al pages 121-126