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 1
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Previous lecture: three determinants of resting potential Major role for K + ions which is described by the Nernst equation This describes a true equilibrium.
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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
•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