Electrophysiology

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Beginning electrophysiology:How the resting potential is generated

•How do we know there’s a resting potential?•Its origins: ionic concentrations inside and outside cells•Ion pumps and ion channels in the membrane•K+ ions and the Nernst equation•Na+ ions and the Goldman-Hodgkin-Katz equation•The role of the Na+/K+ ATPase

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•How do we know there’s a resting potential?

•How was it first measured?

The resting potential

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Cut end of muscle

Muscle (cut in the middle)

Electrode touching cut end(i.e. intracellular)

Electrode touching intact muscle(i.e. extracellular)

Oil

Resting potential first measured by Bernstein (1902)

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•Squid giant axon

More modern approaches

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•A real squid giant axon

More modern approaches

•It’s so big you can push a wire along it!

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More modern approaches

•Methods for smaller neurones

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So how can biological tissue generate electricity?

•Our body fluids contain ions

•A solution of ions is electrically neutral: equal numbers of (+) and (–) ions

•Potential difference can be created by separating (+) and (–) ions

•Cells have a membrane: that’s where the separation happens (membrane lets some charges through and not others)

•(+) and (–) ions are separated there creating a voltage difference across the cell membrane (i.e. a membrane potential)

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Movement of ions across the membrane

•At rest: Charge separationdue to membrane:more (–) insidemore (+) outside

•During action potential:(+) charges move insideleaving excess (–) outside

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Evidence for importance of the membrane (1)

•Advance microelectrode slowly into cell•This is what happens

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Evidence for importance of the membrane (2)

•This is what happens

•Squid axon•Take away everything apart from the membrane!

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Closer look at the cell membrane

Lipid bilayer

Protein molecules

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The cytoskeleton supports the cell membrane

•A simple “fluid mosaic” membrane would have little mechanical strength•Cytoskeletal proteins e.g. actin, spectrin, ankyrin support the bilayer and attach proteins

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How do substances move across the membrane?

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How can ions cross it?- two types of proteins in the membrane

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•How is the resting potential generated?

The resting potential

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–85 mV

•This is what was known in 1902 about ions in biological tissue

Proteins: large anions

Bernstein and the resting potential

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•To create a voltage difference, the membrane has to let some ions cross and stop others from crossing•This happens if only one type of ion channel is open•Let’s see what would happen if only K+ channels are open

Bernstein and the resting potential

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•Begin with no resting potential•K+ ions would start to move randomly•More would move outwards than inwards(because there are more on the inside)

Bernstein and the resting potential

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•Inside would become negative•Outward flow would decrease, inward flow increase

+ –

Bernstein and the resting potential

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•Inside would become negative•Outward flow would decrease, inward flow increase

+ –

Bernstein and the resting potential

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•Inside would become negative•Outward flow would decrease, inward flow increase

+ –+ –

•The inside would become still more negative

Bernstein and the resting potential

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+ –+ –

Bernstein and the resting potential

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+ –+ –+ –

•Process would continue till inward and outward flows are the same: equilibrium•Movement wouldn’t stop: it would be equal and opposite

–85 mV

•This could explain the resting potential

Bernstein and the resting potential

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How to test this?•If we change the outside K+ concentration the potential ought to change

+ –+ –+ –

–85 mV

•We can predict exactly how it ought to change: if [K+]o = [K+]i, then Em should be zero

90 K+

0 mV

30 Na+

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Effect of [K+]o on the resting potential

•Measured in squid axon (using wire pushed down axon)

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Effect of [K+]o on the resting potential

•Squid axon: [K+]i = ~400 mM•So raising [K+]o does bring resting potential nearer to zero•What about a more quantitative prediction?

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The Nernst equation

•Predicts the voltage that would result from different ion concentrations•Looks like this:

•Why does it look like this?•If you want to follow this up, see the derivation on Blackboard

Em: membrane potentialR: the gas constant (8.315 J mol–1 K–1)T: absolute temperature (20 °C = 293 K)z: charge on the ion (z=1 for K+)F: Faraday’s constant (96480 C mol–1)[K+]o, [K+]o: K+ ion concentrations outside and inside cellln: natural logarithm

i

om ]K[

]K[ln

zF

RTE

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What does the Nernst equation predict?

•Prediction 1:If [K+]o < [K+]i then the inside will be negative

•Prediction 2:If [K+]i = [K+]o then Em = 0 mV

•Prediction 3:The more similar [K+]i and [K+]o are, the smaller is Em;so raising [K+]o at constant [K+]i will depolarise

i

om ]K[

]K[ln

zF

RTE

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Does the Nernst equation predict resting potential correctly?

•Back to our earlier measurements•Now we plot these: resting membrane potential against [K+]o

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Resting potential and [K+]o

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•Nernst equation is good at high [K+]o, but not at low [K+]o

•How to account for this?•The membrane is also permeable to Na+

Resting potential and [K+]o

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+ –+ –+ –

–85 mV

+ –+ –

–65 mV

•More Na+ enters than leavesbecause of the concentration gradient and the inside negativity•The cell becomes less negative inside

Effect of the sodium permeability

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becomes the Goldman-Hodgkin-Katz (GHK) equation:

...how can we picture this in physical terms?

The Nernst equation with Na+ permeability

The Nernst equation:

i

om ]K[

]K[ln

zF

RTE

iNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

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+ –+ –

–65 mV

What does the GHK equation mean?

Goldman-Hodgkin-Katz (GHK) equation:

Inward fluxes

Outward fluxesiNaiK

oNaoKm ]Na[]K[

]Na[]K[ln

PP

PP

zF

RTE

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Does this account for the deviation?

•Deviation from Nernst prediction at low [K+]o

is accounted for well by permeability to Na+

•(The GHK equation is a good fit)

GHK prediction

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+ –+ –+ –

–85 mV

+ –+ –

–65 mV

•There is a net gain of Na+

It’s no longer equilibrium...

•and a net loss of K+

•So how does the cell avoid running down?37

Ionic pumping

Passive ionic fluxes

Active pumping

•Passive fluxes of K+ (out) and Na+ (in)are balanced by the Na+/K+ ATPase

•It pumps Na+ out and K+ in

•This keeps ionic concentrations stable

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Ionic pumping is electrogenic(i.e. it changes membrane potential)

3 Na+2 K+

Na+/K+ ATPase

•Two K+ ions move in but 3 Na+ ions go out:So the pumping creates a current

•(+) charge moves out:Inside becomes more negative

•This makes resting potential more negative than GHK prediction

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How ionic pumping affects resting potential

•Recorded from a mollusc neurone

•4 °C: Na+/K+ ATPase is inactive: GHK prediction fits well

•17 °C: Na+/K+ ATPase is active: deviation from GHK prediction - membrane potential is more negative

?

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Summary: 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

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Reading for today’s lectures:

•Purves et al chapter 2

Further reading:•Nicholls et al chapter 5•Kandel et al chapter 7

Next lecture: The action potential

Reading for next lecture:•Purves et al chapter 2 (later part on action potential)

Further reading:•Nicholls et al pages 26-31, 62-63, 91-93

•Kandel et al chapter 842