Electrophysiology 3. The Hodgkin-Huxley model of the action potential

Question 1

What is known by the 1950s?

Answer 1

• negative resting potential
• high internal [K]
• Na needed for nerve and muscle excitability

Question 2

Describe the cell membrane as an electrical circuit

Answer 2

• in steady state (resting Vm) no net inward or outward current.
• ignoring other ionic currents to simplify = IK + INa = 0
• substituting in the ionic currents:
  
  • IK = gK (Vm - EK)
  • INa = gNA (Vm - ENa)
• We get: gK (Vm - EK) + gNa (Vm -ENa) = 0
• Solving for Vm = (ENa x gNa) + (EK x gK)/ gNa + gK

Question 3

Rationale for voltage clamp

Answer 3

-developed by Cole, Hodgkin, Huxley, katz and others 1940s-50s
-reasoned that if Vm could be held clamped at any desired test voltage
-then I ion could be measured and hence g ion determined for that voltage
I ion = g ion (Vm - E ion)

Question 4

Voltage clamp: measuring the ionic currents of the AP

Answer 4

• Clamp Vm to some value that would normally be above threshold
• As membrane ‘tries’ to generate AP, a feedback circuit rapidly detects deviations from the clamp value and injects current to cancel this out
• These currents are equal (and opposite) to the ionic currents flowing across the membrane

Question 5

Action potential: the ionic permeability hypothesis

Answer 5

• the permeability changes during the AP probably consist of a rapid but transient increase in the permeability to sodium and a delayed increase in the permeability to potassium
• it’s suggested that both permeability changed vary with membrane potential in a graded but reversible manner (Hodgkin, 1951)
• Membrane potential Vm, controls g values
• Na channels; low probability of open at rest
• Open probability increases as V in membrane voltage increase in the direction

Question 6

What membrane properties are time dependent?

Answer 6

Membrane capacitance which slows change in membrane not as Vm change

Question 7

Introducing the dimension of time

Answer 7

-total current across the membrane includes an ionic component and a capacitive component

Im = I ion + I C

the capacitative current: I C = C M dVM/dt

Question 8

What is dVm/dt?

Answer 8

-time-derivative of Vm
-can be approximated as change in Vm/change in time
-provided the time step change in time is sufficiently small
change in VM = change in time (I M - I ion)/Cm

Question 9

How to test the ionic permeability hypothesis?

Answer 9

-lonic current is conductance x driving force
Ik = gk(Vm - Ek)
INa =gNa (Vm - ENa)

-Need to measure gion to show V-dependence, then work out lion for any Vm:
change in Vm = change in t (Im - lion) / Cm

-Problem: Vm is changing due to changes in both I and g. impossible to know the underlying changes in I and g during AP from measurement of Vm

Question 10

Ionic current as a function of Vm

Answer 10

Early inward current:
Depends on both driving force and gNa, which in turn is V-dependent
/ Na = g Na (Vm - ENa)

For any Vm g Na can be determined from current measurements
g Na = / Na / (Vm - ENa)

Question 11

Describe voltage dependent activation

Answer 11

Membrane conductance changes are time- and voltage-dependent

• Measure time course of INa and /k from V-clamp
  Sodium conductance (mV)
  Potassium conductance (mV)
  series
• Calculate conductance changes (dots)
• Derive equations for conductance as function of time and Vm (fitted curves)
• Means lion can be worked out for each small time step change in Vm
  Vm = At (/m - lion) / Cm

1. Work out lion for Vm at time t using equations for gion
2. Calculate AVm
3. Vm in next At is Vm + AVm
4. Repeat

Voltage values are step size from resting Vm Note that gNa shows both activation and inactivation with a step change in Vm

Question 12

Describe voltage-dependent inactivation

Answer 12

see graphs

Question 13

What’s the relationship between the sodium pump (Na/K ATPase) and the action potential?

Answer 13

maintains ionic equilibrium potenitals

Question 14

What would happen to the AP waveform if there was voltage-dependent activation of both Na and K channels, but no V-dependent inactivation of Na channels?

Answer 14

x

Question 15

Voltage-gated Na channels show V-dependent activation and V-dependent inactivation, but V-gated K channels show only V-dependent activation. Why?

Answer 15

Membrane potential is positive = K puts Vm down so no inactivation needed = NEGATIVE FEEDBACK

Question 16

What is the rationale for voltage clamp? Explain how data from voltage so no clamp experiments enabled reconstruction of the action potential.

Answer 16

x

Question 17

Hyperkalemia

Answer 17

-changes in resting membrane
-change in equilibrium potential

K: activation (open) -> inactivation (blocked) -> deactivation (closed)

Na: activated (open) <=> deactivation (closed)