Electrophysiology 3. The Hodgkin-Huxley model of the action potential Flashcards
What is known by the 1950s?
- negative resting potential
- high internal [K]
- Na needed for nerve and muscle excitability
Describe the cell membrane as an electrical circuit
- 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
Rationale for voltage clamp
-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)
Voltage clamp: measuring the ionic currents of the AP
- 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
Action potential: the ionic permeability hypothesis
- 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
What membrane properties are time dependent?
Membrane capacitance which slows change in membrane not as Vm change
Introducing the dimension of time
-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
What is dVm/dt?
-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
How to test the ionic permeability hypothesis?
-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
Ionic current as a function of Vm
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)
Describe voltage dependent activation
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
- Work out lion for Vm at time t using equations for gion
- Calculate AVm
- Vm in next At is Vm + AVm
- Repeat
Voltage values are step size from resting Vm Note that gNa shows both activation and inactivation with a step change in Vm
Describe voltage-dependent inactivation
see graphs
What’s the relationship between the sodium pump (Na/K ATPase) and the action potential?
maintains ionic equilibrium potenitals
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?
x
Voltage-gated Na channels show V-dependent activation and V-dependent inactivation, but V-gated K channels show only V-dependent activation. Why?
Membrane potential is positive = K puts Vm down so no inactivation needed = NEGATIVE FEEDBACK
