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  • squid giant axon
  • action potentials don't depend on pumps (can knock them out and still have AP)
  • for action potential, either GNa increases or GK decreases to increase membrane potential towards VNa
    • experimental data indicates GNa goes up
    • but which is cause and which is effect? does action potential cause change in sodium conductance or does change in sodium conductance cause action potential?
  • Space clamp (Curtis)
    • converts 2D to 1D V_m(z,t) \rightarrow V_m(t)
  • Voltage clamp (Hodgkin)
    • Takes space clamp but also fix membrane voltage
    • Can't have action potential if voltage is fixed, but can study membrane response
    • Responses are all graded
  • General strategy of Hodgkin-Huxley
    1. apply voltage step
    2. measure response
    3. make circuit model V_m(t) \rightarrow J_m(t)
    4. run circuit backwards J_m(t) \rightarrow V_m(t)
      • see if get action potential (and win Nobel prize)
  • A voltage step leads to an impulse of current
    • looks like a a capacitor's response
    • membrane is like capacitor ~1μF/cm2
    • capacitive response is linear so can subtract it by adding response to depolarizing step with an equal hyperpolarizing step
    • this gives the non-capacitive response
  • As increase V_m^f (final value of the voltage step)
    • persistent outward current increases
    • transient inward current becomes transient outward current
    • flips about +57mV, close to VNa
      • transient part likely due to Na
    • Set V_m^f=V_{Na} so that the sodium current must be 0. The response then is JK.
    • To get JNa, keep the membrane potential the same but change c^o_{Na} which changes VNa
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