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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 [math]\displaystyle{ G_{Na} }[/math] increases or [math]\displaystyle{ G_{K} }[/math] decreases to increase membrane potential towards [math]\displaystyle{ V_{Na} }[/math]
    • experimental data indicates [math]\displaystyle{ G_{Na} }[/math] 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 [math]\displaystyle{ V_m(z,t) \rightarrow V_m(t) }[/math]
  • 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 [math]\displaystyle{ V_m(t) \rightarrow J_m(t) }[/math]
    4. run circuit backwards [math]\displaystyle{ J_m(t) \rightarrow V_m(t) }[/math]
      • 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 ~1[math]\displaystyle{ \mu }[/math]F/cm[math]\displaystyle{ {}^2 }[/math]
    • 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 [math]\displaystyle{ V_m^f }[/math] (final value of the voltage step)
    • persistent outward current increases
    • transient inward current becomes transient outward current
    • flips about +57mV, close to [math]\displaystyle{ V_{Na} }[/math]
      • transient part likely due to Na
    • Set [math]\displaystyle{ V_m^f=V_{Na} }[/math] so that the sodium current must be 0. The response then is [math]\displaystyle{ J_K }[/math].
    • To get [math]\displaystyle{ J_{Na} }[/math], keep the membrane potential the same but change [math]\displaystyle{ c^o_{Na} }[/math] which changes [math]\displaystyle{ V_{Na} }[/math]