6.021/Notes/2006-10-25

Hodgkin-Huxley

• 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]