6.021/Notes/2006-10-30

Hodgkin-Huxley

• state variables: [math]\displaystyle{ m, n, h, V_m }[/math]
• using [math]\displaystyle{ m(t_0), n(t_0), h(t_0), V_m(t_0) }[/math] and the input [math]\displaystyle{ J_m(t) }[/math] for [math]\displaystyle{ t\gt t_0 }[/math], we can propagate into the future to calculate all of the variables
• For example, [math]\displaystyle{ \frac{dm}{dt}=\frac{m_\infty(V_m)-m(V_m,t)}{\tau_m(V_m)} }[/math]
• To calculate next value of the membrane potential, solve the circuit model
• If you run the HH model by appyling a current, you get an action potential!
• Response to current pulse:
  1. [math]\displaystyle{ J_m \rightarrow \Delta V_m }[/math]
  2. [math]\displaystyle{ V_m\uparrow \rightarrow m\uparrow \rightarrow G_{Na}\uparrow \rightarrow V_m\uparrow }[/math] (positive feedback)
     • Both [math]\displaystyle{ m }[/math] and [math]\displaystyle{ V_m }[/math] increase about exponentially until [math]\displaystyle{ V_m }[/math] about the max ([math]\displaystyle{ V_{Na} }[/math])
  3. Negative feedback until membrae potential drops to below rest
     • [math]\displaystyle{ V_m \gt V_m^o \rightarrow n\uparrow \rightarrow G_K\uparrow \rightarrow V_m\downarrow }[/math]
     • [math]\displaystyle{ V_m \gt V_m^o \rightarrow h\downarrow \rightarrow G_{Na}\downarrow \rightarrow V_m\downarrow }[/math]
  4. n & h need to be reset to original values. Explains why action potential is refractory
• Put HH model of membrane behavior into core conductor model
• assume constant speed of propagation
  • As speed of propagation not part of HH model, guess/fit
• The Hodgkin-Huxley model can account for decrement-free conduction