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  • 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