6.021/Notes/2006-10-30

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Hodgkin-Huxley

  • state variables: m,n,h,Vm
  • using m(t0),n(t0),h(t0),Vm(t0) and the input Jm(t) for t > t0, we can propagate into the future to calculate all of the variables
  • For example, \frac{dm}{dt}=\frac{m_\infty(V_m)-m(V_m,t)}{\tau_m(V_m)}
  • 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. J_m \rightarrow \Delta V_m
    2. V_m\uparrow \rightarrow m\uparrow \rightarrow G_{Na}\uparrow \rightarrow V_m\uparrow (positive feedback)
      • Both m and Vm increase about exponentially until Vm about the max (VNa)
    3. Negative feedback until membrae potential drops to below rest
      • V_m > V_m^o \rightarrow n\uparrow \rightarrow G_K\uparrow \rightarrow V_m\downarrow
      • V_m > V_m^o \rightarrow h\downarrow \rightarrow G_{Na}\downarrow \rightarrow V_m\downarrow
    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
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