6.021/Notes/2006-10-27

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Hodgkin-Huxley

  • assumed conductances on depend on membrane potential and not concentrations
    • used this to determine contribution of Na and K currents by fixing membrane potential and changing concentrations which affect Nernst potentials only
  • persistent current primarily due to K
  • transient current due to Na
  • J_{Na}(V_m,t) = G_{Na}(V_m,t) \cdot (V_m(t) - V_{Na})
  • G_{Na}(V_m,t) = \frac{J_{Na}(V_m,t)}{V_m(t) - V_{Na}}
  • G_{K}(V_m,t) = \frac{J_{K}(V_m,t)}{V_m(t) - V_{K}}
  • Vm(t) − VNa is constant for t > 0 (step in potential). Same for K
    • Thus conductances are simply scaled versions of the current
    • Fit the current responses using following parameters
  • G_{K}(V_m,t) = \overline{G_K} n^4(V_m,t) where
    • n(V_m,t) + \tau_n(V_m)\frac{dn(V_m,t)}{dt} = n_\infty(V_m)
  • G_{Na}(V_m,t) = \overline{G_{Na}} m^3(V_m,t)h(V_m,t) where
    • m(V_m,t) + \tau_m(V_m)\frac{dm(V_m,t)}{dt} = m_\infty(V_m)
    • h(V_m,t) + \tau_h(V_m)\frac{dh(V_m,t)}{dt} = h_\infty(V_m)
  • n_\infty and m_\infty are activating functions
    • are about 0 at negative Vm and has asymptote 1
  • h_\infty is the reverse. =1 for low Vm and 0 for high Vm
  • τm (time constant for activating Na) is much smaller than other time constants
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