6.021/Notes/2006-10-30

Hodgkin-Huxley

 * state variables: $$m, n, h, V_m$$
 * using $$m(t_0), n(t_0), h(t_0), V_m(t_0)$$ and the input $$J_m(t)$$ for $$t>t_0$$, 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:
 * $$J_m \rightarrow \Delta V_m$$
 * $$V_m\uparrow \rightarrow m\uparrow \rightarrow G_{Na}\uparrow \rightarrow V_m\uparrow$$ (positive feedback)
 * Both $$m$$ and $$V_m$$ increase about exponentially until $$V_m$$ about the max ($$V_{Na}$$)
 * Negative feedback until membrae potential drops to below rest
 * $$V_m > V_m^o \rightarrow n\uparrow \rightarrow G_K\uparrow \rightarrow V_m\downarrow$$
 * $$V_m > V_m^o \rightarrow h\downarrow \rightarrow G_{Na}\downarrow \rightarrow V_m\downarrow$$
 * 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