# 6.021/Notes/2006-10-30

## 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