# 6.021/Notes/2006-11-06

### From OpenWetWare

## Threshold in Hodgkin-Huxley model

- threshold is sharp
- change in 10
^{ − 8}− 10^{ − 14}can change AP to non-AP in model - determine threshold in model
- asssume n & h are so slow that and
- Also m is so fast that
- The potassium current is constant as the the potassium conductance doesn't change
- Find that there are 2 stable equilibrium points and 1 unstable point
- The unstable point is the threshold voltage
- We can relax assumption that m is instant and instead obeys the standard HH model for m
- Make phase plane showing m vs
*V*_{m} - To be at equilibrium, must be on isoclines
- These two lines again cross 3 times, with one point being unstable

- The separatrix curve in
*m*−*V*_{m}space determines whether will go to rest or*V*_{Na} - So threshold depends on both m and
*V*_{m} - If instead of fixing h to , we set it to another value, as h decreases, the isoclines change such that thresholds increase until a point when the curves only intersect once at rest
- This explains the relative and absolute refractory period
- The relative refractory period is characterized by higher threshold
- During the absolute refractory period it is impossible to reach threshold no matter the amount of stimulus