# 6.021/Notes/2006-11-27

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## Ion channels

- Gate model
- α: rate of opening
- β: rate of closing

- Theory of absolute reaction rates (Arrhenius)
- potential energy of open ([math]E_O[/math]), closed ([math]E_C[/math]), and intermediate barrier state ([math]E_B[/math])
- [math]\alpha=Ae^{(E_C-E_B)/kT}[/math]
- [math]\beta=Ae^{(E_O-E_B)/kT}[/math]

- If gate has some charge, the potential energy can be function membrane potential
- If assume simple voltage dependence, get similar looking rates as parameters in Hodgkin-Huxley model
- As gate moves, its charge moves, so have extra
**gating current** - [math]q_g[/math]: gating charge
- [math]i_g = \frac{d}{dt}q_g[/math]
- [math]\tilde{i}_g = \frac{d}{dt}\tilde{q}_g[/math]
- [math]\tilde{q}_g[/math] is 0 or Q
- [math]\tilde{i}_g[/math] is impulses of amplitude Q up and down
- At steady state, average of [math]\tilde{i}_g = 0[/math]
- [math]q_g = Qx[/math]
- [math]i_g = E[\tilde{i}_g] = E[\frac{d}{dt}\tilde{q}_g] = \frac{d}{dt}E[\tilde{q}_g] = \frac{d}{dt}Qx = Q\frac{dx}{dt}[/math]
- To measure gating current, disable the ion channel (ionic current)
- Have to separate out capacitance current which is much larger
- Gating current is non-linear while capacitance current is linear so can sum response to equal step up and step down to cancel out capacitive current and leave gating current