# 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 ($E_O$), closed ($E_C$), and intermediate barrier state ($E_B$)
• $\alpha=Ae^{(E_C-E_B)/kT}$
• $\beta=Ae^{(E_O-E_B)/kT}$
• 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
• $q_g$: gating charge
• $i_g = \frac{d}{dt}q_g$
• $\tilde{i}_g = \frac{d}{dt}\tilde{q}_g$
• $\tilde{q}_g$ is 0 or Q
• $\tilde{i}_g$ is impulses of amplitude Q up and down
• At steady state, average of $\tilde{i}_g = 0$
• $q_g = Qx$
• $i_g = E[\tilde{i}_g] = E[\frac{d}{dt}\tilde{q}_g] = \frac{d}{dt}E[\tilde{q}_g] = \frac{d}{dt}Qx = Q\frac{dx}{dt}$
• 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