6.021/Notes/2006-11-27

Ion channels

 * Gate model
 * &alpha;: rate of opening
 * &beta;: 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