$\hbox{GABA}_B$

GABA-B is a much more complex receptor. It involves so-called second messengers. For the other three receptors, the receptor and the ion channel are part of the same protein complex. GABA-B responses occur when the GABA binds to another compound (the G-protein) which in turn binds to a potassium channel and opens it up. It takes 4 of the activated G-proteins to open the channel. For this reason, we must use a second order kinetic scheme to properly model the GABA-B dynamics. The equations are:

$$I_{GABA_B} = \bar{g}_{GABA_B} \frac{s^n}{s^n+K_d} (V-E_K)$$

$$\frac{dr}{dt} = \alpha [T](1-r) - \beta r$$

$$\frac{ds}{dt} = K_3 r -K_4 s$$

where n=4, K_d=5, $\alpha=.09\ mM^{-1} ms^{-1}$, $\beta=.0012 \ ms^{-1}$, $K_3 = .18 \ ms^{-1}$, and $K_4=.034 \ ms^{-1}.$