Dynamical Systems in Neuroscience:

146 Conductance-Based Models0I=9.750I=100.10.1inactivation, h0.20.3h-nullcline-50-600 time, s 2-70 -65 -60 -55 -50 -45membrane voltage, VV-nullclineinactivation, h0.20.3h-nullcline0 time, s 2-70 -65 -60 -55 -50 -45membrane voltage, VFigure 5.10: Rest and sustained subthreshold oscillations in the I h +I Kir -model. Parameters:E K = −80 mV, E h = −43 mV, E L = −50 mV, g Kir = 4, g h = 0.5, g L = 0.44.h-current is the same as in the previous section, except V 1/2 = −65 mV. InstantaneousI Kir has V 1/2 = −76 mV and k = −11.-50-60V-nullclinehyperpolarizationdeactivationof I Kinjecteddc-currentactivationof I Kinactivationof I KirdepolarizationFigure 5.11: Mechanism of generation of sustainedvoltage oscillations in the I K +I Kir -model.many biologists: How can a neuron with only outward K + currents and no inward Na +or Ca 2+ currents fire action potentials?In the I K +I Kir -modelI KirIC ˙V{ }} { { }} K{= I − g Kir h(V − E K ) − g K n(V − E K ) ,ṅ = (n ∞ (V ) − n)/τ n (V ) ,ḣ = (h ∞ (V ) − h)/τ h (V ) ,the amplifying current is I Kir with inactivation gating variable h, and the resonantcurrent is I K with activation variable n. The mechanism of generation of action potentialsis summarized in Fig. 5.11. A strong injected current depolarizes the membranepotential and inactivates (turns off) I Kir , which amplifies the depolarization. Whiledepolarized, the slower K + current I K activates and brings the potential down withpossible hyperpolarization, which is amplified by the deinactivation of I Kir . While themembrane potential is hyperpolarized, I K deactivates and the strong injected current