Dynamical Systems in Neuroscience:

144 Conductance-Based Models0I=0inactivation, h0.20.40.6-50-60-700 time, ms 1000h-nullcline0V-nullcline0.80.06-70 -60 -5010I=-1inactivation, h0.20.40.6-50-60-700 time, ms 1000h-nullcline0V-nullcline0.80.06-70 -60 -501-100 -90 -80 -70 -60 -50membrane voltage, VFigure 5.8: Rest and sustained subthreshold oscillations in the I Na,p +I h -model. Parametersfor currents as in thalamocortical neurons, E Na = 20 mV, E h = −43 mV,E L = −80 mV, g L = 1.3, g Na = 0.9, and g h = 3.5.1.5 I h +I Kir -modelThe persistent Na + current, which amplifies the damped oscillations in the I Na,p +I h -model, can be substituted by the K + inwardly rectifying current I Kir to achieve thesame amplifying effect. The resulting I h +I Kir -modelleak I L IC ˙V{ }} {KirI{ }} { { }} h{= I − g L (V −E L ) − g Kir h Kir (V − E K ) − g h h(V − E h ) ,ḣ Kir = (h Kir,∞ (V ) − h Kir )/τ Kir (V ) ,ḣ = (h ∞ (V ) − h)/τ h (V ) ,can exhibit sustained subthreshold oscillations of membrane voltage via a rather weirdmechanism illustrated in Fig. 5.9. The inwardly rectifying K + current I Kir behavessimilarly to I h , except that it is an outward current. A brief hyperpolarization deinactivates(turns on) the fast outward current I Kir and produces more hyperpolarization