Dynamical Systems in Neuroscience:

Excitability 2557.2.8 Inhibition-induced spikingIn Fig. 7.32, top, we use the I Na,t -model introduced in Chap. 5 to illustrate an interestingproperty of some resonators — inhibition-induced spiking. Recall, that the modelconsists of an Ohmic leak current and a transient Na + current with instantaneous activationand relatively slow inactivation kinetics. It can generate action potentials dueto the interplay between the amplifying gate m and the resonant gate h.We widened the activation function h ∞ (V ) so that Na + current is largely inactivatedat the resting state; see the inset in Fig. 7.32. Indeed, h = 0.27 when I = 0. Eventhough such a system is excitable, it cannot fire repetitive action potentials when apositive step of current, e.g., I = 10, is injected. Depolarization produced by theinjected current inactivates Na + current so much that no repetitive spikes are possible.Such a system is Class 3 excitable.Remarkably, injection of a negative step of current, e.g., I = −15 in the figure,results in a periodic train of action potentials! How is it possible? Inhibition-inducedspiking or bursting are possible in neurons having slow h-current or T-current, such asthe thalamo-cortical relay neurons. (We discuss these and other examples in the nextchapter.) The I Na,t -model does not have such currents, yet it can fire in response toinhibition.Figure 7.33 summarizes the ionic mechanism of inhibition-induced spiking. Theresting state in the model corresponds to the balance of the outward leak current anda partially activated, partially inactivated inward Na + current. When the membranepotential is hyperpolarized by the negative injected current, two processes take place:Na + current deinactivates (variable h increases), and deactivates (variable m = m ∞ (V )decreases). Since m ∞ (V ) is flatter than h ∞ (V ), deinactivation is stronger than deacti-K + activation gate10 mV1 msinhibitorypulseexcitatorypulseinhibitorypulseexcitatorypulse-60 -40 -20membrane potential, mVFigure 7.31: Post-inhibitory facilitation: A subthreshold excitatory pulse can becomesuperthreshold if it is preceded by an inhibitory pulse.