Dynamical Systems in Neuroscience:

Excitability 23720 mV50 msaverage firing frequency, Hz25020015010050F-I curveClass 2 excitabilitynoisewithwithout noise00 500 1000 1500injected dc-current, I (pA)Figure 7.12: Examples of noise-induced low-frequency firings of Class 2 excitable system.The F-I curve may look like the one for Class 1 excitability. Shown are recordingsof brainstem mesV neuron.neuro-computational property: Bistable systems can be switched from one state tothe other by an appropriately timed brief stimulus. Rinzel (1978) predicted such abehavior in the Hodgkin-Huxley model, and then bistability and hysteresis were foundexperimentally in the squid axon (Guttman et al. 1980). What was really surprisingfor many neuroscientists is that neurons can be switched from repetitive spiking toresting by brief depolarizing shock-stimuli.This phenomenon is illustrated in Fig. 7.11. Each shaded area in the figure denotesthe attraction domain of a spiking limit cycle attractor. Obviously, the state of theresting neuron must be pushed into the shaded area to initiate periodic spiking. Similarly,the state of the periodically spiking neuron must be pushed out of the shadedarea to stop the spiking. As the arrows in the figure indicate, both excitatory and inhibitorystimuli can do that, depending on their timing relative to the phase of spikingoscillation. This protocol can be used to test bistability experimentally.Bistable behavior reveals itself indirectly when a neuron is kept close to the bifurcation,e.g., when the injected dc-current is just below the rheobase. Noisy perturbationscan switch the neuron from resting to spiking states thereby creating an irregular spiketrain consisting of short bursts of spikes. Such stuttering spiking have been observedin many neurons, including some regular spiking (RS) and fast spiking (FS) neocorticalneurons, as we discuss in Chap. 8. The mean firing frequency during stutteringis proportional to the amplitude of the injected current and it can be quite low evenfor Class 2 excitable system, as we illustrate in Fig. 7.12. Thus, caution should be