Dynamical Systems in Neuroscience:

Excitability 231layer 5 pyramidal cellbrainstem mesV celltransition20 mVtransition-60 mV-50 mV200 pA3000 pA0 pA500 ms0 pA500 msFigure 7.6: As the magnitude of injected dc-current increases, the neurons bifurcatesfrom resting to repetitive spiking behavior. Shown are recordings of the same neuronsas in Fig. 7.3. Notice that the ratio of the first and last interspike intervals of thepyramidal cell is much greater than that in mes V neuron.trains in another mesV neuron in Fig. 7.3, cannot evoke multiple spikes in this neuron.Similarly, the pyramidal neuron in Fig. 7.5 cannot sustain tonic spiking even when theinjected current is ten times stronger than the neuron’s rheobase. Ironically, neuronsexhibiting such a behavior would most likely be discarded as “sick” or “unhealthy”,though the neurons analyzed in the figures looked normal from any other point of view.We will study the dynamic mechanism of this class of excitability and show that it mayhave nothing to do with sickness.It will be clear shortly that this classification is of limited value except that itpoints to the fact that neurons should be distinguished according not only to ionicmechanisms of excitability, but also to dynamic mechanisms, in particular, to the typeof bifurcation of the rest state.7.1.3 Classes 1 and 2Let us consider the strength of the applied current in Hodgkin’s experiments as beinga bifurcation parameter. Instead of changing the parameter abruptly, as in Fig. 7.3,we change it slowly in Fig. 7.6 using recordings of the same neurons as in the previousfigure. In Sect. 7.1.5 we explain the fundamental difference between these two protocols.When the current ramps up, the rest potential increases until a bifurcation occurs,resulting in loss of stability or disappearance of the equilibrium corresponding to therest state, and the neuron activity becomes oscillatory. Notice that the pyramidalneuron in Fig. 7.6 starts to fire with a small frequency, which then increases accordingto the F-I curve in Fig. 7.3 (a slower current ramp is needed to span the entire frequencyrange of the F-I curve). In contrast, the brainstem neuron starts to fire with a highfrequency that remains relatively constant even though the magnitude of the injectedcurrent increases.