Dynamical Systems in Neuroscience:

266 Excitabilitymembrane potential (mV)interspike period, Ti (ms)40200-20-40-60(a)T 0 T 1 T 2 T 3 T 4 T 5I=300 pA0 pA spike number, i-800 50 time (ms) 100 150(b)interspike frequency, Fi=1000/Ti (Hz)150F120010010080F 160rampF 250 T 0 T40F 3,4,5T 3FT 2 20rampT0T 1 0 00 100 200 3000 100 200 300injected current, I (pA)injected current, I (pA)(c)T i402000 5 10 15Figure 7.43: Spike-frequency adaptation in layer 5 pyramidal cell (see Fig. 7.3). Rampdata is from Fig. 7.6.other types of neurons discussed in the next chapter. In contrast, cortical fast spiking(FS) interneurons (Gibson et al. 1999) exhibit spike-frequency acceleration, depictedin Fig. 7.44, i.e., the instantaneous interspike intervals decrease, and the frequencyincreases with each spike.Whether a neuron exhibits spike frequency adaptation or acceleration depends onthe nature of the slow current or currents and how they affect the spiking limit cycle ofthe fast subsystem. At the first glance, a resonant slow current, e.g., slowly activatingK + or slowly inactivating Na + current, builds up during each spike and provides anegative feedback that should slow down spiking of the fast subsystem. Buildup ofa slow amplifying current, e.g., slowly activating Na + or inactivating K + current, orslow charging of the dendritic tree should have the opposite effect. In Chap. 9, devotedto bursting, we will show that this simple rule works for many models, but there arealso many exceptions. To understand how the slow subsystem modulates repetitivespiking, we need to consider bifurcations of the fast subsystem in (7.2), treating the