Dynamical Systems in Neuroscience:

Simple Models 313LS neuron (in vitro)simple model100 ms20 mVI=200 pAI=150 pAI=125 pAFigure 8.28: Comparison of in vitro recordings of a late spiking (LS) interneuron oflayer 1 rat’s neocortex with simulations of the simple two-compartment model. Soma:20 ˙v = 0.3(v + 66)(v + 40) + 1.2(v d − v) − u + I, ˙u = 0.17{5(v + 66) − u}, if v ≥ 30, thenv ← −45, u ← u+100. Passive dendrite (dotted curve): ˙v d = 0.01(v−v d ). Weak noisewas added to simulations to unmask the subthreshold oscillations. (Recordings werekindly provided by Zhiguo Chu, Mario Galarreta and Shaul Hestrin. Traces I = 125and I = 150 are from one cell, trace I = 200 is from another cell.)and forth and result in irregular stuttering spiking with subthreshold oscillations inthe 10-40 Hz range between the spike trains. Further increase of I shrinks the amplitudeof the unstable limit cycle, results in the subcritical Andronov-Hopf bifurcation ofthe resting state, removes the co-existence of attractors, and leaves only tonic spikingmode.8.2.7 Late spiking (LS) interneuronsWhen stimulated with long pulses of dc-current, late spiking neurons exhibit a longvoltage ramp, barely seen in Fig. 8.28, bottom, and then switch into a tonic firing mode.A stronger stimulation may evoke an immediate (transient) spike followed by a longramp and a long latency to the second spike. There are pronounced fast subthresholdoscillations during the voltage ramp indicating the existence of at least two time scales: