Dynamical Systems in Neuroscience:

Simple Models 303layer 5 neuronsimple modelAHP3421550 pAAHP500 pA21-50 mV370 pA200 msreset21-75 mV12spike-60 mV-75 mVpeakrecovery, u4002000restpeakv-nullclinev-nullcline, I=0300 pAinputinput-80 -60 -40 -20 0membrane potential, v (mV)Figure 8.19: Comparison of in vitro recordings of an intrinsically bursting (IB) neuronwith the simple model 150 ˙v = 1.2(v + 75)(v + 45) − u + I, ˙u = 0.01{5(v + 75) − u},if v ≥ +50, then v ← −56, u ← u + 130. White squares denote the reset pointsnumbered according to the spike number.IB cells. Depending on the strength of the injected dc current and the state of theneuron, the ADP can be large enough to cause another somatic spike, as we illustratein Fig. 7.52. The somatic spike may initiate another dendritic spike, etc., resulting ina burst in Fig. 8.20b. This mechanism is known as the dendritic-somatic ping-pong(Wang 1999) and it occurs in the Pinsky-Rinzel (1994) model of hippocampal CA3 neuron,the sensory neuron of weakly electric fish (Doiron et al. 2002), and in chatteringneurons considered below.Let us build a two-compartment simple model that simulates the somatic and dendriticspike generation of IB neurons. Since we do not know the rheobase, inputresistance, resting and instantaneous threshold potentials of dendritic tree of IB neurons,we cannot determine parameters of the dendritic compartment. Instead, we feedthe somatic recording V (t) in Fig. 8.20a into the model dendritic compartment and