Dynamical Systems in Neuroscience:

Simple Models 305layer 5 neuronsimple modelI=700 pAI=560 pA+50 mV20 mV100 msI=400 pAFigure 8.21: Comparison of in vitro recordings of an intrinsically bursting (IB) neuron(layer 5 of somatosensory cortex of a 4 week old rat at 35C; data was kindly providedby Greg Stuart and Maarten Kole) with the two-compartment simple model. Soma:150 ˙v = 3(v + 70)(v + 45) + 50(v d − v) − u + I, ˙u = 0.01{5(v + 70) − u}, if v ≥ +50,then v ← −52, u ← u + 240. Active dendrite: 30 ˙v d = (v d + 50) 2 + 20(v − v d ) − u d ,˙u d = 3{15(v d + 50) − u d }, if v d ≥ +20, then v d ← −20, u d ← u d + 500.as we do next.8.2.3 Multi-compartment dendritic treeIn Fig. 8.22 we simulate an IB pyramidal neuron having 47 compartments (Fig. 8.22a,b),each described by a simple model with parameters provided in the caption of the figure.Our goal is to illustrate a number of interesting phenomena that occur in neuronalmodels having active dendrites, i.e., dendrites capable of generating action potentials.In Fig. 8.22c we inject a current into compartment 4 on the apical dendrite toevoke an excitatory post-synaptic potential (EPSP) of 4 mV, which is subthresholdfor the spike-generation mechanism. This depolarization produces a current that passivelyspreads to neighboring compartments, and eventually into the somatic compartment.However, the somatic EPSP is much weaker, only 1 mV, reflecting thedistance-dependent attenuation of dendritic synaptic inputs. Notice also that somaticEPSP is delayed and it has a wider time course, which is the result of dendritic low-passfiltering, or smoothing, of subthreshold neuronal signals. The further the stimulationsite is from the soma, the weaker, more delayed, and longer lasting is the somaticEPSP. For many years, dendrites were thought to be passive conductors whose sole