Dynamical Systems in Neuroscience:

304 Simple Models(a)dendriticspike20 mV25 ms(b)somadendriterecorded (in vitro)(c)ADP(d)12345simulated6dendritic recovery variable, udvd-nullcline6resting1reset452evoked bysomatic spikepeak of spike3u d -nullclinedendritic membrane potential, v dFigure 8.20: Somatic and dendritic spike (a) and burst (b) in an IB neuron. Thedendritic spike in (a) is simulated in (c) using the simple model described in Fig. 8.20.Phase portrait (d) describes the geometry of dendritic spike-generation mechanism.(Recordings are from layer 5 of somatosensory cortex of a 4 week old rat at 35C;dendritic electrode is 0.43mm from the soma; data was kindly provided by Greg Stuartand Maarten Kole).fine-tune the parameters so that simulated dendritic spike in Fig. 8.20c “looks like”the recorded one in Fig. 8.20a.The phase portrait in Fig. 8.20d explains the peculiarities of the shape of simulateddendritic spike. Recorded somatic spike quickly depolarizes the dendritic membranepotential from point 1 to point 2, and starts the regenerative process — the up-strokeof a spike. Upon reaching the peak of the spike (3), the dendritic membrane potentialand the recovery variable are reset by the action of fast voltage-gated K + currents,which are not modeled here explicitly. The reset point (4) is near the stable manifoldof the saddle, so the membrane potential slowly repolarizes (5) and returns to theresting state (6).In Fig. 8.21 we put the somatic and dendritic compartment together, adjust someof the parameters, and simulate the response of the IB neuron to pulses of current ofvarious amplitudes. Notice that the model correctly reproduces the transient burstof 2 closely spaced spikes when stimulation is weak, and the rhythmic bursting withdecreasing number of spikes per burst when stimulation is strong. Using this approach,one can build models of pyramidal neurons having multiple dendritic compartments,