Analysis of complex bursting in cortical pyramidal neuron models

Burst "ring is a prominent feature of cortical pyramidal cells and is thought to have signi"cant functional roles in reliable signaling and synaptic plasticity. Modeling studies have successfully elucidated possible biophysical mechanisms underlying complex bursting in pyramidal cells. Based on these results (Pinsky, Rinzel, J. Comput. Neurosci. 1 (1994) 39}60), we have built a simpli"ed two-compartment burst model. Using the fastand slow-variable analysis method, we show that complex bursting is an instance of square-wave bursting, where the dendritic slow potassium conductance is the single slow variable. The coupling parameters between the two compartments change the topological class of bursting thereby altering the "ring patterns of the neuron. These results explain the diverse set of "ring patterns seen with di!erent dendritic morphologies (Mainen, Sejnowski, Nature 382 (1996) 363}366). ( 2000 Elsevier Science B.V. All rights reserved.