Dynamical Systems in Neuroscience:

264 Excitabilitya pulse of current. Of course, these behaviors are difficult to catch experimentally,because the system must be near a codimension-2 bifurcation.200 ms20 mVSSAAAPSAPSFigure 7.42: Proximity to Bogdanov-Takens bifurcation in layer 5 pyramidal neuron ofrat primary visual cortex results in slow subthreshold oscillation before a spike. Shownare hand-drown phase portrait and in vitro recordings obtained while an automatedprocedure was testing the neuronal rheobase.7.3 Slow ModulationSo far we have considered neuronal models having voltage- or Ca 2+ -gated conductancesoperating on a fast time scale comparable with the duration of a spike. Such conductancesparticipate directly or indirectly in the generation of each spike and subsequentrepolarization of the membrane potential. In addition, neurons have dendritic trees andsome slow conductances and currents that may not be involved in the spike-generationmechanism directly , but rather modulate may it. For example, some cortical pyramidalneurons have I h , all thalamocortical neurons have I h and I Ca(T) . Activation andinactivation kinetics of these current is too slow to participate in the generation ofup-stroke or down-stroke of a spike, but the currents can modulate spiking pattern,e.g., they can transform it into bursting.To illustrate the phenomenon of slow modulation, we use the I Na,p +I K +I K(M) -