Dynamical Systems in Neuroscience:

348 Burstingslow dynamicsneuronvoltage-gatedactivationof outwardinactivationof inwardactivationof outwardCa2+-gatedinactivationof inwardreferencesneocortical chatteringneuronsI K(M) I KslowWang (1999)pre-Botzinger complex(respiratory rhythm)I KslowI NaslowButera et al. (1999)thalamic relay neurons I Ca(T) I hHuguenard andMcCormick (1992)thalamic reticularneuronshippocampal CA3neuronsI Ca(T) Destexhe et al. (1994)I AHP Traub et al. (1991)subiculum burstingneuronsI AHP Stanford et al. (1998)midbrain dopaminergicneuronsI K(Ca) ICa(L) Amini et al. (1999)anterior bursting (AB)neuron in lobsterstomatogastric ganglionIK(Ca)I Ca(L)Harris-Warrick andFlamm (1987)Aplysia abdominalganglion R15 neuronI Ca(L)Canavier et al. (1991)Figure 9.7: Slow dynamics in bursting neurons.values of parameters. A bursting model is minimal if removal of any current or gatingvariable eliminates the ability to burst.One way to build a fast-slow minimal model for bursting is to take a minimal modelfor spiking, which consists of an amplifying and a resonant gate, see Fig. 5.17, and addanother slow resonant gate. Since there are many minimal spiking models in Fig. 5.17and four choices of slow resonant gates in Fig. 9.6, there are quite a few combinations,which fill out the squares in Fig. 9.8. We present only a few reasonable models in thefigure and ask the reader to fill in the blanks. Completing the table is an excellent testof one’s knowledge and understanding of how different currents interact to producenon-trivial firing patterns.Some of the minimal models for bursting might seem too bizarre at first glance.Yet the table in Fig. 9.8, upon completion, might prove to be a valuable tool thatcould allow experimenters to formulate various ionic hypotheses. For example, if oneuses pharmacological agents, e.g., TEA or Ba 2+ , to block Ca 2+ -gated K + channelsand show that bursting persists, then the possible electrophysiological mechanisms of