Dynamical Systems in Neuroscience:

346 Burstingvoltage-gatedCa2+-gatedinactivation ofinward currentrestingdeinactivationof inwardcurrentrepolarizationdepolarizationinactivationof inwardcurrentspikingrestingCa 2+bufferingdeinactivationof inwardcurrentrepolarizationdepolarizationinactivationof inwardcurrentCa 2+ influxand buildupspikingactivation ofoutward currentrestingdeactivationof outwardcurrentrepolarizationdepolarizationactivationof outwardcurrentspikingrestingCa 2+bufferingdeactivationof outwardcurrentrepolarizationdepolarizationactivationof outwardcurrentCa 2+ influxand buildupspikingspikingrestingbuildup of resonant gate or [Ca2+]in(activation of outward current)(inactivation of inward current)recovery of resonant gate or [Ca2+]in(deactivation of outward current)(deinactivation of inward current)Figure 9.6: Four major classes of bursting models are defined by the slow resonantgating variable that modulates spiking activity.variable (see Sect. 5.1.1) that modulates the spiking via a slow negative feedback. Theresonant gating variable can describe inactivation of an inward current or activation ofan outward current, both voltage- or Ca 2+ -dependent (see Fig. 5.17). Hence, there arefour major classes of bursting models, summarized in Fig. 9.6:• Voltage-gated inactivation of an inward current, e.g., slow inactivation of persistentNa + current or inactivation of Ca 2+ transient T-current, or inactivation ofthe h-current (most biologists refer to this as activation of the h-current by hyperpolarization).Repetitive spiking slowly inactivates (turns off) the inward currentand makes the neuron less excitable and unable to sustain spiking activity. Aftera while, the spiking stops and the membrane potential repolarizes. The inwardcurrent slowly de-inactivates (turns on) and depolarizes the membrane potential,