Dynamical Systems in Neuroscience:

Bursting 349voltage-gatedCa2+-gatedinactivation of inward currentamplifying gateCa 2+ -gatedvoltage-gatedactivationof inwardcurrentinactivationof outwardcurrentactivationof inwardcurrentinactivationof outwardcurrentresonant gatevoltage-gatedCa 2+ -gatedactivation inactivationof outward of inwardcurrent currentinactivationof inwardcurrentINa,t+IhINa,t(fast and slow)INa,t slow +IKINa,p+IK+Ihactivationof outwardcurrentamplifying gateCa 2+ -gatedvoltage-gatedactivationof inwardcurrentinactivationof outwardcurrentactivationof inwardcurrentinactivationof outwardcurrentresonant gatevoltage-gatedCa 2+ -gatedactivation inactivationof outward of inwardcurrent currentinactivationof inwardcurrentICa(N)ICa(L)+IKactivationof outwardcurrentactivation of outward currentamplifying gateCa 2+ -gatedvoltage-gatedactivationof inwardcurrentinactivationof outwardcurrentactivationof inwardcurrentinactivationof outwardcurrentresonant gatevoltage-gatedCa 2+ -gatedactivation inactivationof outward of inwardcurrent currentinactivationof inwardcurrentINa,t+IK(M)INa,p+IK+IK(M)activationof outwardcurrentamplifying gateCa 2+ -gatedvoltage-gatedactivationof inwardcurrentinactivationof outwardcurrentactivationof inwardcurrentinactivationof outwardcurrentresonant gatevoltage-gatedCa 2+ -gatedactivation inactivationof outward of inwardcurrent currentinactivationof inwardcurrentICa(T)+IAHPICa+IK+IAHPactivationof outwardcurrentFigure 9.8: Some minimal models for bursting.bursting are confined to the left column in Fig. 9.8. Minimal models in this columnwould provide testable hypotheses on the ionic basis of bursting, and they could guidenovel experiments. If block abolishes bursting, we cannot conclude that the blockedcurrent drives the bursting — it may merely be necessary for providing backgroundstimulation.Notice that the I Na,tslow + I K -model and the I Na,t + I K(M) -model in the figure (seethe shaded rectangles) consist of the same gating variables: Na + activation gate m,inactivation gate h, and K + activation gate n. Both models are equivalent to theHodgkin-Huxley model, the only difference being the choice of the slow gate. Thus, incontrast to the common biophysical folklore, the Hodgkin-Huxley model is a minimalmodel for bursting, and there are two fundamentally different ways in which one canmake it burst without any additional currents, as we show in Fig. 9.9. Of course, one