Dopamine Neurons Change the Type of Excitability in Response to Stimuli
Fig 7
The Ih current switches the type of excitability of the DA neuron to type II.
(A) Two-parameter bifurcation diagram. See part (C) for explanations. LC Fold is a saddle-node bifurcation of limit cycles, in which two oscillatory solutions, stable and unstable, emerge. A-H is the Andronov-Hopf bifurcation, in which a limit cycle shrinks in amplitude and merges with an equilibrium state. SN is a saddle-node bifurcation of equilibrium states, in which two equilibria (rest states) emerge. SNIC is a saddle-node bifurcation of equilibria on invariant circle, which is the same SN bifurcation that occurs on a limit cycle and, therefore, interrupts it. (B) F-I curves for three values of gh: gh = 0mS/cm^2, gh = 3.5mS/cm^2 and gh = 7mS/cm^2. (C1-3) Representative one-parameter bifurcation diagrams of three different bifurcation scenarios occurring at gh = 0mS/cm^2, 0<gh<7mS/cm^2 and gh> = 7mS/cm^2. Black curves represent equilibria. Red curves represent minima and maxima along a limit cycle. Solid stands for stable and dashed for unstable solutions. Dotted arrows represent bifurcation transitions. In C1, spiking is blocked as Iapp decreases through the LC Fold bifurcation. If Iapp increases through the same interval, the LC Fold bifurcation stays unnoticed because the equilibrium state remains stable, and only after the A-H bifurcation, spiking emerges. This is called hysteresis, and it creates bistability, in which either spiking or the rest state can be observed depending on the initial conditions for the voltage and Ca2+ concentration. In C2, the curve of equilibrium states folds and two saddle-node bifurcations of equilibria occur. The equilibria interrupt the unstable limit cycle (homoclinic bifurcation), but do not affect the stable limit cycle yet. In C3, the equilibria interrupt the stable limit cycle and destroy it in the SNIC bifurcation.