Figure 1.

(A) Kinetic cycle of the NCX based on Matsuoka et al. (1996). The I₂ inactivated state is Na⁺-independent and relieved by ${\left[\text{C}{\text{a}}^{2+}\right]}_i$ at ≈ 100 nM range with a fast kinetics, the I₁ is Na⁺-dependent and relieved by ${\left[\text{C}{\text{a}}^{2+}\right]}_i$ at ≈ 1 μM level with a slower kinetics. (B) NCX as a trigger. Nullclines of the proposed model with clamped ${\left[\text{N}{\text{a}}^{+}\right]}_i$, blue: dh/dt = 0, red: $d{\left[\text{C}{\text{a}}^{2+}\right]}_i/dt=0$; pale curves: ${\left[\text{N}{\text{a}}^{+}\right]}_i=17$ mM, bold curves: ${\left[\text{N}{\text{a}}^{+}\right]}_i=45$ mM. Attraction domains corresponding to low-Ca²⁺ and high-Ca²⁺ states at ${\left[\text{N}{\text{a}}^{+}\right]}_i=45$ mM are shown in purple and yellow, respectively. Stable equilibria are marked with gray filled circles, an unstable equilibrium is marked with a red open circle. (C) Scheme of the model space, representing a small section of the thin astrocytic process. Resting values for [Na⁺] and [Ca²⁺] are set by Na⁺/K⁺-pump (NKA) and Ca²⁺-pump, NCX can exert either positive or negative influence on ${\left[\text{N}{\text{a}}^{+}\right]}_i$ and ${\left[\text{C}{\text{a}}^{2+}\right]}_i$, depending on the mode. Probing external pulses of Ca²⁺ and Na⁺ are administered through virtual “pipettes” Positive and negative effects are indicated with green and red arrows.