Figure 1.

Six-state model of the BK_Ca-CaV complex with 1:1 stoichiometry and its simplification. (A) Shown here is a scheme indicating the six states and voltage-dependent transitions. C, O, and B refer respectively to closed, open, and inactivated states of the CaV, whereas X and Y indicate the closed and open states of the BK_Ca channel. The subscripts o and c on the horizontal transition rates indicate dependence on the Ca²⁺ concentration below an open (respectively, closed) Ca²⁺ channel. At physiological voltages, the transition to a state with an open BK_Ca channel occurs virtually only when the CaV is open (k⁺_c ≈ 0). The green box indicates states with noninactivated CaVs, whereas the blue box highlights states with inactivated CaVs. The transitions between the colored boxes are slow compared to transitions within boxes. (B) Shown here are simulated CaV open probabilities in response to a voltage step from −80 to 0 mV, obtained from the seven-state Markov chain model (gray; (17)), the three-state Markov chain model C, O, B (black; (27)), the ODE model corresponding to the three-state model ((13), (14), (15); blue), and the corresponding model assuming instantaneous activation m_CaV = m_CaV,∞ (Eq. 20; dash-dotted green). (C) Shown here are simulated open probabilities, in response to a voltage step from −80 to 0 mV, for BK_Ca channels controlled by CaVs in complexes with 1:1 stoichiometry, obtained from the original 70-state Markov chain model (gray; (17)), the six-state Markov chain model (A; black), the ODE model corresponding to the six-state model (Eqs. S6–S11; blue), the simplified Hodgkin-Huxley-type model (Eq. 25; dashed red), and the corresponding model assuming instantaneous activation m_CaV = m_CaV,∞ (dash-dotted green; see main text). In (B) and (C), one-thousand realizations were simulated for the Markov chain models, and the average of these Monte Carlo simulations is shown. To see this figure in color, go online.