Coupling and cooperativity in voltage activation of a limited-state BK channel gating in saturating Ca²⁺

Voltage-dependent gating mechanisms of large conductance Ca²⁺and voltage-activated (BK) channels were investigated using two-dimensional maximum likelihood analysis of single-channel open and closed intervals. To obtain sufficient data at negative as well as positive voltages, single-channel currents were recorded at saturating Ca²⁺ from BK channels mutated to remove the RCK1 Ca²⁺ and Mg²⁺ sensors. The saturating Ca²⁺ acting on the Ca²⁺ bowl sensors of the resulting BK_B channels increased channel activity while driving the gating into a reduced number of states, simplifying the model, Five highly constrained idealized gating mechanisms based on extensions of the Monod-Wyman-Changeux model for allosteric proteins were examined. A 10-state model without coupling between the voltage sensors and the opening/closing transitions partially described the voltage dependence of Po but not the single-channel kinetics. With allowed coupling, the model gave improved descriptions of Po and approximated the single-channel kinetics; each activated voltage sensor increased the opening rate approximately an additional 23-fold while having little effect on the closing rate. Allowing cooperativity among voltage sensors further improved the description of the data: each activated voltage sensor increased the activation rate of the remaining voltage sensors approximately fourfold, with little effect on the deactivation rate. The coupling factor was decreased in models with cooperativity from∼23 to ∼18. Whether the apparent, cooperativity among voltage sensors arises from imposing highly idealized models or from actual cooperativity will require additional studies to resolve. For both cooperative and noncooperative models, allowing transitions to five additional brief (flicker) closed states further improved the description of the data. These observations show that the voltage-dependent single-channel kinetics of BK _B channels can be approximated by highly idealized allosteric models in which voltage sensor movement increases Po mainly through an increase in channel opening rates, with limited effects on closing rates,