BK channels are activated synergistically by Ca²⁺_i and depolarization (Barrett et al., 1982). Po, the percentage of time that the channel is open, is plotted against Ca²⁺_i and membrane potential. Appreciable channel activity requires both depolarization from the typical resting membrane potentials and elevation of Ca²⁺_i above the typical resting level of 0.1 μM.

Schematic diagram of the α subunit of BK channels. The Ca²⁺ bowl, M513, and D362/D367 indicate sites on Ca²⁺ regulatory mechanisms that when mutated decrease the high affinity Ca²⁺ sensitivity. D81 is a similar type of site, but is much less effective. E374/E399 defines a site on a Ca²⁺/Mg²⁺ regulatory mechanism that when mutated decreases the low affinity Ca²⁺/Mg²⁺ sensitivity. VPEI precedes the position of the stop codon at 323 to make a truncated subunit (Piskorowski and Aldrich, 2002). The various named parts of the channel are indicated. The core and tail domain are connected by a nonconserved linker that also connects the RCK1 and the putative RCK2 domains (details in text).

Given the information of one voltage sensor per subunit and at least one Ca²⁺ binding site per subunit (it will be argued later that there are at least three Ca²⁺ binding sites per subunit), what might be the minimal expected kinetic gating mechanism for BK channels? This question was addressed indirectly by Eigen (1968) for hemoglobin (also a ligand binding tetramer) long before the first single-channel recordings. A simplified diagram of the Eigen model (Fersht, 1984), as applied to BK channels, is shown in Scheme I, where there are 25 states. The large numbers of states arise because each of the four subunits can exist in four different configurations. Squares indicate voltage sensors in the relaxed conformation, circles indicate voltage sensors in the active conformation, unshaded squares and circles indicate the absence of bound Ca²⁺, and shaded squares and circles indicate that a Ca²⁺ is bound to the subunit. Since binding and conformational changes would not be expected to occur exactly simultaneously, there are no diagonal pathways connecting the different states. Scheme I is a simplification of the 35–55 possible states that would arise if channels with diagonal and adjacent subunits in different configurations have different properties (Eigen, 1968; Cox et al., 1997; Rothberg and Magleby, 1999). Twenty-five states may seem overwhelming, but this number follows immediately from a tetramer in which each subunit can exist in four different configurations due to activation by voltage and Ca²⁺. Notice in Scheme II that the Eigen model condenses to the 10-state MWC model (Monod et al., 1965) if the four voltage sensors always move in a concerted manner.

Given the information of one voltage sensor per subunit and at least one Ca²⁺ binding site per subunit (it will be argued later that there are at least three Ca²⁺ binding sites per subunit), what might be the minimal expected kinetic gating mechanism for BK channels? This question was addressed indirectly by Eigen (1968) for hemoglobin (also a ligand binding tetramer) long before the first single-channel recordings. A simplified diagram of the Eigen model (Fersht, 1984), as applied to BK channels, is shown in Scheme I, where there are 25 states. The large numbers of states arise because each of the four subunits can exist in four different configurations. Squares indicate voltage sensors in the relaxed conformation, circles indicate voltage sensors in the active conformation, unshaded squares and circles indicate the absence of bound Ca²⁺, and shaded squares and circles indicate that a Ca²⁺ is bound to the subunit. Since binding and conformational changes would not be expected to occur exactly simultaneously, there are no diagonal pathways connecting the different states. Scheme I is a simplification of the 35–55 possible states that would arise if channels with diagonal and adjacent subunits in different configurations have different properties (Eigen, 1968; Cox et al., 1997; Rothberg and Magleby, 1999). Twenty-five states may seem overwhelming, but this number follows immediately from a tetramer in which each subunit can exist in four different configurations due to activation by voltage and Ca²⁺. Notice in Scheme II that the Eigen model condenses to the 10-state MWC model (Monod et al., 1965) if the four voltage sensors always move in a concerted manner.

An alternative method of testing the Eigen and MWC models is to examine whether there is correlation between the durations of adjacent open and closed intervals. In both 0 Ca²⁺_i and saturating Ca²⁺_i, these models predict a linear gating mechanisms, shown by the dashed boxes in Schemes I and II. While the Eigen model (which was for hemoglobin) does not specify which of the states are open and which are closed, if, for purposes of discussion, it is assumed that the top three rows in Scheme I are closed states and the bottom two rows are open states, then the gating mechanism in saturating Ca²⁺_i is given by Scheme III, which has a single transition pathway between the open and closed states. Consequently, this scheme predicts that there would be no correlation between the durations of adjacent intervals (Fredkin et al., 1985; McManus et al., 1985; Colquhoun and Hawkes, 1987). Examination of the durations of adjacent intervals from BK channels in saturating Ca²⁺_i indicates a very pronounced correlation: shorter open intervals are preferentially adjacent to longer closed intervals, and longer open intervals are preferentially adjacent to briefer closed intervals (McManus et al., 1985; Rothberg and Magleby, 1998, 1999). Such a correlation requires that there be at least two independent transition pathways between open and closed states, in contrast to Scheme III from the Eigen model in saturating Ca²⁺, which has a single transition pathway. Thus, the observation under 0 and saturating Ca²⁺ of gating in more than five kinetics states and also of correlations between adjacent open and closed intervals in saturating Ca²⁺ indicates that the Eigen model is too simple to account for the gating of BK channels, and can be rejected. On the same basis, the MWC model (Scheme II) can also be rejected, as it predicts only two states and also no correlations under extreme gating conditions.

If the Eigen model is too simple, how then does the channel gate? Detailed kinetic analysis suggests that the gating at 0 Ca²⁺ (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999; Nimigean and Magleby, 2000; Rothberg and Magleby, 2000) and saturating Ca²⁺ (Rothberg and Magleby, 1999, 2000) are both consistent with at least a 10-state model in each case, as indicated by Schemes IV and V. These schemes are expansions of the Eigen model at the extreme conditions of 0 Ca²⁺_i (Scheme IV) and saturating Ca²⁺_i (Scheme V), with the further assumption that each of the states predicted by the Eigen model can exist in two major conformations: closed (top tier) and open (bottom tier). The requirement for two-tiered gating mechanisms suggests that the Ca²⁺ sensors and voltage sensors move separately from the open-closed conformational change. Such separation of the sensor movement from the opening/closing transitions is also observed for other channels (Marks and Jones, 1992; Rios et al., 1993; McCormack et al., 1994). It immediately follows from Schemes I, IV, and V that the complete gating mechanism for all ranges of Ca²⁺_i, rather than just extreme conditions, would be given by the 50-state two-tiered model in Scheme VI (Horrigan and Aldrich, 1999; Horrigan et al., 1999; Rothberg and Magleby, 1999, 2000; Cox and Aldrich, 2000; Cui and Aldrich, 2000).

If the Eigen model is too simple, how then does the channel gate? Detailed kinetic analysis suggests that the gating at 0 Ca²⁺ (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999; Nimigean and Magleby, 2000; Rothberg and Magleby, 2000) and saturating Ca²⁺ (Rothberg and Magleby, 1999, 2000) are both consistent with at least a 10-state model in each case, as indicated by Schemes IV and V. These schemes are expansions of the Eigen model at the extreme conditions of 0 Ca²⁺_i (Scheme IV) and saturating Ca²⁺_i (Scheme V), with the further assumption that each of the states predicted by the Eigen model can exist in two major conformations: closed (top tier) and open (bottom tier). The requirement for two-tiered gating mechanisms suggests that the Ca²⁺ sensors and voltage sensors move separately from the open-closed conformational change. Such separation of the sensor movement from the opening/closing transitions is also observed for other channels (Marks and Jones, 1992; Rios et al., 1993; McCormack et al., 1994). It immediately follows from Schemes I, IV, and V that the complete gating mechanism for all ranges of Ca²⁺_i, rather than just extreme conditions, would be given by the 50-state two-tiered model in Scheme VI (Horrigan and Aldrich, 1999; Horrigan et al., 1999; Rothberg and Magleby, 1999, 2000; Cox and Aldrich, 2000; Cui and Aldrich, 2000).

If the Eigen model is too simple, how then does the channel gate? Detailed kinetic analysis suggests that the gating at 0 Ca²⁺ (Horrigan and Aldrich, 1999, 2002; Horrigan et al., 1999; Nimigean and Magleby, 2000; Rothberg and Magleby, 2000) and saturating Ca²⁺ (Rothberg and Magleby, 1999, 2000) are both consistent with at least a 10-state model in each case, as indicated by Schemes IV and V. These schemes are expansions of the Eigen model at the extreme conditions of 0 Ca²⁺_i (Scheme IV) and saturating Ca²⁺_i (Scheme V), with the further assumption that each of the states predicted by the Eigen model can exist in two major conformations: closed (top tier) and open (bottom tier). The requirement for two-tiered gating mechanisms suggests that the Ca²⁺ sensors and voltage sensors move separately from the open-closed conformational change. Such separation of the sensor movement from the opening/closing transitions is also observed for other channels (Marks and Jones, 1992; Rios et al., 1993; McCormack et al., 1994). It immediately follows from Schemes I, IV, and V that the complete gating mechanism for all ranges of Ca²⁺_i, rather than just extreme conditions, would be given by the 50-state two-tiered model in Scheme VI (Horrigan and Aldrich, 1999; Horrigan et al., 1999; Rothberg and Magleby, 1999, 2000; Cox and Aldrich, 2000; Cui and Aldrich, 2000).