Figure 9. Modelling of BK channel inactivation and reactivation.

BK channels were modelled with the illustrated scheme. The channel gating in the absence of inactivation has been collapsed to a simple closed (C) - open (O) scheme. The chosen rates reflected the mean open time (12 ms) and fastest closed time (0.14 ms) obtained from dwell time analysis of sustained BK channel activity. A, BK channel inactivation was modelled at a holding potential (V_h) of +40 mV (assuming > 1 μM Ca²⁺). Inactivation occurred as a block of the open channel by an associated particle. Two blocked states were modelled, providing the two open times (0.2 and 3 ms) observed during inactivation (see Figs 1F and 4). The model was initiated with three channels in the primary open state. After approximately 3 s one channel inactivated by initially entering the first blocked state (B1). Brief channel openings (primarily from the B2 state) were observed superimposed on high P_o activity from the other two channels. Governed by the rate entering the blocked state B1, the two remaining channels inactivated, leaving low P_o short duration openings (see Fig. 1). B, BK channel reactivation was modelled at −40 mV, with membrane hyperpolarization increasing the rates for exiting the two blocked states (indicated by *). The transition rate between B2 and B1 was changed to reflect the time to the ‘first opening’ observed in Fig. 5. The rate between the blocked state B1 and the primary open state (O) was increased to reflect the observed time to bursts of activity at −40 mV (see Fig. 5). Both rates indicated by *, would change in exponential fashion with membrane hyperpolarization (see Fig. 5). With these rates, the model was initiated with a single channel residing in the blocked state, B2 (as if the channel was fully inactivated by preceding membrane depolarization). After approximately 30 s, the channel exited the final blocked state (B2) and high P_o activity was observed.