Simulations of BK channel activation were performed by integrating a set of partial differential equations. The differential equations were written in the xppaut syntax and solved using the free xppaut software (Ermentrout, 2002). The steady-state open probability (Po,ss) for a BK channel was taken to be that described by Bao and Cox (eq. 14 in Bao and Cox, 2005). This is a function of [Ca2+] and voltage. At each instant in time, the Po is driven toward this steady-state value at a simple exponential rate (based on an experimentally observed time constant of τ) as Marhl et al. (2006) did but using a different Po. This τ itself is a function of local [Ca2+] and thus is usually changing. Mathematically, dPo/dt = (Po,ss − Po)/τ, where τ is τ(Ca) and Po,ss is Po,ss(Ca, V). As [Ca2+] changes as a result of release from the spark, τ and Po,ss will change. If Po(t) < Po,ss, an activation τ based on the opening rate of BK channels is used; otherwise, a deactivation τ based on the closing rate is used (see Figs.
