Concise Whole-Cell Modeling of BK_Ca-CaV Activity Controlled by Local Coupling and Stoichiometry

Large-conductance Ca²⁺-dependent K⁺ (BK_Ca) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca²⁺ (CaV) channels. Recent stochastic simulations of the BK_Ca-CaV complex with 1:1 stoichiometry have given important insight into the local control of BK_Ca channels by fluctuating nanodomains of Ca²⁺. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BK_Ca-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BK_Ca-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BK_Ca currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BK_Ca description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BK_Ca-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BK_Ca current that respects local interactions in BK_Ca-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.