Large-conductance Ca-dependent K (BK) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca (CaV) channels. Recent stochastic simulations of the BK-CaV complex with 1:1 stoichiometry have given important insight into the local control of BK channels by fluctuating nanodomains of Ca. 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-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BK-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BK 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 description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BK-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BK current that respects local interactions in BK-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

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In this note we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L p , to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann-Stieltjes integral.

We study strictly parabolic stochastic partial differential equations on R d , d ≥ 1, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give sufficient conditions on the correlation of the noise ensuring Hölder continuity for the trajectories of the solution of the equation. For self-adjoint operators with deterministic coefficients, the mild and weak formulation of the equation are related, deriving path properties of the solution to a parabolic Cauchy problem in evolution form.