Modeling the Calcium Gate of Cardiac Gap Junction Channel

Abstract

We addressed the question how Ca²⁺ transients affect gap junction conductance (G_j) during action potential (AP) propagation by constructing a dynamic gap junction model coupled with a cardiac cell model. The kinetics of the Ca²⁺ gate was determined based on published experimental findings that the Hill coefficient for the [Ca²⁺]_i–G_j relationship ranges from 3 to 4, indicating multiple ion bindings. It is also suggested that the closure of the Ca²⁺ gate follows a single exponential time course. After adjusting the model parameters, a two-state (open-closed) model, assuming simultaneous ion bindings, well described both the single exponential decay and the [Ca²⁺]_i–G_j relationship. Using this gap junction model, 30 cardiac cell models were electrically connected in a one-dimensional cable. However, G_j decreased in a cumulative manner by the repetitive Ca²⁺ transients, and a conduction block was observed. We found that a reopening of the Ca²⁺ gate is possible only by assuming a sequential ion binding with one rate limiting step in a multistate model. In this model, the gating time constant (τ) has a bell-shaped dependence on [Ca²⁺]_i, with a peak around the half-maximal concentration of [Ca²⁺]_i. Here we propose a five-state model including four open states and one closed state, which allows normal AP propagation; namely, the G_j is decreased ∼15% by a single Ca²⁺ transient, but well recovers to the control level during diastole. Under the Ca²⁺-overload condition, however, the conduction velocity is indeed decreased as demonstrated experimentally. This new gap junction model may also be useful in simulations of the ventricular arrhythmia.