## Abstract

We present a probability density approach to modeling localized Ca ^{2+} influx via L-type Ca^{2+} channels and Ca ^{2+}-induced Ca^{2+} release mediated by clusters of ryanodine receptors during excitation-contraction coupling in cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca^{2+}] conditioned on "Ca^{2+} release unit" state. When these equations are solved numerically using a high-resolution finite difference scheme and the resulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic and sarcoplasmic reticulum [Ca^{2+}], a realistic but minimal model of cardiac excitation-contraction coupling is produced. Modeling Ca^{2+} release unit activity using this probability density approach avoids the computationally demanding task of resolving spatial aspects of global Ca^{2+} signaling, while accurately representing heterogeneous local Ca^{2+} signals in a population of diadic subspaces and junctional sarcoplasmic reticulum depletion domains. The probability density approach is validated for a physiologically realistic number of Ca^{2+} release units and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. In simulated voltage-clamp protocols, both the probability density and Monte Carlo approaches to modeling local control of excitation-contraction coupling produce high-gain Ca^{2+} release that is graded with changes in membrane potential, a phenomenon not exhibited by so-called "common pool" models. However, a probability density calculation can be significantly faster than the corresponding Monte Carlo simulation, especially when cellular parameters are such that diadic subspace [Ca^{2+}] is in quasistatic equilibrium with junctional sarcoplasmic reticulum [Ca^{2+}] and, consequently, univariate rather than multivariate probability densities may be employed.

Original language | English |
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Pages (from-to) | 2311-2328 |

Number of pages | 18 |

Journal | Biophysical Journal |

Volume | 92 |

Issue number | 7 |

DOIs | |

State | Published - Apr 2007 |

Externally published | Yes |