Probability Density Methods for Modeling Local Control of Calcium- Induced Calcium Release in Cardiac Myocytes <P>

Considerable insight into intracellular Ca responses has been obtained  through the development of whole cell models that are based on  molecular mechanisms, e.g., the kinetics of intracellular Ca channels  and the feedback of Ca upon these channels.  However, a limitation of  most deterministic whole cell models to date is the assumption that  channels are globally coupled by a single [Ca], when in fact channels  experience localized "domain'' Ca concentrations.  More realistic  stochastic Monte Carlo simulations are capable of representing  individual domain Ca concentrations but suffer from increased  computational demand.  In this talk I will discuss a novel probability  approach to modeling Ca-induced Ca release (CICR) in cardiac myocytes.  This approach utilizes advection-reaction equations relating the time- dependent probability density of subsarcolemmal subspace and  junctional sarcoplasmic reticulum [Ca] conditioned on "Ca release  unit'' state. When these equations are coupled to ordinary  differential equations for the bulk myoplasmic and sarcoplasmic  reticulum [Ca], a realistic but minimal whole cell model is produced.   Modeling Ca release unit activity using this probability density  approach avoids the computationally demanding task of resolving  spatial aspects of global Ca signaling, while accurately representing  heterogeneous local Ca signals.