Non-spatial whole cell models of global calcium responses that account for heterogeneous domain calcium concentrations

A limitation of most whole cell models to date is the assumption that intracellular Ca²⁺ channels are globally coupled by a continuously stirred bulk cytosolic [Ca²⁺], when in fact open intracellular Ca²⁺ channels experience elevated domain [Ca²⁺]. Such heterogeneous local [Ca²⁺] can be modeled using 2N+2-compartment model that includes bulk cytosolic and luminal [Ca²⁺] and 2N compartments representing cytosolic and luminal Ca²⁺ domains associated with N stochastically gating intracellular channels. We have introduced an alternative whole cell model formulation that solves a system of advection reaction equations for the probability density of cytosolic and luminal domain [Ca²⁺] jointly distributed with channel state. This probability density formulation and an associated moment closure approach have been used to create computationally efficient models of local control of Ca²⁺-induced Ca²⁺ release in ventricular cardiac myocytes.