Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors

Considerable insight into intracellular Ca²⁺ responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate (IP₃) receptor Ca²⁺ channel. However, a limitation of most whole cell models to date is the assumption that IP₃ receptor Ca²⁺ channels (IP₃Rs) are globally coupled by a “continuously stirred” bulk cytosolic [Ca²⁺], when in fact open IP₃Rs experience elevated “domain” Ca²⁺ concentrations. Here we present a 2N+2-compartment whole cell model of local and global Ca²⁺ responses mediated by N=100,000 diffusely distributed IP₃Rs, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal Ca²⁺ concentrations, and the remaining 2N compartments represent time-dependent cytosolic and luminal Ca²⁺ domains associated with each IP₃R. Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection-reaction equations for the probability density of cytosolic and luminal domain [Ca²⁺] jointly distributed with IP₃R state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [Ca²⁺], a realistic but minimal model of whole cell Ca²⁺ dynamics is produced that accounts for the influence of local Ca²⁺ signaling on channel gating and global Ca²⁺ responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of Ca²⁺ channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of Ca²⁺ domain formation and collapse (both cytosolic and luminal) may influence global Ca²⁺ oscillations, and we derive two reduced models of global Ca²⁺ dynamics that account for the influence of local Ca²⁺ signaling on global Ca²⁺ dynamics when there is a separation of time scales between the stochastic gating of IP₃Rs and the dynamics of domain Ca²⁺.