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

Considerable insight into intracellular Ca 2 + 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 ( IP 3 ) receptor Ca 2 + channel. However, a limitation of most whole cell models to date is the assumption that IP 3 receptor Ca 2 + channels ( IP 3 R s) are globally coupled by a “continuously stirred” bulk cytosolic [ Ca 2 + ], when in fact open IP 3 R s experience elevated “domain” Ca 2 + concentrations. Here we present a 2 N + 2 -compartment whole cell model of local and global Ca 2 + responses mediated by N = 100 , 000 diffusely distributed IP 3 R s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal Ca 2 + concentrations, and the remaining 2 N compartments represent time-dependent cytosolic and luminal Ca 2 + domains associated with each IP 3 R . 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 [ Ca 2 + ] jointly distributed with IP 3 R state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [ Ca 2 + ], a realistic but minimal model of whole cell Ca 2 + dynamics is produced that accounts for the influence of local Ca 2 + signaling on channel gating and global Ca 2 + 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 Ca 2 + channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of Ca 2 + domain formation and collapse (both cytosolic and luminal) may influence global Ca 2 + oscillations, and we derive two reduced models of global Ca 2 + dynamics that account for the influence of local Ca 2 + signaling on global Ca 2 + dynamics when there is a separation of time scales between the stochastic gating of IP 3 R s and the dynamics of domain Ca 2 + .