Ca2+ Dynamics in Apoptosis: Real-Time Data and Mathematical Modeling

Abstract

The time-dependent behavior of Ca2+ in statistically significant number of live apoptotic cells in the same population is measured for the first time (along with behavior of other apoptosis markers phosphatidyl serine and caspase-3/7). The Ca2+ dynamics shows predominantly a single peak behavior at the early stage but also multiple peak behavior in a small fraction of the cells. These data enable for the first time mathematical modeling of the Ca2+ dynamics in apoptosis. Towards this end we propose a physical model motivated by the role of cytochrome c binding to the IP3R in the endoplasmic reticulum membrane thereby enhancing the probability of Ca2+ release as demonstrated by Boehing et al. (Nat Cell Biol, 2003, 5, 1051). The IP3R opening probability under the influence of cytochrome c is modeled as a modification of the probability in its absence in non-apoptotic cells (Mak et al. PNAS, 1998, 95, 15821). Coupled ordinary differential equations for the dynamics of Ca2+ and cytochrome c are formulated and solved for the behavior under nonapoptotic and apoptotic conditions. The results are qualitatively consistent with the overall observed dynamics of Ca2+, including the appearance of multiple peak behavior for certain ranges of the parameter space. The detailed analysis of the model indicates that the binding of cytochrome c to IP3R is the main source of cytosolic Ca2+ elevation in apoptosis while the active pumps on the plasma membrane provide the sink for the elevated cytosolic Ca2+ to return near the base level. The experimentally measured Ca2+ dynamics exhibit a significant cell-to-cell variation inherent to the stochastic nature of the underlying biochemical processes. Such variations are manifest in the modeling in terms of the uncertainites of the initial conditions in different cells upon the intiation of the apoptotic stress.