Fluctuations in Calcium Concentration Alter the Temporal Dynamics of Calcium-Dependent Signaling Cascades

Abstract

Calcium signaling is often localized in spatially restricted “microdomains,” which may involve only 1-100 calcium ions. Fluctuations in the local calcium concentration can arise from calcium influx and association/dissociation with calcium buffers [Weinberg and Smith. Biophys J 106(12): 2693 (2014)]. However it is unclear to what extent these fluctuations alter calcium-dependent signaling cascades. We construct a Markov model of a calcium-dependent signaling cascade and compare the first hitting time distribution for a Markov model that accounts for calcium fluctuations, a phase-type distribution that can be calculated from the infinitesimal generator matrix, with the corresponding model that neglects these fluctuations. In general, when calcium fluctuations are much faster than the characteristic time for the signaling cascade, the distributions for the two processes are similar. However, when the time scale of calcium fluctuations is on the same order as the signaling cascade or slower, the mean and variance of the hitting time is increased, in particular when the number of calcium ions is small, a consequence of a long-tailed hitting time distribution. These “rare events” comprising the long tail can be significant and have a physiological impact. We further study calcium fluctuations in two settings: calcium-dependent synaptic vesicle release [Bollmann et al. Science 289, 953 (2000)] and a calcium-release site model composed of calcium-activated calcium channels [DeRemigio and Smith. Cell Calcium 38: 73 (2005)]. In these models, we demonstrate the conditions for which calcium fluctuations alter the distribution, mean, and variance of the timing for synaptic vesicle release and calcium-release site activation, respectively. Under physiological conditions, the mean hitting time can be increased orders of magnitude when calcium fluctuations are accounted for, demonstrating a significant influence on intracellular signaling.