Mathematical Biology seminar

Greg Smith
Department of Applied Science, College of William and Mary
"Stochastic Automata Network Models of Instantaneously-Coupled Intracellular Calcium Channels"
September 8
3:05pm in LCB 215

Although there is consensus that Ca2+ puffs and sparks arise from the cooperative action of multiple intracellular Ca2+ channels, the precise relationship between single-channel kinetics and the collective phenomena of stochastic Ca2+ excitability is not well understood. Here we present a memory-efficient numerical method by which mathematical models for Ca2+ release sites can be derived from Markov models of single-channel gating that include Ca2+ activation, Ca2+ inactivation, or both. Such models are essentially stochastic automata networks (SANs) that involve a large number of so-called `functional transitions,' that is, the transition probabilities of the infinitesimal generator matrix (or Q-matrix) of one automata (i.e, an individual channel) may depend on the local [Ca2+] and thus the state of the other channels. Simulation and analysis of the SAN descriptors representing homogeneous clusters of intracellular Ca2+ channels show that 1) release site density can modify both the steady-state open probability and stochastic excitability of Ca2+ release sites, 2) Ca2+-inactivation is not a requirement for Ca2+ puffs, and 3) a single channel model with bell-shaped open probability curve does not lead to release site activity that is a biphasic function of release site density. These findings are obtained using iterative, memory-efficient methods (novel in this biophysical context and distinct from Monte Carlo simulation) that leverage the highly structured SAN descriptor to unambiguously calculate the steady-state probability of each release site configuration and puff statistics such as puff duration and inter-puff-interval. The validity of a mean-field approximation that neglects the spatial organization of Ca2+ release sites is also discussed.