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.
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Mathematical Biology Program
Department of Mathematics
University of Utah
155 South 1400 East Room 233
Salt Lake City, UT 84112
rasmusse@math.utah.edu
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