Abstract
Calcium (Ca$^2+$)-induced Ca$^2+$-release (CICR) takes place
in spatially restricted microdomains known as dyads. The length scale
over which CICR occurs is on the order of nanometers and relevant
time scales range from micro- to milliseconds. Quantitative understanding
of CICR therefore requires development of models that are applicable
over a range of spatio-temporal scales. We will present several new
approaches for multiscale modeling of CICR. First, we present a model
of dyad Ca$^2+$ dynamics in which the Fokker-Planck equation
(FPE) is solved for the probability P(x, t) that a Ca$^2+$ ion
is located at dyad position x at time t. Using this model, we demonstrate
that (a) Ca$^2+$ signaling in the dyad is mediated by approximately
tens of Ca$^2+$ ions; (b) these signaling events are noisy due
to the small number of ions involved; and (c) the geometry of the
RyR (ryanodine receptors) protein may function to restrict the diffusion
of and to "funnel" Ca$^2+$ ions to activation-binding sites on
the RyR, thus increasing RyR open probability and excitation-contraction
(EC) coupling gain. Simplification of this model to one in which
the dyadic space is represented using a single compartment yields
the stochastic local-control model of CICR developed previously.
We have shown that this model captures fundamental properties of
CICR, such as graded release and voltage-dependent gain, may be integrated
within a model of the myocyte and may be simulated in reasonable
times using a combination of efficient numerical methods and parallel
computing, but remains too complex for general use in cell simulations.
To address this problem, we show how separation of time scales may
be used to formulate a model in which nearby L-type Ca$^2+$ channels
(LCCs) and RyRs gate as a coupled system that may be described using
low-dimensional systems of ordinary differential equations, thus
reducing computational complexity while capturing fundamentally important
properties of CICR. The simplified model may be solved many orders
of magnitude faster than can either of the more detailed models,
thus enabling incorporation into tissue-level simulations.
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