We present a probability density approach to modeling localized Ca$^2+$
influx via L-type Ca$^2+$ channels and Ca$^2+$-induced Ca$^2+$
release mediated by clusters of ryanodine receptors during excitation-contraction
coupling in cardiac myocytes. Coupled advection-reaction equations
are derived relating the time-dependent probability density of subsarcolemmal
subspace and junctional sarcoplasmic reticulum Ca$^2+$ conditioned
on "Ca$^2+$ release unit" state. When these equations are solved
numerically using a high-resolution finite difference scheme and
the resulting probability densities are coupled to ordinary differential
equations for the bulk myoplasmic and sarcoplasmic reticulum Ca$^2+$,
a realistic but minimal model of cardiac excitation-contraction coupling
is produced. Modeling Ca$^2+$ release unit activity using this
probability density approach avoids the computationally demanding
task of resolving spatial aspects of global Ca$^2+$ signaling,
while accurately representing heterogeneous local Ca$^2+$ signals
in a population of diadic subspaces and junctional sarcoplasmic reticulum
depletion domains. The probability density approach is validated
for a physiologically realistic number of Ca$^2+$ release units
and benchmarked for computational efficiency by comparison to traditional
Monte Carlo simulations. In simulated voltage-clamp protocols, both
the probability density and Monte Carlo approaches to modeling local
control of excitation-contraction coupling produce high-gain Ca$^2+$
release that is graded with changes in membrane potential, a phenomenon
not exhibited by so-called "common pool" models. However, a probability
density calculation can be significantly faster than the corresponding
Monte Carlo simulation, especially when cellular parameters are such
that diadic subspace Ca$^2+$ is in quasistatic equilibrium
with junctional sarcoplasmic reticulum Ca$^2+$ and, consequently,
univariate rather than multivariate probability densities may be
employed.
%0 Journal Article
%1 Will_2007_2311
%A Williams, George S B
%A Huertas, Marco A
%A Sobie, Eric A
%A Jafri, M. Saleet
%A Smith, Gregory D
%D 2007
%J Biophys. J.
%K Action Calcium Calcium; Cardiac; Cardiovascular; Channels; Computer Contraction; Distributions Models, Myocardial Myocytes, Potentials; Signaling; Simulation; Statistical Statistical;
%N 7
%P 2311--2328
%R 10.1529/biophysj.106.099861
%T A probability density approach to modeling local control of calcium-induced
calcium release in cardiac myocytes.
%U http://dx.doi.org/10.1529/biophysj.106.099861
%V 92
%X We present a probability density approach to modeling localized Ca$^2+$
influx via L-type Ca$^2+$ channels and Ca$^2+$-induced Ca$^2+$
release mediated by clusters of ryanodine receptors during excitation-contraction
coupling in cardiac myocytes. Coupled advection-reaction equations
are derived relating the time-dependent probability density of subsarcolemmal
subspace and junctional sarcoplasmic reticulum Ca$^2+$ conditioned
on "Ca$^2+$ release unit" state. When these equations are solved
numerically using a high-resolution finite difference scheme and
the resulting probability densities are coupled to ordinary differential
equations for the bulk myoplasmic and sarcoplasmic reticulum Ca$^2+$,
a realistic but minimal model of cardiac excitation-contraction coupling
is produced. Modeling Ca$^2+$ release unit activity using this
probability density approach avoids the computationally demanding
task of resolving spatial aspects of global Ca$^2+$ signaling,
while accurately representing heterogeneous local Ca$^2+$ signals
in a population of diadic subspaces and junctional sarcoplasmic reticulum
depletion domains. The probability density approach is validated
for a physiologically realistic number of Ca$^2+$ release units
and benchmarked for computational efficiency by comparison to traditional
Monte Carlo simulations. In simulated voltage-clamp protocols, both
the probability density and Monte Carlo approaches to modeling local
control of excitation-contraction coupling produce high-gain Ca$^2+$
release that is graded with changes in membrane potential, a phenomenon
not exhibited by so-called "common pool" models. However, a probability
density calculation can be significantly faster than the corresponding
Monte Carlo simulation, especially when cellular parameters are such
that diadic subspace Ca$^2+$ is in quasistatic equilibrium
with junctional sarcoplasmic reticulum Ca$^2+$ and, consequently,
univariate rather than multivariate probability densities may be
employed.
@article{Will_2007_2311,
abstract = {We present a probability density approach to modeling localized {C}a$^{2+}$
influx via L-type {C}a$^{2+}$ channels and {C}a$^{2+}$-induced {C}a$^{2+}$
release mediated by clusters of ryanodine receptors during excitation-contraction
coupling in cardiac myocytes. Coupled advection-reaction equations
are derived relating the time-dependent probability density of subsarcolemmal
subspace and junctional sarcoplasmic reticulum [{C}a$^{2+}$] conditioned
on "{C}a$^{2+}$ release unit" state. When these equations are solved
numerically using a high-resolution finite difference scheme and
the resulting probability densities are coupled to ordinary differential
equations for the bulk myoplasmic and sarcoplasmic reticulum [{C}a$^{2+}$],
a realistic but minimal model of cardiac excitation-contraction coupling
is produced. Modeling {C}a$^{2+}$ release unit activity using this
probability density approach avoids the computationally demanding
task of resolving spatial aspects of global {C}a$^{2+}$ signaling,
while accurately representing heterogeneous local {C}a$^{2+}$ signals
in a population of diadic subspaces and junctional sarcoplasmic reticulum
depletion domains. The probability density approach is validated
for a physiologically realistic number of {C}a$^{2+}$ release units
and benchmarked for computational efficiency by comparison to traditional
Monte Carlo simulations. In simulated voltage-clamp protocols, both
the probability density and Monte Carlo approaches to modeling local
control of excitation-contraction coupling produce high-gain {C}a$^{2+}$
release that is graded with changes in membrane potential, a phenomenon
not exhibited by so-called "common pool" models. However, a probability
density calculation can be significantly faster than the corresponding
Monte Carlo simulation, especially when cellular parameters are such
that diadic subspace [{C}a$^{2+}$] is in quasistatic equilibrium
with junctional sarcoplasmic reticulum [{C}a$^{2+}$] and, consequently,
univariate rather than multivariate probability densities may be
employed.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Williams, George S B and Huertas, Marco A and Sobie, Eric A and Jafri, M. Saleet and Smith, Gregory D},
biburl = {https://www.bibsonomy.org/bibtex/2a5e243cba4e2cc6f0472b20bf7e5eb1b/hake},
description = {The whole bibliography file I use.},
doi = {10.1529/biophysj.106.099861},
file = {Will_2007_2311.pdf:Will_2007_2311.pdf:PDF},
interhash = {c8759c66266b42823c8d9aef096076d9},
intrahash = {a5e243cba4e2cc6f0472b20bf7e5eb1b},
journal = {Biophys. J.},
keywords = {Action Calcium Calcium; Cardiac; Cardiovascular; Channels; Computer Contraction; Distributions Models, Myocardial Myocytes, Potentials; Signaling; Simulation; Statistical Statistical;},
month = Apr,
number = 7,
pages = {2311--2328},
pdf = {Will_2007_2311.pdf},
pii = {biophysj.106.099861},
pmid = {17237200},
timestamp = {2009-06-03T11:21:37.000+0200},
title = {A probability density approach to modeling local control of calcium-induced
calcium release in cardiac myocytes.},
url = {http://dx.doi.org/10.1529/biophysj.106.099861},
volume = 92,
year = 2007
}