BME Seminar Series
Presents
Raimond L. Winslow, Ph.D.
Professor of Biomedical Engineering,
Johns Hopkins University School of Medicine
Director of the Institute for Computational Medicine
Multi-Scale Modeling of Calcium Signaling in the Cardiac
Dyad
Friday, February 23, 2007
2:00 - 3:00 p.m.
BME Lecture Hall (Room 1041), MR-5
ABSTRACT
In cardiac ventricular myocytes, events crucial to
excitation-contraction (EC) coupling take place in spatially restricted
microdomains known as dyads. The length-scale over which this
Ca2+ signaling occurs is a few tens of
nanometers and the time-scale of these events spans the range of msecs to
msecs. Quantitative understanding of the functional consequences of these
signaling events therefore requires development of models that are
applicable over a range of spatio-temporal scales. We will present
several new approaches for developing such multi-scale models of EC
coupling.
We will begin our analyses at the nano-scale level by presenting a model
of dyad Ca2+ dynamics in which the
Fokker-Planck equation is solved for the probability P(x,
t) that a Ca2+ ion is located at
position x at time t (Tanskanen et al, SIAM J. MMS,
in press). The model will describe: a) dyad geometry; b) membrane surface
charges; c) geometry and space-filling properties of the RyR (cryo-em),
L-Type Ca2+ channel (LCC) and calmodulin
proteins (crystal structures); d) stochastic gating of and
Ca2+ flux through LCCs; and d)
Ca2+ binding to RyR
activation/inactivation sites, stochastic gating and
Ca2+ flux through RyRs. Using this model,
we will demonstrate that: a) Ca2+
signaling in the dyad is mediated by ~ tens of
Ca2+ ions; b) these signaling events are
noisy due to the small number of ions involved; and c) the geometry of
the RyR protein may function to restrict the diffusion of and to “funnel”
Ca2+ ions to
Ca2+ activation sites on the RyR, thus
increasing RyR open probability and EC coupling gain.
The computational complexity of the above model prevents its
incorporation into integrative models of the myocyte. Simplification of
this model to one in which the dyadic space is represented using a single
compartment yields what we have referred to previously as the stochastic
local-control model of EC coupling (Biophys. J. 83: 2918). We will
show that this model captures the fundamental EC coupling properties of
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
that in general is not well suited for single cell simulations. To
address this problem, we will show how “separation of time-scales” may be
used to formulate what we refer to as the coupled LCC-RyR gating model
(Biophys. J. 87: 3723). In this model, nearby LCCs and RyRs
function gate as a coupled system that may be described using
low-dimensional systems of ordinary differential equations, thus reducing
computational complexity dramatically while still capturing fundamentally
important EC coupling properties. The simplified model may be solved many
orders of magnitude faster than can the stochastic model, thus enabling
incorporation into tissue level simulations (Biophys. J. 90:
77).