Biophysical Models of the Cardiovascular System - Systems Biology: Networks, Models, and Applications - page 276

subspace, and regulation of inactivation of the LCC. When this newly
revealed balance between voltage- and Ca 2+ -dependent inactivation is
incorporated into common pool models, the models become unstable,
exhibiting alternating short and long duration APs. An example of
this behavior is shown in figure 9.5d. The reason for this is intuitively
clear: since JSR Ca 2+ release is all-or-none in these models, Ca 2+ -
dependent inactivation of LCCs is all-or-none, depending on whether
release has or has not occurred. Since L-type Ca 2+ current is a major
contributor to inward current during the plateau phase of the AP
(see figure 9.2), its biphasic inactivation leads to instability of AP
duration. This, unfortunately, constitutes a fatal weakness of biophysi-
cally based common pool models.

Challenges for Single Myocyte Modeling
The fundamental failure of common pool models described above
demonstrates that capturing the property of graded release is critically
important for modeling dynamics of single cardiac myocytes.
Understanding of the mechanisms by which Ca 2+ influx via LCCs
triggers Ca 2+ release from the JSR has advanced tremendously with
the development of experimental techniques for simultaneous meas-
urement of LCC currents and Ca 2+ transients and detection of local
Ca 2+ transients, and this has given rise to the local control hypothesis
of CICR [35,39-41]. This hypothesis asserts that opening of an
individual LCC in the T-tubular membrane triggers Ca 2+ release from
the small cluster of RyRs located in the closely apposed JSR membrane
(see figure 9.1b). Thus, the local control hypothesis asserts that release
is all-or-none at the level of these individual groupings of LCCs
and RyRs. However, LCC:RyR clusters are physically separated at the
ends of the sarcomeres [42]. These clusters therefore function in an
approximately independent fashion. The local control hypothesis asserts
that graded control of SR Ca 2+ release is achieved by the statistical

recruitment of elementary Ca 2+ release events in these independent

dyadic spaces.
We have recently implemented a local control model of myocyte
function [43]. As a compromise between structural and biophysical
detail versus tractability, a “minimal model” of local control of Ca 2+
release, referred to as the Ca 2+ release unit (CaRU) model, was devel-
oped. This model is intended to mimic the properties of Ca 2+ sparks
in the T-tubule/SR (T-SR) junction (Ca 2+ sparks are elementary SR
Ca 2+ release events arising from opening of a cluster of RyRs [44]).
Each CaRU in this model consists of a dyadic space, 4 LCCs and 20
RyRs in the JSR and sarcolemmal membranes, respectively. All 20 RyRs
in the CaRU communicate via Ca 2+ diffusion within the single local
JSR (dyadic) volume. The 5:1 RyR to LCC stoichiometry is chosen to be
consistent with recent estimates indicating that a single LCC typically