Biophysical Models of the Cardiovascular System - Systems Biology: Networks, Models, and Applications - page 277

triggers the opening of 4-6 RyRs [45]. Since LCC:RyR clusters are
physically separated [42], each model CaRU is assumed to function
independently of other CaRUs.
Simulation of the dynamics of the CaRU model requires both
numerical integration of the ordinary differential equations (ODEs)
describing time-varying global Ca 2+ , Na + , and K + concentrations and
K + and Na + channel states in the myocyte model as well as Monte Carlo
simulation of LCC and RyR channel gating in the approximately
~12,500 CaRUs in the cell (yielding ~50,000 LCCs per ventricular
myocyte). The state of each LCC and RyR channel is described by a
set of discrete valued random variables that evolve in time as described
by Markov processes. Time steps for CaRU simulations are adaptive
and are chosen to be sufficiently small based on channel transition
rates. The CaRU simulations occur within the (larger) time step used
for the numerical integration of the system of ordinary differential
equations describing the time evolution of the global state variables.
As a result of the embedded Monte Carlo simulation, all model state
variables and ionic currents/fluxes will contain a component of
stochastic noise. These fluctuations introduce a degree of variability
to simulation output.
Figure 9.6 shows macroscopic properties of APs and SR Ca 2+ release
in this CaRU model. Figure 9.6a shows relative balance between
the fraction of LCCs not voltage-inactivated (dotted line) and not
Ca 2+ -inactivated (dashed line) during the simulated AP (solid line).
These fractions were designed to fit the experimental data of Linz
and Meyer [38] showing that Ca 2+ -dependent inactivation is stronger
than is voltage-dependent inactivation. The solid line shows an AP
predicted by the local control model. This AP should be contrasted
with those produced by the common pool mode (figure 9.5d) when
the same relationship between LCC voltage- and Ca 2+ -dependent
inactivation shown in figure 9.6a is used. Clearly, the local control
model exhibits stable APs whereas the common pool model does not.
Figure 9.6b shows the voltage-dependence of peak LCC Ca 2+ influx
( F LCC(max), closed circles, ordinate) and peak RyR Ca 2+ release flux
( F RyR(max), open circles, ordinate) in response to voltage-clamp steps to
the indicated potentials (mV, abscissa). These data demonstrate graded
release, as Ca 2+ release flux is a smooth and continuous function of
membrane potential and hence triggers Ca 2+ flux through LCCs.
These simulations offer an intriguing glimpse of how the colocal-
ization and stochastic gating of individual channel complexes can
have a profound effect on the overall, integrative behavior of the cell.
The results also point out that a key challenge remains. That is, com-
putational models of the ventricular myocyte incorporating a
phenomenological description of CICR have reduced predictive power
as they do not describe the biophysical basis of the release process.