Biomedical Engineering Reference
In-Depth Information
evolution of 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 variabil-
ity to simulation output.
Figures 4C-F show macroscopic properties of APs and SR Ca
2+
release in
this hybrid stochastic/ODE model. Figure 4C shows the relative balance be-
tween the fraction of LCCs
not
voltage-inactivated (dotted line) and
not
Ca
2+
-
inactivated (dashed line) during the AP. These fractions were designed to fit the
experimental data of Linz and Meyer (53). The solid line shows a local-control
model AP. This AP should be contrasted with those produced by the common
pool model when the same relationship between LCC voltage- and Ca
2+
-
dependent inactivation as shown in Figure 4C is used. Clearly, the local-control
model exhibits stable APs whereas the common pool model does not. Figure 4E
shows the voltage dependence of peak LCC Ca
2+
influx (
F
LCC(max)
= filled 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). Ca
2+
release flux is a smooth and continuous function of membrane potential, and
hence triggers Ca
2+
, as shown by the experimental data in Figure 4D. EC cou-
pling gain may be defined as by Wier et al. (50), as the ratio
F
RyR(max)
/
F
LCC(max)
, and
is plotted as a function of voltage in Figure 4F (triangles). EC coupling gain is
monotonically decreasing with increasing membrane potential, and agrees with
corresponding experimental measurements made by Wier (50). The role of inter-
subspace coupling on gain is demonstrated in Figure 4F, by comparison of con-
trol simulations (triangles) to those in the absence of inter-subspace coupling
(squares). With inter-subspace coupling intact, EC coupling gain is greater at all
potentials, but the increase in gain is most dramatic at more negative potentials.
In this negative voltage range, LCC open probability is submaximal, leading to
sparse LCC openings. However, unitary current magnitude is relatively high, so
that in the presence of Ca
2+
diffusion within the CaRU the rise in local Ca
2+
due
to the triggering action of a single LCC can recruit and activate RyRs in adjacent
subspace compartments within the same T-SR junction. The net effect of inter-
subspace coupling is therefore to increase the magnitude and slope of the gain
function preferentially in the negative voltage range. These simulations therefore
offer an intriguing glimpse of how the co-localization and stochastic gating of
individual channel complexes can have a profound effect on the overall integra-
tive behavior of the cell.
3.
MODELS OF THE CARDIAC VENTRICLES
Computational models of the cardiac myocyte have contributed greatly to
our understanding of myocyte function. This is in large part due to a rich inter-
play between experiment and modeling—an interplay in which experiments
