Abstract
The consequences of cardiac excitation-contraction coupling by calcium-induced
calcium release were studied theoretically, using a series of idealized
models solved by analytic and numerical methods. "Common-pool" models,
those in which the trigger calcium and released calcium pass through
a common cytosolic pool, gave nearly all-or-none regenerative calcium
releases (in disagreement with experiment), unless their loop gain
was made sufficiently low that it provided little amplification of
the calcium entering through the sarcolemma. In the linear (small
trigger) limit, it was proven rigorously that no common-pool model
can give graded high amplification unless it is operated on the verge
of spontaneous oscillation. To circumvent this problem, we considered
two types of "local-control" models. In the first type, the local
calcium from a sarcolemmal L-type calcium channel directly stimulates
a single, immediately opposed SR calcium release channel. This permits
high amplification without regeneration, but requires high conductance
of the SR channel. This problem is avoided in the second type of
local control model, in which one L-type channel triggers a regenerative
cluster of several SR channels. Statistical recruitment of clusters
results in graded response with high amplification. In either type
of local-control model, the voltage dependence of SR calcium release
is not exactly the same as that of the macroscopic sarcolemmal calcium
current, even though calcium is the only trigger for SR release.
This results from the existence of correlations between the stochastic
openings of individual sarcolemmal and SR channels. Propagation of
regenerative calcium-release waves (under conditions of calcium overload)
was analyzed using analytically soluble models in which SR calcium
release was treated phenomenalogically. The range of wave velocities
observed experimentally is easily explained; however, the observed
degree of refractoriness to wave propagation requires either a strong
dependence of SR calcium release on the rate of rise of cytosolic
calcium or localization of SR release sites to one point in the sarcomere.
We conclude that the macroscopic behavior of calcium-induced calcium
release depends critically on the spatial relationships among sarcolemmal
and SR calcium channels, as well as on their kinetics.
- 11203466
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