Abstract
We present a mathematical model of calcium cycling that takes into
account the spatially localized nature of release events that correspond
to experimentally observed calcium sparks. This model naturally incorporates
graded release by making the rate at which calcium sparks are recruited
proportional to the whole cell L-type calcium current, with the total
release of calcium from the sarcoplasmic reticulum (SR) being just
the sum of local releases. The dynamics of calcium cycling is studied
by pacing the model with a clamped action potential waveform. Experimentally
observed calcium alternans are obtained at high pacing rates. The
results show that the underlying mechanism for this phenomenon is
a steep nonlinear dependence of the calcium released from the SR
on the diastolic SR calcium concentration (SR load) and/or the diastolic
calcium level in the cytosol, where the dependence on diastolic calcium
is due to calcium-induced inactivation of the L-type calcium current.
In addition, the results reveal that the calcium dynamics can become
chaotic even though the voltage pacing is periodic. We reduce the
equations of the model to a two-dimensional discrete map that relates
the SR and cytosolic concentrations at one beat and the previous
beat. From this map, we obtain a condition for the onset of calcium
alternans in terms of the slopes of the release-versus-SR load and
release-versus-diastolic-calcium curves. From an analysis of this
map, we also obtain an understanding of the origin of chaotic dynamics.
- 14645059
- animals,
- biological,
- biophysics,
- calcium
- calcium,
- cardiac,
- cell
- channels,
- cytosol,
- diffusion,
- factors,
- gov't,
- heart
- ions,
- l-type,
- membrane,
- models,
- myocytes,
- non-u.s.
- p.h.s.,
- research
- reticulum,
- sarcoplasmic
- sodium,
- statistical,
- support,
- time
- u.s.
- ventricles,
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