aheadofpub,
Stochastic binding of Ca$^2+$ ions in the dyadic cleft; continuous vs Random walk description of diffusion.
(February 2008)
DOI: 10.1529/biophysj.106.103523
Abstract
Ca$^2+$ signalling in the dyadic cleft in ventricular myocytes
is fundamentally discrete and stochastic. We study the stochastic
binding of single Ca ions to receptors in the cleft using two different
models of diffusion: a stochastic and discrete Random Walk (RW) model,
and a deterministic continuous model. We investigate whether the
latter model, together with a stochastic receptor model, can reproduce
binding events registered in fully stochastic RW simulations. By
evaluating the continuous model goodness-of-fit, for a large range
of parameters, we present evidence that it can. Further, we show
that the large fluctuations in binding rate observed at the level
of single time steps are integrated and smoothed at the larger time
scale of binding events, which explains the continuous model goodness-of-fit.
With these results we demonstrate that the stochasticity and discreteness
of the Ca$^2+$ signalling in the dyadic cleft, determined by
single binding events, can be described using a deterministic model
of Ca$^2+$ diffusion together with a stochastic model of the
binding events, for a specific range of physiological relevant parameters.
Time-consuming RW simulations can thus be avoided. We also present
a new analytical model of bi-molecular binding probabilities, which
we use in the RW simulations and the statistical analysis.
