@misc{12211,
  author = {Johan Hake and Glenn Lines},
  title = {Modelling the Mesoscopic Length Scale of EC Coupling: the Diadic Cleft},
  abstract = {Ca2+ signalling in the dyadic cleft plays an important role in the excitation contraction (EC) coupling in ventricular myocytes. The cleft is a fuzzy space between the T-tubule and the Sarcoplasmic reticulum (SR). An action potential triggers the opening of L-type Ca2+ channels that let Ca2+ ions into the cleft. Most of the ions diffuses into the cytosole; but some bind to Ryanodine receptors (RyR), which are situated in clusters at the SR membrane, triggering further Ca 2+ release from SR. The signal is conveyed by a small number of diffusing Ca2+ ions, and is therefor fundamentally stochastic. The small number of Ca2+ ions involved in the process would suggest that diffusion in the dyadic cleft have to be modelled using Random Walk methods, making a deterministic and continuous model of diffusion useless. However the signal is not conveyed by Ca2+ ions in the cleft but rather by Ca2+ ions binding to single RyRs. To study the mesoscopic scale for this process we compared the event of single Ca2+ ions binding to RyRs 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. The large fluctuations in binding rate observed at the level of single time steps are integrated and smoothed at the larger time scale of single binding events, explaining the continuous model goodness-of-fit. Three parameters, which are combined into a dimensionless parameter: the diffusion constant of Ca2+, the binding rate of Ca2+ to the RyRs, and the diffusion length of the RW model, defines an upper limit for the agreement between the two models. As a result these parameters set the mesoscopic scale for the EC coupling.},
  year = {2008},
  journal = {Invited talk at {\textquoteright}European Conference on Mathematical and Theoretical Biology{\textquoteright}},
  month = {june},
}