Probability of Exocytosis in Pancreatic β-Cells: Dependence on Ca2+ Sensing Latency Times, Ca2+ Channel Kinetic Parameters, and Channel Clustering

The fusion of secretory vesicles and granules with the cell membrane prior to the release of their content into the extracellular space requires a transient increase of free Ca2+ concentration in the vicinity of the fusion site. Usually there is a short temporal delay in the onset of the actual fusion of membranes with reference to the rising free Ca2+ levels. This delay is described as a latency time of the Ca2+-sensing system of the secretory machinery and has been observed in several cell types, including pancreatic β-cells. The presence of a delay time of a finite length inherent to the secretory machinery of the cell has an essential effect on the probability for a certain granule to fuse with the cell membrane and to release its contents into the extracellular space during the action potential. We investigate here, theoretically and by numerical simulations, the extent of this influence and its dependence on the parameters of Ca2+ channels, channel clustering, the Ca2+-sensing system, and the length of depolarizing pulses.We use a linear probabilistic model for a random opening and closing of channels that yields an explicit expression for the Laplace transforms of the waiting time distributions for an event that at least one channel is open during the latency time. This allows one in principle to calculate the probability that a vesicle will fuse with the cell membrane during the action potential. We compare our theoretical results with numerical simulatio © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.