Frequency of elemental events of intracellular Ca²⁺ dynamics

The dynamics of intracellular Ca²⁺ is driven by random events called Ca²⁺ puffs, in which Ca²⁺ is liberated from intracellular stores. We show that the emergence of Ca²⁺ puffs can be mapped to an escape process. The mean first passage times that correspond to the stochastic fraction of puff periods are computed from a novel master equation and two Fokker-Planck equations. Our results demonstrate that the mathematical modeling of Ca²⁺ puffs has to account for the discrete character of the Ca²⁺ release sites and does not permit a continuous description of the number of open channels.

Stability of membrane bound reactions

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active sub-region of the cluster. Linear stability analysis reveals that diffusion is one of the ma jor determinants of the stability of the dynamics. We illustrate the model concept with Ca²⁺ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca²⁺ dynamics are caused by fluctuations due to the small number of channels per cluster.