Frequency of elemental events of intracellular Ca��⁺ dynamics

The dynamics of intracellular Ca��⁺ is driven by random events called Ca��⁺ puffs, in which Ca��⁺ is liberated from intracellular stores. We show that the emergence of Ca��⁺ 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 Ca��⁺ puffs has to account for the discrete character of the Ca��⁺ release sites and does not permit a continuous description of the number of open channels.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca��⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca��⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca��⁺ liberation is modulated by the Ca��⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Towards a predictive model of Ca��⁺ puffs

We investigate key characteristics of Ca��⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca��⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca��⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca��⁺ concentrations eliminate Ca��⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca��⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca��⁺ puffs and hence the stochastic time scale of intracellular Ca��⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca��⁺ oscillations.