How noise can generate calcium spike-type oscillations in deterministic equilibrium modes

Stochastic excitability of spiking oscillatory regimes in the calcium kinetics is studied on the basis of the Li-Rinzel conceptual model. The probabilistic mechanisms of the noise-induced generation of large-amplitude oscillations in parametric zones, where the original deterministic model has only stable equilibria, are investigated numerically and analytically. A parametric statistical description of interspike intervals is curried out and the phenomenon of coherence resonance is discussed. For the analytical study of the stochastic excitement, the confidence domain method using a stochastic sensitivity technique is applied. In this analysis, a key role of mutual arrangement of the confidence ellipses and separatrices detaching the sub- and supercritical regions is demonstrated. It is shown that in the Li-Rinzel model such separatrices are the stable manifolds of the saddle equilibria and the transient semiattractors.

Automated summary

The stochastic excitability of spiking oscillatory regimes in calcium kinetics is investigated using the Li-Rinzel conceptual model. The probabilistic mechanisms of noise-induced generation of large-amplitude oscillations in parametric zones are studied numerically and analytically. The phenomenon of coherence resonance is discussed, and a parametric statistical description of interspike intervals is applied. The role of confidence ellipses and separatrices in determining sub- and supercritical regions is demonstrated.