Spiral breakup and defect dynamics in a model for intracellular Ca²⁺ dynamics

Pattern formation is investigated near the breakup instability of rotating spiral waves in a model for intracellular Ca²⁺ dynamics. Our results show that spiral breakup is strongly dependent on the inactivation parameter of the inositol 1,4,5 triphosphate receptor ion channel. We compute the pulse train instability reponsible for spiral breakup and investigate the influence of the system size. The instability of planar pulse trains is a long wavelength (with respect to the perturbations) Eckhaus instability, that appears upon decrease of the wavelength of the pulse train. Secondly, we study the dynamics of topological defects in the spatiotemporally chaotic state emerging from the spiral breakup. This regime is charcterized by a variance of the number of defects that is considerably smaller than the corresponding mean value. Global characteristics like the creation and annihilation rate and the probability distribution of the number of defects are calculated. The defect transport is characterized by its diffusivity. Most defects move subdiffusively within their lifetime as a consequence of meandering.