Exploring oscillations in a point model of the intracellular Ca²⁺ concentration

Intracellular calcium (Ca²⁺) oscillations are a key signaling mechanism in most cell types. A prominent approach to modeling intracellular Ca²⁺ oscillations is the use of ordinary differential equations (ODEs), which treat the intracellular Ca²⁺ concentration as spatially homogenous. Although ODEs cannot account for the interaction of Ca²⁺ microdomains to form cell-wide Ca²⁺ patterns, modelers still choose ODEs because (a) the study of ODEs is computationally cheap, and a large body of techniques is available to investigate ODEs in great detail, or (b) sufficient experimental data are not available to develop a spatially extended model. Irrespective of the reason, analyzing ODEs is a key instrument in the toolbox of modelers. In this protocol, we look at a well-known model for Ca²⁺ oscillations, the De Young-Keizer model, along with the Li-Rinzel approximation of the De Young-Keizer model. The main emphasis of this protocol is the use of the open source software package XPPAUT to numerically study ODEs. The knowledge gained here can be directly transferred to other ODE systems and therefore may serve as a template for future studies.