Oscillations in a point models of the intracellular Ca2+ concentration - Thul, Ruediger (Cold Spring Harbor Laboratory Press, 2014)
Oscillations in the intracellular calcium (Ca2+) concentration form one of the main pathways by which cells translate external stimuli into physiological responses (Thul et al. 2008; Dupont et al. 2011; Parekh 2011). The mechanisms that underlie the generation of Ca2+ oscillations are still actively debated in the modeling community, but there is growing evidence that Ca2+ oscillations result from the spatio-temporal summation of subcellular Ca2+ release events (Thurley et al. 2012). Nevertheless, one prominent modeling approach to 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 since (a) the study of ODEs is computationally cheap, and a large body of techniques is available to investigate ODEs in great detail, or (b) there might not be sufficient experimental data 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 wellknown model for Ca2+ oscillations (De Young and Keizer 1992; Li and Rinzel 1994). The main emphasis of this protocol is the use of the open source software package XPPaut to numerically study ODEs (Ermentrout 2002). The knowledge gained here can be directly transferred to other ODE systems and therefore may serve as a template for future studies. For a general background on analysing ODEs in the context of Mathematical Cell Physiology, I refer the reader to (Keener and Sneyd 2001; Fall et al. 2002; Britton 2002; Murray 2013).