Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics

Abstract

A range of representative models of intracellular calcium dynamics are surveyed, with the aim of determining which model characteristics are qualitatively unchanged by changes to details of the model components. Techniques from geometric singular perturbation theory are used to investigate the role of separation of timescales in determining model dynamics, with particular emphasis on identifying parameter regimes in which mixed mode oscillations are present as a result of the separation of timescales. We find that the number of distinct timescales and the number of variables evolving on each timescale varies between models and depends on both the model assumptions and on the parameter regime of interest within the model, but in all cases, the presence of canards and associated mixed mode oscillations provides a mechanism by which the models can robustly exhibit complex oscillations, with the frequency of oscillation depending sensitively on parameter values. We find that analysis of the number and nature of the distinct timescales in a model allows us to make useful predictions about the dynamics associated with the model, and that this may give us more information about the model dynamics than a classification according to the modelling assumptions made about different cellular mechanisms in deriving the models.