Dynamical Probing of the Mechanisms Underlying Calcium Oscillations

Understanding anomalous delays in a model of intracellular calcium dynamics

“…As reported in [6], under certain conditions a Class I model can respond to an IP 3 pulse by exhibiting a small number of faster oscillations, followed by a long delay, before recovering to the initial oscillatory pattern. This is a highly non-intuitive result: in Class I models the oscillation frequency is an increasing function of the IP 3 concentration (assuming that transients have died away), and thus a temporary increase in the IP 3 concentration might be expected to lead to a temporary increase in oscillation frequency, not to a long delay.…”

“…This inherent multiple time-scale structure provides us with a simple necessary condition for Class I and Class II dynamics by calculating a dimensionless quantity 1 representing the ratio of the different time scales involved. This is most easily illustrated using a representative model, the Atri model [1,6], which we will use as an example throughout this paper, and which has the following dimensionless form [9]:…”

“…However, more detailed mathematical investigations [6] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of Class I, Class II and Hybrid models of calcium oscillations.…”

“…However, more detailed mathematical studies of these models [6] have shown that the situation is more complex than appeared at first, and there are situations in which a Class I model can look remarkably like a Class II model, making interpretation of the experimental data ambiguous and difficult. Here we perform a detailed mathematical study of Class I and Class II models, investigate how they respond to a pulse of IP 3 , and provide a detailed explanation of why Class I and Class II models cannot necessarily be easily distinguished by the IP 3 pulse experiment.…”

“…It has been suggested [16] that the mechanisms underlying the generation and control of such oscillations can be determined by means of a simple experiment, whereby a single exogenous pulse of inositol trisphosphate (IP 3 ) is applied to the cell.However, more detailed mathematical investigations [6] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of Class I, Class II and Hybrid models of calcium oscillations.…”