Bifurcations and limit cycles in cytosolic yeast calcium

Calcium homeostasis is a fundamental cellular process in yeast. The regulation of the cytosolic calcium concentration is required for volume preservation and to regulate many vital calcium dependent processes such as mating and response to stress. The homeostatic mechanism is often studied by applying calcium pulses: sharply changing the calcium concentration in the yeast environment and observing the cellular response. To address these experimental investigations, several mathematical models have been proposed to describe this response. In this article we demonstrate that a previously studied model for this response predicts the presence of limit point instabilities and limit cycles in the dynamics of the calcium homeostasis system. We discuss the ways in which such dynamic characteristics can be observed with luminometric techniques. We contrast these predictions with experimentally observed responses and find that the experiments reveal a number of features that are consistent with modeling predictions. In particular, we find that equilibrium cytosolic concentrations have a sharp change in behavior as pulse size changes in the micromolar range. We show that such change is consistent with the presence of limit point instabilities. Additionally, we find that the response of synchronized yeast cells to millimolar range pulses is non-monotonic in its late stages. This response has characteristics similar to those associated with limit cycles.