Mathematical Studies of Intracellular Calcium Dynamics

Abstract

Calcium (Ca2+) is thought to be an essential player in almost all cell types, acting as a second messenger that controls many cellular processes including cell growth, muscle contraction, neuronal firing, cellular secretion, and cell death [15]. The central fact of Ca2+ signalling is that the cytosolic Ca2+ concentration ([Ca2+]i) oscillates, in a way that is highly regulated, and the signal is contained in the frequency (or sometimes the amplitude) of these oscillations. It is thus of great scientific interest to understand the cellular mechanisms that generate Ca2+ oscillations. This thesis investigates features of Ca2+ oscillations in two different intracellular context: in microdomains between intracellular Ca2+ stores, and in the cytosol of a salivary ductal cell line. Within a cell, two organelles may come in close proximity with each other and form membrane contact sites (i.e., microdomains). Recently, microdomains between two types of intracellular Ca2+ stores, lysosomes and the endoplasmic reticulum (ER), have been identified in cultured human fibroblasts [93]. We develop a mathematical model to study the role of microdomains in the regulation of global Ca2+ dynamics. Our model simulations suggest that lysosomal Ca2+ fluxes into the microdomains can either trigger or modulate Ca2+ signals, depending on the density and distribution of lysosomal Ca2+ channels. It has been conjectured that Ca2+ oscillations in HSY cells, a salivary ductal cell line from the parotid gland, are primarily produced by Ca2+ feedback on the inositol 1,4,5-trisphosphate (IP3) receptors, a type of Ca2+ channel on the ER membrane [184]. We investigate this hypothesis by constructing a mathematical model that captures the essential features of Ca2+ dynamics in HSY cells, and studying model behaviours. The model is validated through a combination of simulations and experiments, indicating that the model can provide useful insight into mechanisms underlying Ca2+ behaviours in HSY cells. A new set of model simulations is carried out, then confirmed through experimental verification. The study of model behaviours suggests a possible cellular mechanism in HSY cells that modulates oscillation frequencies. We find that perturbing Ca2+ oscillations in a reduced HSY cell Ca2+ model with a pulse of IP3 induces systematically di↵erent responses, depending on the state of [Ca2+]i. If the pulse is applied when [Ca2+]i is near the peak of a spike, [Ca2+]i evolves on a plateau for some time before returning to an oscillatory phase with a higher frequency. The pulse given right after a Ca2+ spike causes a transient delay in oscillations. Lastly, if the pulse is applied some time after a Ca2+ spike, it is immediately followed by faster oscillations. We describe each response in relation to model dynamics, and suggest possible mechanisms that underlie the result. Experimental data are presented to show that HSY cells and airway smooth muscle cells exhibit similar responses as in the model. We conjecture that there may be a common cellular mechanism shared by these two types of cells.