Mathematical Modeling of Inositol Trisphosphate Receptor and Calcium Oscillations in Airway Smooth Muscle Cells

Abstract

Oscillations in cytoplasmic calcium concentration ([Ca2+]i) in airway smooth muscle cells (ASMC), primarily mediated by repetitive openings and closings of inositol trisphosphate receptor (IP3R) channels situated in the sarcoplasmic reticulum membrane, have been found to be important in generating and maintaining airway contractile force. However, it has been unclear about the mechanisms accounting for such oscillations, especially how the IP3R behaves in living cells to perform its function. In light of the extensive existence of calcium oscillations in many other cell types, although this thesis focuses on modeling calcium oscillations in ASMC due to their importance for the study of pathology of asthma, it also aims to solve some major questions in a wider context: • What is the mechanism for the formation of the repetitive calcium releases? How is the mechanism connected to the dynamics of the IP3R? • How best (or simply) should the IP3R be modeled for performing its function? • Should we care about the channel stochasticity when making model predictions? That is, does the deterministic model (which is easier and faster to solve) have the same predictive power as the stochastic model? In this thesis, by mathematical modeling, our primary achievements are • First, based on a very recent IP3R model and available single-channel data, we developed a new IP3R model by introducing time-dependent interstate transitions, and showed that the time-dependent feature is crucial for a quantitatively reproduction of behaviors and statistical properties of localized calcium events (called calcium puffs). • Second, we showed that the existing 6-state IP3R model could be reduced down to a simple 2-state model without losing its function. This result leads us around full circle of 20 years of detailed studies and modeling of the IP3R, back to an early formulation where the calcium oscillations arise as a fast-slow dynamical system extensively seen in physiological processes. • Third, we compared a stochastic ASMC calcium model and its associated deterministic form, and showed that both of the models successfully predicted the trends of frequency change in response to a number of experimentally testable parameter perturbations. This allows a reliable use of deterministic models in making predictions.