Mathematical Modeling of Calcium Dynamics in Airway Smooth Muscle Cells

Abstract

Oscillations in the concentration of free cytoplasmic calcium ([Ca²⁺] _i ) play a vital role in the generation and maintenance of force by airway smooth muscle (ASM) cells. Mathematical models have an important role to play in the study of such complex dynamic phenomena, and can be used to construct and test hypotheses for how such oscillations might occur, and how properties such as the oscillation period might be controlled. We briefly discuss the underlying principles of the construction of mathematical models of calcium dynamics, and show how our current model can be used to understand how oscillations of [Ca²⁺] _i in ASM are the result of a complex interplay between inositol trisphosphate receptors (IP₃R) and ryanodine receptors (RyRs). Agonist-stimulated production of inositol trisphosphate (IP₃) opens IP₃R, resulting in the release of Ca²⁺ from the endoplasmic reticulum (ER). This released Ca²⁺ stimulates the release of additional Ca²⁺ from both IP₃R and RyR, leading to cycles of Ca²⁺ release and reuptake from the ER. In the absence of IP₃ (no agonist), when the ER is overloaded with Ca²⁺ these cycles of release and reuptake are mediated primarily by the RyR. Conversely, in the presence of IP₃ (with agonist), when the ER is partially depleted of Ca²⁺, these cycles are mediated primarily by the IP₃R. Thus, an understanding of both IP₃R and RyR is required for an understanding of how [Ca²⁺] _i oscillations are controlled in ASM.