A Mathematical Analysis of Agonist- and KCl-Induced Ca2+ Oscillations in Mouse Airway Smooth Muscle Cells

Abstract

Airway hyperresponsiveness is a major characteristic of asthma and is generally ascribed to excessive airway narrowing associated with the contraction of airway smooth muscle cells (ASMCs). ASMC contraction is initiated by a rise in intracellular calcium concentration ([Ca2+]i), observed as oscillatory Ca2+ waves that can be induced by either agonist or high extracellular K+ (KCl). In this work, we present a model of oscillatory Ca2+ waves based on experimental data that incorporate both the inositol trisphosphate receptor and the ryanodine receptor. We then combined this Ca2+ model and our modified actin-myosin cross-bridge model to investigate the role and contribution of oscillatory Ca2+ waves to contractile force generation in mouse ASMCs. The model predicts that: 1), the difference in behavior of agonist- and KCl-induced Ca2+ waves results principally from the fact that the sarcoplasmic reticulum is depleted during agonist-induced oscillations, but is overfilled during KCl-induced oscillations; 2), regardless of the order in which agonist and KCl are added into the cell, the resulting [Ca2+]i oscillations will always be the short-period, agonist-induced-like oscillations; and 3), both the inositol trisphosphate receptor and the ryanodine receptor densities are higher toward one end of the cell. In addition, our results indicate that oscillatory Ca2+ waves generate less contraction than whole-cell Ca2+ oscillations induced by the same agonist concentration. This is due to the spatial inhomogeneity of the receptor distributions.