A mathematical analysis of agonist- and KCl-induced Ca(2+) 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 ([Ca(2+)](i)), observed as oscillatory Ca(2+) waves that can be induced by either agonist or high extracellular K(+) (KCl). In this work, we present a model of oscillatory Ca(2+) waves based on experimental data that incorporate both the inositol trisphosphate receptor and the ryanodine receptor. We then combined this Ca(2+) model and our modified actin-myosin cross-bridge model to investigate the role and contribution of oscillatory Ca(2+) waves to contractile force generation in mouse ASMCs. The model predicts that: 1), the difference in behavior of agonist- and KCl-induced Ca(2+) 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 [Ca(2+)](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 Ca(2+) waves generate less contraction than whole-cell Ca(2+) oscillations induced by the same agonist concentration. This is due to the spatial inhomogeneity of the receptor distributions.

Figure 1

Schematic diagram of the Ca²⁺ model. Ca²⁺ can be released from the sarcoplasmic reticulum (SR) though the inositol trisphosphate receptor (IPR), the ryanodine receptor (RyR), and a generic leak. Binding of agonist to the receptor in the outer cell membrane stimulates IP₃ production. IP₃ binds to the IPR in the SR, thus opening the receptor and leading to Ca²⁺ release. Initially, this has a positive feedback on the IPR and RyR open probabilities, thus triggering the release of more Ca²⁺ into the cytoplasm. At higher [Ca²⁺]_i, this feedback loop becomes negative and closes the IPR. The increase in [Ca²⁺] in the SR also has a positive feedback on the RyR open probability. Ca²⁺ can be pumped into the SR through the SERCA pump and out of the cell via the ATPase pump. Ca²⁺ enters the cell through voltage-gated Ca²⁺ channels or arachidonic-acid-operated channels (AAOC). The Ca²⁺ fluxes are denoted by solid lines. The dashed lines represent the feedback effects on various mechanisms in the cell.

Figure 2

Agonist-induced oscillations. (A) Experimental result from Perez and Sanderson (10), which represents mouse airway smooth muscle cells (ASMCs) stimulated with 1 μM acetylcholine (ACh). (B and D) Numerical simulations of our Ca²⁺ model. (C) Expanded region of 1 min, indicated by the lower bar in panel A. (E) Changes in [Ca²⁺] in the sarcoplasmic reticulum (SR). (F and G) Fluxes from the SR via the inositol trisphosphate receptor (IPR) and the ryanodine receptor (RyR), respectively. To simulate the experimental addition and removal of agonist, the increase and decrease in p required 50 s to reach its maximum level. Parameter values are shown in the Supporting Material with p = 0.35 μM and V = –60 mV.

Figure 3

KCl-induced oscillations. (A) Experimental result from Perez and Sanderson (10), which represents mouse airway smooth muscle cells (ASMCs) stimulated with 100 mM KCl. (B) Numerical solution with p = 0 μM and V = –30 mV. (C) Changes in [Ca²⁺] in the SR. (D and E) Fluxes from the sarcoplasmic reticulum (SR) via the inositol trisphosphate receptor (IPR) and the ryanodine receptor (RyR), respectively. Parameter values are shown in the Supporting Material.

Figure 4

Model prediction. (A and B) Numerical simulations of [Ca²⁺] oscillations in the cytosol and sarcoplasmic reticulum (SR), respectively. In this simulation, V = –40 mV and p is set to be 0.35 μM at t = 250 s. (C) Experimental result of [Ca²⁺]_i oscillations induced by 50 mM KCl and 200 nM methacholine (MCh) that were consecutively added to the mouse airway smooth muscle cell (ASMC). (D and E) Numerical simulations with p = 0.35 μM and V set to –40 mV at t = 80 s. (F) [Ca²⁺]_i oscillations corresponding to the reverse order of stimuli. Parameter values are shown in the Supporting Material.

Figure 5

Ca²⁺ waves and elemental Ca²⁺ events in ASMCs induced by agonist and KCl. (A) Experimental results of line scans from the longitudinal axes of single mouse ASMC during simulation with 1 μM 5-hydroxytryptamine (5-HT), 1 μM acetylcholine (ACh), and 50 mM KCl (10). The line scans show ∼13 μm along the center of the cell. The elemental Ca²⁺ events in the KCl-induced Ca²⁺ wave are indicated by arrows. It was assumed that a smooth muscle cell is ∼40-μm-long in our model. (B and C) Numerical results showing Ca²⁺ waves close to the center of the smooth muscle cell (15–30 μm) induced by agonist and KCl, respectively. The slopes of the open lines in panel A as well as the colored lines in panels B and C indicate the velocity and direction of the Ca²⁺ waves in the mouse airway smooth muscle cell (ASMC). (D and E) Distributions of inositol trisphosphate receptor (IPR) and the ryanodine receptor (RyR) densities along the cell length u, respectively. Parameter values are shown in the Supporting Material.

Figure 6

Steady-state mean relative force generated by both Ca²⁺ waves and whole-cell Ca²⁺ oscillations represented by stars and circles in all plots, respectively. (A) Relationships between mean relative isometric force and increases in agonist level (p μM). (B and C) Changes in oscillation frequency and average [Ca²⁺]_i corresponding to varied levels of p, respectively. (D) Data are taken from Wang et al. (14), their Fig. 8 C, and shows the contractile response of airway to Ca²⁺ oscillations (i.e., square waves) with different average [Ca²⁺]_i. Note that smaller mean relative airway area corresponds to stronger contraction. For comparison, the area obtained from a constant Ca²⁺ signal of equal average is shown (dashed line). The dot-dashed line gives the mean area for the limit case at high frequency oscillations (for detailed calculation, see Wang et al. (14)). In all panels, Ca²⁺ waves (marked as stars) and whole-cell Ca²⁺ oscillations (marked as circles) induced by p ∼0.32 μM (red) and p ∼0.6 μM (blue). Parameter values are shown in the Supporting Material.