Effect of CPA on dynamics.

<p>(A) Fluorescence imaging of in ASMC of a mouse lung slice treated with agonist and CPA. Agonist removal leads to decrease. (B–D) Model simulations of the experiments shown in (A), assuming that (B) CPA quickly blocks the SERCA, (C) CPA slowly blocks the SERCA, (D) CPA partially blocks the SERCA but reaches maximum strength rather quickly. Black solid and dashed curves (left y-axis) represent respectively and ; blue and red curves (right y-axis) show respectively the fraction of open SOCC and the fraction of operating SERCA (that is, , where is given by Eq. (0c)).</p

Fluorescence image of part of a mouse airway wall obtained by two-photon laser scanning microscopy.

<p>The yellow square shows a typical region, within an ASMC, from which dynamics is imaged.</p

Influence of SOCE on agonist-induced oscillations.

<p>Amplitude (black) and frequency (red) of oscillations as a function of (A) SOCE maximum rate, , and (B) STIM affinity for SR , . Dotted lines indicate the “normal” parameter values (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069598#pone-0069598-t001" target="_blank">Table 1</a>, Figs. 3D–F). As in Fig. 4, only the frequency of the large-amplitude stable oscillations is shown.</p

Experimental evidence that CPA does not fully empty the SR of ASMC.

<p>Tests of the model predictions shown in Fig. 6B–D, performed with mouse lung slices. (A) Significantly longer exposure to agonist+CPA and to CPA than in Fig. 6A still fails to maintain SOCE. (B) Same experiment as in (A) except that extracellular is removed before agonist is applied a second time, confirming the residual presence of in the SR and hence the partial efficacy of CPA to inhibit SERCA (scenario of Fig. 6D). (Insets show magnifications of selected time windows).</p

dynamics in ASMC: experiment and model.

<p>(A)–(C): Fluorescence imaging of dynamics in an ASMC within a human lung slice, during the following 3-step experiment: (A) Agonist stimulation, (B) Rya-Caf treatment, and (C) second agonist stimulation. Following the irreversible Rya-Caf treatment in (B), agonist stimulation (C) is no longer able to elicit oscillations, nor does it perturb the new elevated equilibrium. <i>Reprinted from </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069598#pone.0069598-Ressmeyer1" target="_blank">[<i>2</i>] </a><i>under a CC BY license, with permission of the American Thoracic Society, original copyright 2010. Cite: Ressmeyer et al. /2010/Am J Respir Cell Mol Biol/43/179–191. Official journal of the American Thoracic Society. This modified figure is based on the original figure available from </i><a href="http://www.atsjournals.org" target="_blank">www.atsjournals.org</a>. (D)–(F): Simulations of the experiments in (A)–(C) using Eqs. 114–12 and the parameter values in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069598#pone-0069598-t001" target="_blank">Table 1</a>. The evolution of , , and (fraction of open SOCC) are shown (cf. legend in (E)).</p

Literature-based and estimated parameter values used in the ASM growth model.

<p>(^* indicates the values estimated from <i>in vitro</i> experiments.)</p

The role of individual inflammation history in the case of slow inflammation resolution (IR <<1).

<p>(a–c) ASM population size dynamics (<i>c</i>-cells, red; <i>p</i>-cells, blue; total population <i>s</i>, black) and (d–f) the corresponding inflammatory status evolution (μ, solid black; inflammatory thresholds μ₁ and μ₂, dashed), characterized by the same inflammation resolution rate, magnitude and average stimulus frequency (λ_d/λ_p  = 0.08, <i>a</i>/μ₁  = 0.5, ω/λ_p  = 0.25). (d) Regular series of inflammatory events; (e–f) two realisations of a series of inflammatory events at random times for the same mean frequency (about once a fortnight) as in (d). (g) Distribution of fold-increase in ASM mass after 300 days for a random sequence of inflammatory events with the same characteristics as in panels (b, c); arrows indicate the fold-increase corresponding to (a–c). (h) The distribution of outcomes with an increase of 25% in the inflammation resolution rate (λ_d/λ_p  = 0.1). (The outcome histograms (g,h) are computed for <i>N</i> = 1000 instances).</p

Survey of ASM growth scenarios, showing fold-increase in ASM population size after 300 days (colour scale) as a function of the inflammation resolution rate IR = λ_d/λ_p and (a) inflammation magnitude <i>a</i>/μ₁ (for fixed frequency ω/λ_p = 0.25) or (b) inflammation frequency ω/λ_p (for fixed magnitude <i>a</i>/μ₁ = 5).

<p>White dots indicate the growth regimes shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090162#pone-0090162-g002" target="_blank">Fig. 2</a>. Solid black lines are the computed isolines of the 2- and 8-fold ASM growth, which agree with the theoretically predicted dependence λ_d ∼ ω log <i>a</i>/μ₂ (dashed white lines; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090162#pone.0090162.s001" target="_blank">Materials S1</a>).</p

A schematic of the model design.

<p>(a) Schematic representation of the model with <i>p</i> being the amount of ASM cells in proliferating state, <i>c</i> the amount of non-proliferative cells and μ the inflammatory status; λ_p is the proliferation rate, λ_a is the apoptosis rate, λ_cp and λ_pc are the switching rates between non-proliferative and proliferative states, λ_d is the inflammation clearance rate, and <i>f</i>(<i>t</i>) is a time-dependent external inflammatory stimulus. (b) Dependence of the model parameters on the inflammatory status μ (three levels of inflammation are characterised by the thresholds μ₁ and μ₂; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090162#pone-0090162-t001" target="_blank">Table 1</a> for reference values). Rates are plotted on a logarithmic vertical scale. (c) An illustration of the inflammatory status dynamics induced by a series of environmental stimuli such as shown in (a), illustrating graphically the parameters λ_d, <i>a</i>, and ω. (d) A simulation of the ASM cell population response (<i>p</i>, blue dash-dotted; <i>c</i>, red dashed; <i>s</i> = <i>p</i>+<i>c</i>, thick black solid) to a stepwise variation in the inflammation status (thin solid); the arrows show the direction of change in the ASM subpopulations. Although the inflammatory status returns to its initial state at the end of the simulation, the total ASM cell population has irreversibly increased, showing thereby “effective” hysteresis. Only the time spent in “severe” regime (μ>μ₂) contributes to substantial growth (over weeks); however, the “moderate” regime (μ₁<μ<μ₂) can also give rise to substantial growth over a longer timescale (months). Note that the proportion of proliferative cells (blue dash-dotted) is significant only during the “severe inflammation” regime (3).</p

Possible pathways of chronic ASM mass accumulation in asthma (solid lines indicate the mechanisms included in the mathematical model).

<p>Possible pathways of chronic ASM mass accumulation in asthma (solid lines indicate the mechanisms included in the mathematical model).</p