COPD association results in stage 1 and 2 for lung function sentinel variants analysed in stage 2.

<p>COPD association results in stage 1 and 2 for lung function sentinel variants analysed in stage 2.</p

Collapsing methods results for most significant loci in stage 2.

<p>Collapsing methods results for most significant loci in stage 2.</p

Flow chart of the variant selection process.

<p>Flow chart of the variant selection process.</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

Representative ASM cell population growth dynamics over a period of 300 days, starting from a “healthy” state (<i>c</i> = 0.1, <i>p</i> = 0.01), for different values of normalised inflammation magnitude <i>a</i>/μ₁, frequency ω/λ_p and inflammation resolution rate λ_d/λ_p: <i>a</i>/μ₁ = {2 (a), 5 (b,c), 8 (d), 1.5 (e)}, ω/λ_p = {0.25 (a,c–e), 0.125 (b)} and λ_d/λ_p = {7 (a), 5 (b,c), 2 (d), 0.22 (e)}.

<p>(a,b) show no substantial ASM accumulation, (c,e) show “moderate” and (d) “severe” ASM hyperplasia. The amount of <i>c</i>-cells is depicted by the red line, <i>p</i>-cells (blue) and total population size <i>s</i> = <i>p</i>+<i>c</i> (thick black). Insets plot the corresponding inflammatory status μ (solid black) and the inflammation level thresholds (horizontal dashed lines).</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

Characteristics of Gedling and replication COPD cases and controls.

<p>Characteristics of Gedling and replication COPD cases and controls.</p