Fig. 2.

Overview of the biochemical mechanisms. Allergen or contractile agonist challenges, f(t), specified to occur at times $t_i$, drive evolution of an inflammatory factor, $\mu$, and contractile agonist concentration, k. The magnitude and rate of clearance of $\mu$ and k are determined by constants $a_{\mu }$, $a_k$, and $c_{\mathrm{d}\mu },c_{\mathrm{d}k}$, respectively. Inflammation leads to global release of contractile agonist at rate $a_{k\mu }$. Contractile agonist induces local ASMC contraction, and the resulting increased mechanical stress $\tau$ releases further cytokines, with contractile agonist properties, at rate $a_{\mathrm{c}}$. Contractile ASMCs undergo apoptosis ($c_{\mathrm{a}}$) and switching to a proliferative phenotype ($c_{\mathrm{cp}}$). The proliferative ASMCs divide ($c_{\mathrm{p}}$) and switch to a contractile phenotype at a (high) constant rate ($c_{\mathrm{pc}}$). Both inflammation and mechanical stress drive increases (from a baseline) in the contractile to proliferative switching rate ($c_{\mathrm{cp}}(\mu ,\tau )$), and increasing mechanical stress drives increases in the proliferation or recruitment rate ($c_{\mathrm{p}}(\tau )$). ECM proteins degrade ($c_{\mathrm{de}}$) and are deposited ($c_{\mathrm{be}}(\mu )$) at baseline rates during normal tissue maintenance, with the latter increasing with inflammation. Proliferating ASMCs produce additional ECM proteins (with rate $c_{\mathrm{pe}}$). Blue dotted arrows indicate how constituent volume fractions are required for computation of the mechanical stress ($\tau$), as illustrated in Fig. 1. Rate constants are given in Online Resource 2