Modelling cell–matrix interactions in airway smooth muscle cells

Tissues, in both humans and animals, consist of cells embedded in a dynamic scaffold known as the extracellular matrix (ECM). Cells interact with the ECM through the process of cell–matrix adhesion, and these interactions, mediated by transmembrane proteins called integrins, are fundamental in regulating a diverse range of physiological processes. The focus of this thesis is on airway smooth muscle (ASM) cell–matrix adhesion, which regulates the transmission of contractile forces generated within ASM cells to the ECM. This is of particular importance in the context of asthma, where contraction of ASM cells, and the subsequent transmission of contractile forces to the surrounding tissue, leads to a narrowing of the airways called bronchoconstriction. In this thesis, we develop mathematical models of ASM cell–matrix adhesion; our objective is to investigate how integrin-mediated adhesions are affected by the dynamic mechanical environment of the in vivo airway. In particular, we aim to gain insight into how integrins respond to tidal breathing and deep inspirations (DIs), since changes in integrin dynamics may affect the extent of airway narrowing during bronchoconstriction. Firstly, we develop a discrete stochastic–elastic model and a multiscale continuum model (Chapter 2), both able to account for detailed integrin binding kinetics alongside material deformations at the cell level. With these models we observe two distinct adhesion regimes in response to oscillatory loading, where either adhesion formation or adhesion rupture dominate (Chapter 3). For intermediate oscillation amplitudes we observe bistability due to shared loading and, as a result, we find that perturbations in the loading amplitude, mimicking DIs, can lead to different outcomes for the level of adhesion. This will affect the level of attainable force transmission during ASM cell contraction, and we discuss the possible consequences for airway narrowing. There is strong qualitative agreement between our discrete and continuum model results, and we consider several extensions of the continuum model (Chapter 4) to allow for activation, diffusion and strain-dependent reinforcement of integrins. In addition to theoretical results, we present and analyse experimental data from atomic force microscopy experiments (Chapter 5). In the experiments, cells were subject to vertical oscillatory loading of varying amplitudes. By extending the continuum model to support vertical motion, we mimic the experimental protocol and, in agreement with the data, we obtain two distinct temporal patterns in adhesion force. Our simulations provide insight into the underlying integrin dynamics and the resulting cell deformation; these cannot currently be measured by experiments but are predicted by the model. We use cluster analysis techniques to study force timecourses from individual cells and, in some cases, we observe switching behaviours that could be an indicator for bistability. The integrin response to oscillatory loading affects how contractile forces are transmitted from ASM cells to the ECM. However, it is also known that oscillatory loading affects the generation of contractile force (which is mediated by actomyosin crossbridges within the cell). In order to fully understand the consequences for bronchoconstriction, it is therefore important to consider how these processes interact. To investigate this, we couple our model of cell–matrix adhesion to a well-established model of contractile force generation (Chapter 6). Our results demonstrate a close mechanical coupling between the two processes and show that both force transmission (via integrins) and force generation (via crossbridges) are modulated by oscillatory loading. Moreover, there is feedback between the two processes and a regulatory mechanism due to negative feedback. We observe two regions of bistability: one as reported in our earlier results, due to shared loading between integrins, and a second due to analogous mechanisms for the crossbridges. These both introduce hysteresis and can result, in each case, in reduced levels of total contractile force after large amplitude oscillations. It is known from experiments that deep inspirations can induce either transient or sustained bronchodilation, and that these responses differ in asthmatics and non-asthmatics. Because of the hysteresis in total contractile force, we hypothesise that bistability could be an underlying mechanism by which sustained bronchodilation occurs. Furthermore, we show that the bistability can be lost for changes in the passive cell stiffness or in the relative crossbridge to integrin strength; a loss of bistability would result in an inability to obtain sustained reductions in contractile force, which could correspond to the transient bronchodilation seen in asthmatics