A thermodynamically motivated investigation of cell and tissue remodelling
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The overall objective of this thesis is to provide a new understanding of the mechanisms that drive cell spreading and remodelling, and to extend this understanding to remodelling at a tissue and organ level. A steady-state adaptation of the thermodynamically motivated stress fibre (SF) model of Vigliotti et al. (2015) is implemented in a non-local finite element setting, where global conservation of cytoskeletal proteins and binding integrins is considered. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell, to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experimental measurements. Experiments of cells adhering to “V-shaped” and “Y-shaped” ligand patches are also simulated, and analysis reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations. The equilibrium statistical mechanics framework developed by Shishvan et al. (2018) allows for the simulation of the homeostatic ensemble for cells on an elastic substrate. This framework is expanded to describe the free energy associated with formation of focal adhesions between the cell and substrate. The extended model is shown to predict the effects of substrate stiffness and surface collagen density on the response of spread cells, as reported experimentally by Engler et al. (2003). Alteration of the surface collagen density directly affects formation of adhesion complexes and the associated free energy. At a low collagen density there is a high probability cells will assume rounded morphologies with low spread areas. With increasing collagen densities, the probability of cells becoming highly spread with irregular morphologies increases. The influence of substrate stiffness is shown to be highly coupled with surface collagen density. Elastic free energy associated with substrate deformation lowers the probability of observing a highly spread cell, thereby altering the tractions that influence assembly of adhesion complexes. The homeostatic ensemble for cells, expanded to include focal adhesion formation, provides new insight into observed cell behaviour on deformable collagen coated substrates. The active cytoskeleton is known to play an important mechanistic role in cellular structure, spreading, and contractility. Contractility is actively generated by SFs, which continuously remodel in response to physiological dynamic loading conditions. The influence of actin-myosin cross-bridge cycling on SF remodelling under dynamic loading conditions has not previously been uncovered. A novel SF cross-bridge cycling model is developed to predict transient active force generation in cells subjected to dynamic loading. Rates of formation of cross-bridges within SFs are governed by the chemical potentials of attached and unattached myosin heads. This transient cross-bridge cycling model is coupled with a thermodynamically motivated framework for SF remodelling to analyse the influence of transient force generation on cytoskeletal evolution. The model is shown to correctly predict complex patterns of active cell force generation under a range of dynamic loading conditions, as reported in previous experimental studies. In order to bridge the gap between cell and organ level remodeling, a thorough understanding of the passive tissue mechanics is required. While the anisotropic behaviour of the complex composite myocardial tissue has been well characterized in recent years, the compressibility of the tissue has not been rigorously investigated to date. Experimental evidence is presented that passive excised porcine myocardium exhibits volume change under tensile and confined compression loading conditions. To simulate the multi-axial passive behaviour of the myocardium a nonlinear volumetric hyperelastic component is combined with the well-established Holzapfel-Ogden anisotropic hyperelastic component for myocardium fibres. This framework is shown to describe the experimentally observed behaviour of porcine and human tissues under shear and biaxial loading conditions. A representative volumetric element (RVE) of myocardium tissue is constructed to parse the contribution of the tissue vasculature to observed volume change under confined compression loading. Simulations of the myocardium microstructure suggest that the vasculature cannot fully account for the experimentally measured volume change. Additionally, the RVE is subjected to six modes of shear loading to investigate the influence of micro-scale fibre alignment and dispersion on tissue-scale mechanical behaviour. Hypertrophy of the ventricular myocardium develops following a change in cardiovascular loading conditions. The current understanding is that disease progression may be stress or strain driven, but the multi-scale nature of the cellular remodelling processes have yet to be uncovered. A model of the contractile left ventricle is developed, with active cell tension described by a thermodynamically motivated cross-bridge cycling model. Simulation of the transient recruitment of myosin results in correct patterns of ventricular pressure predicted over a cardiac cycle. A myofibril remodelling framework is coupled with the cross-bridge cycling model to investigate how deviations in the transient force generation drive restructuring of cellular myofibrils in the heart wall. Analyses reveal that pathological loading conditions can significantly alter actin-myosin cross-bridge cycling over the course of the cardiac cycle. The resultant alteration in sarcomere stress pushes an imbalance between the internal free energy of the myofibril and that of unbound contractile proteins, which onsets remodelling. Myofibril remodelling associated with concentric and eccentric hypertrophy is predicted to occur following periods of hypertension and volume overload, respectively. The link between cross-bridge thermodynamics and myofibril remodelling proposed may significantly advance current understanding of cardiac disease onset.
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