William Ronan

Numerical investigation of the active role of the actin cytoskeleton in the compression resistance of cells.

Numerous in-vitro studies have established that cells react to their physical environment and to applied mechanical loading. However, the mechanisms underlying such phenomena are poorly understood. Previous modelling of cell compression considered the cell as a passive homogenous material, requiring an artificial increase in the stiffness of spread cells to replicate experimentally measured forces. In this study, we implement a fully 3D active constitutive formulation that predicts the distribution, remodelling, and contractile behaviour of the cytoskeleton. Simulations reveal that polarised and axisymmetric spread cells contain stress fibres which form dominant bundles that are stretched during compression. These dominant fibres exert tension; causing an increase in computed compression forces compared to round cells. In contrast, fewer stress fibres are computed for round cells and a lower resistance to compression is predicted. The effect of different levels of cellular contractility associated with different cell phenotypes is also investigated. Highly contractile cells form more dominant circumferential stress fibres and hence provide greater resistance to compression. Computed predictions correlate strongly with published experimentally observed trends of compression resistance as a function of cellular contractility and offer an insight into the link between cell geometry, stress fibre distribution and contractility, and cell deformability. Importantly, it is possible to capture the behaviour of both round and spread cells using a given, unchanged set of material parameters for each cell type. Finally, it is demonstrated that stress distributions in the cell cytoplasm and nucleus computed using the active formulation differ significantly from those computed using passive material models.

The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force–indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force–indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force–indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force–indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling–experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

Numerous experimental studies have established that cells can sense the stiffness of underlying substrates and have quantified the effect of substrate stiffness on stress fibre formation, focal adhesion area, cell traction, and cell shape. In order to capture such behaviour, the current study couples a mixed mode thermodynamic and mechanical framework that predicts focal adhesion formation and growth with a material model that predicts stress fibre formation, contractility, and dissociation in a fully 3D implementation. Simulations reveal that SF contractility plays a critical role in the substrate-dependent response of cells. Compliant substrates do not provide sufficient tension for stress fibre persistence, causing dissociation of stress fibres and lower focal adhesion formation. In contrast, cells on stiffer substrates are predicted to contain large amounts of dominant stress fibres. Different levels of cellular contractility representative of different cell phenotypes are found to alter the range of substrate stiffness that cause the most significant changes in stress fibre and focal adhesion formation. Furthermore, stress fibre and focal adhesion formation evolve as a cell spreads on a substrate and leading to the formation of bands of fibres leading from the cell periphery over the nucleus. Inhibiting the formation of FAs during cell spreading is found to limit stress fibre formation. The predictions of this mutually dependent material-interface framework are strongly supported by experimental observations of cells adhered to elastic substrates and offer insight into the inter-dependent biomechanical processes regulating stress fibre and focal adhesion formation.

Experimental and Computational Investigation of the Role of Stress Fiber Contractility in the Resistance of Osteoblasts to Compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell’s actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.

Computational investigation of in situ chondrocyte deformation and actin cytoskeleton remodelling under physiological loading.

Previous experimental studies have determined local strain fields for both healthy and degenerate cartilage tissue during mechanical loading. However, the biomechanical response of chondrocytes in situ, in particular the response of the actin cytoskeleton to physiological loading conditions, is poorly understood. In the current study a three-dimensional (3-D) representative volume element (RVE) for cartilage tissue is created, comprising a chondrocyte surrounded by a pericellular matrix and embedded in an extracellular matrix. A 3-D active modelling framework incorporating actin cytoskeleton remodelling and contractility is implemented to predict the biomechanical behaviour of chondrocytes. Physiological and abnormal strain fields, based on the experimental study of Wong and Sah (J. Orthop. Res. 2010; 28: 1554-1561), are applied to the RVE. Simulations demonstrate that the presence of a focal defect significantly affects cellular deformation, increases the stress experienced by the nucleus, and alters the distribution of the actin cytoskeleton. It is demonstrated that during dynamic loading cyclic tension reduction in the cytoplasm causes continuous dissociation of the actin cytoskeleton. In contrast, during static loading significant changes in cytoplasm tension are not predicted and hence the rate of dissociation of the actin cytoskeleton is reduced. It is demonstrated that chondrocyte behaviour is affected by the stiffness of the pericellular matrix, and also by the anisotropy of the extracellular matrix. The findings of the current study are of particular importance in understanding the biomechanics underlying experimental observations such as actin cytoskeleton dissociation during the dynamic loading of chondrocytes.

On the role of the actin cytoskeleton and nucleus in the biomechanical response of spread cells

Micropipette aspiration (MA) has been used extensively in biomechanical investigations of un-adhered cells suspended in media. In the current study, a custom MA system is developed to aspirate substrate adhered spread cells. Additionally, the system facilitates immuno-fluorescent staining of aspirated cells to investigate stress fibre redistribution and nucleus deformation during MA. In response to an applied pressure, significantly lower aspiration length is observed for untreated contractile cells compared to cells in which actin polymerisation is chemically inhibited, demonstrating the important contribution of stress fibres in the biomechanical behaviour of spread cells. Additional experiments are performed in which untreated contractile cells are subjected to a range of applied pressures. Computational finite element simulations reveal that a viscoelastic material model for the cell cytoplasm is incapable of accurately predicting the observed aspiration length over the range of applied pressures. It is demonstrated that an active computational framework that incorporates stress fibre remodelling and contractility must be used in order to accurately simulate MA of untreated spread cells. Additionally, the stress fibre distribution observed in immuno-fluorescent experimental images of aspirated cells is accurately predicted using the active stress fibre modelling framework. Finally, a detailed experimental-computational investigation of the nucleus mechanical behaviour demonstrates that the nucleus is highly deformable in cyto, reaching strain levels in excess of 100% during MA. The characterisation of stress fibres and nucleus biomechanics in spread cells presented in the current study can potentially be used to guide tissue engineering strategies to control cell behaviour and gene expression.

Simulation of the mechanical response of cells on micropost substrates.

Experimental studies where cells are seeded on micropost arrays in order to quantify their contractile behavior are becoming increasingly common. Interpretation of the data generated by this experimental technique is difficult, due to the complexity of the processes underlying cellular contractility and mechanotransduction. In the current study, a coupled framework that considers strain rate dependent contractility and remodeling of the cytoskeleton is used in tandem with a thermodynamic model of tension dependent focal adhesion formation to investigate the biomechanical response of cells adhered to micropost arrays. Computational investigations of the following experimental studies are presented: cell behavior on different sized arrays with a range of post stiffness; stress fiber and focal adhesion formation in irregularly shaped cells; the response of cells to deformations applied locally to individual posts; and the response of cells to equibiaxial stretching of micropost arrays. The predicted stress fiber and focal adhesion distributions; in addition to the predicted post tractions are quantitatively and qualitatively supported by previously published experimental data. The computational models presented in this study thus provide a framework for the design and interpretation of experimental micropost studies.

Modelling the degradation and elastic properties of poly(lactic-co-glycolic acid) films and regular open-cell tissue engineering scaffolds

Scaffolding plays a critical rule in tissue engineering and an appropriate degradation rate and sufficient mechanical integrity are required during degradation and healing of tissue. This paper presents a computational investigation of the molecular weight degradation and the mechanical performance of poly(lactic-co-glycolic acid) (PLGA) films and tissue engineering scaffolds. A reaction-diffusion model which predicts the degradation behaviour is coupled with an entropy-based mechanical model which relates Young׳s modulus and the molecular weight. The model parameters are determined based on experimental data for in-vitro degradation of a PLGA film. Microstructural models of three different scaffold architectures are used to investigate the degradation and mechanical behaviour of each scaffold. Although the architecture of the scaffold does not have a significant influence on the degradation rate, it determines the initial stiffness of the scaffold. It is revealed that the size of the scaffold strut controls the degradation rate and the mechanical collapse. A critical length scale due to competition between diffusion of degradation products and autocatalytic degradation is determined to be in the range 2-100μm. Below this range, slower homogenous degradation occurs; however, for larger samples monomers are trapped inside the sample and faster autocatalytic degradation occurs.

Cooperative contractility: the role of stress fibres in the regulation of cell-cell junctions

We present simulations of cell-cell adhesion as reported in a recent study [Liu et al., 2010, PNAS, 107(22), 9944-9] for two cells seeded on an array of micro-posts. The micro-post array allows for the measurement of forces exerted by the cell and these show that the cell-cell tugging stress is a constant and independent of the cell-cell junction area. In the current study, we demonstrate that a material model which includes the underlying cellular processes of stress fibre contractility and adhesion formation can capture these results. The simulations explain the experimentally observed phenomena whereby the cell-cell junction forces increase with junction size but the tractions exerted by the cell on the micro-post array are independent of the junction size. Further simulations on different types of micro-post arrays and cell phenotypes are presented as a guide to future experiments.

Effects of material thickness and processing method on poly(lactic-co-glycolic acid) degradation and mechanical performance

In this study, the effects of material thickness and processing method on the degradation rate and the changes in the mechanical properties of poly(lactic-co-glycolic acid) material during simulated physiological degradation were investigated. Two types of poly(lactic-co-glycolic acid) materials were considered: 0.12 mm solvent-cast films and 1 mm compression-moulded plates. The experimental results presented in this study were compared to the experimental results of Shirazi et al. (Acta Biomaterialia 10(11):4695–703, 2014) for 0.25 mm solvent-cast films. These experimental observations were used to validate the computational modelling predictions of Shirazi et al. (J Mech Behav Biomed Mater 54: 48–59, 2016) on critical diffusion length scale and also to refine the model parameters. The specific material processing methods considered here did not have a significant effect on the degradation rate and the changes in mechanical properties during degradation; however, they influenced the initial molecular weight and they determined the stiffness and hardness of the poly(lactic-co-glycolic acid) material. The experimental observations strongly supported the computational modelling predictions that showed no significant difference in the degradation rate and the changes in the elastic modulus of poly(lactic-co-glycolic acid) films for thicknesses larger than 100 μm.