Cells experience different mechanical cues from their local environment, including shear flow, forces applied by neighbouring cells, and substrate stiffness. These external signals influence cell behaviour, also in embryonic stem (ES) cells, where they could potentially affect pluripotency or differentiation. The precise effects of external forces on ES cells are confounded by forces inducing secondary changes to attachment or cell-cell signalling, which themselves can also influence cell behaviour. In this study we developed a set-up to attach cells to elastic membranes using a novel functionalisation technique, and exposed them to single or cyclic stretch. We used this method to study the mechanosensitive response of ES cells. We found that stretching caused an immediate increase in the concentration of intracellular calcium, followed by a rapid decrease in some cells. On timescales of 1 - 2 h, stretching induced an increase in the expression of the immediate and early genes, but then cells became temporarily insensitive to subsequent mechanical signals. Stretching did not have a substantial impact on pluripotency and differentiation, as we showed using gene expression studies and a Rex1 reporter. To study how ES cells' susceptibility to mechanical signals depended on media condition, stretch duration and stretch type, we performed RNA sequencing and used gene ontology techniques to investigate the involvement of specific pathways. We found that forces have a broad impact on the overall transcriptome that is highly culture media-dependent. However, a core transcriptional response, including the biosynthesis of membrane components and stress pathways, was largely preserved across the different conditions. We supplemented our experimental findings with a conceptual model of force propagation in disordered environments, such as the nucleus of a cell. Using computational simulations, we studied how the large-scale behaviour of a disordered system depends on the microscopic structure. Contrary to common wisdom, we showed that disordered systems exhibit both positive and negative Poisson's ratios with equal probability. Overall, on short timescales, stretching affected ES cells' calcium concentration and transcription. On longer timescales, ES cells' response was small in magnitude but broad in scope, with limited effects on pluripotency. As such, our results suggest that mechanosensitivity in ES cells is mediated primarily by tissue-wide changes to morphology and attachment.

When the states of a system can be described by the extrema of a high-dimensional function, the characterisation of its complexity, i.e. the enumeration of the accessible stable states, can be reduced to a sampling problem. In this thesis a robust numerical protocol is established, capable of producing numerical estimates of the total number of stable states for a broad class of systems, and of computing the a-priori probability of observing any given state. The approach is demonstrated within the context of the computation of the configurational entropy of two and three-dimensional jammed packings. By means of numerical simulation we show the extensivity of the granular entropy as proposed by S.F. Edwards for three-dimensional jammed soft-sphere packings and produce a direct test of the Edwards conjecture for the equivalent two dimensional systems. We find that Edwards’ hypothesis of equiprobability of all jammed states holds only at the (un)jamming density, that is precisely the point of practical significance for many granular systems. Furthermore, two new recipes for the computation of high-dimensional volumes are presented, that improve on the established approach by either providing more statistically robust estimates of the volume or by exploiting the trajectories of the paths of steepest descent. Both methods also produce as a natural by-product unprecedented details on the structures of high-dimensional basins of attraction. Finally, we present a novel Monte Carlo algorithm to tackle problems with fluctuating weight functions. The method is shown to improve accuracy in the computation of the ‘volume’ of high dimensional ‘fluctuating’ basins of attraction and to be able to identify transition states along known reaction coordinates. We argue that the approach can be extended to the optimisation of the experimental conditions for observing certain phenomena, for which individual measurements are stochastic and provide little guidance.

The goal of this thesis has been to find a means of i) designing an active square particle, and ii) continuously varying its degree of activity with the objective of understanding the effects of activity on the various phases of granular matter. The motivations, results and limitations of our methods of creating active particles are discussed in this thesis. The applicability of a stochastic model based on the Langevin equation in 2D as well as implications for future experiments are also discussed.