Spreading and locomotion enable the cells to explore their microenvironments during the interphase period of the cell cycle (24-48 hours after cell seeding and prior to cell division). The morphologies adopted by cells in this period dictate orientational ordering, direction and speed of migration, lineage of differentiation and apoptosis. It is well established that cells display a fluctuating response in their microenvironments, and no two cells evolve in the same manner despite being cultured under identical conditions. However, the statistics of cell spreading (i.e. morphometrics such as cell area, aspect ratio, etc.) are remarkably reproducible when experiments are performed over a large number of cells. A mechanistic understanding of this stochastic behaviour of cells will have far-reaching implications in aiding the interpretation of a wide range of cell functionalities.

The aim of this thesis is to model the response of single cells to mechanical, chemical and geometric cues in their microenvironment. In the first part of the thesis, we study the contact guidance of myofibroblasts on adhesive stripes of different widths. Contact guidance—the widely-known phenomenon of cell alignment induced by anisotropic environmental features—plays a crucial role in the micro-architecture of tissues and dictates their biological and mechanical functioning. However, the mechanisms by which cells achieve this orientational ordering remain unclear. To examine the mechanisms underpinning contact guidance, we combine detailed morphometric analysis of cells and their subcellular components with the novel homeostatic mechanics framework that recognises the non-thermal fluctuating response of living cells. We show that similar to nematic ordering in liquid crystals, orientational ordering of cells on micropatterns is driven, rather counter-intuitively, by the tendency of cells to maximise morphological disorder. This finding reveals an alternative, entropy-mediated mechanism for explaining the response of cells to anisotropic environmental cues besides the often-invoked mechanisms that are predicated on very specific biochemical feedback pathways.

In the second part of the thesis, we extend the framework to investigate the role of substrate curvature in the orientational ordering of myofibroblasts. We propose that the microtubules are the primary cytoskeletal component involved in curvature sensing. Using detailed morphometric analysis, we confirm our hypothesis, and additionally verify that the microtubules control the patterns of stress-fibres formed in cells, in turn controlling cell polarisation and alignment. We also observe that the absence of microtubules results in reduced guidance on the curved substrates, concomitant with increased cellular traction forces.

The variability in morphometrics (such as cell shape, area, cytoskeletal protein arrangements and traction forces) also reflects in other critical cell functionality. In particular, the fluctuating response of stem cells on mechanical, chemical and geometric cues has been shown to direct lineage commitment and differentiation. In the third part of the thesis, we apply the homeostatic mechanics framework to forecast the differentiation of human mesenchymal stem cells (hMSCs) in response to a range of environmental cues including sizes of adhesive islands, stiffness of substrates, and treatment with ROCK inhibitors in both growth and mixed media. The cytoskeletal free-energy, which succinctly parameterises the biochemical state of the cell, is shown to capture hMSC commitment over a range of environments while simple morphological factors such as cell shape, tractions on their own are unable to correlate with lineages hMSCs adopt.

Finally, we summarize the key insights from viewing contact guidance and stem cell differentiation through the lens of the homeostatic mechanics framework. Inspired by the success of the framework in capturing diverse biophysical phenomena, we provide suggestions for future work that can further enhance the versatility of the framework.