Dr Carina Dunlop

We here consider modelling tissue growth and mechanotransduction, utilising a continuum approach based on the theory of elasticity. Our models are valid for both unhealthy and healthy tissues and assume a spherical symmetry is present. In principal, there are a number of tissue types which can be modelled using our framework, however, we choose to focus on three main tissue paradigms; epithelial cysts, ovarian follicles and avascular tumour spheroids, which all share common geometric features of a central core, surrounded by a proliferating rim of cells. In all cases, the tissues are embedded in a constraining outer gel. We show that growth within the tissue leads to the build-up of internal stress, and we find potential mechanotransductive mechanisms occurring as a result of this growth. These mechanisms are deemed switching points and we show that they can occur both as a result of the internal stress and of the associated strains. We also find that, for systems with a deformable central core, this core can expand and shrink passively as a result of growth within the surrounding material in parameter regimes that we identify. We also relax the assumption that the inner core is non-growing and consider that both phases of the tissue undergo growth. This leads to a competition of growth and we show that switching still occurs, but is now dependent upon the growth in both regions. This is considered specifically in the case of ovarian follicles, where we further observe that the cuboidalisation of cells can be produced as a consequence of the mechanics within the system. We next consider the addition of the effect of contractility upon the linear model using two techniques of implementation. The necessity of the use of nonlinear elasticity is then tested, from which we show that for most parameters within the realms of soft biological tissues, the linear approximation to the nonlinear model is of a sufficient likeness to warrant the use of the linear scheme. We find that the ratio of the Young's modulus of the tissue and the surrounding medium is key in determining the effectiveness of the linear model. These studies consistently highlight the importance of the mechanical properties of the tissue and surrounding extracellular matrix, specifically stressing the significance of the Young's modulus upon tissue growth dynamics.

Syncytial embryos develop through cycles of nuclear division and rearrangement within a common cytoplasm. A paradigm example is Drosophila melanogaster in which nuclei form an ordered array in the embryo surface over cell cycles 10-13. This ordering process is assumed to be essential for subsequent cellularisation. Using quantitative tissue analysis, it has previously been shown that the regrowth of actin and microtubule networks after nuclear division generates reordering forces that counteract its disordering effect (Kanesaki et al., 2011). We present here an individual-based computer simulation modelling the nuclear dynamics. In contrast to similar modelling approaches e.g. epithelial monolayers or tumour spheroids, we focus not on the spatial dependence, but rather on the time-dependence of the interaction laws. We show that appropriate phenomenological inter-nuclear force laws reproduce the experimentally observed dynamics provided that the cytoskeletal network regrows sufficiently quickly after mitosis. Then repulsive forces provided by the actin system are necessary and sufficient to regain the observed level of order in the system, after the strong disruption resulting from cytoskeletal network disassembly and spindle formation. We also observe little mixing of nuclei through cell cycles. Our study highlights the importance of the dynamics of cytoskeletal forces during this critical phase of syncytial development and emphasises the need for real-time experimental data at high temporal resolution. © 2014 Elsevier Ltd.

There is increasing experimental interest in mechanotransduction in multi-cellular tissues as opposed to single cells. This is driven by a growing awareness of the importance of physiologically relevant three-dimensional culture and of cell-cell and cell-gel interactions in directing growth and development. The paradigm biophysical technique for investigating tissue level mechanobiology in this context is to grow model tissues in artificial gels with well-defined mechanical properties. These studies often indicate that the sti↵ness of the encapsulating gel can significantly alter cellular behaviours. We demonstrate here potential mechanisms linking tissue growth with sti↵ness-mediated mechanotransduction. We show how tissue growth in gel systems generates points at which there is a significant qualitative change in the cellular stress and strain experienced. We show analytically how these potential switching points depend on the mechanical properties of the constraining gel and predict when they will occur. Significantly, we identify distinct mechanisms that act separately in each of the stress and strain fields at di↵erent times. These observations suggest growth as a potential physical mechanism coupling gel sti↵ness with cellular mechanotransduction in three-dimensional tissues. We additionally show that non-proliferating areas, in the case that the constraining gel is soft compared with the tissue, will expand and contract passively as a result of growth. Central compartment size is thus seen to not be a reliable indicator on its own for growth initiation or active behaviour.

The ability of cells to sense and respond to the mechanical properties of their environments is fundamental to a range of cellular behaviours, with substrate stiffness increasingly being found to be a key signalling factor. Although active contractility of the cytoskeleton is clearly necessary for stiffness sensing in cells, the physical mechanisms connecting contractility with mechanosensing and molecular conformational change are not well understood. Here we present a contractility-driven mechanism for linking changes in substrate stiffness with internal conformational changes. Cellular contractility is often assumed to imply an associated compressive strain. We show, however, that where the contractility is non-uniform, localized areas of internal stretch can be generated as stiffer substrates are encountered. This suggests a physical mechanism for the stretch-activation of mechanotransductive molecules on stiffer substrates. Importantly, the areas of internal stretch occur deep within the cell and not near the cellular perimeter, which region is more traditionally associated with stiffness sensing through e.g. focal adhesions. This supports recent experimental results on whole-cell mechanically-driven mechanotransduction. Considering cellular shape we show that aspect ratio acts as an additional control parameter, so that the onset of positive strain moves to higher stiffness values in elliptical cells.

Maintenance and activation of the limited supply of primordial follicles in the ovary are important determinants of reproductive lifespan. Currently, the molecular programme that maintains the primordial phenotype and the early events associated with follicle activation are not well defined. Here we have systematically analysed these events using microscopy and detailed image analysis. Using the immature mouse ovary as a model, we demonstrate that the onset of granulosa cell (GC) proliferation results in increased packing density on the oocyte surface and consequent GC cuboidalisation. These events precede oocyte growth and nuclear translocation of FOXO3a, a transcription factor important in follicle activation. Immunolabelling of the TGF signalling mediators and transcription factors, SMAD2/3, revealed a striking expression pattern specific to GCs of small follicles. SMAD2/3 was expressed in the nuclei of primordial GCs but was mostly excluded in early growing follicles. In activated follicles, GC nuclei lacking SMAD2/3 generally expressed Ki67. These findings suggest that the first phenotypic changes during follicle activation are observed in GCs, and that TGF signalling is fundamental for regulating GC arrest and the onset of proliferation.

It is known that cells grown in 3D are more tolerant to drug treatment than those grown in dispersion but the mechanism for this is still not clear; cells grown in 3D have opportunities to develop inter-cell communication, but are also closely packed which may impede diffusion. In this study we examine methods for dielectrophoresis-based cell aggregation of both suspension and adherent cell lines and compare the effect of various drugs on cells grown in 3D and 2D. Comparing viability of pharmacological interventions on 3D cell clusters against both suspension cells and adherent cells grown in monolayer, as well as against a unicellular organism with no propensity for intracellular communication, we suggest that 3D aggregates of adherent cells, compared to suspension cells, show a substantially different drug response to cells grown in monolayer, which increases as the IC50 is approached. Further, a mathematical model of the system for each agent demonstrates that changes to drug response are due to inherent changes in the system of adherent cells from the 2D to 3D state. Finally, differences within electrophysiological membrane properties of the adherent cell type suggest this parameter plays an important role in the differences found in the 3D drug response.

Cooperation is acting in the interests of one’s social group, often at a cost to yourself. When the level of cooperation is observed in the laboratory, people cooperate more often, and at higher levels than are predicted by standard theories. In this thesis I find two novel ways in which cooperation on multilayered populations is increased. These models contribute to an understanding of how people cooperate in real-world social situations, and help us to explain why people cooperate as much as they are observed to do. In each study I model the tension between the individual and the group using the public goods game. This game is played on a structured population defined by a multilayered network. Each layer represents a different sphere of influence on the player’s decision to cooperate or defect. The first model studies the effect of a player choosing whether to cooperate or defect on either all layers simultaneously (synchronously) or on one layer at a time (asynchronously). Updating asynchronously leads to increased cooperation across a number of different parameter regimes. This demonstrates a new way in which cooperation can be increased in a system with multiple influences, and also helps to understand exactly why cooperation is increased in multilayered systems. Inspired by empirical examples, the second model adds to the standard model of the public goods game on networks in two ways. The first is to include conditional cooperators, and the second is the addition of a layer of social influence. This combination of economic and social influence has not been considered in previous models of the public goods game, and I find that this additional layer of influence results in high levels of cooperation. In the final chapter, I study these dynamics on more realistic network structures, with results echoing empirical findings under certain parameters.