Cells often chemotax, directing their motion in response to a chemical signal. We develop models of strategies for chemotaxis in complex environments. Groups of cells may cooperate to sense a chemical signal. One strategy is to specialize into leader cells that sense the gradient and follower cells that follow the clusters direction. We find that this specialization can speed up cluster migration in steep gradients, where a few cells have much more information than the other cells in the cluster. Surprisingly, specialization may also be optimal in shallow gradients. There are tradeoffs between cluster speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters. In addition, single cells can express multiple types of receptors with varying affinities for the same signal. Will this help chemotactic accuracy? If the environment is not variable, using multiple receptor types is less effective than a single receptor type tuned to the environment. However, as environmental variability increases, cells should hedge their bets by expressing multiple receptor types adapted to varying environments. Cells can make several measurements of the signal over time, combining them to make a consistent estimate. Remarkably, time-integration for multiple receptor types is qualitatively different from a single type, allowing cells to extract orders of magnitude more information by using a maximum likelihood estimate.

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Developing effective cancer treatment presents a unique challenge due to the overwhelming variability in tumour cell behaviour and spatial heterogeneity. Virotherapy is a type of cancer treatment that uses genetically engineered viruses to infect and lyse cancerous cells. When these viruses are administered with immune cells or immunostimulatory cytokines, an antitumour immune response is instigated. Developing a hybrid PDE/agent-based modelling for the treatment of glioblastoma (a type brain cancer), we predicted the variability in glioblastoma cells that hinders the efficacy of oncolytic virotherapy. We then show how this treatment could be improved for the majority of patients. Recently, gel-based mediums have been used to improve the efficacy of oncolytic virotherapy by providing a sustained therapeutic delivery of the vectors . Using a system of ODEs and a genetic algorithm, we show how this treatment could be further optimised by changing the gel-material to reduce the immune cell release rate. Overall, this talk aims to demonstrate complementing mathematical models and their applications in oncolytic virotherapy.

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In general, the mechanisms by which walled cells specify their shapes are not fully understood. This project is a case study towards understanding the cell-shape formation during tip-cell elongation at the early developmental stage of mosses. We have developed a mathematical method that decomposes cell wall areal growth and cell wall stretching based on imaging data of cell outlines with and without turgor pressure. The decomposition illustrates how these two mechanisms influence cell shapes from two different cell types of mosses: faster-extending caulonema versus slower-extending choloronema. Joint work with: Danush Chelladurai, Giulia Galotto, Luis Vidali, and Jocelyn Petitto