| Summary: | Collective cell migration is the defining characteristic of many biological events involved in morphogenesis, regeneration, and pathology. This abundance, together with the immense clinical and therapeutic advances that would arise from the ability to control collective migration in specific applications in regenerative medicine and oncology, has led to an enormous increase in the number of studies on collective cell migration. Yet, the integration of large biological data sets with modelling has proven challenging. In this thesis, we address three main challenges: connecting mathematical models with high-dimensional data, leveraging biological data to learn new mathematical models, and controlling biological systems using mathematical models. In our first case study, we combine individual-based models with computational Bayesian statistics to identify links between genetic perturbations and cellular phenotypes in a large siRNA screen. We propose a new approach to approximate Bayesian computation (ABC) and show that it is possible to identify the functional impact of a range of different genetic perturbations. Second, in the context of Madin-Darby canine kidney (MDCK) epithelial monolayers, we use a continuum mechanics model to characterise the role of mechanical power expenditure in regulating active cellular forces. We then utilise this knowledge in a continuum model for collective electrotaxis which takes into account energy expenditure during migration, and develop an optimal control framework to achieve experimentally desirable outcomes. By deriving a Keller-Segel type model of collective electrotaxis, we propose design of optimal electric fields that vary in space and in time. Finally, by combining single-cell tracking with deep attention networks, we discover a set of genes critical for the invasion of c8161 melanoma cells: failure to express these genes leads to abnormal leader-follower dynamics. Together, the contributions of this thesis are towards developing new approaches to data-driven mathematical modelling, using the derived models to control biological systems, and understanding the underlying mechanisms.
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