Modelling of Epithelial-to-Mesenchymal Transition in Invading Cells

Cell migration is at the core of many biological processes in development and cancer progression. Epithelial-to-mesenchymal transition (EMT), i.e. the temporary and reversible switching between epithelial and mesenchymal phenotypes, plays a crucial role in increasing the motility and invasiveness of cells, representing a potential therapeutic target in many biomedical areas. With the surge of omics data, we are now more than ever able to characterise the phenotypic properties of cells and require theoretical frameworks which can effectively integrate such information to help us predict tissue-level behaviours for optimisation of therapeutic interventions.My project is devoted to the development of such a theoretical framework, in which cell migration through the extracellular matrix (ECM) is mediated by the cell phenotypic state which may change guided by mechanistic rules for EMT, incorporating information on the cell phenotypic state coming from omics data.I will focus on mathematical models comprising nonlocal partial differential equations of the evolutionary dynamics of space- and phenotype-structured cell populations. By representing cell phenotypes on a continuum, the models can capture intratumour heterogeneity and hybrid phenotypes, and may be directly linked with transcriptomic and proteomic data. This project will tackle the analytical and numerical challenges stemming from movement in physical space, modelling heterogeneous cell motion in the ECM, and complex phenotypic drifts, incorporating a description of core regulatory circuits for EMT, yet to be investigated in a unified framework. Moreover, we will address the inverse problem of employing transcriptomic data to infer the nonlinear impact of environmental factors on the core regulatory circuit mediating phenotypic changes, to this day an open problem.The outcomes of the project will advance mathematical, biomedical and interdisciplinary research.