Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualizing the emergent behavior of cells. We first review how this inference problem has been addressed in freely migrating cells on two-dimensional substrates and in structured, confining systems. Moreover, we discuss how data-driven methods can be connected with molecular mechanisms, either by integrating mechanistic bottom-up biophysical models, or by performing inference on subcellular degrees of freedom. Finally, we provide an overview of applications of data-driven modelling in developing frameworks for cell-to-cell variability in behaviours, and for learning the collective dynamics of multicellular systems. Specifically, we review inference and machine learning approaches to recover cell-cell interactions and collective dynamical modes, and how these can be integrated into physical active matter models of collective migration.