Modeling Collective Cell Migration in a Data-Rich Age: Challenges and Opportunities for Data-Driven Modeling

Mathematical modeling has a long history in the context of collective cell migration, with applications throughout development, disease, and regenerative medicine. The aim of modeling in this context is to provide a framework in which to mathematically encode experimentally derived mechanistic hypotheses and then to test and validate them to provide new insights and understanding. Traditionally, mathematical models have consisted of systems of partial differential equations that model the evolution of cell density over time, together with the dynamics of any associated biochemical signals or the underlying substrate. The various terms in the model are usually chosen to provide simplified, phenomenological descriptions of the underlying biology and follow long-standing conventions in the field. However, with the recent development of a plethora of new experimental technologies that provide quantitative data on collective cell migration processes, we now have the opportunity to leverage statistical and machine learning tools to determine mathematical models directly from the data. This article aims to provide an overview of recently developed data-driven modeling approaches, outlining the main methodologies and the challenges involved in using them to interrogate real-world data relating to collective cell migration.