Inverse modeling unveils governing law of mechano-chemical dynamics of epithelial migration.

Collective cell migration is fundamental to tissue homeostasis and underlies biological processes such as wound healing and cancer invasion. Previous work has proposed governing equations to describe how chemical and mechanical inputs regulate these movements, but the quantitative validity of such models remains to be thoroughly assessed. Here, we developed a machine-learning framework that infers the governing equation from live-cell imaging data. Applied to epithelial sheet migration driven by MAPK/ERK, our approach quantitatively predicted single-cell movement from local chemical and mechanical cues. Examination of the learned equations further indicated that cells process environmental signals by computing their spatiotemporal derivatives. Moreover, when applied to individual cells, our framework revealed cell-cell heterogeneity in the underlying migratory rules. Our framework offers a powerful tool for predictive modeling of multicellular dynamics in both physiological and pathological settings.