Kalman-filter force inference: an estimation framework for cellular forces from temporal evolution of epithelial...

Epithelial morphogenesis is orchestrated by cellular forces, including cell junctional tension and cellular pressure. Elucidating their spatio-temporal dynamics is paramount for understanding morphogenesis during development. While various methods have been proposed to infer cellular forces from the shape and geometry of cells within epithelial tissues, most rely on the assumption of static force balance, which neglects cell deformation, thereby limiting their applicability to tissues undergoing dynamic deformation. To address this, we develop a novel method to accurately infer cellular forces from time-lapse imaging data by explicitly accounting for tissue dynamics. Our method rests on two fundamental assumptions. First, cellular forces balance dissipative forces (viscous and frictional forces) arising from cell deformation, termed the dynamic force balance. Second, cellular forces evolve smoothly. A Bayesian formalization of these assumptions yields a new force inference approach: Kalman-filter force inference. We evaluated our method using synthetic data from cell vertex model simulations. The results demonstrated accurate estimation of cellular force dynamics across diverse cell mechanical parameters. Furthermore, the method proved robust to observation noise. Our method will broaden the applicability of force inference and provide new insights into the mechanical principles underlying epithelial morphogenesis.