Kalman-filter Force Inference: an estimation framework for cellular forces from temporal evolution of epithelial morphogenesis

Abstract

Epithelial morphogenesis is orchestrated by cellular forces, such as cell junctional tension and cellular pressure. Therefore, elucidating the spatiotemporal distribution of these forces and their dynamics is paramount to understand morphogenesis during development. Over the past decade, various force inference methods have been proposed to estimate cellular forces based on the shape and geometry of cells within epithelial tissues. Most of these methods were developed under the assumption of static force balance, which neglects the cell deformation, thereby limiting their applicability to tissue undergoing dynamic deformation. To address this issue, we develop a novel method to accurately infer cellular forces from time-lapse imaging data of epithelial deformation, without relying on the static force balance assumption. Our method is based on two fundamental assumptions. First, the forces exerted by cells are balanced with dissipative forces (such as viscous and frictional forces) at each vertex arising from cell deformation, referred to as the dynamic force balance. Second, cellular forces vary smoothly over time. By formalizing these assumptions using a Bayesian framework, we construct a new approach of force inference, named Kalman-filter Force Inference (KFI). The effectiveness of our method is evaluated using synthetic data of a deforming tissue generated by numerical simulations of the cell vertex model. The results demonstrate the accurate estimation of cellular force dynamics. Furthermore, our systematic evaluation reveals the capability of our method to accurately estimate cellular forces across tissues with diverse mechanical parameters. Finally, we assessed the robustness of our method to observation noise. We anticipate that Kalman-filter Force Inference will broaden the applicability of force inference techniques and significantly contribute to our understanding of epithelial mechanics.