Bayesian inference of force dynamics during morphogenesis.

During morphogenesis, cells push and pull each other to trigger precise deformations of a tissue to shape the body. Therefore, to understand the development of animal forms, it is essential to analyze how mechanical forces coordinate behaviors of individual cells that underlie tissue deformations. However, the lack of a direct and non-invasive force-measurement method has hampered our ability to identify the underlying physical principles required to regulate morphogenesis. In this study, by employing Bayesian statistics, we develop a novel inverse problem framework to estimate the pressure of each cell and the tension of each contact surface from the observed geometry of the cells. We confirmed that the true and estimated values of forces fit well in artificially generated data sets. Moreover, estimates of forces in Drosophila epithelial tissues are consistent with other readouts of forces obtained by indirect or invasive methods such as laser-induced destruction of cortical actin cables. Using the method, we clarify the developmental changes in the patterns of tensile force in the Drosophila dorsal thorax. In summary, the batch and noninvasive nature of the described force-estimation method will enable us to analyze the mechanical control of morphogenesis at an unprecedented quantitative level.