We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply Bayesian inversion stress microscopy to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi one-dimensional geometry
We study the closure dynamics of a large number of well-controlled circular apertures within an epithelial monolayer, where the collective cell migration responsible for epithelization is triggered by the removal of a spatial constraint rather than by scratching. Based on experimental observations, we propose a physical model that takes into account border forces, friction with the substrate, and tissue rheology. Border protrusive activity drives epithelization despite the presence of a contractile actomyosin cable at the periphery of the wound. The closure dynamics is quantified by an epithelization coefficient, defined as the ratio of protrusive stress to tissue-substrate friction, that allows classification of different phenotypes. The same analysis demonstrates a distinct signature for human cells bearing the oncogenic RasV12 mutation, demonstrating the potential of the approach to quantitatively characterize metastatic transformations.
During development, epithelial tissues undergo extensive morphogenesis based on coordinated changes of cell shape and position over time. Continuum mechanics describes tissue mechanical state and shape changes in terms of strain and stress. It accounts for individual cell properties using only a few spatially averaged material parameters. To determine the mechanical state and parameters in the Drosophila pupa dorsal thorax epithelium, we severed in vivo the adherens junctions around a disc-shaped domain comprising typically a hundred cells. This enabled a direct measurement of the strain along different orientations at once. The amplitude and the anisotropy of the strain increased during development. We also measured the stress-to-viscosity ratio and similarly found an increase in amplitude and anisotropy. The relaxation time was of the order of 10 s. We propose a space – time, continuous model of the relaxation. Good agreement with experimental data validates the description of the epithelial domain as a continuous, linear, visco-elastic material. We discuss the relevant time and length scales. Another material parameter, the ratio of external friction to internal viscosity, is estimated by fitting the initial velocity profile. Together, our results contribute to quantify forces and displacements, and their time evolution, during morphogenesis.
Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.