Abstract
Cellular mechanics drives epithelial morphogenesis, the process wherein cells collectively rearrange to produce tissue-scale deformations that determine organismal shape. However, quantitative understanding of tissue mechanics is impaired by the difficulty of direct measurement of stress in vivo. This difficulty has spurred the development of image-based inference algorithms that estimate stress from snapshots of epithelial geometry. Such methods are challenged by sensitivity to measurement error and thus require accurate geometric segmentation for practical use. We overcome this difficulty by introducing a novel approach—the variational method of stress inference (VMSI)—which exploits the fundamental duality between stress and geometry at equilibrium of discrete mechanical networks that model confluent cellular layers. We approximate the apical geometry of an epithelial tissue by a 2D tiling with circular arc polygons in which arcs represent intercellular interfaces defined by the balance of local line tension and pressure differentials between adjacent cells. The mechanical equilibrium of such networks imposes extensive local constraints on circular arc polygon geometry. These constraints provide the foundation of VMSI which, starting with images of epithelial monolayers, simultaneously approximates both tissue geometry and internal forces, subject to the constraint of equilibrium. We find VMSI to be more robust than previous methods. Specifically, the VMSI performance is validated by the comparison of the predicted cellular and mesoscopic scale stress with the measured myosin II patterns during early Drosophila embryogenesis. VMSI prediction of a mesoscopic stress tensor correlates at the 80% level with the measured myosin distribution and reveals that most of the myosin activity in that case is involved in a static internal force balance within the epithelial layer. In addition to insight into cell mechanics, this study provides a practical method for nondestructive estimation of stress in live epithelial tissue.
6 More- Received 6 February 2019
- Revised 10 September 2019
- Accepted 16 December 2019
DOI:https://doi.org/10.1103/PhysRevX.10.011072
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Morphogenesis, the process by which a developing embryo shapes itself, requires precise orchestration of growth and cell rearrangements. Mechanical interactions between cells play a prominent role in controlling morphogenesis, but their study has been impeded by the difficulty of directly measuring mechanical stress in live tissues. One promising solution is based on highly developed fluorescent imaging of live tissues and aims to infer mechanical stress from the observed 2D geometry of cells. Current algorithms for this sort of inference are hindered by image noise and the quality of the underlying image analysis. Here, we present a new approach to inferring mechanical stress from tissue images that overcomes these hurdles.
Our approach is based on a novel parametrization of cellular packings (in epithelial tissues) in terms of polygonal tilings with circular arc edges. These polygons represent the equilibrium geometry of an array of cells, allowing us to identify the observable constraints on the tiling geometry that are imposed by the force balance needed for mechanical equilibrium. Implementing these constraints into the image analysis of single layers of epithelial cells, we formulate a robust algorithm that can infer cell-scale stress over the whole surface of the tissue. Testing our algorithm on data for the embryonic development of fruit flies, we find that the inferred stress strongly matches the measured global pattern of myosin II, a molecular motor known to generate mechanical forces within tissue.
Our algorithm should be immediately useful to researchers studying the mechanics of tissue and organ development, providing a practical and nondestructive approach to measuring stress in live tissue.