Force inference predicts local and tissue-scale stress patterns in epithelia

Morphogenesis relies on the active generation of forces, and the transmission of these forces to surrounding cells and tissues. Hence measuring forces directly in developing embryos is an essential task to study the mechanics of development. Among the experimental techniques that have emerged to measure forces in epithelial tissues, force inference is particularly appealing. Indeed it only requires a snapshot of the tissue, as it relies on the topology and geometry of cell contacts, assuming that forces are balanced at each vertex. However, establishing force inference as a reliable technique requires thorough validation in multiple conditions. Here we performed systematic comparisons of force inference with laser ablation experiments in three distinct Drosophila epithelia. We show that force inference accurately predicts single junction tensions, tension patterns in stereotyped groups of cells, and tissue-scale stress patterns, in wild type and mutant conditions. We emphasize its ability to capture the distribution of forces at different scales from a single image, which gives it a critical advantage over perturbative techniques such as laser ablation. Our results demonstrate that force inference is a reliable and efficient method to quantify the mechanics of epithelial tissues during morphogenesis.

[1]  P. Lenne,et al.  Measuring forces and stresses in situ in living tissues , 2016, Development.

[2]  S. Hilgenfeldt,et al.  Physical modeling of cell geometric order in an epithelial tissue , 2008, Proceedings of the National Academy of Sciences.

[3]  Timothy A. Davis,et al.  Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization , 2011, TOMS.

[4]  Frank Jülicher,et al.  The Influence of Cell Mechanics, Cell-Cell Interactions, and Proliferation on Epithelial Packing , 2007, Current Biology.

[5]  Luca Ambrogioni,et al.  Dynamic decomposition of spatiotemporal neural signals , 2016, PLoS Comput. Biol..

[6]  C. Heisenberg,et al.  Forces in Tissue Morphogenesis and Patterning , 2013, Cell.

[7]  Jeff Hasty,et al.  Streaming instability in growing cell populations. , 2010, Physical review letters.

[8]  Xiaoyan Ma,et al.  Probing embryonic tissue mechanics with laser hole drilling , 2008, Physical biology.

[9]  Andrew Balmford,et al.  Walk on the Wild Side: Estimating the Global Magnitude of Visits to Protected Areas , 2015, PLoS biology.

[10]  Richard W. Carthew,et al.  Surface mechanics mediate pattern formation in the developing retina , 2004, Nature.

[11]  E. Wieschaus,et al.  Measurement of cortical elasticity in Drosophila melanogaster embryos using ferrofluids , 2017, Proceedings of the National Academy of Sciences.

[12]  Pierre Saramito,et al.  Geometry can provide long-range mechanical guidance for embryogenesis , 2016, bioRxiv.

[13]  Jan Huisken,et al.  Mechanical Coupling between Endoderm Invagination and Axis Extension in Drosophila , 2015, PLoS biology.

[14]  Jean-Léon Maître,et al.  Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells , 2012, Science.

[15]  François Graner,et al.  Cell adhesion and cortex contractility determine cell patterning in the Drosophilaretina , 2007, Proceedings of the National Academy of Sciences.

[16]  C. Collinet,et al.  Viscoelastic Dissipation Stabilizes Cell Shape Changes during Tissue Morphogenesis , 2017, Current Biology.

[17]  Françoise Brochard-Wyart,et al.  Aspiration , 2019, Differential Diagnosis of Cardiopulmonary Disease.

[18]  T. Lecuit,et al.  Distinct contributions of tensile and shear stress on E-cadherin levels during morphogenesis , 2018, bioRxiv.

[19]  Kenneth A. Brakke,et al.  The Surface Evolver , 1992, Exp. Math..

[20]  Pierre-François Lenne,et al.  Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis , 2008, Nature Cell Biology.

[21]  P. Lenne,et al.  Probing cell mechanics with subcellular laser dissection of actomyosin networks in the early developing Drosophila embryo. , 2015, Methods in molecular biology.

[22]  Philippe Marcq,et al.  Mechanical state, material properties and continuous description of an epithelial tissue , 2012, Journal of The Royal Society Interface.

[23]  Kaoru Sugimura,et al.  Bayesian inference of force dynamics during morphogenesis. , 2012, Journal of theoretical biology.

[24]  Kaoru Sugimura,et al.  Unified quantitative characterization of epithelial tissue development , 2015, eLife.

[25]  Frank Jülicher,et al.  Cell Flow Reorients the Axis of Planar Polarity in the Wing Epithelium of Drosophila , 2010, Cell.

[26]  Pierre-François Lenne,et al.  Direct laser manipulation reveals the mechanics of cell contacts in vivo , 2015, Proceedings of the National Academy of Sciences.

[27]  Jennifer A Zallen,et al.  Myosin II dynamics are regulated by tension in intercalating cells. , 2009, Developmental cell.

[28]  G. Wayne Brodland,et al.  CellFIT: A Cellular Force-Inference Toolkit Using Curvilinear Cell Boundaries , 2014, PloS one.

[29]  L. Sulak,et al.  Myosin-dependent junction remodelling controls planar cell intercalation and axis elongation , 2004, Nature.

[30]  G. Batchelor,et al.  The stress system in a suspension of force-free particles , 1970, Journal of Fluid Mechanics.

[31]  F Graner,et al.  Comparative study of non-invasive force and stress inference methods in tissue , 2013, The European physical journal. E, Soft matter.

[32]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Sriram Narasimhan,et al.  Video force microscopy reveals the mechanics of ventral furrow invagination in Drosophila , 2010, Proceedings of the National Academy of Sciences.

[34]  David J. Anderson,et al.  Ventromedial hypothalamic neurons control a defensive emotion state , 2015, eLife.

[35]  Lars Hufnagel,et al.  Supplementary Information for Mechanical Stress Inference for Two Dimensional Cell Arrays , 2012 .

[36]  Pierre-François Lenne,et al.  Local and tissue-scale forces drive oriented junction growth during tissue extension , 2015, Nature Cell Biology.

[37]  T. Lecuit,et al.  Distinct contributions of tensile and shear stress on E-cadherin levels during morphogenesis , 2018, Nature Communications.

[38]  Payam Rowghanian,et al.  In vivo quantification of spatially varying mechanical properties in developing tissues , 2016, Nature Methods.

[39]  David S. Lorberbaum,et al.  Genetic evidence that Nkx2.2 acts primarily downstream of Neurog3 in pancreatic endocrine lineage development , 2017, eLife.

[40]  Eunice HoYee Chan,et al.  Patterned cortical tension mediated by N-cadherin controls cell geometric order in the Drosophila eye , 2017, eLife.