A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia

Apico-basal cell intercalations (scutoids) optimize packing and energy expenditure in curved epithelia. Further consequences of this new paradigm of tissue packing remain uncharacterized. In particular, how scutoids modify the 3D cellular connectivity is an open question. This property is crucial for understanding epithelial architecture and is instrumental for regulating the biological function of tissues. Here, we address this problem by means of a computational model of epithelial tubes and a biophysical approach that links geometrical descriptors with the energetic cost required to increase the cellular connectivity. Our results predict that epithelial tubes satisfy a novel quantitative principle: the “Flintstones’ law”. In short, cellular connectivity increases with tissue thickness/curvature in a logistic way. We confirm experimentally the existence of this principle using Drosophila’s salivary glands. Our study provides methodological advances to analyze tissue packing in 3D and, more importantly, unveils a morphogenetic principle with key biological consequences.

[1]  Hans Clevers,et al.  Modeling Development and Disease with Organoids , 2016, Cell.

[2]  Konrad Basler,et al.  EpiTools: An Open-Source Image Analysis Toolkit for Quantifying Epithelial Growth Dynamics , 2016, Developmental cell.

[3]  Lennart Kester,et al.  Differential proliferation rates generate patterns of mechanical tension that orient tissue growth , 2013, The EMBO journal.

[4]  Weimiao Yu,et al.  Geometric constraints alter cell arrangements within curved epithelial tissues , 2017, Molecular biology of the cell.

[5]  E. Siggia,et al.  Self-organization of stem cells into embryos: A window on early mammalian development , 2019, Science.

[6]  S. Shvartsman,et al.  Complex structures from patterned cell sheets , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[7]  Ruth E Baker,et al.  Vertex models of epithelial morphogenesis. , 2014, Biophysical journal.

[8]  David A. Weitz,et al.  Physical forces during collective cell migration , 2009 .

[9]  D. Devenport,et al.  Epithelial geometry regulates spindle orientation and progenitor fate during formation of the mammalian epidermis , 2019, eLife.

[10]  Celeste M Nelson,et al.  Geometric control of tissue morphogenesis. , 2009, Biochimica et biophysica acta.

[11]  B. Tripathi,et al.  The wing imaginal disc , 2022, Genetics.

[12]  A. Hoppe,et al.  Tissue Fluidity Promotes Epithelial Wound Healing , 2019, Nature physics.

[13]  Guillaume Salbreux,et al.  Myosin II Controls Junction Fluctuations to Guide Epithelial Tissue Ordering , 2016, bioRxiv.

[14]  Andrew J Ewald,et al.  Cellular foundations of mammary tubulogenesis. , 2014, Seminars in cell & developmental biology.

[15]  G. Schoenwolf,et al.  Towards a cellular and molecular understanding of neurulation , 2001, Developmental dynamics : an official publication of the American Association of Anatomists.

[16]  Yara E. Sánchez-Corrales,et al.  Radially patterned cell behaviours during tube budding from an epithelium , 2018, bioRxiv.

[17]  S. Okuda,et al.  Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity. , 2019, Biophysical journal.

[18]  K. Röper,et al.  Controlling cell shape changes during salivary gland tube formation in Drosophila. , 2014, Seminars in cell & developmental biology.

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

[20]  N. Perrimon,et al.  The emergence of geometric order in proliferating metazoan epithelia , 2006, Nature.

[21]  M. Leptin,et al.  Cell shape changes during gastrulation in Drosophila. , 1990, Development.

[22]  I. Robinson,et al.  Revealing the large-scale network organization of growth hormone-secreting cells. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[23]  A. Martinez-Arias,et al.  The hope and the hype of organoid research , 2017, Development.

[24]  H. Honda.  Description of cellular patterns by Dirichlet domains: the two-dimensional case. , 1978, Journal of theoretical biology.

[25]  G. Beitel,et al.  Tubulogenesis: An Inside Job , 2006, Current Biology.

[26]  Dapeng Bi,et al.  Energy barriers and cell migration in densely packed tissues. , 2013, Soft matter.

[27]  Guillaume Salbreux,et al.  Vertex models: from cell mechanics to tissue morphogenesis , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[28]  Yanlan Mao,et al.  Fundamental physical cellular constraints drive self‐organization of tissues , 2016, The EMBO journal.

[29]  T. Adachi,et al.  Epithelial tissue folding pattern in confined geometry , 2019, Biomechanics and modeling in mechanobiology.

[30]  Madhav Mani,et al.  QuBiT: a quantitative tool for analyzing epithelial tubes reveals unexpected patterns of organization in the Drosophila trachea , 2019, Development.

[31]  I. Kevrekidis,et al.  Cell Division Induces and Switches Coherent Angular Motion within Bounded Cellular Collectives. , 2017, Biophysical journal.

[32]  D. Lubensky,et al.  Vertex stability and topological transitions in vertex models of foams and epithelia , 2016, The European physical journal. E, Soft matter.

[33]  J. Kitajewski,et al.  Tips, stalks, tubes: notch-mediated cell fate determination and mechanisms of tubulogenesis during angiogenesis. , 2012, Cold Spring Harbor perspectives in medicine.

[34]  K. Röper.  Quantitative Imaging and the Effect of Tissue Topology on Morphogenesis. , 2018, Developmental cell.

[35]  H. Sebastian Seung,et al.  Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification , 2017, Bioinform..

[36]  Luis M. Escudero,et al.  Scutoids are a geometrical solution to three-dimensional packing of epithelia , 2018, Nature Communications.

[37]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[38]  F. T. Lewis,et al.  The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis , 1928 .

[39]  T. Lecuit,et al.  Compartmentalized morphogenesis in epithelia: From cell to tissue shape , 2005, Developmental dynamics : an official publication of the American Association of Anatomists.

[40]  G. Bassel,et al.  Mechanical constraints imposed by 3D cellular geometry and arrangement modulate growth patterns in the Arabidopsis embryo , 2014, Proceedings of the National Academy of Sciences.

[41]  Donald E Ingber,et al.  Quantifying cell-generated mechanical forces within living embryonic tissues , 2013, Nature Methods.

[42]  Payam Rowghanian,et al.  A fluid-to-solid jamming transition underlies vertebrate body axis elongation , 2018, Nature.

[43]  Jaume Casademunt,et al.  Dynamics and Mechanical Stability of the Developing Dorsoventral Organizer of the Wing Imaginal Disc , 2011, PLoS Comput. Biol..

[44]  T. Adachi,et al.  Polarized cellular mechano-response system for maintaining radial size in developing epithelial tubes , 2019, Development.

[45]  X. Trepat,et al.  Active wetting of epithelial tissues , 2018, Nature Physics.

[46]  G. Wetzel.  Zur entwicklungsmechanischen Analyse des einfachen prismatischen Epithels , 2005, Wilhelm Roux' Archiv für Entwicklungsmechanik der Organismen.

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

[48]  Radhika Nagpal,et al.  Control of the Mitotic Cleavage Plane by Local Epithelial Topology , 2011, Cell.

[49]  T. Margaritis,et al.  Tubuloids derived from human adult kidney and urine for personalized disease modeling , 2019, Nature Biotechnology.

[50]  Sarah Machado,et al.  LimeSeg: a coarse-grained lipid membrane simulation for 3D image segmentation , 2019, BMC Bioinformatics.

[51]  Christopher Gribben,et al.  Tissue curvature and apicobasal mechanical tension imbalance instruct cancer morphogenesis , 2019, Nature.

[52]  M. Iruela-Arispe,et al.  Tubulogenesis , 2013, Development.

[53]  Eric F. Wieschaus,et al.  Quantitative 4D analyses of epithelial folding during Drosophila gastrulation , 2014, Development.

[54]  Benoit Ladoux,et al.  Active superelasticity in three-dimensional epithelia of controlled shape , 2018, Nature.

[55]  Johannes E. Schindelin,et al.  Fiji: an open-source platform for biological-image analysis , 2012, Nature Methods.

[56]  Matthias Merkel,et al.  Correlating cell shape and cellular stress in motile confluent tissues , 2017, Proceedings of the National Academy of Sciences.

[57]  Forces-in-tissue workshop participants.  Measuring forces and stresses in situ in living tissues , 2015, bioRxiv.

[58]  Karl Reinhardt.  Über die Zerlegung der Ebene in Polygone , 1918 .

[59]  Luis M. Escudero,et al.  Dual role of myosin II during Drosophila imaginal disc metamorphosis , 2013, Nature Communications.

[60]  Amsha Proag,et al.  Apoptotic forces in tissue morphogenesis , 2017, Mechanisms of Development.

[61]  D. Weaire,et al.  Demonstration and interpretation of ‘scutoid’ cells formed in a quasi-2D soap froth , 2018, Philosophical Magazine Letters.

[62]  K D Irvine,et al.  Cell intercalation during Drosophila germband extension and its regulation by pair-rule segmentation genes. , 1994, Development.

[63]  Alexander A Spector,et al.  Emergent patterns of growth controlled by multicellular form and mechanics. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[64]  E. O'Duibhir.  Stochastic Gene Expression , 2010 .

[65]  Dapeng Bi,et al.  A density-independent rigidity transition in biological tissues , 2014, Nature Physics.

[66]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[67]  M. Fürthauer,et al.  Delta/Notch signaling controls neuroepithelial morphogenesis in the zebrafish spinal cord , 2019, bioRxiv.

[68]  Complex Structures , 2000, Science.