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Mimura T, Inoue Y. Cell-center-based model for simulating three-dimensional monolayer tissue deformation. J Theor Biol 2023; 571:111560. [PMID: 37315765 DOI: 10.1016/j.jtbi.2023.111560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Revised: 04/25/2023] [Accepted: 06/07/2023] [Indexed: 06/16/2023]
Abstract
The shape of the epithelial monolayer can be depicted as a curved tissue in three-dimensional (3D) space, where individual cells are tightly adhered to one another. The 3D morphogenesis of these tissues is governed by cell dynamics, and a variety of mathematical modeling and simulation studies have been conducted to investigate this process. One promising approach is the cell-center model, which can account for the discreteness of cells. The cell nucleus, which is considered to correspond to the cell center, can be observed experimentally. However, there has been a shortage of cell-center models specifically tailored for simulating 3D monolayer tissue deformation. In this study, we developed a mathematical model based on the cell-center model to simulate 3D monolayer tissue deformation. Our model was confirmed by simulating the in-plane deformation, out-of-plane deformation, and invagination due to apical constriction.
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Affiliation(s)
- Tomohiro Mimura
- Department of Micro Engineering, Graduate School of Engineering, Kyoto University, 615-8540 Kyoto, Japan.
| | - Yasuhiro Inoue
- Department of Micro Engineering, Graduate School of Engineering, Kyoto University, 615-8540 Kyoto, Japan.
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2
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Gómez-Gálvez P, Vicente-Munuera P, Anbari S, Tagua A, Gordillo-Vázquez C, Andrés-San Román JA, Franco-Barranco D, Palacios AM, Velasco A, Capitán-Agudo C, Grima C, Annese V, Arganda-Carreras I, Robles R, Márquez A, Buceta J, Escudero LM. A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia. Cell Syst 2022; 13:631-643.e8. [PMID: 35835108 DOI: 10.1016/j.cels.2022.06.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Revised: 02/15/2022] [Accepted: 06/15/2022] [Indexed: 01/26/2023]
Abstract
Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.
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Affiliation(s)
- Pedro Gómez-Gálvez
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain.
| | - Pablo Vicente-Munuera
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Samira Anbari
- Chemical and Biomolecular Engineering Department, Lehigh University, Bethlehem, PA 18018, USA
| | - Antonio Tagua
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Carmen Gordillo-Vázquez
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Jesús A Andrés-San Román
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Daniel Franco-Barranco
- Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), San Sebastian, Spain; Donostia International Physics Center (DIPC), San Sebastian, Spain
| | - Ana M Palacios
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Antonio Velasco
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain
| | - Carlos Capitán-Agudo
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain
| | - Clara Grima
- Departamento de Matemática Aplicada I, Universidad de Sevilla, Seville 41012, Spain
| | - Valentina Annese
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain
| | - Ignacio Arganda-Carreras
- Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), San Sebastian, Spain; Donostia International Physics Center (DIPC), San Sebastian, Spain; Ikerbasque, Basque Foundation for Science, Bilbao, Spain
| | - Rafael Robles
- Departamento de Matemática Aplicada I, Universidad de Sevilla, Seville 41012, Spain
| | - Alberto Márquez
- Departamento de Matemática Aplicada I, Universidad de Sevilla, Seville 41012, Spain
| | - Javier Buceta
- Institute for Integrative Systems Biology (I2SysBio), CSIC-UV, Paterna 46980, Spain.
| | - Luis M Escudero
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain; Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), Madrid, Spain.
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Impact of environmental asymmetry on epithelial morphogenesis. Sci Rep 2022; 12:11326. [PMID: 35790869 PMCID: PMC9256595 DOI: 10.1038/s41598-022-15343-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 06/22/2022] [Indexed: 11/29/2022] Open
Abstract
Epithelial folding is a universal biological phenomenon in morphogenesis, typical examples being brain gyri, villi of the intestinal tract, and imaginal discs in invertebrates. During epithelial morphogenesis, the physical constraints imposed by the surrounding microenvironment on epithelial tissue play critical roles in folding morphology. In this study, we focused on the asymmetry of the environmental constraints sandwiching the epithelial sheet and introduced the degree of asymmetry, which indicates whether the basal or apical side of the epithelium is closer to the constraint wall. Then, we investigated the relationship between the degree of asymmetry and epithelial folding morphology using three-dimensional vertex simulations. The results show that the folding patterns of the epithelial sheets change from spot patterns to labyrinth patterns and then to hole patterns as the degree of asymmetry changes. Furthermore, we examined the pattern formation in terms of the equation of out-of-plane displacement of the sheet derived from the mechanical energy functional.
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Van Liedekerke P, Gannoun L, Loriot A, Johann T, Lemaigre FP, Drasdo D. Quantitative modeling identifies critical cell mechanics driving bile duct lumen formation. PLoS Comput Biol 2022; 18:e1009653. [PMID: 35180209 PMCID: PMC8856558 DOI: 10.1371/journal.pcbi.1009653] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 11/16/2021] [Indexed: 02/07/2023] Open
Abstract
Biliary ducts collect bile from liver lobules, the smallest functional and anatomical units of liver, and carry it to the gallbladder. Disruptions in this process caused by defective embryonic development, or through ductal reaction in liver disease have a major impact on life quality and survival of patients. A deep understanding of the processes underlying bile duct lumen formation is crucial to identify intervention points to avoid or treat the appearance of defective bile ducts. Several hypotheses have been proposed to characterize the biophysical mechanisms driving initial bile duct lumen formation during embryogenesis. Here, guided by the quantification of morphological features and expression of genes in bile ducts from embryonic mouse liver, we sharpened these hypotheses and collected data to develop a high resolution individual cell-based computational model that enables to test alternative hypotheses in silico. This model permits realistic simulations of tissue and cell mechanics at sub-cellular scale. Our simulations suggest that successful bile duct lumen formation requires a simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size. The initial step in bile duct development is the formation of a biliary lumen, a process which involves several cellular mechanisms, such as cell division and polarization, and secretion of fluid. However, how these mechanisms are orchestrated in time and space is difficult to understand. Here, we built a computational model of biliary lumen formation which represents every cell and its function in detail. With the model we can simulate the effect of biophysical aspects that affect duct formation. We have tested the individual and combined effects of directed cell division, apical constriction, and osmotic effects on lumen expansion by varying the parameters that control their relative strength. Our simulations suggest that successful bile duct lumen formation requires the simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.
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Affiliation(s)
- Paul Van Liedekerke
- Inria Saclay Île-De-France, Palaiseau, France
- de Duve Institute, Université Catholique de Louvain, Brussels, Belgium
- Inria de Paris & Sorbonne Université LJLL, Paris, France
- * E-mail: (PVL); (DD)
| | - Lila Gannoun
- de Duve Institute, Université Catholique de Louvain, Brussels, Belgium
| | - Axelle Loriot
- de Duve Institute, Université Catholique de Louvain, Brussels, Belgium
| | - Tim Johann
- Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, Dortmund, Germany
| | | | - Dirk Drasdo
- Inria Saclay Île-De-France, Palaiseau, France
- Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, Dortmund, Germany
- Inria de Paris & Sorbonne Université LJLL, Paris, France
- * E-mail: (PVL); (DD)
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Rozman J, Krajnc M, Ziherl P. Morphologies of compressed active epithelial monolayers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:99. [PMID: 34287727 DOI: 10.1140/epje/s10189-021-00094-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
Using a three-dimensional active vertex model, we numerically study the shapes of strained unsupported epithelial monolayers subject to active junctional noise due to stochastic binding and unbinding of myosin. We find that while uniaxial, biaxial, and isotropic in-plane compressive strains do lead to the formation of longitudinal, herringbone pattern, and labyrinthine folds, respectively, the villus morphology characteristic of, e.g., the small intestine appears only if junctional tension fluctuations are strong enough to fluidize the tissue. Moreover, the fluidized epithelium features villi even in the absence of compressive strain provided that the apico-basal differential surface tension is large enough. We analyze several details of the different epithelial forms including the role of strain rate and the modulation of tissue thickness across folds. Our results show that even unsupported, non-patterned epithelia can form nontrivial morphologies.
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Affiliation(s)
- Jan Rozman
- Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia.
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
| | - Matej Krajnc
- Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Primož Ziherl
- Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
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Computational analyses decipher the primordial folding coding the 3D structure of the beetle horn. Sci Rep 2021; 11:1017. [PMID: 33441712 PMCID: PMC7806817 DOI: 10.1038/s41598-020-79757-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 12/07/2020] [Indexed: 01/18/2023] Open
Abstract
The beetle horn primordium is a complex and compactly folded epithelial sheet located beneath the larval cuticle. Only by unfolding the primordium can the complete 3D shape of the horn appear, suggesting that the morphology of beetle horns is encoded in the primordial folding pattern. To decipher the folding pattern, we developed a method to manipulate the primordial local folding on a computer and clarified the contribution of the folding of each primordium region to transformation. We found that the three major morphological changes (branching of distal tips, proximodistal elongation, and angular change) were caused by the folding of different regions, and that the folding mechanism also differs according to the region. The computational methods we used are applicable to the morphological study of other exoskeletal animals.
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Gómez-Gálvez P, Vicente-Munuera P, Anbari S, Buceta J, Escudero LM. The complex three-dimensional organization of epithelial tissues. Development 2021; 148:148/1/dev195669. [PMID: 33408064 DOI: 10.1242/dev.195669] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Understanding the cellular organization of tissues is key to developmental biology. In order to deal with this complex problem, researchers have taken advantage of reductionist approaches to reveal fundamental morphogenetic mechanisms and quantitative laws. For epithelia, their two-dimensional representation as polygonal tessellations has proved successful for understanding tissue organization. Yet, epithelial tissues bend and fold to shape organs in three dimensions. In this context, epithelial cells are too often simplified as prismatic blocks with a limited plasticity. However, there is increasing evidence that a realistic approach, even from a reductionist perspective, must include apico-basal intercalations (i.e. scutoidal cell shapes) for explaining epithelial organization convincingly. Here, we present an historical perspective about the tissue organization problem. Specifically, we analyze past and recent breakthroughs, and discuss how and why simplified, but realistic, in silico models require scutoidal features to address key morphogenetic events.
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Affiliation(s)
- Pedro Gómez-Gálvez
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain.,Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031 Madrid, Spain
| | - Pablo Vicente-Munuera
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain.,Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031 Madrid, Spain
| | - Samira Anbari
- Chemical and Biomolecular Engineering Department, Lehigh University, Bethlehem, PA 18018, USA
| | - Javier Buceta
- Institute for Integrative Systems Biology (I2SysBio), CSIC-UV, 46980 Paterna (Valencia), Spain
| | - Luis M Escudero
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013 Seville, Spain .,Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031 Madrid, Spain
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