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Ferme LC, Ryan AQ, Haase R, Modes CD, Norden C. Timely neurogenesis drives the transition from nematic to crystalline nuclear packing during retinal morphogenesis. SCIENCE ADVANCES 2025; 11:eadu6843. [PMID: 40344072 PMCID: PMC12063663 DOI: 10.1126/sciadv.adu6843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/17/2024] [Accepted: 04/03/2025] [Indexed: 05/11/2025]
Abstract
Correct organogenesis depends on the timely coordination of developmental processes, such as cell proliferation, differentiation, and migration. This coordination is particularly critical in crowded tissues, such as pseudostratified epithelia (PSE) that are often found as organ precursors. They are composed of elongated epithelial cells with densely packed nuclei aligned along the apicobasal axis. While cell cycle-dependent nuclear movements in PSE are well studied, less is known about how nuclear packing influences tissue morphogenesis. To investigate this, we analyzed nuclear shapes, sizes, and neighborhood statistics in zebrafish neuroepithelia, focusing on the retinal PSE. We found that nuclei exhibit elongated shapes and biaxial nematic-like orientational order but remain positionally disordered. During retinal development, nuclear packing density increases, approaching theoretical limits. This occurs when the tissue transitions to a laminated structure and nuclear shapes are remodeled. Timely neurogenesis is critical as failure to initiate neurogenesis leads to tissue deformations. These findings highlight the influence of nuclear shape and positioning for organ morphogenesis.
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Affiliation(s)
- Lucrezia C. Ferme
- Gulbenkian Institute for Molecular Medicine, rua da Quinta Grande 6, 2780-156 Oeiras, Portugal (formerly Instituto Gulbenkian de Ciência, IGC)
| | - Allyson Q. Ryan
- Max-Planck Institute for Molecular Cell Biology and Genetics, MPI-CBG, Pfotenhauerstrasse 108, 01307 Dresden, Germany
- Excellence Cluster, Physics of Life, Technische Universität Dresden, Arnoldstrasse 18, 01307 Dresden, Germany
- Center for Systems Biology, Pfotenhauerstrasse 108, 01307 Dresden, Germany
| | - Robert Haase
- Excellence Cluster, Physics of Life, Technische Universität Dresden, Arnoldstrasse 18, 01307 Dresden, Germany
- Data Science Center, Leipzig University, Humboldtstraße 25, 04105 Leipzig, Germany
- Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Dresden/Leipzig, Germany
| | - Carl D. Modes
- Max-Planck Institute for Molecular Cell Biology and Genetics, MPI-CBG, Pfotenhauerstrasse 108, 01307 Dresden, Germany
- Excellence Cluster, Physics of Life, Technische Universität Dresden, Arnoldstrasse 18, 01307 Dresden, Germany
- Center for Systems Biology, Pfotenhauerstrasse 108, 01307 Dresden, Germany
| | - Caren Norden
- Gulbenkian Institute for Molecular Medicine, rua da Quinta Grande 6, 2780-156 Oeiras, Portugal (formerly Instituto Gulbenkian de Ciência, IGC)
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2
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Brown PJ, Green JEF, Binder BJ, Osborne JM. Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation. Math Biosci 2025; 380:109367. [PMID: 39732162 DOI: 10.1016/j.mbs.2024.109367] [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: 04/02/2024] [Revised: 12/11/2024] [Accepted: 12/13/2024] [Indexed: 12/30/2024]
Abstract
A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell-stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.
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Affiliation(s)
- Phillip J Brown
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, Australia
| | - J Edward F Green
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, Australia
| | - Benjamin J Binder
- School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, Australia
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia.
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3
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Cano-Fernández H, Tissot T, Brun-Usan M, Salazar-Ciudad I. A mathematical model of development shows that cell division, short-range signaling and self-activating gene networks increase developmental noise while long-range signaling and epithelial stiffness reduce it. Dev Biol 2025; 518:85-97. [PMID: 39622312 DOI: 10.1016/j.ydbio.2024.11.014] [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: 07/25/2024] [Revised: 09/27/2024] [Accepted: 11/29/2024] [Indexed: 12/06/2024]
Abstract
The position of cells during development is constantly subject to noise, i.e. cell-level noise. We do not yet fully understand how cell-level noise coming from processes such as cell division or movement leads to morphological noise, i.e. morphological differences between genetically identical individuals developing in the same environment. To address this question we constructed a large ensemble of random genetic networks regulating cell behaviors (contraction, adhesion, etc.) and cell signaling. We simulated them with a general computational model of development, EmbryoMaker. We identified and studied the dynamics, under cell-level noise, of those networks that lead to the development of animal-like morphologies from simple blastula-like initial conditions. We found that growth by cell division is a major contributor to morphological noise. Self-activating gene network loops also amplified cell-level noise into morphological noise while long-range signaling and epithelial stiffness tended to reduce morphological noise.
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Affiliation(s)
- Hugo Cano-Fernández
- Genomics, Bioinformatics and Evolution Group, Departament de Genètica i Microbiologia, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra (Cerdanyola del Vallès), Barcelona, Spain
| | - Tazzio Tissot
- Electronics and Computer Science Department, University of Southampton, University Road, Southampton, SO17 1BJ, UK
| | - Miguel Brun-Usan
- Departamento de Biologia, Universidad Autónoma de Madrid, Darwin St., 2, Fuencarral-El Pardo, 28049, Madrid, Spain
| | - Isaac Salazar-Ciudad
- Genomics, Bioinformatics and Evolution Group, Departament de Genètica i Microbiologia, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra (Cerdanyola del Vallès), Barcelona, Spain; Centre de Recerca Matemàtica (CRM), Edifici C, 08193, Bellaterra (Cerdanyola del Vallès), Barcelona, Spain.
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4
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Tu JJ, Zang YY, Shi YS, Teng XY. The TMEM63B Channel Facilitates Intestinal Motility and Enhances Proliferation of Intestinal Stem Cells. Cells 2024; 13:1784. [PMID: 39513891 PMCID: PMC11545518 DOI: 10.3390/cells13211784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2024] [Revised: 10/24/2024] [Accepted: 10/26/2024] [Indexed: 11/16/2024] Open
Abstract
The intestines are in a constant state of motion and self-renewal. The mechanical breakdown of food facilitates intestinal movement and aids digestion. It is believed that mechanical stimulation, triggered by changes in osmotic pressure within the intestines, plays a crucial role in regulating gastrointestinal motility. While TRPs and PIEZO1/2 have been identified as mechanosensitive ion channels involved in this process, there still exist numerous unidentified channels with similar properties. In this study, we demonstrate that the TMEM63B expressed in intestinal stem cells contributes to the regulation of intestinal motility and digestion. The deletion of TMEM63B in intestinal stem cells not only decelerates intestinal motility and impairs digestion but also attenuates the proliferation of intestinal stem cells and exacerbates DSS-induced colitis in mice. Collectively, our findings unveil the pivotal role of TMEM63B in governing optimal digestive function and modulating intestinal motility.
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Affiliation(s)
- Jing-Jing Tu
- Model Animal Research Center, Jiangsu Key Laboratory of Molecular Medicine, Medical School, Nanjing University, Nanjing 210093, China; (J.-J.T.); (Y.-Y.Z.)
| | - Yan-Yu Zang
- Model Animal Research Center, Jiangsu Key Laboratory of Molecular Medicine, Medical School, Nanjing University, Nanjing 210093, China; (J.-J.T.); (Y.-Y.Z.)
| | - Yun Stone Shi
- Model Animal Research Center, Jiangsu Key Laboratory of Molecular Medicine, Medical School, Nanjing University, Nanjing 210093, China; (J.-J.T.); (Y.-Y.Z.)
- Guangdong Institute of Intelligence Science and Technology, Hengqin, Zhuhai 519031, China
| | - Xiao-Yu Teng
- Model Animal Research Center, Jiangsu Key Laboratory of Molecular Medicine, Medical School, Nanjing University, Nanjing 210093, China; (J.-J.T.); (Y.-Y.Z.)
- Guangdong Institute of Intelligence Science and Technology, Hengqin, Zhuhai 519031, China
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5
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Rigato A, Meng H, Chardes C, Runions A, Abouakil F, Smith RS, LeGoff L. A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis. PLoS Biol 2024; 22:e3002662. [PMID: 38870210 PMCID: PMC11175506 DOI: 10.1371/journal.pbio.3002662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 05/03/2024] [Indexed: 06/15/2024] Open
Abstract
The polygonal shape of cells in proliferating epithelia is a result of the tensile forces of the cytoskeletal cortex and packing geometry set by the cell cycle. In the larval Drosophila epidermis, two cell populations, histoblasts and larval epithelial cells, compete for space as they grow on a limited body surface. They do so in the absence of cell divisions. We report a striking morphological transition of histoblasts during larval development, where they change from a tensed network configuration with straight cell outlines at the level of adherens junctions to a highly folded morphology. The apical surface of histoblasts shrinks while their growing adherens junctions fold, forming deep lobules. Volume increase of growing histoblasts is accommodated basally, compensating for the shrinking apical area. The folded geometry of apical junctions resembles elastic buckling, and we show that the imbalance between the shrinkage of the apical domain of histoblasts and the continuous growth of junctions triggers buckling. Our model is supported by laser dissections and optical tweezer experiments together with computer simulations. Our analysis pinpoints the ability of histoblasts to store mechanical energy to a much greater extent than most other epithelial cell types investigated so far, while retaining the ability to dissipate stress on the hours time scale. Finally, we propose a possible mechanism for size regulation of histoblast apical size through the lateral pressure of the epidermis, driven by the growth of cells on a limited surface. Buckling effectively compacts histoblasts at their apical plane and may serve to avoid physical harm to these adult epidermis precursors during larval life. Our work indicates that in growing nondividing cells, compressive forces, instead of tension, may drive cell morphology.
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Affiliation(s)
- Annafrancesca Rigato
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
- Aix Marseille Univ, CNRS, IBDM UMR7288, Turing Center for Living Systems, Marseille, France
| | - Huicheng Meng
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
| | - Claire Chardes
- Aix Marseille Univ, CNRS, IBDM UMR7288, Turing Center for Living Systems, Marseille, France
| | - Adam Runions
- Department of Computer Science, University of Calgary, Calgary, Canada
| | - Faris Abouakil
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
| | - Richard S. Smith
- John Innes Centre, Norwich Research Park, Norwich, United Kingdom
| | - Loïc LeGoff
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
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6
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Guerrero P, Perez-Carrasco R. Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models. Philos Trans R Soc Lond B Biol Sci 2024; 379:20230051. [PMID: 38432320 PMCID: PMC10909505 DOI: 10.1098/rstb.2023.0051] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 12/06/2023] [Indexed: 03/05/2024] Open
Abstract
To understand the mechanisms that coordinate the formation of biological tissues, the use of numerical implementations is necessary. The complexity of such models involves many assumptions and parameter choices that result in unpredictable consequences, obstructing the comparison with experimental data. Here, we focus on vertex models, a family of spatial models used extensively to simulate the dynamics of epithelial tissues. Usually, in the literature, the choice of the friction coefficient is not addressed using quasi-static deformation arguments that generally do not apply to realistic scenarios. In this manuscript, we discuss the role that the choice of friction coefficient has on the relaxation times and consequently in the conditions of cell cycle progression and division. We explore the effects that these changes have on the morphology, growth rate and topological transitions of the tissue dynamics. These results provide a deeper understanding of the role that an accurate mechanical description plays in the use of vertex models as inference tools. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.
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Affiliation(s)
- Pilar Guerrero
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
| | - Ruben Perez-Carrasco
- Department of Life Sciences, Imperial College London, South Kensington, London, SW7 2AZ, UK
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Melo S, Guerrero P, Moreira Soares M, Bordin JR, Carneiro F, Carneiro P, Dias MB, Carvalho J, Figueiredo J, Seruca R, Travasso RDM. The ECM and tissue architecture are major determinants of early invasion mediated by E-cadherin dysfunction. Commun Biol 2023; 6:1132. [PMID: 37938268 PMCID: PMC10632478 DOI: 10.1038/s42003-023-05482-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 10/18/2023] [Indexed: 11/09/2023] Open
Abstract
Germline mutations of E-cadherin cause Hereditary Diffuse Gastric Cancer (HDGC), a highly invasive cancer syndrome characterised by the occurrence of diffuse-type gastric carcinoma and lobular breast cancer. In this disease, E-cadherin-defective cells are detected invading the adjacent stroma since very early stages. Although E-cadherin loss is well established as a triggering event, other determinants of the invasive process persist largely unknown. Herein, we develop an experimental strategy that comprises in vitro extrusion assays using E-cadherin mutants associated to HDGC, as well as mathematical models epitomising epithelial dynamics and its interaction with the extracellular matrix (ECM). In vitro, we verify that E-cadherin dysfunctional cells detach from the epithelial monolayer and extrude basally into the ECM. Through phase-field modelling we demonstrate that, aside from loss of cell-cell adhesion, increased ECM attachment further raises basal extrusion efficiency. Importantly, by combining phase-field and vertex model simulations, we show that the cylindrical structure of gastric glands strongly promotes the cell's invasive ability. Moreover, we validate our findings using a dissipative particle dynamics simulation of epithelial extrusion. Overall, we provide the first evidence that cancer cell invasion is the outcome of defective cell-cell linkages, abnormal interplay with the ECM, and a favourable 3D tissue structure.
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Affiliation(s)
- Soraia Melo
- i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal
- Ipatimup - Institute of Molecular Pathology and Immunology of the University of Porto, University of Porto, Porto, Portugal
| | - Pilar Guerrero
- Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Leganés, Spain
| | - Maurício Moreira Soares
- Oslo Center for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo, Oslo, Norway
| | - José Rafael Bordin
- Department of Physics, Institute of Physics and Mathematics, Federal University of Pelotas, Capão do Leão, Rio Grande do Sul, Brazil
| | - Fátima Carneiro
- i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal
- Ipatimup - Institute of Molecular Pathology and Immunology of the University of Porto, University of Porto, Porto, Portugal
- Department of Pathology, Faculty of Medicine, University of Porto, Porto, Portugal
| | - Patrícia Carneiro
- i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal
- Ipatimup - Institute of Molecular Pathology and Immunology of the University of Porto, University of Porto, Porto, Portugal
| | - Maria Beatriz Dias
- CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal
| | - João Carvalho
- CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal
| | - Joana Figueiredo
- i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal.
- Ipatimup - Institute of Molecular Pathology and Immunology of the University of Porto, University of Porto, Porto, Portugal.
- Department of Pathology, Faculty of Medicine, University of Porto, Porto, Portugal.
| | - Raquel Seruca
- i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal
- Ipatimup - Institute of Molecular Pathology and Immunology of the University of Porto, University of Porto, Porto, Portugal
- Department of Pathology, Faculty of Medicine, University of Porto, Porto, Portugal
| | - Rui D M Travasso
- CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal.
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Maleki F, Najafi A. Instabilities in a growing system of active particles: scalar and vectorial systems. SOFT MATTER 2023; 19:8157-8163. [PMID: 37850327 DOI: 10.1039/d3sm00880k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2023]
Abstract
The physics of micron-scale biological colonies usually benefits from different out-of-equilibrium sources. In bacterial colonies and cellular tissues, the growth process is among the important active sources that determine the dynamics. In this article, we study the generic dynamical instabilities associated with the growth phenomena that may arise in both scalar and vectorial systems. In vectorial systems, where the rotational degrees of particles play a role, a phenomenological growth-mediated torque can affect the rotational dynamics of individual particles. We show that such a growth-mediated torque can result in active traveling waves in the bulk of a growing system. In addition to the bulk properties, we analyze the instabilities in the shape of growing interfaces in both scalar and vectorial systems.
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Affiliation(s)
- Forouh Maleki
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
| | - Ali Najafi
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
- Research Center for Basic Sciences & Modern Technologies (RBST), Institute for Advanced Studies in Basic Sciences, Zanjan, Iran.
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9
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Jiang J, Aegerter CM. An integrated vertex model of the mesoderm invagination during the embryonic development of Drosophila. J Theor Biol 2023; 572:111581. [PMID: 37481232 DOI: 10.1016/j.jtbi.2023.111581] [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: 03/22/2023] [Revised: 07/05/2023] [Accepted: 07/16/2023] [Indexed: 07/24/2023]
Abstract
The mesoderm invagination of the Drosophila embryo is known as an archetypal morphogenic process. To explore the roles of the active cellular forces and the regulation of these forces, we developed an integrated vertex model that combines the regulation of morphogen expression with cell movements and tissue mechanics. Our results suggest that a successful furrow formation requires an apical tension gradient, decreased basal tension, and increased lateral tension, which corresponds to apical constriction, basal expansion, and apicobasal shortening respectively. Our model also considers the mechanical feedback which leads to an ectopic twist expression with external compression as observed in experiments. Our model predicts that ectopic invagination could happen if an external compressive gradient is applied.
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Affiliation(s)
- Jianfei Jiang
- Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Christof M Aegerter
- Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
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10
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Hoehme S, Hammad S, Boettger J, Begher-Tibbe B, Bucur P, Vibert E, Gebhardt R, Hengstler JG, Drasdo D. Digital twin demonstrates significance of biomechanical growth control in liver regeneration after partial hepatectomy. iScience 2022; 26:105714. [PMID: 36691615 PMCID: PMC9860368 DOI: 10.1016/j.isci.2022.105714] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 06/23/2022] [Accepted: 11/29/2022] [Indexed: 12/12/2022] Open
Abstract
Partial liver removal is an important therapy option for liver cancer. In most patients within a few weeks, the liver is able to fully regenerate. In some patients, however, regeneration fails with often severe consequences. To better understand the control mechanisms of liver regeneration, experiments in mice were performed, guiding the creation of a spatiotemporal 3D model of the regenerating liver. The model represents cells and blood vessels within an entire liver lobe, a macroscopic liver subunit. The model could reproduce the experimental data only if a biomechanical growth control (BGC)-mechanism, inhibiting cell cycle entrance at high compression, was taken into account and predicted that BGC may act as a short-range growth inhibitor minimizing the number of proliferating neighbor cells of a proliferating cell, generating a checkerboard-like proliferation pattern. Model-predicted cell proliferation patterns in pigs and mice were found experimentally. The results underpin the importance of biomechanical aspects in liver growth control.
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Affiliation(s)
- Stefan Hoehme
- Interdisciplinary Centre for Bioinformatics (IZBI), University of Leipzig, Haertelstraße 16-18, 04107 Leipzig, Germany,Institute of Computer Science, University of Leipzig, Haertelstraße 16-18, 04107 Leipzig, Germany,Saxonian Incubator for Clinical Research (SIKT), Philipp-Rosenthal-Straße 55, 04103 Leipzig, Germany
| | - Seddik Hammad
- Section Molecular Hepatology, Department of Medicine II, Medical Faculty Mannheim, Heidelberg University, Germany,Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, 44139 Dortmund, Germany,Department of Forensic Medicine and Veterinary Toxicology, Faculty of Veterinary Medicine, South Valley University, Qena, Egypt
| | - Jan Boettger
- Faculty of Medicine, Rudolf-Schoenheimer-Institute of Biochemistry, Leipzig University, 04103 Leipzig, Germany
| | - Brigitte Begher-Tibbe
- Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, 44139 Dortmund, Germany
| | - Petru Bucur
- Unité INSERM 1193, Centre Hépato-Biliaire, Villejuif, France,Service de Chirurgie Digestive, CHU Trousseau, Tours, France
| | - Eric Vibert
- Unité INSERM 1193, Centre Hépato-Biliaire, Villejuif, France
| | - Rolf Gebhardt
- Faculty of Medicine, Rudolf-Schoenheimer-Institute of Biochemistry, Leipzig University, 04103 Leipzig, Germany
| | - Jan G. Hengstler
- Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, 44139 Dortmund, Germany
| | - Dirk Drasdo
- Interdisciplinary Centre for Bioinformatics (IZBI), University of Leipzig, Haertelstraße 16-18, 04107 Leipzig, Germany,Leibniz Research Centre for Working Environment and Human Factors at the Technical University Dortmund, 44139 Dortmund, Germany,Inria Paris & Sorbonne Université LJLL, 75012 Paris, France,Correspondence:
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11
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Abstract
The vertebrate intestine experiences a range of intrinsically generated and external forces during both development and adult homeostasis. It is increasingly understood how the coordination of these forces shapes the intestine through organ-scale folding and epithelial organization into crypt-villus compartments. Moreover, accumulating evidence shows that several cell types in the adult intestine can sense and respond to forces to regulate key cellular processes underlying adult intestinal functions and self-renewal. In this way, transduction of forces may direct both intestinal homeostasis as well as adaptation to external stimuli, such as food ingestion or injury. In this review, we will discuss recent insights from complementary model systems into the force-dependent mechanisms that establish and maintain the unique architecture of the intestine, as well as its homeostatic regulation and function throughout adult life.
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12
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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: 8] [Impact Index Per Article: 2.7] [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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Mathias S, Coulier A, Hellander A. CBMOS: a GPU-enabled Python framework for the numerical study of center-based models. BMC Bioinformatics 2022; 23:55. [PMID: 35100968 PMCID: PMC8805507 DOI: 10.1186/s12859-022-04575-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 01/11/2022] [Indexed: 11/24/2022] Open
Abstract
BACKGROUND Cell-based models are becoming increasingly popular for applications in developmental biology. However, the impact of numerical choices on the accuracy and efficiency of the simulation of these models is rarely meticulously tested. Without concrete studies to differentiate between solid model conclusions and numerical artifacts, modelers are at risk of being misled by their experiments' results. Most cell-based modeling frameworks offer a feature-rich environment, providing a wide range of biological components, but are less suitable for numerical studies. There is thus a need for software specifically targeted at this use case. RESULTS We present CBMOS, a Python framework for the simulation of the center-based or cell-centered model. Contrary to other implementations, CBMOS' focus is on facilitating numerical study of center-based models by providing access to multiple ordinary differential equation solvers and force functions through a flexible, user-friendly interface and by enabling rapid testing through graphics processing unit (GPU) acceleration. We show-case its potential by illustrating two common workflows: (1) comparison of the numerical properties of two solvers within a Jupyter notebook and (2) measuring average wall times of both solvers on a high performance computing cluster. More specifically, we confirm that although for moderate accuracy levels the backward Euler method allows for larger time step sizes than the commonly used forward Euler method, its additional computational cost due to being an implicit method prohibits its use for practical test cases. CONCLUSIONS CBMOS is a flexible, easy-to-use Python implementation of the center-based model, exposing both basic model assumptions and numerical components to the user. It is available on GitHub and PyPI under an MIT license. CBMOS allows for fast prototyping on a central processing unit for small systems through the use of NumPy. Using CuPy on a GPU, cell populations of up to 10,000 cells can be simulated within a few seconds. As such, it will substantially lower the time investment for any modeler to check the crucial assumption that model conclusions are independent of numerical issues.
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Affiliation(s)
- Sonja Mathias
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Adrien Coulier
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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14
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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: 1.8] [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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15
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Mechanical compartmentalization of the intestinal organoid enables crypt folding and collective cell migration. Nat Cell Biol 2021; 23:745-757. [PMID: 34155382 PMCID: PMC7611697 DOI: 10.1038/s41556-021-00699-6] [Citation(s) in RCA: 112] [Impact Index Per Article: 28.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Accepted: 05/12/2021] [Indexed: 02/06/2023]
Abstract
Intestinal organoids capture essential features of the intestinal epithelium such as crypt folding, cellular compartmentalization and collective movements. Each of these processes and their coordination require patterned forces that are at present unknown. Here we map three-dimensional cellular forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the extracellular matrix and folds through apical constriction, whereas the transit amplifying zone pulls the extracellular matrix and elongates through basal constriction. The size of the stem cell compartment depends on the extracellular-matrix stiffness and endogenous cellular forces. Computational modelling reveals that crypt shape and force distribution rely on cell surface tensions following cortical actomyosin density. Finally, cells are pulled out of the crypt along a gradient of increasing tension. Our study unveils how patterned forces enable compartmentalization, folding and collective migration in the intestinal epithelium.
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16
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Tallapragada NP, Cambra HM, Wald T, Keough Jalbert S, Abraham DM, Klein OD, Klein AM. Inflation-collapse dynamics drive patterning and morphogenesis in intestinal organoids. Cell Stem Cell 2021; 28:1516-1532.e14. [PMID: 33915079 DOI: 10.1016/j.stem.2021.04.002] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2020] [Revised: 12/29/2020] [Accepted: 04/01/2021] [Indexed: 02/07/2023]
Abstract
How stem cells self-organize to form structured tissues is an unsolved problem. Intestinal organoids offer a model of self-organization as they generate stem cell zones (SCZs) of typical size even without a spatially structured environment. Here we examine processes governing the size of SCZs. We improve the viability and homogeneity of intestinal organoid cultures to enable long-term time-lapse imaging of multiple organoids in parallel. We find that SCZs are shaped by fission events under strong control of ion channel-mediated inflation and mechanosensitive Piezo-family channels. Fission occurs through stereotyped modes of dynamic behavior that differ in their coordination of budding and differentiation. Imaging and single-cell transcriptomics show that inflation drives acute stem cell differentiation and induces a stretch-responsive cell state characterized by large transcriptional changes, including upregulation of Piezo1. Our results reveal an intrinsic capacity of the intestinal epithelium to self-organize by modulating and then responding to its mechanical state.
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Affiliation(s)
- Naren P Tallapragada
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, MA 02115, USA
| | - Hailey M Cambra
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, MA 02115, USA
| | - Tomas Wald
- Program in Craniofacial Biology and Department of Orofacial Sciences, University of California, San Francisco, San Francisco, CA, USA; Department of Pediatrics and Institute for Human Genetics, University of California, San Francisco, San Francisco, CA, USA
| | - Samantha Keough Jalbert
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, MA 02115, USA
| | - Diana M Abraham
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, MA 02115, USA
| | - Ophir D Klein
- Program in Craniofacial Biology and Department of Orofacial Sciences, University of California, San Francisco, San Francisco, CA, USA; Department of Pediatrics and Institute for Human Genetics, University of California, San Francisco, San Francisco, CA, USA
| | - Allon M Klein
- Department of Systems Biology, Blavatnik Institute, Harvard Medical School, Boston, MA 02115, USA.
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17
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Mathias S, Coulier A, Bouchnita A, Hellander A. Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models. Bull Math Biol 2020; 82:132. [PMID: 33025278 PMCID: PMC7538447 DOI: 10.1007/s11538-020-00810-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Accepted: 09/21/2020] [Indexed: 12/17/2022]
Abstract
Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.
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Affiliation(s)
- Sonja Mathias
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Adrien Coulier
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Anass Bouchnita
- Department of Information Technology, Uppsala University, Uppsala, Sweden
- Present Address: Ecole Centrale Casablanca, Bouskoura, Morocco
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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18
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Trushko A, Di Meglio I, Merzouki A, Blanch-Mercader C, Abuhattum S, Guck J, Alessandri K, Nassoy P, Kruse K, Chopard B, Roux A. Buckling of an Epithelium Growing under Spherical Confinement. Dev Cell 2020; 54:655-668.e6. [PMID: 32800097 PMCID: PMC7497624 DOI: 10.1016/j.devcel.2020.07.019] [Citation(s) in RCA: 66] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Revised: 04/26/2020] [Accepted: 07/22/2020] [Indexed: 12/19/2022]
Abstract
Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires measurement of the stress field and the material properties of the tissue, which are currently inaccessible in vivo. Here, we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelial growth in three-dimensional confinement are sufficient to drive folding by buckling.
A proliferating epithelium encapsulated in a hollow sphere spontaneously invaginates Epithelial proliferation generates compressive stresses that deform the elastic shell Coupling between stress and folding shape shows that folding arises from buckling Epithelial elastic moduli are inferred from buckling theory and experiments
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Affiliation(s)
- Anastasiya Trushko
- Department of Biochemistry, University of Geneva, CH-1211 Geneva, Switzerland
| | - Ilaria Di Meglio
- Department of Biochemistry, University of Geneva, CH-1211 Geneva, Switzerland
| | - Aziza Merzouki
- Department of Computer Science, University of Geneva, CH-1211 Geneva, Switzerland
| | - Carles Blanch-Mercader
- Department of Biochemistry, University of Geneva, CH-1211 Geneva, Switzerland; Department of Theoretical Physics, University of Geneva, CH-1211 Geneva, Switzerland
| | - Shada Abuhattum
- Biotechnology Center, Technische Universität Dresden, D-01307 Dresden, Germany; JPK Instruments AG, 12099 Berlin, Germany
| | - Jochen Guck
- Biotechnology Center, Technische Universität Dresden, D-01307 Dresden, Germany; Max Planck Institute for the Science of Light & Max-Planck-Zentrum für Physik und Medizin, Staudtstr. 2, D-91058 Erlangen, Germany
| | - Kevin Alessandri
- Laboratoire Photonique Numérique et Nanosciences, CNRS UMR 5298, Université de Bordeaux and Institut d'Optique, F-33400 Talence, France
| | - Pierre Nassoy
- Laboratoire Photonique Numérique et Nanosciences, CNRS UMR 5298, Université de Bordeaux and Institut d'Optique, F-33400 Talence, France
| | - Karsten Kruse
- Department of Biochemistry, University of Geneva, CH-1211 Geneva, Switzerland; Department of Theoretical Physics, University of Geneva, CH-1211 Geneva, Switzerland; National Center of Competence in Research Chemical Biology, University of Geneva, CH-1211 Geneva, Switzerland
| | - Bastien Chopard
- Department of Computer Science, University of Geneva, CH-1211 Geneva, Switzerland
| | - Aurélien Roux
- Department of Biochemistry, University of Geneva, CH-1211 Geneva, Switzerland; National Center of Competence in Research Chemical Biology, University of Geneva, CH-1211 Geneva, Switzerland.
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19
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Stalidzans E, Zanin M, Tieri P, Castiglione F, Polster A, Scheiner S, Pahle J, Stres B, List M, Baumbach J, Lautizi M, Van Steen K, Schmidt HH. Mechanistic Modeling and Multiscale Applications for Precision Medicine: Theory and Practice. NETWORK AND SYSTEMS MEDICINE 2020. [DOI: 10.1089/nsm.2020.0002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Egils Stalidzans
- Computational Systems Biology Group, University of Latvia, Riga, Latvia
- Latvian Biomedical Reasearch and Study Centre, Riga, Latvia
| | - Massimiliano Zanin
- Centro de Tecnología Biomédica, Universidad Politécnica de Madrid, Pozuelo de Alarcón, Spain
| | - Paolo Tieri
- CNR National Research Council, IAC Institute for Applied Computing, Rome, Italy
| | - Filippo Castiglione
- CNR National Research Council, IAC Institute for Applied Computing, Rome, Italy
| | | | - Stefan Scheiner
- Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria
| | - Jürgen Pahle
- BioQuant, Heidelberg University, Heidelberg, Germany
| | - Blaž Stres
- Department of Animal Science, University of Ljubljana, Ljubljana, Slovenia
- Faculty of Civil and Geodetic Engineering, University of Ljubljana, Ljubljana, Slovenia
- Department of Automation, Biocybernetics and Robotics, Jozef Stefan Institute, Ljubljana, Slovenia
| | - Markus List
- Big Data in BioMedicine Research Group, Chair of Experimental Bioinformatics, TUM School of Weihenstephan, Technical University of Munich, Freising, Germany
| | - Jan Baumbach
- Chair of Experimental Bioinformatics, TUM School of Weihenstephan, Technical University of Munich, Freising, Germany
| | - Manuela Lautizi
- Computational Systems Medicine Research Group, Chair of Experimental Bioinformatics, TUM School of Weihenstephan, Technical University of Munich, Freising, Germany
| | - Kristel Van Steen
- BIO-Systems Genetics, GIGA-R, University of Liège, Liège, Belgium
- BIO3—Systems Medicine, Department of Human Genetics, KU Leuven, Leuven, Belgium
| | - Harald H.H.W. Schmidt
- Department of Pharmacology and Personalised Medicine, Faculty of Health, Medicine and Life Science, Maastricht University, Maastricht, The Netherlands
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20
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Guerrero P, Perez-Carrasco R, Zagorski M, Page D, Kicheva A, Briscoe J, Page KM. Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium. Development 2019; 146:dev.176297. [PMID: 31784457 PMCID: PMC6918779 DOI: 10.1242/dev.176297] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Accepted: 11/01/2019] [Indexed: 01/04/2023]
Abstract
Cell division, movement and differentiation contribute to pattern formation in developing tissues. This is the case in the vertebrate neural tube, in which neurons differentiate in a characteristic pattern from a highly dynamic proliferating pseudostratified epithelium. To investigate how progenitor proliferation and differentiation affect cell arrangement and growth of the neural tube, we used experimental measurements to develop a mechanical model of the apical surface of the neuroepithelium that incorporates the effect of interkinetic nuclear movement and spatially varying rates of neuronal differentiation. Simulations predict that tissue growth and the shape of lineage-related clones of cells differ with the rate of differentiation. Growth is isotropic in regions of high differentiation, but dorsoventrally biased in regions of low differentiation. This is consistent with experimental observations. The absence of directional signalling in the simulations indicates that global mechanical constraints are sufficient to explain the observed differences in anisotropy. This provides insight into how the tissue growth rate affects cell dynamics and growth anisotropy and opens up possibilities to study the coupling between mechanics, pattern formation and growth in the neural tube. Summary: A mechanical model of the vertebrate neuroepithelium, based on experimental observations, suggests that the rate of neuronal differentiation influences tissue growth and the shape of lineage-related clones.
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Affiliation(s)
- Pilar Guerrero
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
| | - Ruben Perez-Carrasco
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
| | | | - David Page
- Myrtle Software, Second Floor, 50 St. Andrew's Street, Cambridge CB2 3AH, UK
| | - Anna Kicheva
- IST Austria, Am Campus 1, A - 3400 Klosterneuburg, Austria
| | - James Briscoe
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK
| | - Karen M Page
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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21
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Inoue Y, Tateo I, Adachi T. Epithelial tissue folding pattern in confined geometry. Biomech Model Mechanobiol 2019; 19:815-822. [PMID: 31728791 PMCID: PMC7203093 DOI: 10.1007/s10237-019-01249-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Accepted: 10/28/2019] [Indexed: 11/30/2022]
Abstract
The primordium of the exoskeleton of an insect is epithelial tissue with characteristic patterns of folds. As the insect develops from larva to pupa, the spreading of these folds produces the three-dimensional shape of the exoskeleton of the insect. It is known that the three-dimensional exoskeleton shape has already been encoded in characteristic patterns of folds in the primordium; however, a description of how the epithelial tissue forms with the characteristic patterns of folds remains elusive. The present paper suggests a possible mechanism for the formation of the folding pattern. During the primordium development, because of the epithelial tissue is surrounded by other tissues, cell proliferation proceeds within a confined geometry. To elucidate the mechanics of the folding of the epithelial tissue in the confined geometry, we employ a three-dimensional vertex model that expresses tissue deformations based on cell mechanical behaviors and apply the model to examine the effects of cell divisions and the confined geometry on epithelial folding. Our simulation results suggest that the orientation of the axis of cell division is sufficient to cause different folding patterns in silico and that the restraint of out-of-plane deformation due to the confined geometry determines the interspacing of the folds.
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Affiliation(s)
- Yasuhiro Inoue
- Department of Micro Engineering, Kyoto University, Kyoto, Japan.
| | - Itsuki Tateo
- Department of Micro Engineering, Kyoto University, Kyoto, Japan
| | - Taiji Adachi
- Department of Micro Engineering, Kyoto University, Kyoto, Japan.,Institute for Frontier Life and Medical Sciences, Kyoto University, Kyoto, Japan
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22
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Kirkegaard JB, Nielsen BF, Trusina A, Sneppen K. Self-assembly, buckling and density-invariant growth of three-dimensional vascular networks. J R Soc Interface 2019; 16:20190517. [PMID: 31640503 PMCID: PMC6833333 DOI: 10.1098/rsif.2019.0517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Accepted: 10/02/2019] [Indexed: 12/19/2022] Open
Abstract
The experimental actualization of organoids modelling organs from brains to pancreases has revealed that much of the diverse morphologies of organs are emergent properties of simple intercellular 'rules' and not the result of top-down orchestration. In contrast to other organs, the initial plexus of the vascular system is formed by aggregation of cells in the process known as vasculogenesis. Here we study this self-assembling process of blood vessels in three dimensions through a set of simple rules that align intercellular apical-basal and planar cell polarity. We demonstrate that a fully connected network of tubes emerges above a critical initial density of cells. Through planar cell polarity, our model demonstrates convergent extension, and this polarity furthermore allows for both morphology-maintaining growth and growth-induced buckling. We compare this buckling with the special vasculature of the islets of Langerhans in the pancreas and suggest that the mechanism behind the vascular density-maintaining growth of these islets could be the result of growth-induced buckling.
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23
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Walter C, Davis JT, Mathur J, Pathak A. Physical defects in basement membrane-mimicking collagen-IV matrices trigger cellular EMT and invasion. Integr Biol (Camb) 2019; 10:342-355. [PMID: 29790537 DOI: 10.1039/c8ib00034d] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
In fibrosis and cancer, degradation of basement membrane (BM) and cell invasion are considered as key outcomes of a cellular transformation called epithelial-mesenchymal transition (EMT). Here, we pose a converse question - can preexisting physical defects in the BM matrix cause EMT in normal epithelial cells? On a BM-mimicking matrix of collagen-IV-coated polyacrylamide (PA) gel, we have discovered a reverse phenomenon in which preexisting defects trigger EMT in normal epithelial cells. Through spatiotemporal measurements and simulations in silico, we demonstrate that the EMT precedes cellular mechanoactivation on defective matrices, but they occur concurrently on stiff matrices. The defect-dependent EMT caused cell invasion though a stroma-mimicking collagen-I layer, which could be disabled through MMP9 inhibition. Our findings reveal that the known BM degradation caused by cellular EMT and invasion is not a one-way process. Instead, normal epithelial cells can exploit physical defects in the BM matrix to undergo disease-like cellular transformations.
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Affiliation(s)
- Christopher Walter
- Department of Biomedical Engineering, Washington University, St. Louis, USA
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24
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Mathur J, Sarker B, Pathak A. Predicting Collective Migration of Cell Populations Defined by Varying Repolarization Dynamics. Biophys J 2018; 115:2474-2485. [PMID: 30527449 PMCID: PMC6302036 DOI: 10.1016/j.bpj.2018.11.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2018] [Revised: 11/06/2018] [Accepted: 11/12/2018] [Indexed: 01/23/2023] Open
Abstract
Collective migration of heterogeneous cell populations is an essential aspect of fundamental biological processes, including morphogenesis, wound healing, and tumor invasion. Through experiments and modeling, it has been shown that cells attain front-rear polarity, generate forces, and form adhesions to migrate. However, it remains unclear how the ability of individual cells in a population to dynamically repolarize themselves into new directions could regulate the collective response. We present a vertex-based model in which each deformable cell randomly chooses a new polarization direction after every defined time interval, elongates, proportionally generates forces, and causes collective migration. Our simulations predict that cell types that repolarize at longer time intervals attain more elongated shapes, migrate faster, deform the cell sheet, and roughen the leading edge. By imaging collectively migrating epithelial cell monolayers at high temporal resolution, we found longer repolarization intervals and elongated shapes of cells at the leading edge compared to those within the monolayer. Based on these experimental measurements and simulations, we defined aggressive mutant leader cells by long repolarization interval and minimal intercellular contact. The cells with frequent and random repolarization were defined as normal cells. In simulations with uniformly dispersed leader cells in a normal cell population at a 1:10 ratio, the resulting migration and deformation of the heterogeneous cell sheet remained low. However, when the 10% mutant leaders were placed only at the leading edge, we predicted a rise in the migration of an otherwise normal cell sheet. Our model predicts that a repolarization-based definition of leader cells and their placement within a healthy population can generate myriad modes of collective cell migration, which can enhance our understanding of collective cell migration in disease and development.
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Affiliation(s)
- Jairaj Mathur
- Department of Mechanical Engineering & Materials Science, Washington University, St. Louis, Missouri
| | - Bapi Sarker
- Department of Mechanical Engineering & Materials Science, Washington University, St. Louis, Missouri
| | - Amit Pathak
- Department of Mechanical Engineering & Materials Science, Washington University, St. Louis, Missouri.
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25
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Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma. Bull Math Biol 2018; 80:1134-1171. [PMID: 29568983 DOI: 10.1007/s11538-017-0375-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 11/27/2017] [Indexed: 12/11/2022]
Abstract
Recently, hepatocyte-sinusoid alignment (HSA) has been identified as a mechanism that supports the coordination of hepatocytes during liver regeneration to reestablish a functional micro-architecture (Hoehme et al. in Proc Natl Acad Sci 107(23):10371-10376, 2010). HSA means that hepatocytes preferentially align along the closest micro-vessels. Here, we studied whether this mechanism is still active in early hepatocellular tumors. The same agent-based spatiotemporal model that previously correctly predicted HSA in liver regeneration was further developed to simulate scenarios in early tumor development, when individual initiated hepatocytes gain increased proliferation capacity. The model simulations were performed under conditions of realistic liver micro-architectures obtained from 3D reconstructions of confocal laser scanning micrographs. Interestingly, the established model predicted that initiated hepatocytes at first arrange in elongated patterns. Only when the tumor progresses to cell numbers of approximately 4000, does it adopt spherical structures. This prediction may have relevant consequences, since elongated tumors may reach critical structures faster, such as larger vessels, compared to a spherical tumor of similar cell number. Interestingly, this model prediction was confirmed by analysis of the spatial organization of initiated hepatocytes in a rat liver tumor initiation study using single doses of 250 mg/kg of the genotoxic carcinogen N-nitrosomorpholine (NNM). Indeed, small clusters of GST-P positive cells induced by NNM were elongated, almost columnar, while larger GDT-P positive foci of approximately the size of liver lobuli adopted spherical shapes. From simulations testing numerous possible mechanisms, only HSA could explain the experimentally observed initial deviation from spherical shape. The present study demonstrates that the architecture of small cell clusters of hepatocytes early after initiation is still controlled by physiological mechanisms. However, this coordinating influence is lost when the tumor grows to approximately 4000 cells, leading to further growth in spherical shape. Our findings stress the potential importance of organ micro-architecture in understanding tumor phenotypes.
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26
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Wong KK. Three-dimensional discrete element method for the prediction of protoplasmic seepage through membrane in a biological cell. J Biomech 2017; 65:115-124. [DOI: 10.1016/j.jbiomech.2017.10.023] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2017] [Revised: 10/09/2017] [Accepted: 10/15/2017] [Indexed: 12/15/2022]
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27
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An exactly solvable, spatial model of mutation accumulation in cancer. Sci Rep 2016; 6:39511. [PMID: 28004754 PMCID: PMC5177951 DOI: 10.1038/srep39511] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2016] [Accepted: 11/24/2016] [Indexed: 12/17/2022] Open
Abstract
One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.
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Ciasca G, Papi M, Minelli E, Palmieri V, De Spirito M. Changes in cellular mechanical properties during onset or progression of colorectal cancer. World J Gastroenterol 2016; 22:7203-7214. [PMID: 27621568 PMCID: PMC4997642 DOI: 10.3748/wjg.v22.i32.7203] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Revised: 07/11/2016] [Accepted: 08/01/2016] [Indexed: 02/06/2023] Open
Abstract
Colorectal cancer (CRC) development represents a multistep process starting with specific mutations that affect proto-oncogenes and tumour suppressor genes. These mutations confer a selective growth advantage to colonic epithelial cells that form first dysplastic crypts, and then malignant tumours and metastases. All these steps are accompanied by deep mechanical changes at the cellular and the tissue level. A growing consensus is emerging that such modifications are not merely a by-product of the malignant progression, but they could play a relevant role in the cancer onset and accelerate its progression. In this review, we focus on recent studies investigating the role of the biomechanical signals in the initiation and the development of CRC. We show that mechanical cues might contribute to early phases of the tumour initiation by controlling the Wnt pathway, one of most important regulators of cell proliferation in various systems. We highlight how physical stimuli may be involved in the differentiation of non-invasive cells into metastatic variants and how metastatic cells modify their mechanical properties, both stiffness and adhesion, to survive the mechanical stress associated with intravasation, circulation and extravasation. A deep comprehension of these mechanical modifications may help scientist to define novel molecular targets for the cure of CRC.
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Hirashima T. Mathematical study on robust tissue pattern formation in growing epididymal tubule. J Theor Biol 2016; 407:71-80. [PMID: 27396360 DOI: 10.1016/j.jtbi.2016.07.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 07/05/2016] [Indexed: 11/27/2022]
Abstract
Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation.
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Affiliation(s)
- Tsuyoshi Hirashima
- Institute for Frontier Medical Sciences, Kyoto University, Kyoto 606-8507, Japan; Institute for Virus Research, Kyoto University, Kyoto 606-8507, Japan.
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Kunche S, Yan H, Calof AL, Lowengrub JS, Lander AD. Feedback, Lineages and Self-Organizing Morphogenesis. PLoS Comput Biol 2016; 12:e1004814. [PMID: 26989903 PMCID: PMC4798729 DOI: 10.1371/journal.pcbi.1004814] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2015] [Accepted: 02/15/2016] [Indexed: 01/31/2023] Open
Abstract
Feedback regulation of cell lineage progression plays an important role in tissue size homeostasis, but whether such feedback also plays an important role in tissue morphogenesis has yet to be explored. Here we use mathematical modeling to show that a particular feedback architecture in which both positive and negative diffusible signals act on stem and/or progenitor cells leads to the appearance of bistable or bi-modal growth behaviors, ultrasensitivity to external growth cues, local growth-driven budding, self-sustaining elongation, and the triggering of self-organization in the form of lamellar fingers. Such behaviors arise not through regulation of cell cycle speeds, but through the control of stem or progenitor self-renewal. Even though the spatial patterns that arise in this setting are the result of interactions between diffusible factors with antagonistic effects, morphogenesis is not the consequence of Turing-type instabilities.
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Affiliation(s)
- Sameeran Kunche
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
| | - Huaming Yan
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Anne L. Calof
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, United States of America
- Department of Anatomy and Neurobiology, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
| | - John S. Lowengrub
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
| | - Arthur D. Lander
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
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Štorgel N, Krajnc M, Mrak P, Štrus J, Ziherl P. Quantitative Morphology of Epithelial Folds. Biophys J 2016; 110:269-77. [PMID: 26745429 PMCID: PMC4825108 DOI: 10.1016/j.bpj.2015.11.024] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Revised: 10/08/2015] [Accepted: 11/12/2015] [Indexed: 12/21/2022] Open
Abstract
The shape of spatially modulated epithelial morphologies such as villi and crypts is usually associated with the epithelium-stroma area mismatch leading to buckling. We propose an alternative mechanical model based on intraepithelial stresses generated by differential tensions of apical, lateral, and basal sides of cells as well as on the elasticity of the basement membrane. We use it to theoretically study longitudinal folds in simple epithelia and we identify four types of corrugated morphologies: compact, invaginated, evaginated, and wavy. The obtained tissue contours and thickness profiles are compared to epithelial folds observed in invertebrates and vertebrates, and for most samples, the agreement is within the estimated experimental error. Our model establishes the groove-crest modulation of tissue thickness as a morphometric parameter that can, together with the curvature profile, be used to estimate the relative differential apicobasal tension in the epithelium.
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Affiliation(s)
- Nick Štorgel
- Jožef Stefan Institute, Ljubljana, Slovenia; Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
| | | | - Polona Mrak
- Biotechnical Faculty, University of Ljubljana, Ljubljana, Slovenia
| | - Jasna Štrus
- Biotechnical Faculty, University of Ljubljana, Ljubljana, Slovenia
| | - Primož Ziherl
- Jožef Stefan Institute, Ljubljana, Slovenia; Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia; Erwin Schrödinger International Institute for Mathematical Physics, University of Vienna, Vienna, Austria
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Fumoto K, Takigawa-Imamura H, Sumiyama K, Kaneiwa T, Kikuchi A. Modulation of apical constriction by Wnt signaling is required for lung epithelial shape transition. Development 2016; 144:151-162. [DOI: 10.1242/dev.141325] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Accepted: 11/21/2016] [Indexed: 01/09/2023]
Abstract
In lung development the apically constricted columnar epithelium forms numerous buds during the pseudoglandular stage and subsequently changes the shape into flat or cuboidal pneumocytes that compose the air sacs during the canalicular and saccular (canalicular-saccular) stages, yet the impact of cell shapes on tissue morphogenesis remains unclear. The expression of Wnt components were decreased in the canalicular-saccular stages, and genetically constitutive activation of Wnt signaling impaired air sac formation by inducing apical constriction in the epithelium as seen in the pseudoglandular stage. Organ culture models also demonstrated that Wnt signaling induces apical constriction through the apical actomyosin cytoskeletal organization. Mathematical modeling revealed that apical constriction induces bud formation and loss of apical constriction is required for the formation of an air sac-like structure. MAP/Microtubule affinity-regulating kinase (MARK1) was identified as a downstream molecule of Wnt signaling and required for the apical cytoskeletal organization and bud formation. These results suggest that Wnt signaling is required for bud formation by inducing apical constriction during the pseudoglandular stage, while loss of Wnt signaling is for air sac formation in the canalicular-saccular stages.
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Affiliation(s)
- Katsumi Fumoto
- Departments of Molecular Biology and Biochemistry, Graduate School of Medicine, Osaka University, 2-2 Yamadaoka, Suita 565-0871, Japan
| | - Hisako Takigawa-Imamura
- Anatomy and cell biology, Graduate school of medical sciences, Kyushu University, Fukuoka 812-8582, Japan
| | - Kenta Sumiyama
- Laboratory for Mouse Genetic Engineering, RIKEN Quantitative Biology Center, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Tomoyuki Kaneiwa
- Departments of Molecular Biology and Biochemistry, Graduate School of Medicine, Osaka University, 2-2 Yamadaoka, Suita 565-0871, Japan
| | - Akira Kikuchi
- Departments of Molecular Biology and Biochemistry, Graduate School of Medicine, Osaka University, 2-2 Yamadaoka, Suita 565-0871, Japan
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Gardiner BS, Joldes GR, Wong KKL, Tan CW, Smith DW. Controlling seepage in discrete particle simulations of biological systems. Comput Methods Biomech Biomed Engin 2015; 19:1160-70. [PMID: 26629728 DOI: 10.1080/10255842.2015.1115022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
It is now commonplace to represent materials in a simulation using assemblies of discrete particles. Sometimes, one wishes to maintain the integrity of boundaries between particle types, for example, when modelling multiple tissue layers. However, as the particle assembly evolves during a simulation, particles may pass across interfaces. This behaviour is referred to as 'seepage'. The aims of this study were (i) to examine the conditions for seepage through a confining particle membrane and (ii) to define some simple rules that can be employed to control seepage. Based on the force-deformation response of spheres with various sizes and stiffness, we develop analytic expressions for the force required to move a 'probe particle' between confining 'membrane particles'. We analyse the influence that particle's size and stiffness have on the maximum force that can act on the probe particle before the onset of seepage. The theoretical results are applied in the simulation of a biological cell under unconfined compression.
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Affiliation(s)
- Bruce S Gardiner
- a School of Engineering and Information Technology , Murdoch University , Perth , Australia
| | - Grand R Joldes
- b Intelligent Systems for Medicine Laboratory , School of Mechanical and Chemical Engineering, The University of Western Australia , Perth , Australia
| | - Kelvin K L Wong
- c Engineering Computational Biology, School of Computer Science and Software Engineering , The University of Western Australia , Perth , Australia
| | - Chin Wee Tan
- d Structural Biology Division , The Walter and Eliza Hall Institute of Medical Research , Victoria , Australia.,e Department of Medical Biology , University of Melbourne , Victoria , Australia
| | - David W Smith
- c Engineering Computational Biology, School of Computer Science and Software Engineering , The University of Western Australia , Perth , Australia
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Pin C, Parker A, Gunning AP, Ohta Y, Johnson IT, Carding SR, Sato T. An individual based computational model of intestinal crypt fission and its application to predicting unrestrictive growth of the intestinal epithelium. Integr Biol (Camb) 2015; 7:213-28. [PMID: 25537618 DOI: 10.1039/c4ib00236a] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Intestinal crypt fission is a homeostatic phenomenon, observable in healthy adult mucosa, but which also plays a pathological role as the main mode of growth of some intestinal polyps. Building on our previous individual based model for the small intestinal crypt and on in vitro cultured intestinal organoids, we here model crypt fission as a budding process based on fluid mechanics at the individual cell level and extrapolated predictions for growth of the intestinal epithelium. Budding was always observed in regions of organoids with abundant Paneth cells. Our data support a model in which buds are biomechanically initiated by single stem cells surrounded by Paneth cells which exhibit greater resistance to viscoelastic deformation, a hypothesis supported by atomic force measurements of single cells. Time intervals between consecutive budding events, as simulated by the model and observed in vitro, were 2.84 and 2.62 days, respectively. Predicted cell dynamics was unaffected within the original crypt which retained its full capability of providing cells to the epithelium throughout fission. Mitotic pressure in simulated primary crypts forced upward migration of buds, which simultaneously grew into new protruding crypts at a rate equal to 1.03 days(-1) in simulations and 0.99 days(-1) in cultured organoids. Simulated crypts reached their final size in 4.6 days, and required 6.2 days to migrate to the top of the primary crypt. The growth of the secondary crypt is independent of its migration along the original crypt. Assuming unrestricted crypt fission and multiple budding events, a maximal growth rate of the intestinal epithelium of 0.10 days(-1) is predicted and thus approximately 22 days are required for a 10-fold increase of polyp size. These predictions are in agreement with the time reported to develop macroscopic adenomas in mice after loss of Apc in intestinal stem cells.
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Affiliation(s)
- Carmen Pin
- Gut Health and Food Safety Research Programme, Institute of Food Research, Norwich, NR4 7UA, UK.
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35
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Waclaw B, Bozic I, Pittman ME, Hruban RH, Vogelstein B, Nowak MA. A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity. Nature 2015; 525:261-4. [PMID: 26308893 PMCID: PMC4782800 DOI: 10.1038/nature14971] [Citation(s) in RCA: 352] [Impact Index Per Article: 35.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Accepted: 07/23/2015] [Indexed: 01/01/2023]
Abstract
Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.
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Affiliation(s)
- Bartlomiej Waclaw
- School of Physics and Astronomy, University of Edinburgh, JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Ivana Bozic
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
- Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA
| | - Meredith E Pittman
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
| | - Ralph H Hruban
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
| | - Bert Vogelstein
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
- Ludwig Center and Howard Hughes Medical Institute, Johns Hopkins Kimmel Cancer Center, 1650 Orleans Street, Baltimore, Maryland 21287, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
- Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, Massachusetts 02138, USA
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Abstract
Mechanical forces shape biological tissues. They are the effectors of the developmental programs that orchestrate morphogenesis. A lot of effort has been devoted to understanding morphogenetic processes in mechanical terms. In this review, we focus on the interplay between tissue mechanics and growth. We first describe how tissue mechanics affects growth, by influencing the orientation of cell divisions and the signaling pathways that control the rate of volume increase and proliferation. We then address how the mechanical state of a tissue is affected by the patterns of growth. The forward and reverse interactions between growth and mechanics must be investigated in an integrative way if we want to understand how tissues grow and shape themselves. To illustrate this point, we describe examples in which growth homeostasis is achieved by feedback mechanisms that use mechanical forces.
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Affiliation(s)
- Loïc LeGoff
- National Center for Scientific Research, Developmental Biology Institute of Marseille-Luminy, Aix Marseille Université, 13009 Marseille, France
| | - Thomas Lecuit
- National Center for Scientific Research, Developmental Biology Institute of Marseille-Luminy, Aix Marseille Université, 13009 Marseille, France
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37
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Rieger H, Welter M. Integrative models of vascular remodeling during tumor growth. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2015; 7:113-29. [PMID: 25808551 PMCID: PMC4406149 DOI: 10.1002/wsbm.1295] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2014] [Revised: 02/05/2015] [Accepted: 02/19/2015] [Indexed: 02/02/2023]
Abstract
UNLABELLED Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature that is in many respects different from the hierarchically organized arterio-venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. WIREs Syst Biol Med 2015, 7:113-129. doi: 10.1002/wsbm.1295 For further resources related to this article, please visit the WIREs website. CONFLICT OF INTEREST The authors have declared no conflicts of interest for this article.
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Affiliation(s)
- Heiko Rieger
- Department of Theoretical Physics, Saarland UniversitySaarbrücken, Germany
| | - Michael Welter
- Department of Theoretical Physics, Saarland UniversitySaarbrücken, Germany
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38
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Ciarletta P, Balbi V, Kuhl E. Pattern selection in growing tubular tissues. PHYSICAL REVIEW LETTERS 2014; 113:248101. [PMID: 25541805 DOI: 10.1103/physrevlett.113.248101] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2014] [Indexed: 06/04/2023]
Abstract
Tubular organs display a wide variety of surface morphologies including circumferential and longitudinal folds, square and hexagonal undulations, and finger-type protrusions. Surface morphology is closely correlated to tissue function and serves as a clinical indicator for physiological and pathological conditions, but the regulators of surface morphology remain poorly understood. Here, we explore the role of geometry and elasticity on the formation of surface patterns. We establish morphological phase diagrams for patterns selection and show that increasing the thickness or stiffness ratio between the outer and inner tubular layers induces a gradual transition from circumferential to longitudinal folding. Our results suggest that physical forces act as regulators during organogenesis and give rise to the characteristic circular folds in the esophagus, the longitudinal folds in the valves of Kerckring, the surface networks in villi, and the crypts in the large intestine.
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Affiliation(s)
- P Ciarletta
- CNRS and Sorbonne Universités, Université Paris 6, Institut Jean le Rond d'Alembert, UMR 7190, 4 Place Jussieu case 162, 75005 Paris, France and MOX and Fondazione CEN, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - V Balbi
- CNRS and Sorbonne Universités, Université Paris 6, Institut Jean le Rond d'Alembert, UMR 7190, 4 Place Jussieu case 162, 75005 Paris, France
| | - E Kuhl
- Living Matter Laboratory, Stanford University, 496 Lomita Mall, Stanford, California 94305, USA
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Castiglione F, Pappalardo F, Bianca C, Russo G, Motta S. Modeling biology spanning different scales: an open challenge. BIOMED RESEARCH INTERNATIONAL 2014; 2014:902545. [PMID: 25143952 PMCID: PMC4124842 DOI: 10.1155/2014/902545] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2014] [Accepted: 06/25/2014] [Indexed: 02/03/2023]
Abstract
It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.
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Affiliation(s)
- Filippo Castiglione
- Institute for Applied Mathematics, National Research Council of Italy, Rome, Italy
| | | | - Carlo Bianca
- Theoretical Physics of Condensed Matter, Sorbonne Universities, UPMC Univ Paris 6, 75252 Paris Cedex 05, France
- UMR 7600 LPTMC, CNRS, 75252 Paris Cedex 05, France
| | - Giulia Russo
- Department of Pharmaceutical Sciences, University of Catania, Catania, Italy
| | - Santo Motta
- Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy
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40
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Hannezo E, Prost J, Joanny JF. Growth, homeostatic regulation and stem cell dynamics in tissues. J R Soc Interface 2014; 11:20130895. [PMID: 24478279 DOI: 10.1098/rsif.2013.0895] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The regulation of cell growth in animal tissues is a question of critical importance: most tissues contain different types of cells in interconversion and the fraction of each type has to be controlled in a precise way, by mechanisms that remain unclear. Here, we provide a theoretical framework for the homeostasis of stem-cell-containing epithelial tissues using mechanical equations, which describe the size of the tissue and kinetic equations, which describe the interconversions of the cell populations. We show that several features, such as the evolution of stem cell fractions during intestinal development, the shape of a developing intestinal wall, as well as the increase in the proliferative compartment in cancer initiation, can be studied and understood from generic modelling which does not rely on a particular regulatory mechanism. Finally, inspired by recent experiments, we propose a model where cell division rates are regulated by the mechanical stresses in the epithelial sheet. We show that pressure-controlled growth can, in addition to the previous features, also explain with few parameters the formation of stem cell compartments as well as the morphologies observed when a colonic crypt becomes cancerous. We also discuss optimal strategies of wound healing, in connection with experiments on the cornea.
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Affiliation(s)
- E Hannezo
- Physicochimie Curie (Institut Curie/CNRS-UMR168/UPMC), Institut Curie, Centre de Recherche, , 26 rue d'Ulm, 75248 Paris Cedex 05, France
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41
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Fogle C, Rowat AC, Levine AJ, Rudnick J. Shape transitions in soft spheres regulated by elasticity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052404. [PMID: 24329276 DOI: 10.1103/physreve.88.052404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Indexed: 06/03/2023]
Abstract
We study elasticity-driven morphological transitions of soft spherical core-shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.
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Affiliation(s)
- Craig Fogle
- Department of Physics, UCLA, Los Angeles, California 90095-1596, USA
| | - Amy C Rowat
- Department of Integrative Biology and Physiology, UCLA, Los Angeles, California 90095, USA and Department of Bioengineering, UCLA, Los Angeles, California 90095, USA
| | - Alex J Levine
- Department of Physics, UCLA, Los Angeles, California 90095-1596, USA and Department of Chemistry & Biochemistry, UCLA, Los Angeles, California 90095-1596, USA and Department of Biomathematics, UCLA, Los Angeles, California 90095-1596, USA
| | - Joseph Rudnick
- Department of Physics, UCLA, Los Angeles, California 90095-1596, USA
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Fletcher AG, Osborne JM, Maini PK, Gavaghan DJ. Implementing vertex dynamics models of cell populations in biology within a consistent computational framework. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2013; 113:299-326. [DOI: 10.1016/j.pbiomolbio.2013.09.003] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2012] [Revised: 09/18/2013] [Accepted: 09/25/2013] [Indexed: 10/26/2022]
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Nelson MR, King JR, Jensen OE. Buckling of a growing tissue and the emergence of two-dimensional patterns. Math Biosci 2013; 246:229-41. [PMID: 24128749 PMCID: PMC3863975 DOI: 10.1016/j.mbs.2013.09.008] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2013] [Revised: 09/24/2013] [Accepted: 09/27/2013] [Indexed: 12/21/2022]
Abstract
We model the growth of gut epithelial cells cultured upon a deformable substrate. Growth generates buckling instabilities, contributing to crypt formation in vivo. Variations in mechanical properties have little effect on resulting configurations. Configurations are controlled by growth patterns & interactions with strata below. The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity.
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Affiliation(s)
- M R Nelson
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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van der Wath RC, Gardiner BS, Burgess AW, Smith DW. Cell organisation in the colonic crypt: a theoretical comparison of the pedigree and niche concepts. PLoS One 2013; 8:e73204. [PMID: 24069177 PMCID: PMC3771985 DOI: 10.1371/journal.pone.0073204] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2013] [Accepted: 07/17/2013] [Indexed: 12/23/2022] Open
Abstract
The intestinal mucosa is a monolayer of rapidly self-renewing epithelial cells which is not only responsible for absorption of water and nutrients into the bloodstream but also acts as a protective barrier against harmful microbes entering the body. New functional epithelial cells are produced from stem cells, and their proliferating progeny. These stem cells are found within millions of crypts (tubular pits) spaced along the intestinal tract. The entire intestinal epithelium is replaced every 2–3 days in mice (3–5 days in humans) and hence cell production, differentiation, migration and turnover need to be tightly regulated. Malfunctions in this regulation are strongly linked to inflammatory bowel diseases and to the formation of adenomas and ultimately cancerous tumours. Despite a great deal of biological experimentation and observation, precisely how colonic crypts are regulated to produce mature colonocytes remains unclear. To assist in understanding how cell organisation in crypts is achieved, two very different conceptual models of cell behaviour are developed here, referred to as the ‘pedigree’ and the ‘niche’ models. The pedigree model proposes that crypt cells are largely preprogrammed and receive minimal prompting from the environment as they move through a routine of cell differentiation and proliferation to become mature colonocytes. The niche model proposes that crypt cells are primarily influenced by the local microenvironments along the crypt, and that predetermined cell behaviour plays a negligible role in their development. In this paper we present a computational model of colonic crypts in the mouse, which enables a comparison of the quality and controllability of mature coloncyte production by crypts operating under these two contrasting conceptual models of crypt regulation.
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Affiliation(s)
- Richard C. van der Wath
- School of Computer Science and Software Engineering, University of Western Australia, Perth, Western Australia, Australia
- * E-mail:
| | - Bruce S. Gardiner
- School of Computer Science and Software Engineering, University of Western Australia, Perth, Western Australia, Australia
| | - Antony W. Burgess
- Ludwig Institute for Cancer Research, Royal Melbourne Hospital, Melbourne, Victoria, Australia
- The Walter and Eliza Hall Institute of Medical Research, Melbourne, Victoria, Australia
| | - David W. Smith
- School of Computer Science and Software Engineering, University of Western Australia, Perth, Western Australia, Australia
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Ovadia J, Nie Q. Stem cell niche structure as an inherent cause of undulating epithelial morphologies. Biophys J 2013; 104:237-46. [PMID: 23332076 PMCID: PMC3540249 DOI: 10.1016/j.bpj.2012.11.3807] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2012] [Revised: 11/21/2012] [Accepted: 11/27/2012] [Indexed: 01/07/2023] Open
Abstract
The spatial organization of stem cells into a niche is a key factor for growth and continual tissue renewal during development, sustenance, and regeneration. Stratified epithelia serve as a great context to study the spatial aspects of the stem cell niche and cell lineages by organizing into layers of different cell types. Several types of stratified epithelia develop morphologies with advantageous, protruding structures where stem cells reside, such as rete pegs and palisades of Vogt. Here, multistage, spatial cell lineage models for epithelial stratification are used to study how the stem cell niche influences epithelial morphologies. When the stem cell niche forms along a rigid basal lamina, relatively regular morphologies are maintained. In contrast, stem cell niche formation along a free-moving basal lamina may prompt distorted epithelial morphologies with stem cells accumulating at the tips of fingerlike structures that form. The correspondence between our simulated morphologies and developmental stages of the human epidermis is also explored. Overall, our work provides an understanding of how stratified epithelia may attain distorted morphologies and sheds light on the importance of the spatial aspects of the stem cell niche.
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Affiliation(s)
| | - Qing Nie
- Center for Mathematical and Computational Biology, Center for Complex Biological Systems, Department of Mathematics, University of California, Irvine, California
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Buske P, Przybilla J, Loeffler M, Sachs N, Sato T, Clevers H, Galle J. On the biomechanics of stem cell niche formation in the gut - modelling growing organoids. FEBS J 2012; 279:3475-87. [DOI: 10.1111/j.1742-4658.2012.08646.x] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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De Matteis G, Graudenzi A, Antoniotti M. A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development. J Math Biol 2012. [PMID: 22565629 DOI: 10.1007/s00285‐012‐0539‐4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.
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Affiliation(s)
- Giovanni De Matteis
- Department of Mathematics "F. Enriques", University of Milan, Via Saldini 50, 20133 Milan, Italy
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A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development. J Math Biol 2012; 66:1409-62. [PMID: 22565629 DOI: 10.1007/s00285-012-0539-4] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2011] [Revised: 04/11/2012] [Indexed: 02/06/2023]
Abstract
Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.
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Nelson MR, Howard D, Jensen OE, King JR, Rose FRAJ, Waters SL. Growth-induced buckling of an epithelial layer. Biomech Model Mechanobiol 2011; 10:883-900. [PMID: 21191628 DOI: 10.1007/s10237-010-0280-0] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2010] [Accepted: 12/07/2010] [Indexed: 12/13/2022]
Abstract
We use a proof-of-concept experiment and two mathematical models to explore growth-induced tissue buckling, as may occur in colorectal crypt formation. Our experiment reveals how growth of a cultured epithelial monolayer on a thin flexible substrate can cause out-of-plane substrate deflections. We describe this system theoretically using a 'bilayer' model in which a growing cell layer adheres to a thin compressible elastic beam. We compare this with the 'supported-monolayer' model due to Edwards and Chapman (Bull Math Biol 69:1927-1942, 2007) for an incompressible expanding beam (representing crypt epithelium), which incorporates viscoelastic tethering to underlying stroma. We show that the bilayer model can exhibit buckling via parametric growth (in which the system passes through a sequence of equilibrium states, parameterised by the total beam length); in this case, non-uniformities in cell growth and variations in cell-substrate adhesion are predicted to have minimal effect on the shape of resulting buckled states. The supported-monolayer model reveals how competition between lateral supports and stromal adhesion influences the wavelength of buckled states (in parametric growth), and how non-equilibrium relaxation of tethering forces influences post-buckled shapes. This model also predicts that non-uniformities in growth patterns have a much weaker influence on buckled shapes than non-uniformities in material properties. Together, the experiment and models support the concept of patterning by growth-induced buckling and suggest that targeted softening of a growing cell layer provides greater control in shaping tissues than non-uniform growth.
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Affiliation(s)
- M R Nelson
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
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