1
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Osborne JM. An adaptive numerical method for multi-cellular simulations of tissue development and maintenance. J Theor Biol 2024; 594:111922. [PMID: 39111542 DOI: 10.1016/j.jtbi.2024.111922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 07/26/2024] [Accepted: 08/01/2024] [Indexed: 08/22/2024]
Abstract
In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.
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Affiliation(s)
- James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Melbourne, 3010, Victoria, Australia.
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2
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Boscq S, Billoud B, Theodorou I, Joemmanbaks T, Dufourt T, Charrier B. MUM, a maternal unknown message, inhibits early establishment of the medio-lateral axis in the embryo of the kelp Saccharina latissima. Development 2024; 151:dev202732. [PMID: 39190296 DOI: 10.1242/dev.202732] [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: 01/25/2024] [Accepted: 07/30/2024] [Indexed: 08/28/2024]
Abstract
Brown algae are multicellular photosynthetic organisms that have evolved independently of plants and other algae. Here, we have studied the determinism of body axis formation in the kelp Saccharina latissima. After microdissection of the embryo, we show that the stalk, an empty cell that retains the embryo on the maternal tissue, represses longitudinal cell divisions in the early embryo, thereby reinforcing the establishment of the initial apico-basal axis. In addition, it promotes cell growth and controls cell shape and arrangement in the flat oblong embryo composed of cells aligned in rows and columns. Although the stalk persists for several weeks until the embryo reaches at least 500 cells, proper embryogenesis requires connection to maternal tissue only during the first 4 days after fertilisation, i.e. before the embryo reaches the 8-cell stage. Transplantation experiments indicate that the maternal signal is not diffused in seawater, but requires contact between the embryo and the maternal tissue. This first global quantitative study of brown algal embryogenesis highlights the role of MUM, an unknown maternal message, in the control of growth axes and tissue patterning in kelp embryos.
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Affiliation(s)
- Samuel Boscq
- Morphogenesis of Macro Algae, UMR8227, CNRS - Sorbonne University, Station Biologique de Roscoff, Place Georges Teissier, 29680 Roscoff, France
| | - Bernard Billoud
- Morphogenesis of Macro Algae, UMR8227, CNRS - Sorbonne University, Station Biologique de Roscoff, Place Georges Teissier, 29680 Roscoff, France
| | - Ioannis Theodorou
- Morphogenesis of Macro Algae, UMR8227, CNRS - Sorbonne University, Station Biologique de Roscoff, Place Georges Teissier, 29680 Roscoff, France
| | - Tanweer Joemmanbaks
- Morphogenesis of Macro Algae, UMR8227, CNRS - Sorbonne University, Station Biologique de Roscoff, Place Georges Teissier, 29680 Roscoff, France
| | - Tanguy Dufourt
- Institut de Génomique Fonctionnelle de Lyon (IGFL), UMR5242, ENS-Lyon, CNRS, INRAE, UCBL, 32-34 Avenue Tony Garnier, 69007 Lyon, France
| | - Bénédicte Charrier
- Morphogenesis of Macro Algae, UMR8227, CNRS - Sorbonne University, Station Biologique de Roscoff, Place Georges Teissier, 29680 Roscoff, France
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3
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Belousov R, Savino S, Moghe P, Hiiragi T, Rondoni L, Erzberger A. Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting. PHYSICAL REVIEW LETTERS 2024; 132:248401. [PMID: 38949349 DOI: 10.1103/physrevlett.132.248401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 04/10/2024] [Indexed: 07/02/2024]
Abstract
Cellular Potts models are broadly applied across developmental biology and cancer research. We overcome limitations of the traditional approach, which reinterprets a modified Metropolis sampling as ad hoc dynamics, by introducing a physical timescale through Poissonian kinetics and by applying principles of stochastic thermodynamics to separate thermal and relaxation effects from athermal noise and nonconservative forces. Our method accurately describes cell-sorting dynamics in mouse-embryo development and identifies the distinct contributions of nonequilibrium processes, e.g., cell growth and active fluctuations.
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Affiliation(s)
- R Belousov
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - S Savino
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstraße 1, 69117 Heidelberg, Germany
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
| | - P Moghe
- Hubrecht Institute, Uppsalalaan 8, 3584 CT Utrecht, Netherlands
- Developmental Biology Unit, European Molecular Biology Laboratory, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - T Hiiragi
- Hubrecht Institute, Uppsalalaan 8, 3584 CT Utrecht, Netherlands
- Institute for the Advanced Study of Human Biology (WPI-ASHBi), Kyoto University, Kyoto, Japan
- Department of Developmental Biology, Graduate School of Medicine, Kyoto University, Kyoto 606-8501, Japan
| | - L Rondoni
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
- INFN, Sezione di Torino, Turin 10125, Italy
| | - A Erzberger
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstraße 1, 69117 Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, 69120 Heidelberg, Germany
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4
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Blom E, Engblom S. Morphological Stability for in silico Models of Avascular Tumors. Bull Math Biol 2024; 86:75. [PMID: 38758501 DOI: 10.1007/s11538-024-01297-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: 09/14/2023] [Accepted: 04/16/2024] [Indexed: 05/18/2024]
Abstract
The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.
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Affiliation(s)
- Erik Blom
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 751 05, Uppsala, Sweden
| | - Stefan Engblom
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 751 05, Uppsala, Sweden.
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5
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Boscq S, Billoud B, Charrier B. Cell-Autonomous and Non-Cell-Autonomous Mechanisms Concomitantly Regulate the Early Developmental Pattern in the Kelp Saccharina latissima Embryo. PLANTS (BASEL, SWITZERLAND) 2024; 13:1341. [PMID: 38794413 PMCID: PMC11125204 DOI: 10.3390/plants13101341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2024] [Revised: 05/08/2024] [Accepted: 05/09/2024] [Indexed: 05/26/2024]
Abstract
Brown algae are multicellular organisms that have evolved independently from plants and animals. Knowledge of the mechanisms involved in their embryogenesis is available only for the Fucus, Dictyota, and Ectocarpus, which are brown algae belonging to three different orders. Here, we address the control of cell growth and cell division orientation in the embryo of Saccharina latissima, a brown alga belonging to the order Laminariales, which grows as a stack of cells through transverse cell divisions until growth is initiated along the perpendicular axis. Using laser ablation, we show that apical and basal cells have different functions in the embryogenesis of this alga, with the apical cell being involved mainly in growth and basal cells controlling the orientation of cell division by inhibiting longitudinal cell division and thereby the widening of the embryo. These functions were observed in the very early development before the embryo reached the 8-cell stage. In addition, the growth of the apical and basal regions appears to be cell-autonomous, because there was no compensation for the loss of a significant part of the embryo upon laser ablation, resulting in smaller and less elongated embryos compared with intact embryos. In contrast, the orientation of cell division in the apical region of the embryo appears to be controlled by the basal cell only, which suggests a polarised, non-cell-autonomous mechanism. Altogether, our results shed light on the early mechanisms of growth rate and growth orientation at the onset of the embryogenesis of Saccharina, in which non-cell-specific cell-autonomous and cell-specific non-cell-autonomous processes are involved. This complex control differs from the mechanisms described in the other brown algal embryos, in which the establishment of embryo polarity depends on environmental cues.
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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: 0] [Impact Index Per Article: 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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7
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Ma T, Liu X, Su H, Shi Q, He Y, Wu F, Gao C, Li K, Liang Z, Zhang D, Zhang X, Hu K, Li S, Wang L, Wang M, Yue S, Hong W, Chen X, Zhang J, Zheng L, Deng X, Wang P, Fan Y. Coupling of Perinuclear Actin Cap and Nuclear Mechanics in Regulating Flow-Induced Yap Spatiotemporal Nucleocytoplasmic Transport. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024; 11:e2305867. [PMID: 38161226 PMCID: PMC10953556 DOI: 10.1002/advs.202305867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Revised: 11/10/2023] [Indexed: 01/03/2024]
Abstract
Mechanical forces, including flow shear stress, govern fundamental cellular processes by modulating nucleocytoplasmic transport of transcription factors like Yes-associated Protein (YAP). However, the underlying mechanical mechanism remains elusive. In this study, it is reported that unidirectional flow induces biphasic YAP transport with initial nuclear import, followed by nuclear export as actin cap formation and nuclear stiffening. Conversely, pathological oscillatory flow induces slight actin cap formation, nuclear softening, and sustained YAP nuclear localization. To elucidate the disparately YAP spatiotemporal distribution, a 3D mechanochemical model is developed, which integrates flow sensing, cytoskeleton organization, nucleus mechanotransduction, and YAP transport. The results unveiled that despite the significant localized nuclear stress imposed by the actin cap, its inherent stiffness counteracts the dispersed contractile stress exerted by conventional fibers on the nuclear membrane. Moreover, alterations in nuclear stiffness synergistically regulate nuclear deformation, thereby governing YAP transport. Furthermore, by expanding the single-cell model to a collective vertex framework, it is revealed that the irregularities in actin cap formation within individual cells have the potential to induce topological defects and spatially heterogeneous YAP distribution in the cellular monolayer. This work unveils a unified mechanism of flow-induced nucleocytoplasmic transport, providing a linkage between transcription factor localization and mechanical stimulation.
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Affiliation(s)
- Tianxiang Ma
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Xiao Liu
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Haoran Su
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Qiusheng Shi
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Yuan He
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Fan Wu
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Chenxing Gao
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Kexin Li
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Zhuqing Liang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Dongrui Zhang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Xing Zhang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Ke Hu
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Shangyu Li
- Biomedical Pioneering Innovation Center (BIOPIC)Peking UniversityBeijing100871China
- Academy for Advanced Interdisciplinary StudiesPeking UniversityBeijing100871China
| | - Li Wang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Min Wang
- Department of Gynecology and ObstetricsStrategic Support Force Medical CenterBeijing100101China
| | - Shuhua Yue
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Weili Hong
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Xun Chen
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Jing Zhang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Lisha Zheng
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Xiaoyan Deng
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Pu Wang
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
| | - Yubo Fan
- Key Laboratory of Biomechanics and Mechanobiology (Beihang University), Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical EngineeringBeihang UniversityBeijing100083China
- School of Engineering MedicineBeihang UniversityBeijing100083China
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8
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Wang X, Jenner AL, Salomone R, Warne DJ, Drovandi C. Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation. J Math Biol 2024; 88:28. [PMID: 38358410 PMCID: PMC10869399 DOI: 10.1007/s00285-024-02045-4] [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: 06/28/2023] [Revised: 10/25/2023] [Accepted: 12/27/2023] [Indexed: 02/16/2024]
Abstract
Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.
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Affiliation(s)
- Xiaoyu Wang
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia.
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia.
| | - Adrianne L Jenner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - Robert Salomone
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
- School of Computer Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - David J Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD, Australia
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9
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Pak TF, Pitt-Francis J, Baker RE. A mathematical framework for the emergence of winners and losers in cell competition. J Theor Biol 2024; 577:111666. [PMID: 37956955 DOI: 10.1016/j.jtbi.2023.111666] [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: 03/16/2023] [Revised: 09/27/2023] [Accepted: 11/06/2023] [Indexed: 11/21/2023]
Abstract
Cell competition is a process in multicellular organisms where cells interact with their neighbours to determine a "winner" or "loser" status. The loser cells are eliminated through programmed cell death, leaving only the winner cells to populate the tissue. Cell competition is context-dependent; the same cell type can win or lose depending on the cell type it is competing against. Hence, winner/loser status is an emergent property. A key question in cell competition is: how do cells acquire their winner/loser status? In this paper, we propose a mathematical framework for studying the emergence of winner/loser status based on a set of quantitative criteria that distinguishes competitive from non-competitive outcomes. We apply this framework in a cell-based modelling context, to both highlight the crucial role of active cell death in cell competition and identify the factors that drive cell competition.
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Affiliation(s)
- Thomas F Pak
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
| | - Joe Pitt-Francis
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK
| | - Ruth E Baker
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
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10
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Kiemen AL, Wu PH, Braxton AM, Cornish TC, Hruban RH, Wood L, Wirtz D, Zwicker D. Power-law growth models explain incidences and sizes of pancreatic cancer precursor lesions and confirm spatial genomic findings. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.12.01.569633. [PMID: 38105957 PMCID: PMC10723372 DOI: 10.1101/2023.12.01.569633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2023]
Abstract
Pancreatic ductal adenocarcinoma is a rare but lethal cancer. Recent evidence reveals that pancreatic intraepithelial neoplasms (PanINs), the microscopic precursor lesions in the pancreatic ducts that can give rise to invasive pancreatic cancer, are significantly larger and more prevalent than previously believed. Better understanding of the growth law dynamics of PanINs may improve our ability to understand how a miniscule fraction of these lesions makes the transition to invasive cancer. Here, using artificial intelligence (AI)-based three-dimensional (3D) tissue mapping method, we measured the volumes of >1,000 PanIN and found that lesion size is distributed according to a power law with a fitted exponent of -1.7 over > 3 orders of magnitude. Our data also suggest that PanIN growth is not very sensitive to the pancreatic microenvironment or an individual's age, family history, and lifestyle, and is rather shaped by general growth behavior. We analyze several models of PanIN growth and fit the predicted size distributions to the observed data. The best fitting models suggest that both intraductal spread of PanIN lesions and fusing of multiple lesions into large, highly branched structures drive PanIN growth patterns. This work lays the groundwork for future mathematical modeling efforts integrating PanIN incidence, morphology, genomic, and transcriptomic features to understand pancreas tumorigenesis, and demonstrates the utility of combining experimental measurement of human tissues with dynamic modeling for understanding cancer tumorigenesis.
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Affiliation(s)
- Ashley L. Kiemen
- Department of Pathology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- Department of Oncology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Pei-Hsun Wu
- Department of Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Alicia M. Braxton
- Department of Comparative Medicine, Medical University of South Carolina, Charleston, SC
| | - Toby C. Cornish
- Department of Pathology, University of Colorado School of Medicine, Aurora, CO
| | - Ralph H. Hruban
- Department of Pathology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- Department of Oncology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Laura Wood
- Department of Pathology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- Department of Oncology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Denis Wirtz
- Department of Pathology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- Department of Oncology, The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- Department of Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - David Zwicker
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
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11
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Tervonen A, Korpela S, Nymark S, Hyttinen J, Ihalainen TO. The Effect of Substrate Stiffness on Elastic Force Transmission in the Epithelial Monolayers over Short Timescales. Cell Mol Bioeng 2023; 16:475-495. [PMID: 38099211 PMCID: PMC10716100 DOI: 10.1007/s12195-023-00772-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 06/26/2023] [Indexed: 12/17/2023] Open
Abstract
Purpose The importance of mechanical forces and microenvironment in guiding cellular behavior has been widely accepted. Together with the extracellular matrix (ECM), epithelial cells form a highly connected mechanical system subjected to various mechanical cues from their environment, such as ECM stiffness, and tensile and compressive forces. ECM stiffness has been linked to many pathologies, including tumor formation. However, our understanding of the effect of ECM stiffness and its heterogeneities on rapid force transduction in multicellular systems has not been fully addressed. Methods We used experimental and computational methods. Epithelial cells were cultured on elastic hydrogels with fluorescent nanoparticles. Single cells were moved by a micromanipulator, and epithelium and substrate deformation were recorded. We developed a computational model to replicate our experiments and quantify the force distribution in the epithelium. Our model further enabled simulations with local stiffness gradients. Results We found that substrate stiffness affects the force transduction and the cellular deformation following an external force. Also, our results indicate that the heterogeneities, e.g., gradients, in the stiffness can substantially influence the strain redistribution in the cell monolayers. Furthermore, we found that the cells' apico-basal elasticity provides a level of mechanical isolation between the apical cell-cell junctions and the basal focal adhesions. Conclusions Our simulation results show that increased ECM stiffness, e.g., due to a tumor, can mechanically isolate cells and modulate rapid mechanical signaling between cells over distances. Furthermore, the developed model has the potential to facilitate future studies on the interactions between epithelial monolayers and elastic substrates. Supplementary Information The online version of this article (10.1007/s12195-023-00772-0) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Aapo Tervonen
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Arvo Ylpön katu 34, 33520 Tampere, Finland
- Department of Biological and Environmental Science, Faculty of Mathematics and Science, University of Jyväskylä, Survontie 9 C, 40500 Jyväskylä, Finland
| | - Sanna Korpela
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Arvo Ylpön katu 34, 33520 Tampere, Finland
| | - Soile Nymark
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Arvo Ylpön katu 34, 33520 Tampere, Finland
| | - Jari Hyttinen
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Arvo Ylpön katu 34, 33520 Tampere, Finland
| | - Teemu O. Ihalainen
- BioMediTech, Faculty of Medicine and Health Technology, Tampere University, Arvo Ylpön katu 34, 33520 Tampere, Finland
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12
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Khan AK, Muñoz-Castro G, Muñoz JJ. Single and two-cells shape analysis from energy functionals for three-dimensional vertex models. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3766. [PMID: 37551449 DOI: 10.1002/cnm.3766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 07/10/2023] [Accepted: 07/21/2023] [Indexed: 08/09/2023]
Abstract
Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the definition of an energy functional, which fully determines the cellular response and conclusions. While two-dimensional vertex models have been widely employed, three-dimensional models are far more scarce, mainly due to the large amount of configurations that they may adopt and the complex geometrical transitions they undergo. We here investigate the shape of single and two-cells configurations as a function of the energy terms, and we study the dependence of the final shape on the model parameters: namely the exponent of the term penalising cell-cell adhesion and surface contractility. In single cell analysis, we deduce analytically the radius and limit values of the contractility for linear and quadratic surface energy terms, in 2D and 3D. In two-cells systems, symmetrical and asymmetrical, we deduce the evolution of the aspect ratio and the relative radius. While in functionals with linear surface terms yield the same aspect ratio in 2D and 3D, the configurations when using quadratic surface terms are distinct. We relate our results with well-known solutions from capillarity theory, and verify our analytical findings with a three-dimensional vertex model.
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Affiliation(s)
- Ahmad K Khan
- Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Guillem Muñoz-Castro
- Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Jose J Muñoz
- Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
- Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya, Barcelona, Spain
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain
- Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech), Barcelona, Spain
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13
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Rozman J, Yeomans JM, Sknepnek R. Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model. PHYSICAL REVIEW LETTERS 2023; 131:228301. [PMID: 38101347 DOI: 10.1103/physrevlett.131.228301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 06/26/2023] [Accepted: 10/20/2023] [Indexed: 12/17/2023]
Abstract
We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.
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Affiliation(s)
- Jan Rozman
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Rastko Sknepnek
- School of Science and Engineering, University of Dundee, Dundee DD1 4HN, United Kingdom
- School of Life Sciences, University of Dundee, Dundee DD1 5EH, United Kingdom
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14
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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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15
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Sego TJ, Comlekoglu T, Peirce SM, Desimone DW, Glazier JA. General, open-source vertex modeling in biological applications using Tissue Forge. Sci Rep 2023; 13:17886. [PMID: 37857673 PMCID: PMC10587242 DOI: 10.1038/s41598-023-45127-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: 05/02/2023] [Accepted: 10/16/2023] [Indexed: 10/21/2023] Open
Abstract
Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering open-source, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in the C, C++ and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.
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Affiliation(s)
- T J Sego
- Department of Medicine, University of Florida, Gainesville, FL, USA.
| | - Tien Comlekoglu
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - Shayn M Peirce
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Douglas W Desimone
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - James A Glazier
- Department of Intelligent Engineering and Biocomplexity Institute, Indiana University, Bloomington, IN, USA
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16
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Germano DPJ, Zanca A, Johnston ST, Flegg JA, Osborne JM. Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems. Bull Math Biol 2023; 85:111. [PMID: 37805982 PMCID: PMC10560655 DOI: 10.1007/s11538-023-01214-8] [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: 06/05/2023] [Accepted: 09/11/2023] [Indexed: 10/10/2023]
Abstract
Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.
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Affiliation(s)
- Domenic P. J. Germano
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Adriana Zanca
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Stuart T. Johnston
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - Jennifer A. Flegg
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
| | - James M. Osborne
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010 Australia
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17
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Gou J, Zhang T, Othmer HG. The Interaction of Mechanics and the Hippo Pathway in Drosophila melanogaster. Cancers (Basel) 2023; 15:4840. [PMID: 37835534 PMCID: PMC10571775 DOI: 10.3390/cancers15194840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 09/10/2023] [Accepted: 09/15/2023] [Indexed: 10/15/2023] Open
Abstract
Drosophila melanogaster has emerged as an ideal system for studying the networks that control tissue development and homeostasis and, given the similarity of the pathways involved, controlled and uncontrolled growth in mammalian systems. The signaling pathways used in patterning the Drosophila wing disc are well known and result in the emergence of interaction of these pathways with the Hippo signaling pathway, which plays a central role in controlling cell proliferation and apoptosis. Mechanical effects are another major factor in the control of growth, but far less is known about how they exert their control. Herein, we develop a mathematical model that integrates the mechanical interactions between cells, which occur via adherens and tight junctions, with the intracellular actin network and the Hippo pathway so as to better understand cell-autonomous and non-autonomous control of growth in response to mechanical forces.
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Affiliation(s)
- Jia Gou
- Department of Mathematics, University of California, Riverside, CA 92507, USA;
| | - Tianhao Zhang
- School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;
| | - Hans G. Othmer
- School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;
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18
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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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19
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Wu Y, Sun SX. Mechanics of cell-cell junctions. Biophys J 2023; 122:3354-3368. [PMID: 37475215 PMCID: PMC10465726 DOI: 10.1016/j.bpj.2023.07.011] [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: 02/02/2023] [Revised: 06/01/2023] [Accepted: 07/17/2023] [Indexed: 07/22/2023] Open
Abstract
Tissue cells in epithelial or endothelial monolayers are connected through cell-cell junctions, which are stabilized by transmembrane E-cadherin bonds and intracellular actin filaments. These bonds and junctions play a crucial role in maintaining the barrier function of epithelia and endothelia and are believed to transmit forces between cells. Additionally, E-cadherin bonds can impact the shape of cell-cell junctions. In this study, we develop a continuum mechanical model of the cell-cell junction by explicitly incorporating the cell membrane, distributions of E-cadherin bonds, cytoplasmic fluid pressure, and F-actin dynamics. The static force-balanced version of the model is able to analyze the influences of cell cortical tension, actin dynamics, and cytoplasmic pressure on the junction shape and E-cadherin bonds. Furthermore, an extended model that incorporates fluid flow, across the cell boundary as well as around the cell, is also examined. This model can couple cell-shape changes with cell cortical tension and fluid flow, and predicts the additional effect of fluid motion on cell-cell junction mechanics. Taken together, our models serve as an intermediate link between molecular-scale models of cell-junction molecules and cell-scale models of tissue and epithelia.
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Affiliation(s)
- Yufei Wu
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland; Institute for NanoBioTechnology, Johns Hopkins University, Baltimore, Maryland
| | - Sean X Sun
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland; Institute for NanoBioTechnology, Johns Hopkins University, Baltimore, Maryland; Center for Cell Dynamics, Johns Hopkins School of Medicine, Baltimore, Maryland.
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20
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Schmidt A, Finegan T, Häring M, Kong D, Fletcher AG, Alam Z, Grosshans J, Wolf F, Peifer M. Polychaetoid/ZO-1 strengthens cell junctions under tension while localizing differently than core adherens junction proteins. Mol Biol Cell 2023; 34:ar81. [PMID: 37163320 PMCID: PMC10398881 DOI: 10.1091/mbc.e23-03-0077] [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: 03/01/2023] [Revised: 05/02/2023] [Accepted: 05/03/2023] [Indexed: 05/11/2023] Open
Abstract
During embryonic development, dramatic cell shape changes and movements reshape the embryonic body plan. These require robust but dynamic linkage between the cell-cell adherens junctions and the force-generating actomyosin cytoskeleton. Our view of this linkage has evolved, and we now realize linkage is mediated by mechanosensitive multiprotein complexes assembled via multivalent connections. Here we combine genetic, cell biological, and modeling approaches to define the mechanism of action and functions of an important player, Drosophila polychaetoid, homologue of mammalian ZO-1. Our data reveal that Pyd reinforces cell junctions under elevated tension, and facilitates cell rearrangements. Pyd is important to maintain junctional contractility and in its absence cell rearrangements stall. We next use structured illumination microscopy to define the molecular architecture of cell-cell junctions during these events. The cadherin-catenin complex and Cno both localize to puncta along the junctional membrane, but are differentially enriched in different puncta. Pyd, in contrast, exhibits a distinct localization to strands that extend out from the region occupied by core junction proteins. We then discuss the implications for the protein network at the junction-cytoskeletal interface, suggesting different proteins localize and function in distinct ways, perhaps in distinct subcomplexes, but combine to produce robust connections.
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Affiliation(s)
- Anja Schmidt
- Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3280
| | - Tara Finegan
- Department of Biology, University of Rochester, Rochester, New York 14627-0211
| | - Matthias Häring
- Göttingen Campus Institute for Dynamics of Biological Networks, Georg August University, 37075 Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Max Planck Institute for Multidisciplinary Sciences, 37075 Göttingen, Germany
- Institute for Dynamics of Complex Systems, Georg August University, 37077 Göttingen, Germany
| | - Deqing Kong
- Department of Biology, Philipps University, 35043 Marburg, Germany
| | - Alexander G Fletcher
- School of Mathematics and Statistics and Bateson Centre, University of Sheffield, Sheffield S10 2TN, United Kingdom
| | - Zuhayr Alam
- Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3280
| | - Jörg Grosshans
- Department of Biology, Philipps University, 35043 Marburg, Germany
| | - Fred Wolf
- Göttingen Campus Institute for Dynamics of Biological Networks, Georg August University, 37075 Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Max Planck Institute for Multidisciplinary Sciences, 37075 Göttingen, Germany
- Institute for Dynamics of Complex Systems, Georg August University, 37077 Göttingen, Germany
| | - Mark Peifer
- Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3280
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21
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Dow LP, Parmar T, Marchetti MC, Pruitt BL. Engineering tools for quantifying and manipulating forces in epithelia. BIOPHYSICS REVIEWS 2023; 4:021303. [PMID: 38510344 PMCID: PMC10903508 DOI: 10.1063/5.0142537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Accepted: 04/20/2023] [Indexed: 03/22/2024]
Abstract
The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.
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Affiliation(s)
| | - Toshi Parmar
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
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22
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Sego T, Comlekoglu T, Peirce SM, Desimone D, Glazier JA. General, Open-Source Vertex Modeling in Biological Applications Using Tissue Forge. RESEARCH SQUARE 2023:rs.3.rs-2886960. [PMID: 37214822 PMCID: PMC10197754 DOI: 10.21203/rs.3.rs-2886960/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering opensource, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in the C , C + + and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.
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Affiliation(s)
- T.J. Sego
- Department of Medicine, University of Florida, Gainesville, FL, USA
| | - Tien Comlekoglu
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - Shayn M. Peirce
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Douglas Desimone
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - James A. Glazier
- Department of Intelligent Engineering and Biocomplexity Institute, Indiana University,Bloomington, IN, USA
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23
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Selvamani P, Chelakkot R, Nandi A, Inamdar MM. Emergence of Spatial Scales and Macroscopic Tissue Dynamics in Active Epithelial Monolayers. Cells Tissues Organs 2023; 213:269-282. [PMID: 37044075 DOI: 10.1159/000528501] [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: 06/05/2022] [Accepted: 11/22/2022] [Indexed: 04/14/2023] Open
Abstract
Migrating cells in tissues are often known to exhibit collective swirling movements. In this paper, we develop an active vertex model with polarity dynamics based on contact inhibition of locomotion (CIL). We show that under this dynamics, the cells form steady-state vortices in velocity, polarity, and cell stress with length scales that depend on polarity alignment rate (ζ), self-motility (v0), and cell-cell bond tension (λ). When the ratio λ/v0 becomes larger, the tissue reaches a near jamming state because of the inability of the cells to exchange their neighbors, and the length scale associated with tissue kinematics increases. A deeper examination of this jammed state provides insights into the mechanism of sustained swirl formation under CIL rule that is governed by the feedback between cell polarities and deformations. To gain additional understanding of how active forcing governed by CIL dynamics leads to large-scale tissue dynamics, we systematically coarse-grain cell stress, polarity, and motility and show that the tissue remains polar even on larger length scales. Overall, we explore the origin of swirling patterns during collective cell migration and obtain a connection between cell-level dynamics and large-scale cellular flow patterns observed in epithelial monolayers.
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Affiliation(s)
- Padmalochini Selvamani
- Center for Research in Nanotechnology and Science, Indian Institute of Technology Bombay, Mumbai, India
| | | | - Amitabha Nandi
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, India
| | - Mandar M Inamdar
- Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India
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24
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Schmidt A, Finegan T, Häring M, Kong D, Fletcher AG, Alam Z, Grosshans J, Wolf F, Peifer M. Polychaetoid/ZO-1 strengthens cell junctions under tension while localizing differently than core adherens junction proteins. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.03.01.530634. [PMID: 36909597 PMCID: PMC10002719 DOI: 10.1101/2023.03.01.530634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
Abstract
During embryonic development dramatic cell shape changes and movements re-shape the embryonic body plan. These require robust but dynamic linkage between the cell-cell adherens junctions and the force-generating actomyosin cytoskeleton. Our view of this linkage has evolved, and we now realize linkage is mediated by a mechanosensitive multiprotein complex assembled via multivalent connections. Here we combine genetic, cell biological and modeling approaches to define the mechanism of action and functions of an important player, Drosophila Polychaetoid, homolog of mammalian ZO-1. Our data reveal that Pyd reinforces cell junctions under elevated tension, and facilitates cell rearrangements. Pyd is important to maintain junctional contractility and in its absence cell rearrangements stall. We next use structured illumination microscopy to define the molecular architecture of cell-cell junctions during these events. The cadherin-catenin complex and Cno both localize to puncta along the junctional membrane, but are differentially enriched in different puncta. Pyd, in contrast, exhibits a distinct localization to strands that extend out from the region occupied by core junction proteins. We then discuss the implications for the protein network at the junction-cytoskeletal interface, suggesting different proteins localize and function in distinct ways but combine to produce robust connections.
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Affiliation(s)
- Anja Schmidt
- Department of Biology, University of North Carolina at Chapel Hill, CB#3280, Chapel Hill, NC 27599-3280, USA
| | - Tara Finegan
- Department of Biology, University of Rochester, Rochester, New York, USA 14627-0211
| | - Matthias Häring
- Göttingen Campus Institute for Dynamics of Biological Networks, Georg August University, Hermann Rein Str. 3, 37075 Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
- Max Planck Institute for Multidisciplinary Sciences, Hermann Rein St. 3, 37075 Göttingen, German
- Institute for Dynamics of Complex Systems, Georg August University, Friedrich Hund Pl. 1, 37077 Göttingen, Germany
| | - Deqing Kong
- Department of Biology, Philipps University, Karl-von-Frisch-Straße 8, 35043 Marburg, Germany
| | - Alexander G Fletcher
- School of Mathematics and Statistics & Bateson Centre, University of Sheffield, Sheffield, UK
| | - Zuhayr Alam
- Department of Biology, University of North Carolina at Chapel Hill, CB#3280, Chapel Hill, NC 27599-3280, USA
| | - Jörg Grosshans
- Department of Biology, Philipps University, Karl-von-Frisch-Straße 8, 35043 Marburg, Germany
| | - Fred Wolf
- Göttingen Campus Institute for Dynamics of Biological Networks, Georg August University, Hermann Rein Str. 3, 37075 Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
- Max Planck Institute for Multidisciplinary Sciences, Hermann Rein St. 3, 37075 Göttingen, German
- Institute for Dynamics of Complex Systems, Georg August University, Friedrich Hund Pl. 1, 37077 Göttingen, Germany
| | - Mark Peifer
- Department of Biology, University of North Carolina at Chapel Hill, CB#3280, Chapel Hill, NC 27599-3280, USA
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25
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Picchi Scardaoni M. Energetic convenience of cell division in biological tissues. Phys Rev E 2022; 106:054405. [PMID: 36559362 DOI: 10.1103/physreve.106.054405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 10/25/2022] [Indexed: 11/16/2022]
Abstract
A typical feature of living tissues is proliferation by division: it is a fundamental aspect of many biological processes, including embryonic development, morphogenesis, and cancer growth. Here, we study the energetics of cell division occurring in epithelia, highlighting the interplay of the key parameters ruling mitosis. We find the existence of a region, in the parameter space, which is independent of the cell elasticity and weakly dependent on the ratio between mother and daughter cells areas. In this region, cell division is energetically favorable. Our results may lead to an exact characterization of cells having anomalous proliferation.
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Affiliation(s)
- Marco Picchi Scardaoni
- Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 2, 56122 Pisa, Italy
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26
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Germano DPJ, Johnston ST, Crampin EJ, Osborne JM. Modelling realistic 3D deformations of simple epithelia in dynamic homeostasis. Math Biosci 2022; 352:108895. [PMID: 36037860 DOI: 10.1016/j.mbs.2022.108895] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Revised: 08/19/2022] [Accepted: 08/19/2022] [Indexed: 10/15/2022]
Abstract
The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue's shape must remain relatively unchanged. Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, there are few models which accurately describe how these tissues maintain a stable structure. Here, we present a novel, 3D, deformable, multilayer, cell-centre model of a simple epithelium. Cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. We show that the model is capable of maintaining a consistent tissue structure while undergoing self renewal. We also demonstrate the model's robustness under tissue renewal, cell migration and cell removal. The model presented here is a valuable advancement towards the modelling of tissues and organs with complex and generalised structures.
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Affiliation(s)
- Domenic P J Germano
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia; Systems Biology Laboratory, School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia; Department of Biomedical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - Stuart T Johnston
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia; Systems Biology Laboratory, School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia; Department of Biomedical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - Edmund J Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia; Department of Biomedical Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia; School of Medicine, Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia.
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27
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Johnson CGM, Fletcher AG, Soyer OS. ChemChaste: Simulating spatially inhomogeneous biochemical reaction-diffusion systems for modeling cell-environment feedbacks. Gigascience 2022; 11:giac051. [PMID: 35715874 PMCID: PMC9205757 DOI: 10.1093/gigascience/giac051] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2021] [Revised: 03/31/2022] [Accepted: 05/30/2022] [Indexed: 01/21/2023] Open
Abstract
BACKGROUND Spatial organization plays an important role in the function of many biological systems, from cell fate specification in animal development to multistep metabolic conversions in microbial communities. The study of such systems benefits from the use of spatially explicit computational models that combine a discrete description of cells with a continuum description of one or more chemicals diffusing within a surrounding bulk medium. These models allow the in silico testing and refinement of mechanistic hypotheses. However, most existing models of this type do not account for concurrent bulk and intracellular biochemical reactions and their possible coupling. CONCLUSIONS Here, we describe ChemChaste, an extension for the open-source C++ computational biology library Chaste. ChemChaste enables the spatial simulation of both multicellular and bulk biochemistry by expanding on Chaste's existing capabilities. In particular, ChemChaste enables (i) simulation of an arbitrary number of spatially diffusing chemicals, (ii) spatially heterogeneous chemical diffusion coefficients, and (iii) inclusion of both bulk and intracellular biochemical reactions and their coupling. ChemChaste also introduces a file-based interface that allows users to define the parameters relating to these functional features without the need to interact directly with Chaste's core C++ code. We describe ChemChaste and demonstrate its functionality using a selection of chemical and biochemical exemplars, with a focus on demonstrating increased ability in modeling bulk chemical reactions and their coupling with intracellular reactions. AVAILABILITY AND IMPLEMENTATION ChemChaste version 1.0 is a free, open-source C++ library, available via GitHub at https://github.com/OSS-Lab/ChemChaste under the BSD license, on the Zenodo archive at zendodo doi, as well as on BioTools (biotools:chemchaste) and SciCrunch (RRID:SCR022208) databases.
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Affiliation(s)
- Connah G M Johnson
- Mathematics of Real-World Systems Doctoral Training Centre, University of Warwick, Coventry, CV35 9EF, UK
- School of Life Sciences, University of Warwick, Coventry, CV35 9EF, UK
| | - Alexander G Fletcher
- School of Mathematics & Statistics, University of Sheffield, Sheffield, S3 7RH, UK
- Bateson Centre, University of Sheffield, Sheffield, S10 2TN, UK
| | - Orkun S Soyer
- School of Life Sciences, University of Warwick, Coventry, CV35 9EF, UK
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28
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Lee SW, Morishita Y. Two types of critical cell density for mechanical elimination of abnormal cell clusters from epithelial tissue. PLoS Comput Biol 2022; 18:e1010178. [PMID: 35696420 PMCID: PMC9232172 DOI: 10.1371/journal.pcbi.1010178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 06/24/2022] [Accepted: 05/07/2022] [Indexed: 11/18/2022] Open
Abstract
Recent technological advances in high-resolution imaging and artificial modulation of genetic functions at different times and regions have enabled direct observations of the formation and elimination of abnormal cell populations. A recent trend in cell competition research is the incorporation of cell mechanics. In different tissues and species, abnormal cells developing in epithelial tissues are mechanically eliminated by cell contraction via actomyosin accumulation at the interface between normal and abnormal cells. This mechanical cell elimination process has attracted attention as a potential universal defense mechanism. Here, we theoretically examined the conditions for mechanical elimination of growing abnormal cell populations. Simulations and mathematical analyses using a vertex dynamics model revealed two types of critical cell density associated with mechanical elimination of abnormal cell clusters. One is a subtype of homeostatic density, in which the frequencies of spontaneous mechanical cell elimination and proliferation are balanced, even if no explicit dependence of proliferation or apoptosis on the cell density is assumed. This density is related to the mechanical stability of a single cell. The other is density related to mechanical stability as a cell population under external pressure. Both density types are determined by tissue mechanical properties. In solid tissues, the former type is reached first as the intensity of interfacial contraction increases, and it functions as a critical density. On the other hand, the latter type becomes critical when tissues are highly fluid. The derived analytical solution explicitly reveals the dependence of critical contractile force and density on different parameters. We also found a negative correlation between the proliferation rate of abnormal cells and the likelihood of the abnormal cell population expanding by escaping elimination. This is counterintuitive because in the context of cell competition, fast-growing cell populations generally win. These findings provide new insight into, and interpretation of, the results from experimental studies. High-resolution imaging techniques have revealed that abnormal cells developing in epithelial tissues are mechanically eliminated via contraction at the interface between the abnormal cells and normal surrounding cells. This phenomenon is seen in various species and tissues and thus is regarded as a primitive defense system against precancerous cells common to all animals. For comprehensive understanding of this potential defense system, we derived mathematical conditions to achieve mechanical elimination of growing abnormal cell populations. We identified two characteristic cell density types associated with successful mechanical elimination of abnormal cell clusters. Both are determined by tissue physical properties, and the smaller of the two functions as a critical density above which abnormal cell populations cannot exist. We also found a counterintuitive phenomenon in which slower proliferation of abnormal cells promotes their growth as a population. Our results will help elucidate the mechanisms of intrinsic tissue defenses against cancer from the perspective of cell mechanics.
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Affiliation(s)
- Sang-Woo Lee
- Laboratory for Developmental Morphogeometry, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
| | - Yoshihiro Morishita
- Laboratory for Developmental Morphogeometry, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
- * E-mail:
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29
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Bajpai S, Chelakkot R, Prabhakar R, Inamdar MM. Role of Delta-Notch signalling molecules on cell-cell adhesion in determining heterogeneous chemical and cell morphological patterning. SOFT MATTER 2022; 18:3505-3520. [PMID: 35438097 DOI: 10.1039/d2sm00064d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Cell mechanics and motility are responsible for collective motion of cells that result in overall deformation of epithelial tissues. On the other hand, contact-dependent cell-cell signalling is responsible for generating a large variety of intricate, self-organized, spatial patterns of the signalling molecules. Moreover, it is becoming increasingly clear that the combined mechanochemical patterns of cell shape/size and signalling molecules in the tissues, for example, in cancerous and sensory epithelium, are governed by mechanochemical coupling between chemical signalling and cell mechanics. However, a clear quantitative picture of how these two aspects of tissue dynamics, i.e., signalling and mechanics, lead to pattern and form is still emerging. Although, a number of recent experiments demonstrate that cell mechanics, cell motility, and cell-cell signalling are tightly coupled in many morphogenetic processes, relatively few modeling efforts have focused on an integrated approach. We extend the vertex model of an epithelial monolayer to account for contact-dependent signalling between adjacent cells and between non-adjacent neighbors through long protrusional contacts with a feedback mechanism wherein the adhesive strength between adjacent cells is controlled by the expression of the signalling molecules in those cells. Local changes in cell-cell adhesion lead to changes in cell shape and size, which in turn drives changes in the levels of signalling molecules. Our simulations show that even this elementary two-way coupling of chemical signalling and cell mechanics is capable of giving rise to a rich variety of mechanochemical patterns in epithelial tissues. In particular, under certain parametric conditions, bimodal distributions in cell size and shape are obtained, which resemble experimental observations in cancerous and sensory tissues.
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Affiliation(s)
- Supriya Bajpai
- IITB-Monash Research Academy, Mumbai 400076, India.
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia.
- Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Raghunath Chelakkot
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Ranganathan Prabhakar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia.
| | - Mandar M Inamdar
- Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.
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30
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Mukhtar N, Cytrynbaum EN, Edelstein-Keshet L. A Multiscale computational model of YAP signaling in epithelial fingering behaviour. Biophys J 2022; 121:1940-1948. [DOI: 10.1016/j.bpj.2022.04.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Revised: 01/03/2022] [Accepted: 04/06/2022] [Indexed: 11/26/2022] Open
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31
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Mohammad RZ, Murakawa H, Svadlenka K, Togashi H. A numerical algorithm for modeling cellular rearrangements in tissue morphogenesis. Commun Biol 2022; 5:239. [PMID: 35304570 PMCID: PMC8933555 DOI: 10.1038/s42003-022-03174-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 02/16/2022] [Indexed: 11/15/2022] Open
Abstract
Among morphological phenomena, cellular patterns in developing sensory epithelia have gained attention in recent years. Although physical models for cellular rearrangements are well-established thanks to a large bulk of experimental work, their computational implementation lacks solid mathematical background and involves experimentally unreachable parameters. Here we introduce a level set-based computational framework as a tool to rigorously investigate evolving cellular patterns, and study its mathematical and computational properties. We illustrate that a compelling feature of the method is its ability to correctly handle complex topology changes, including frequent cell intercalations. Combining this accurate numerical scheme with an established mathematical model, we show that the proposed framework features minimum possible number of parameters and is capable of reproducing a wide range of tissue morphological phenomena, such as cell sorting, engulfment or internalization. In particular, thanks to precise mathematical treatment of cellular intercalations, this method succeeds in simulating experimentally observed development of cellular mosaic patterns in sensory epithelia. A numerical algorithm handles complex cell topology changes and reproduces tissue morphological phenomena without relying on nonphysical parameters.
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Affiliation(s)
- Rhudaina Z Mohammad
- Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan.,Institute of Mathematics, College of Science, University of the Philippines Diliman, Quezon City, Philippines
| | - Hideki Murakawa
- Applied Mathematics and Informatics Course, Faculty of Advanced Science and Technology, Ryukoku University, Otsu, Japan
| | - Karel Svadlenka
- Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan. .,Mathematical Institute, Czech Academy of Sciences, Prague, Czech Republic.
| | - Hideru Togashi
- JST PRESTO (Precursory Research for Embryonic Science and Technology), Kobe, Japan.,Department of Biochemistry and Molecular Biology, Kobe University Graduate School of Medicine, Kobe, Japan
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32
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Lin SZ, Merkel M, Rupprecht JF. Implementation of cellular bulk stresses in vertex models of biological tissues. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:4. [PMID: 35038043 DOI: 10.1140/epje/s10189-021-00154-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 12/01/2021] [Indexed: 06/14/2023]
Abstract
Vertex models describe biological tissues as tilings of polygons. In standard vertex models, the tissue dynamics result from a balance between isotropic stresses, which are associated with the bulk of the cells, and tensions associated with cell-cell interfaces. However, in this framework it is less obvious how to describe anisotropic stresses arising from the bulk of cells. In epithelia, such bulk anisotropic stresses could arise for instance through medial myosin fluctuations. Two recent publications-Tlili et al. (Proc Natl Acad Sci USA 116(51):25430-25439, 2019) and Comelles et al. (eLife 10:e57730, 2021)-have proposed different schemes to implement bulk anisotropic stresses in vertex models. Here we show that while both schemes transform in the same way under affine deformations, they lead to significantly different tissue dynamics. Our results are consistent with the interpretation that the Tilli et al. scheme describes bulk stresses that are uniform within each cell, while the Comelles et al. scheme corresponds to non-uniform bulk stresses. Finally, we wondered whether a standard vertex model can be fully expressed in terms of bulk cellular stresses alone. We find that, in general, neither scheme can mimic the vertex forces created by cell-cell interface tensions.
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Affiliation(s)
- Shao-Zhen Lin
- CNRS and Turing Center for Living Systems, Centre de Physique Théorique, Aix Marseille Univ, Université de Toulon, 13009, Marseille, France
| | - Matthias Merkel
- CNRS and Turing Center for Living Systems, Centre de Physique Théorique, Aix Marseille Univ, Université de Toulon, 13009, Marseille, France
| | - Jean-Francois Rupprecht
- CNRS and Turing Center for Living Systems, Centre de Physique Théorique, Aix Marseille Univ, Université de Toulon, 13009, Marseille, France.
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33
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Fletcher AG, Osborne JM. Seven challenges in the multiscale modeling of multicellular tissues. WIREs Mech Dis 2022; 14:e1527. [PMID: 35023326 DOI: 10.1002/wsbm.1527] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 11/23/2020] [Accepted: 03/25/2021] [Indexed: 11/11/2022]
Abstract
The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.
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Affiliation(s)
- Alexander G Fletcher
- School of Mathematics and Statistics, University of Sheffield, Sheffield, UK.,Bateson Centre, University of Sheffield, Sheffield, UK
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia
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34
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Chen Y, Gao Q, Li J, Mao F, Tang R, Jiang H. Activation of Topological Defects Induces a Brittle-to-Ductile Transition in Epithelial Monolayers. PHYSICAL REVIEW LETTERS 2022; 128:018101. [PMID: 35061486 DOI: 10.1103/physrevlett.128.018101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
Epithelial monolayers are subjected to various mechanical forces, such as stretching, shearing, and compression. Thus, its mechanical response to external loadings is essential for its biological functions. However, the mechanism of the fracture failure of the epithelial monolayer remains poorly understood. Here, by introducing a new type of topological transition, i.e., detach transition or T4 transition, we develop a modified cellular vertex model to investigate the rupture of the cell monolayer. Interestingly, we find a brittle-to-ductile transition in epithelial monolayers, which is controlled by the mechanical properties of single cells and cell-cell contacts. We reveal that the external loadings can activate cell rearrangement in ductile cell monolayers. The plastic deformation results from the nucleation and propagation of "pentagon-heptagon defects" in analogy with the topological defects commonly seen in 2D materials. By using a simplified four-cell model, we further demonstrate that the brittle-to-ductile transition is induced by the competition between cell rearrangement and cell detachment. Our work provides a new theoretical framework to study the rupture of living tissues and may have important implications for many other biological processes, such as wound healing and tissue morphogenesis.
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Affiliation(s)
- Yixia Chen
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qigan Gao
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jingchen Li
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Fangtao Mao
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruowen Tang
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hongyuan Jiang
- Hefei National Laboratory for Physical Science at the Microscale, CAS Key Laboratory of Mechanical Behavior and Design of Materials, CAS Center for Excellence in Complex System Mechanics, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
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35
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Lötstedt P. Derivation of continuum models from discrete models of mechanical forces in cell populations. J Math Biol 2021; 83:75. [PMID: 34878601 PMCID: PMC8654724 DOI: 10.1007/s00285-021-01697-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Revised: 07/23/2021] [Accepted: 11/16/2021] [Indexed: 11/14/2022]
Abstract
In certain discrete models of populations of biological cells, the mechanical forces between the cells are center based or vertex based on the microscopic level where each cell is individually represented. The cells are circular or spherical in a center based model and polygonal or polyhedral in a vertex based model. On a higher, macroscopic level, the time evolution of the density of the cells is described by partial differential equations (PDEs). We derive relations between the modelling on the micro and macro levels in one, two, and three dimensions by regarding the micro model as a discretization of a PDE for conservation of mass on the macro level. The forces in the micro model correspond on the macro level to a gradient of the pressure scaled by quantities depending on the cell geometry. The two levels of modelling are compared in numerical experiments in one and two dimensions.
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Affiliation(s)
- Per Lötstedt
- Division of Scientific Computing, Department of Information Technology, Uppsala University, 751 05, Uppsala, Sweden.
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36
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Weakening of resistance force by cell-ECM interactions regulate cell migration directionality and pattern formation. Commun Biol 2021; 4:808. [PMID: 34183779 PMCID: PMC8239002 DOI: 10.1038/s42003-021-02350-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 06/11/2021] [Indexed: 02/06/2023] Open
Abstract
Collective migration of epithelial cells is a fundamental process in multicellular pattern formation. As they expand their territory, cells are exposed to various physical forces generated by cell-cell interactions and the surrounding microenvironment. While the physical stress applied by neighbouring cells has been well studied, little is known about how the niches that surround cells are spatio-temporally remodelled to regulate collective cell migration and pattern formation. Here, we analysed how the spatio-temporally remodelled extracellular matrix (ECM) alters the resistance force exerted on cells so that the cells can expand their territory. Multiple microfabrication techniques, optical tweezers, as well as mathematical models were employed to prove the simultaneous construction and breakage of ECM during cellular movement, and to show that this modification of the surrounding environment can guide cellular movement. Furthermore, by artificially remodelling the microenvironment, we showed that the directionality of collective cell migration, as well as the three-dimensional branch pattern formation of lung epithelial cells, can be controlled. Our results thus confirm that active remodelling of cellular microenvironment modulates the physical forces exerted on cells by the ECM, which contributes to the directionality of collective cell migration and consequently, pattern formation.
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37
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Sadhukhan S, Nandi SK. Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue. Phys Rev E 2021; 103:062403. [PMID: 34271700 DOI: 10.1103/physreve.103.062403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 05/14/2021] [Indexed: 01/23/2023]
Abstract
Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex-model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes theoretical development difficult. The cellular Potts model (CPM) of confluent monolayers provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of the CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first-order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within the CPM is qualitatively similar to that in the VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P_{0} is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. The fragility of the system decreases with increasing P_{0} in the low-P_{0} regime, whereas the dynamics is independent of P_{0} in the other regime. The rigidity transition, found in the VM, is absent within the CPM; this difference seems to come from the nonequilibrium nature of the former. We show that the CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.
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Affiliation(s)
- Souvik Sadhukhan
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Saroj Kumar Nandi
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
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38
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Durney CH, Feng JJ. A three-dimensional vertex model for Drosophilasalivary gland invagination. Phys Biol 2021; 18. [PMID: 33882465 DOI: 10.1088/1478-3975/abfa69] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 04/21/2021] [Indexed: 11/12/2022]
Abstract
During epithelial morphogenesis, force generation at the cellular level not only causes cell deformation, but may also produce coordinated cell movement and rearrangement on the tissue level. In this paper, we use a novel three-dimensional vertex model to explore the roles of cellular forces during the formation of the salivary gland in theDrosophilaembryo. Representing the placode as an epithelial sheet of initially columnar cells, we focus on the spatial and temporal patterning of contractile forces due to three actomyosin pools: the apicomedial actomyosin in the pit of the placode, junctional actomyosin arcs outside the pit, and a supracellular actomyosin cable along the circumference of the placode. In anin silico'wild type' model, these pools are activated at different times according to experimental data. To identify the role of each myosin pool, we have also simulated variousin silico'mutants' in which only one or two of the myosin pools are activated. We find that the apicomedial myosin initiates a small dimple in the pit, but this is not essential for the overall invagination of the placode. The myosin arcs are the main driver of invagination and are responsible for the internalization of the apical surface. The circumferential actomyosin cable acts to constrict the opening of the developing tube, and is responsible for forming a properly shaped lumen. Cell intercalation tends to facilitate the invagination, but the geometric constraints of our model only allow a small number of intercalations, and their effect is minor. The placode invagination predicted by the model is in general agreement with experimental observations. It confirms some features of the current 'belt-and-braces' model for the process, and provides new insights on the separate roles of the various myosin pools and their spatio-temporal coordination.
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Affiliation(s)
- Clinton H Durney
- Department of Mathematics, University of British Columbia, Vancouver, Canada
| | - James J Feng
- Department of Mathematics, University of British Columbia, Vancouver, Canada.,Department of Chemical and Biomedical Engineering, University of British Columbia, Vancouver, Canada
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39
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Conrad L, Runser SVM, Fernando Gómez H, Lang CM, Dumond MS, Sapala A, Schaumann L, Michos O, Vetter R, Iber D. The biomechanical basis of biased epithelial tube elongation in lung and kidney development. Development 2021; 148:261770. [PMID: 33946098 PMCID: PMC8126414 DOI: 10.1242/dev.194209] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 03/16/2021] [Indexed: 01/16/2023]
Abstract
During lung development, epithelial branches expand preferentially in a longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How this bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme, of preferential turnover of the extracellular matrix at the bud tips and of FGF signalling. There is also no evidence for actin-rich filopodia at the bud tips. Rather, we find epithelial tubes to be collapsed during early lung and kidney development, and we observe fluid flow in the narrow tubes. By simulating the measured fluid flow inside segmented narrow epithelial tubes, we show that the shear stress levels on the apical surface are sufficient to explain the reported bias in cell shape and outgrowth. We use a cell-based vertex model to confirm that apical shear forces, unlike constricting forces, can give rise to both the observed bias in cell shapes and tube elongation. We conclude that shear stress may be a more general driver of biased tube elongation beyond its established role in angiogenesis. This article has an associated 'The people behind the papers' interview.
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Affiliation(s)
- Lisa Conrad
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Steve Vincent Maurice Runser
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Harold Fernando Gómez
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Christine Michaela Lang
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Mathilde Sabine Dumond
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Aleksandra Sapala
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Laura Schaumann
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Odyssé Michos
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Roman Vetter
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstraße 26, 4058 Basel, Switzerland.,Swiss Institute of Bioinformatics (SIB), Mattenstraße 26, 4058 Basel, Switzerland
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40
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Bajpai S, Prabhakar R, Chelakkot R, Inamdar MM. Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling. J R Soc Interface 2021; 18:20200825. [PMID: 33561375 DOI: 10.1098/rsif.2020.0825] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell-cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell-cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell-cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta-Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.
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Affiliation(s)
- Supriya Bajpai
- IITB-Monash Research Academy, Mumbai 400076, India.,Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.,Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800, Australia
| | - Ranganathan Prabhakar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800, Australia
| | - Raghunath Chelakkot
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Mandar M Inamdar
- Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
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41
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Kai Y. Intestinal villus structure contributes to even shedding of epithelial cells. Biophys J 2021; 120:699-710. [PMID: 33453270 DOI: 10.1016/j.bpj.2021.01.003] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Revised: 01/04/2021] [Accepted: 01/08/2021] [Indexed: 12/14/2022] Open
Abstract
In the intestinal epithelium, proliferated epithelial cells ascend the crypts and villi and shed at the villus tips into the gut lumen. In this study, we theoretically investigate the roles of the villi on cell turnover. We present a stochastic model that focuses on the duration over which cells migrate the shortest paths between the crypt orifices and the villus tips, where shedding cells are randomly chosen from among those older than the shortest-path cell migration times. By extending the length of the shortest path to delay cell shedding, the finger-like shape of the villus would tightly regulate shedding-cell ages compared with flat surfaces and shorter projections; the villus allows epithelial cells to shed at around the same age, which limits them from shedding early or staying in the epithelium for long periods. Computational simulations of cell dynamics agreed well with the predictions. We also examine various mechanical conditions of cells and confirm that coordinated collective cell migration supports the predictions. These results suggest the important roles of the villi in homeostatic maintenance of the small intestine, and we discuss the applicability of our approach to other tissues with collective cell movement.
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Affiliation(s)
- Yuto Kai
- Department of Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan.
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42
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Gonay L, Spourquet C, Baudoin M, Lepers L, Lemoine P, Fletcher AG, Hanert E, Pierreux CE. Modelling of Epithelial Growth, Fission and Lumen Formation During Embryonic Thyroid Development: A Combination of Computational and Experimental Approaches. Front Endocrinol (Lausanne) 2021; 12:655862. [PMID: 34163435 PMCID: PMC8216395 DOI: 10.3389/fendo.2021.655862] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 04/22/2021] [Indexed: 12/18/2022] Open
Abstract
Organogenesis is the phase of embryonic development leading to the formation of fully functional organs. In the case of the thyroid, organogenesis starts from the endoderm and generates a multitude of closely packed independent spherical follicular units surrounded by a dense network of capillaries. Follicular organisation is unique and essential for thyroid function, i.e. thyroid hormone production. Previous in vivo studies showed that, besides their nutritive function, endothelial cells play a central role during thyroid gland morphogenesis. However, the precise mechanisms and biological parameters controlling the transformation of the multi-layered thyroid epithelial primordium into a multitude of single-layered follicles are mostly unknown. Animal studies used to improve understanding of organogenesis are costly and time-consuming, with recognised limitations. Here, we developed and used a 2-D vertex model of thyroid growth, angiogenesis and folliculogenesis, within the open-source Chaste framework. Our in silico model, based on in vivo images, correctly simulates the differential growth and proliferation of central and peripheral epithelial cells, as well as the morphogen-driven migration of endothelial cells, consistently with our experimental data. Our simulations further showed that reduced epithelial cell adhesion was critical to allow endothelial invasion and fission of the multi-layered epithelial mass. Finally, our model also allowed epithelial cell polarisation and follicular lumen formation by endothelial cell abundance and proximity. Our study illustrates how constant discussion between theoretical and experimental approaches can help us to better understand the roles of cellular movement, adhesion and polarisation during thyroid embryonic development. We anticipate that the use of in silico models like the one we describe can push forward the fields of developmental biology and regenerative medicine.
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Affiliation(s)
- Leolo Gonay
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | | | - Matthieu Baudoin
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | - Ludovic Lepers
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
| | | | - Alexander G. Fletcher
- School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
| | - Emmanuel Hanert
- Earth and Life Institute, UCLouvain, Louvain-La-Neuve, Belgium
| | - Christophe E. Pierreux
- de Duve Institute, UCLouvain, Woluwé-Saint-Lambert, Belgium
- *Correspondence: Christophe E. Pierreux,
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43
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Buttenschön A, Edelstein-Keshet L. Bridging from single to collective cell migration: A review of models and links to experiments. PLoS Comput Biol 2020; 16:e1008411. [PMID: 33301528 PMCID: PMC7728230 DOI: 10.1371/journal.pcbi.1008411] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.
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Affiliation(s)
- Andreas Buttenschön
- Department of Mathematics, University of British Columbia, Vancouver, Canada
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44
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Germano DPJ, Osborne JM. A mathematical model of cell fate selection on a dynamic tissue. J Theor Biol 2020; 514:110535. [PMID: 33259848 DOI: 10.1016/j.jtbi.2020.110535] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 10/27/2020] [Accepted: 11/02/2020] [Indexed: 11/27/2022]
Abstract
Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the tissue. This dynamic homeostasis is maintaned by numerous governing mechanisms which are finely tuned in such a way that the tissue remains in a homeostatic state, even across large timescales. Some of these governing mechanisms include cell motion, and cell fate selection through inter cellular signalling. However, it is not yet clear how to link these two processes, or how they may affect one another across the tissue. In this paper, we present a multicellular, multiscale model, which brings together the two phenomena of cell motility, and inter cellular signalling, to describe cell fate selection on a dynamic tissue. We find that the affinity for cellular signalling to occur greatly influences a cells ability to differentiate. We also find that our results support claims that cell differentiation is a finely tuned process within dynamic tissues at homeostasis, with excessive cell turnover rates leading to unhealthy (undifferentiated and unpatterned) tissues.
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Affiliation(s)
- Domenic P J Germano
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia.
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45
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Koyama H, Fujimori T. Isotropic expansion of external environment induces tissue elongation and collective cell alignment. J Theor Biol 2020; 496:110248. [PMID: 32275986 DOI: 10.1016/j.jtbi.2020.110248] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 02/17/2020] [Accepted: 03/16/2020] [Indexed: 12/01/2022]
Abstract
Cell movement is crucial for morphogenesis in multicellular organisms. Growing embryos or tissues often expand isotropically, i.e., uniformly, in all dimensions. On the surfaces of these expanding environments, which we call "fields," cells are subjected to frictional forces and move passively in response. However, the potential roles of isotropically expanding fields in morphogenetic events have not been investigated well. Our previous mathematical simulations showed that a tissue was elongated on an isotropically expanding field (Imuta et al., 2014). However, the underlying mechanism remains unclarified, and how cells behave during tissue elongation was not investigated. In this study, we mathematically analyzed the effect of isotropically expanding fields using a vertex model, a standard type of multi-cellular model. We found that cells located on fields were elongated along a similar direction each other and exhibited a columnar configuration with nearly single-cell width. Simultaneously, it was confirmed that the cell clusters were also elongated, even though field expansion was absolutely isotropic. We then investigated the mechanism underlying these counterintuitive phenomena. In particular, we asked whether the dynamics of elongation was predominantly determined by the properties of the field, the cell cluster, or both. Theoretical analyses involving simplification of the model revealed that cell clusters have an intrinsic ability to asymmetrically deform, leading to their elongation. Importantly, this ability is effective only under the non-equilibrium conditions provided by field expansion. This may explain the elongation of the notochord, located on the surface of the growing mouse embryo. We established the mechanism underlying tissue elongation induced by isotropically expanding external environments, and its involvement in collective cell alignment with cell elongation, providing key insight into morphogenesis involving multiple adjacent tissues.
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Affiliation(s)
- Hiroshi Koyama
- Division of Embryology, National Institute for Basic Biology, 5-1 Higashiyama, Myodaiji, Okazaki, Aichi 444-8787, Japan; SOKENDAI (The Graduate University for Advanced Studies), Japan.
| | - Toshihiko Fujimori
- Division of Embryology, National Institute for Basic Biology, 5-1 Higashiyama, Myodaiji, Okazaki, Aichi 444-8787, Japan; SOKENDAI (The Graduate University for Advanced Studies), Japan
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46
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Self-sustained planar intercalations due to mechanosignaling feedbacks lead to robust axis extension during morphogenesis. Sci Rep 2020; 10:10973. [PMID: 32620834 PMCID: PMC7334228 DOI: 10.1038/s41598-020-67413-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2019] [Accepted: 06/04/2020] [Indexed: 12/31/2022] Open
Abstract
Tissue elongation is a necessary process in metazoans to implement their body plans that is not fully understood. Here we propose a mechanism based on the interplay between cellular mechanics and primordia patterning that results in self-sustained planar intercalations. Thus, we show that a location-dependent modulation of the mechanical properties of cells leads to robust axis extension. To illustrate the plausibility of this mechanism, we test it against different patterning models by means of computer simulations of tissues where we implemented mechano-signaling feedbacks. Our results suggest that robust elongation relies on a trade-off between cellular and tissue strains that is orchestrated through the cleavage orientation. In the particular context of axis extension in Turing-patterned tissues, we report that different directional cell activities cooperate synergetically to achieve elongation. Altogether, our findings help to understand how the axis extension phenomenon emerges from the dynamics of individual cells.
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47
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Khataee H, Czirok A, Neufeld Z. Multiscale modelling of motility wave propagation in cell migration. Sci Rep 2020; 10:8128. [PMID: 32424155 PMCID: PMC7235313 DOI: 10.1038/s41598-020-63506-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Accepted: 03/26/2020] [Indexed: 12/16/2022] Open
Abstract
The collective motion of cell monolayers within a tissue is a fundamental biological process that occurs during tissue formation, wound healing, cancerous invasion, and viral infection. Experiments have shown that at the onset of migration, the motility is self-generated as a polarisation wave starting from the leading edge of the monolayer and progressively propagates into the bulk. However, it is unclear how the propagation of this motility wave is influenced by cellular properties. Here, we investigate this question using a computational model based on the Potts model coupled to the dynamics of intracellular polarisation. The model captures the propagation of the polarisation wave and suggests that the cells cortex can regulate the migration modes: strongly contractile cells may depolarise the monolayer, whereas less contractile cells can form swirling movement. Cortical contractility is further found to limit the cells motility, which (i) decelerates the wave speed and the leading edge progression, and (ii) destabilises the leading edge. Together, our model describes how different mechanical properties of cells can contribute to the regulation of collective cell migration.
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Affiliation(s)
- Hamid Khataee
- School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia.
| | - Andras Czirok
- Department of Biological Physics, Eotvos University, Budapest, 1053, Hungary.,Department of Anatomy and Cell Biology, University of Kansas Medical Center, Kansas City, KS, 66160, USA
| | - Zoltan Neufeld
- School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia
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48
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Hosseini ZS, Hashemi Golpayegani SMR. Esophageal epithelium modeling based on globally coupled map: an approach toward precancerous lesion diagnosis. Med Biol Eng Comput 2020; 58:1297-1308. [PMID: 32239347 DOI: 10.1007/s11517-020-02151-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Accepted: 02/19/2020] [Indexed: 11/25/2022]
Abstract
Esophageal squamous cell carcinoma is the most predominant malignancy of the esophagus. Its histological precursors (dysplasia) emerge in the esophageal epithelium that their progression into the underlying layers leads to cancer. The epithelium is the origin of many solid cancers and, accordingly, the focus of numerous computational models. In this work, we proposed a framework to establish a two-dimensional, globally coupled map to model the epithelium dynamics. The model aims at diagnosing the early stage of dysplasia based on microscopic images of endoscopic biopsies. We used the logistic map as a black-box model for the epithelial cells. By relating between the structure and dynamic of the epithelium, we defined the coupling function and proposed a case-dependent model in which the parameters were adjusted based on fractal geometry of each pathological image. Thus, by assigning different attractors to the cells' behavior, the lattice dynamic was investigated by the Lyapunov exponent. The decreasing pattern of Lyapunov exponent variations across the epithelium thickness had reasonable performance in diagnosing the normal specimens from the low-grade dysplasia ones. The results showed that there could be a direct relationship between the structural complexity of this system and its uncertainty of dynamics. Graphical abstract The modeling process of the esophageal epithelium to classify the experimental data at normal and LGD stages.
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Affiliation(s)
- Zahra Sadat Hosseini
- Complex Systems and Cybernetic Control Lab, Biomedical Engineering Department, Amirkabir University of Technology, P.O. Box 1591634311, Tehran, Iran
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49
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Rens EG, Edelstein-Keshet L. From energy to cellular forces in the Cellular Potts Model: An algorithmic approach. PLoS Comput Biol 2019; 15:e1007459. [PMID: 31825952 PMCID: PMC6927661 DOI: 10.1371/journal.pcbi.1007459] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2019] [Revised: 12/23/2019] [Accepted: 10/05/2019] [Indexed: 11/30/2022] Open
Abstract
Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian. Using the fact that a force field is easily derived from a scalar energy (F = −∇H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We predict the traction forces exerted by single cells of various shapes and sizes on a 2D substrate. While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we approximate the force field inside the cell domain using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces exerted by cells on one another in classic cell-sorting experiments. Cells exert forces on their surroundings and on one another. In simulations of cell shape using the Cellular Potts Model (CPM), the dynamics of deforming cell shapes is traditionally represented by an energy-minimization method. We use this CPM energy, the Hamiltonian, to derive and visualize the corresponding forces exerted by the cells. We use the fact that force is the negative gradient of energy to assign forces to the CPM cell edges, and then extend the results to approximate interior forces by interpolation. We show that this method works for single as well as multiple interacting model cells, both static and motile. Finally, we show favorable comparison between predicted forces and real forces measured experimentally.
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Affiliation(s)
- Elisabeth G. Rens
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
| | - Leah Edelstein-Keshet
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
- * E-mail:
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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: 11] [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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