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Yin X, Liu YQ, Zhang LY, Liang D, Xu GK. Emergence, Pattern, and Frequency of Spontaneous Waves in Spreading Epithelial Monolayers. NANO LETTERS 2024; 24:3631-3637. [PMID: 38466240 DOI: 10.1021/acs.nanolett.3c04876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2024]
Abstract
A striking phenomenon of collective cell motion is that they can exhibit a spontaneously emerging wave during epithelia expansions. However, the fundamental mechanism, governing the emergence and its crucial characteristics (e.g., the eigenfrequency and the pattern), remains an enigma. By introducing a mechanochemical feedback loop, we develop a highly efficient discrete vertex model to investigate the spatiotemporal evolution of spreading epithelia. We find both numerically and analytically that expanding cell monolayers display a power-law dependence of wave frequency on the local heterogeneities (i.e., cell density) with a scaling exponent of -1/2. Moreover, our study demonstrates the quantitative capability of the proposed model in capturing distinct X-, W-, and V-mode wave patterns. We unveil that the phase transition between these modes is governed by the distribution of active self-propulsion forces. Our work provides an avenue for rigorous quantitative investigations into the collective motion and pattern formation of cell groups.
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Affiliation(s)
- Xu Yin
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, SVL, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yong-Quan Liu
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, SVL, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Li-Yuan Zhang
- School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
| | - Dong Liang
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, SVL, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Guang-Kui Xu
- Laboratory for Multiscale Mechanics and Medical Science, Department of Engineering Mechanics, SVL, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
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Mori F, Bhattacharyya S, Yeomans JM, Thampi SP. Viscoelastic confinement induces periodic flow reversals in active nematics. Phys Rev E 2023; 108:064611. [PMID: 38243430 DOI: 10.1103/physreve.108.064611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 11/22/2023] [Indexed: 01/21/2024]
Abstract
We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behavior of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest experiments to study the role of viscoelastic confinement in the spatiotemporal organization and control of active matter.
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Affiliation(s)
- Francesco Mori
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Saraswat Bhattacharyya
- 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
| | - Sumesh P Thampi
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai-36, India
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Gupta RK, Kant R, Soni H, Sood AK, Ramaswamy S. Active nonreciprocal attraction between motile particles in an elastic medium. Phys Rev E 2022; 105:064602. [PMID: 35854487 DOI: 10.1103/physreve.105.064602] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
We show from experiments and simulations on vibration-activated granular matter that self-propelled polar rods in an elastic medium on a substrate turn and move towards each other. We account for this effective attraction through a coarse-grained theory of a motile particle as a moving point-force density that creates elastic strains in the medium that reorient other particles. Our measurements confirm qualitatively the predicted features of the distortions created by the rods, including the |x|^{-1/2} tail of the trailing displacement field and nonreciprocal sensing and pursuit. A discrepancy between the magnitudes of displacements along and transverse to the direction of motion remains. Our theory should be of relevance to the interaction of motile cells in the extracellular matrix or in a supported layer of gel or tissue.
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Affiliation(s)
- Rahul Kumar Gupta
- Tata Institute of Fundamental Research, Gopanpally, Hyderabad 500 107, India
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
- Institut für Theoretische Physik II - Soft Matter Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
| | - Raushan Kant
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Harsh Soni
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Sriram Ramaswamy
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
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Maitra A, Ramaswamy S. Oriented Active Solids. PHYSICAL REVIEW LETTERS 2019; 123:238001. [PMID: 31868448 DOI: 10.1103/physrevlett.123.238001] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Revised: 09/08/2019] [Indexed: 06/10/2023]
Abstract
We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.
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Affiliation(s)
- Ananyo Maitra
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005 Paris, France
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, 560 012 Bangalore, India
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Blanch-Mercader C, Yashunsky V, Garcia S, Duclos G, Giomi L, Silberzan P. Turbulent Dynamics of Epithelial Cell Cultures. PHYSICAL REVIEW LETTERS 2018; 120:208101. [PMID: 29864293 DOI: 10.1103/physrevlett.120.208101] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Revised: 02/12/2018] [Indexed: 05/23/2023]
Abstract
We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.
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Affiliation(s)
- C Blanch-Mercader
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - V Yashunsky
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - S Garcia
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - G Duclos
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - P Silberzan
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
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Abstract
Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.
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Affiliation(s)
- Shunsuke Yabunaka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan.
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Blanch-Mercader C, Casademunt J. Hydrodynamic instabilities, waves and turbulence in spreading epithelia. SOFT MATTER 2017; 13:6913-6928. [PMID: 28825077 DOI: 10.1039/c7sm01128h] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.
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Affiliation(s)
- C Blanch-Mercader
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain. and Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS, 26 rue d' Ulm, 75005 Paris, France
| | - J Casademunt
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain. and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain
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Yabunaka S, Marcq P. Cell growth, division, and death in cohesive tissues: A thermodynamic approach. Phys Rev E 2017; 96:022406. [PMID: 28950491 DOI: 10.1103/physreve.96.022406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2016] [Indexed: 04/26/2023]
Abstract
Cell growth, division, and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a nonzero rate of variation of cell density. We show how linear nonequilibrium thermodynamics allows us to express this rate as a combination of relevant thermodynamic forces: chemical potential, velocity divergence, and activity. We illustrate the resulting effects of the nonconservation of cell density on simple examples inspired by recent experiments on cell monolayers, considering first the velocity of a spreading front, and second an instability leading to mechanical waves.
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Affiliation(s)
- Shunsuke Yabunaka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan
| | - Philippe Marcq
- Sorbonne Universités, UPMC Université Paris 6, Institut Curie, CNRS, UMR 168, Laboratoire Physico Chimie Curie, Paris, France
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Tlili S, Gay C, Graner F, Marcq P, Molino F, Saramito P. Colloquium: Mechanical formalisms for tissue dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:121. [PMID: 25957180 DOI: 10.1140/epje/i2015-15033-4] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2013] [Revised: 12/22/2014] [Accepted: 03/09/2015] [Indexed: 06/04/2023]
Abstract
The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.
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Affiliation(s)
- Sham Tlili
- Laboratoire Matière et Systèmes Complexes, Université Denis Diderot - Paris 7, CNRS UMR 7057, 10 rue Alice Domon et Léonie Duquet, F-75205, Paris Cedex 13, France
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