1
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Tang Y, Chen S, Bowick MJ, Bi D. Cell Division and Motility Enable Hexatic Order in Biological Tissues. PHYSICAL REVIEW LETTERS 2024; 132:218402. [PMID: 38856284 PMCID: PMC11267118 DOI: 10.1103/physrevlett.132.218402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Accepted: 04/19/2024] [Indexed: 06/11/2024]
Abstract
Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.
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Affiliation(s)
- Yiwen Tang
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
- Center for Theoretical Biological Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Siyuan Chen
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - Mark J Bowick
- Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA
- Kavli Institute of Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - Dapeng Bi
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
- Center for Theoretical Biological Physics, Northeastern University, Boston, Massachusetts 02115, USA
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2
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Armengol-Collado JM, Carenza LN, Giomi L. Hydrodynamics and multiscale order in confluent epithelia. eLife 2024; 13:e86400. [PMID: 38189410 PMCID: PMC10963026 DOI: 10.7554/elife.86400] [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: 01/24/2023] [Accepted: 01/05/2024] [Indexed: 01/09/2024] Open
Abstract
We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) orders, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power-law scaling regimes, reflecting both the hexagonal geometry of small cells clusters and the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.
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Affiliation(s)
| | | | - Luca Giomi
- Instituut-Lorentz, Leiden UniversityLeidenNetherlands
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3
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Eckert J, Ladoux B, Mège RM, Giomi L, Schmidt T. Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density. Nat Commun 2023; 14:5762. [PMID: 37717032 PMCID: PMC10505199 DOI: 10.1038/s41467-023-41449-6] [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: 11/01/2022] [Accepted: 08/30/2023] [Indexed: 09/18/2023] Open
Abstract
Changes in tissue geometry during developmental processes are associated with collective migration of cells. Recent experimental and numerical results suggest that these changes could leverage on the coexistence of nematic and hexatic orientational order at different length scales. How this multiscale organization is affected by the material properties of the cells and their substrate is presently unknown. In this study, we address these questions in monolayers of Madin-Darby canine kidney cells having various cell densities and molecular repertoires. At small length scales, confluent monolayers are characterized by a prominent hexatic order, independent of the presence of E-cadherin, monolayer density, and underlying substrate stiffness. However, all three properties affect the meso-scale tissue organization. The length scale at which hexatic order transits to nematic order, the "hexanematic" crossover scale, strongly depends on cell-cell adhesions and correlates with monolayer density. Our study demonstrates how epithelial organization is affected by mechanical properties, and provides a robust description of tissue organization during developmental processes.
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Affiliation(s)
- Julia Eckert
- Physics of Life Processes, Leiden Institute of Physics, Universiteit Leiden, 2333 CC, Leiden, The Netherlands
- Centre for Cell Biology of Chronic Disease, Institute for Molecular Bioscience, The University of Queensland, St. Lucia, Brisbane, QLD, 4072, Australia
| | - Benoît Ladoux
- Université Paris Cité, CNRS, Institut Jacques Monod, F-75013, Paris, France
| | - René-Marc Mège
- Université Paris Cité, CNRS, Institut Jacques Monod, F-75013, Paris, France
| | - Luca Giomi
- Instituut-Lorentz, Leiden Institute of Physics, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, The Netherlands
| | - Thomas Schmidt
- Physics of Life Processes, Leiden Institute of Physics, Universiteit Leiden, 2333 CC, Leiden, The Netherlands.
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4
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Cislo DJ, Yang F, Qin H, Pavlopoulos A, Bowick MJ, Streichan SJ. Active cell divisions generate fourfold orientationally ordered phase in living tissue. NATURE PHYSICS 2023; 19:1201-1210. [PMID: 37786880 PMCID: PMC10545346 DOI: 10.1038/s41567-023-02025-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 03/15/2023] [Indexed: 10/04/2023]
Abstract
Morphogenesis, the process through which genes generate form, establishes tissue-scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fuelled by cell proliferation, which, naively, should destroy order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order-rather than annihilate it-remains an outstanding question in animal development. We show that cell divisions are the primary drivers of tissue flow, leading to a fourfold orientationally ordered phase. Waves of anisotropic cell proliferation propagate across the embryo with precise patterning. Defects introduced into the nascent lattice by cell divisions are moved out of the tissue bulk towards the boundary by subsequent divisions. Specific cell proliferation rates and orientations enable cell divisions to organize rather than fluidize the tissue. We observe this using live imaging and tissue cartography to analyse the dynamics of fourfold tissue ordering in the trunk segmental ectoderm of the crustacean Parhyale hawaiensis beginning 72 h after egg lay. The result is a robust, active mechanism for generating global orientational order in a non-equilibrium system that sets the stage for the subsequent development of shape and form.
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Affiliation(s)
- Dillon J. Cislo
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
- Center for Studies in Physics and Biology, Rockefeller University, New York, NY, USA
| | - Fengshuo Yang
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
- The T.C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD, USA
| | - Haodong Qin
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
- Department of Physics, University of California, San Diego, La Jolla, CA, USA
| | - Anastasios Pavlopoulos
- Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology Hellas, Heraklion, Greece
| | - Mark J. Bowick
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
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5
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Li R, Moazzeni S, Liu L, Lin H. Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks. PHYSICAL REVIEW LETTERS 2023; 130:188201. [PMID: 37204891 PMCID: PMC10586522 DOI: 10.1103/physrevlett.130.188201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 03/03/2023] [Indexed: 05/21/2023]
Abstract
We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=⟨p⟩/2, where ⟨p⟩ is the mean pressure of the tessellation, for general randomized lattices.
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Affiliation(s)
- Ran Li
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, USA
| | - Seyedsajad Moazzeni
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, USA
| | - Liping Liu
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, USA
- Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
| | - Hao Lin
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, USA
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6
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Hopkins A, Chiang M, Loewe B, Marenduzzo D, Marchetti MC. Local Yield and Compliance in Active Cell Monolayers. PHYSICAL REVIEW LETTERS 2022; 129:148101. [PMID: 36240394 DOI: 10.1103/physrevlett.129.148101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.
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Affiliation(s)
- Austin Hopkins
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael Chiang
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Benjamin Loewe
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
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7
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Duclut C, Paijmans J, Inamdar MM, Modes CD, Jülicher F. Active T1 transitions in cellular networks. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:29. [PMID: 35320447 PMCID: PMC8942949 DOI: 10.1140/epje/s10189-022-00175-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 02/14/2022] [Indexed: 05/20/2023]
Abstract
In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.
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Affiliation(s)
- Charlie Duclut
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 8, 01187, Dresden, Germany
| | - Joris Paijmans
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 8, 01187, Dresden, Germany
| | - Mandar M Inamdar
- Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
| | - Carl D Modes
- Max Planck Institute for Molecular Cell Biology and Genetics (MPI-CBG), 01307, Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307, Dresden, Germany
- Cluster of Excellence, Physics of Life, TU Dresden, 01307, Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 8, 01187, Dresden, Germany.
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307, Dresden, Germany.
- Cluster of Excellence, Physics of Life, TU Dresden, 01307, Dresden, Germany.
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8
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Downs JG, Smith ND, Mandadapu KK, Garrahan JP, Smith MI. Topographic Control of Order in Quasi-2D Granular Phase Transitions. PHYSICAL REVIEW LETTERS 2021; 127:268002. [PMID: 35029468 DOI: 10.1103/physrevlett.127.268002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Accepted: 10/21/2021] [Indexed: 06/14/2023]
Abstract
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.
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Affiliation(s)
- J G Downs
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - N D Smith
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - K K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - M I Smith
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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9
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James M, Suchla DA, Dunkel J, Wilczek M. Emergence and melting of active vortex crystals. Nat Commun 2021; 12:5630. [PMID: 34561437 PMCID: PMC8463610 DOI: 10.1038/s41467-021-25545-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/18/2021] [Indexed: 11/09/2022] Open
Abstract
Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.
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Affiliation(s)
- Martin James
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany
| | - Dominik Anton Suchla
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany.,Faculty of Physics, University of Göttingen, Göttingen, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany. .,Faculty of Physics, University of Göttingen, Göttingen, Germany.
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10
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Durand M. Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime. PLoS Comput Biol 2021; 17:e1008576. [PMID: 34398883 PMCID: PMC8389523 DOI: 10.1371/journal.pcbi.1008576] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Revised: 08/26/2021] [Accepted: 07/06/2021] [Indexed: 12/29/2022] Open
Abstract
Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.
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Affiliation(s)
- Marc Durand
- Université de Paris, CNRS, UMR 7057, Matière et Systèmes Complexes (MSC), Paris, France
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11
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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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12
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Villemot F, Calmettes A, Durand M. Thermal shape fluctuations of a two-dimensional compressible droplet. SOFT MATTER 2020; 16:10358-10367. [PMID: 33052997 DOI: 10.1039/d0sm01113d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Analysis of thermal capillary waves on the surface of a liquid usually assumes incompressibility of the bulk fluid. However, for droplets or bubbles with submicronic size, or for epithelial cells whose out-of-plane elongation can be modeled by an effective 2D bulk modulus, compressibility of the internal fluid must be taken into account for the characterization of their shape fluctuations. We present a theoretical analysis of the fluctuations of a two-dimensional compressible droplet. Analytical expressions for area, perimeter and energy fluctuations are derived and compared with Cellular Potts Model (CPM) simulations. This comparison shows a very good agreement between theory and simulations, and offers a precise calibration method for CPM simulations.
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Affiliation(s)
- François Villemot
- Université de Paris, CNRS, UMR 7057, Matière et Systèmes Complexes (MSC), F-75006 Paris, France.
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13
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Loewe B, Chiang M, Marenduzzo D, Marchetti MC. Solid-Liquid Transition of Deformable and Overlapping Active Particles. PHYSICAL REVIEW LETTERS 2020; 125:038003. [PMID: 32745423 DOI: 10.1103/physrevlett.125.038003] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 04/24/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.
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Affiliation(s)
- Benjamin Loewe
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael Chiang
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
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14
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Pasupalak A, Yan-Wei L, Ni R, Pica Ciamarra M. Hexatic phase in a model of active biological tissues. SOFT MATTER 2020; 16:3914-3920. [PMID: 32270837 DOI: 10.1039/d0sm00109k] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In many biological processes, such as wound healing, cell tissues undergo an epithelial-to-mesenchymal transition, which is a transition from a more rigid to a more fluid state. Here, we investigate the solid/fluid transition of cell tissues within the framework of the self-propelled Voronoi model, which accounts for the deformability of the cells, for their many-body interactions, and for their polarized motility. The transition is controlled by two parameters, respectively accounting for the strength of the self-propelling force of the cells, and for the mechanical rigidity of the cells. We find the melting transition to occur via a continuous solid-hexatic transition followed by a continuous hexatic-liquid transition, as in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario. This finding indicates that the hexatic phase may have an unexpected biological relevance.
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Affiliation(s)
- Anshuman Pasupalak
- School of Physical and Mathematical Science, Nanyang Technological University, Singapore.
| | - Li Yan-Wei
- School of Physical and Mathematical Science, Nanyang Technological University, Singapore.
| | - Ran Ni
- School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore.
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Science, Nanyang Technological University, Singapore. and CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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