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Sutlive J, Liu BS, Kwan SA, Pan JM, Gou K, Xu R, Ali AB, Khalil HA, Ackermann M, Chen Z, Mentzer SJ. Buckling forces and the wavy folds between pleural epithelial cells. Biosystems 2024; 240:105216. [PMID: 38692427 PMCID: PMC11139554 DOI: 10.1016/j.biosystems.2024.105216] [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: 12/11/2023] [Revised: 04/15/2024] [Accepted: 04/15/2024] [Indexed: 05/03/2024]
Abstract
Cell shapes in tissues are affected by the biophysical interaction between cells. Tissue forces can influence specific cell features such as cell geometry and cell surface area. Here, we examined the 2-dimensional shape, size, and perimeter of pleural epithelial cells at various lung volumes. We demonstrated a 1.53-fold increase in 2-dimensional cell surface area and a 1.43-fold increase in cell perimeter at total lung capacity compared to residual lung volume. Consistent with previous results, close inspection of the pleura demonstrated wavy folds between pleural epithelial cells at all lung volumes. To investigate a potential explanation for the wavy folds, we developed a physical simulacrum suggested by D'Arcy Thompson in On Growth and Form. The simulacrum suggested that the wavy folds were the result of redundant cell membranes unable to contract. To test this hypothesis, we developed a numerical simulation to evaluate the impact of an increase in 2-dimensional cell surface area and cell perimeter on the shape of the cell-cell interface. Our simulation demonstrated that an increase in cell perimeter, rather than an increase in 2-dimensional cell surface area, had the most direct impact on the presence of wavy folds. We conclude that wavy folds between pleural epithelial cells reflects buckling forces arising from the excess cell perimeter necessary to accommodate visceral organ expansion.
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Affiliation(s)
- Joseph Sutlive
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Betty S Liu
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Stacey A Kwan
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Jennifer M Pan
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Kun Gou
- Department of Computational, Engineering, and Mathematical Sciences, Texas A&M University-San Antonio, San Antonio, TX, USA
| | - Rongguang Xu
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Ali B Ali
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Hassan A Khalil
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA
| | - Maximilian Ackermann
- Institute of Functional and Clinical Anatomy, University Medical Center of the Johannes Gutenberg-University, Mainz, Germany
| | - Zi Chen
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA.
| | - Steven J Mentzer
- Laboratory of Adaptive and Regenerative Biology, Brigham & Women's Hospital, Harvard Medical School, Boston, MA, USA.
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2
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Atia L, Fredberg JJ. A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming. BIOPHYSICS REVIEWS 2023; 4:041304. [PMID: 38156333 PMCID: PMC10751956 DOI: 10.1063/5.0179719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2023] [Accepted: 11/17/2023] [Indexed: 12/30/2023]
Abstract
Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.
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Affiliation(s)
- Lior Atia
- Ben Gurion University of the Negev, Beer Sheva, Israel
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3
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Li X, Bi D. Nature-inspired designs for disordered acoustic bandgap materials. SOFT MATTER 2023; 19:8221-8227. [PMID: 37859575 DOI: 10.1039/d3sm00419h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2023]
Abstract
We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self-assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides.
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Affiliation(s)
- Xinzhi Li
- Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Dapeng Bi
- Department of Physics, Northeastern University, Boston, MA 02115, USA.
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4
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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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5
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Li R, Ibar C, Zhou Z, Moazzeni S, Norris AN, Irvine KD, Liu L, Lin H. E 2 and Gamma distributions in polygonal networks. PHYSICAL REVIEW RESEARCH 2021; 3:L042001. [PMID: 35340565 PMCID: PMC8950099 DOI: 10.1103/physrevresearch.3.l042001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
From solar supergranulation to salt flat in Bolivia, from veins on leaves to cells on Drosophila wing discs, polygon-based networks exhibit great complexities, yet similarities and consistent patterns emerge. Based on analysis of 99 polygonal tessellations of a wide variety of physical origins, this work demonstrates the ubiquity of an exponential distribution in the squared norm of the deformation tensor, E2, which directly leads to the ubiquitous presence of Gamma distributions in polygon aspect ratio as recently demonstrated by Atia et al. [Nat. Phys. 14, 613 (2018)]. In turn an analytical approach is developed to illustrate its origin. E2 relates to most energy forms, and its Boltzmann-like feature allows the definition of a pseudo-temperature that promises utility in a thermodynamic ensemble framework.
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Affiliation(s)
- Ran Li
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey
| | - Consuelo Ibar
- Waksman Institute and Department of Molecular Biology and Biochemistry, Rutgers, The State University of New Jersey
| | - Zhenru Zhou
- Waksman Institute and Department of Molecular Biology and Biochemistry, Rutgers, The State University of New Jersey
| | - Seyedsajad Moazzeni
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey
| | - Andrew N. Norris
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey
| | - Kenneth D. Irvine
- Waksman Institute and Department of Molecular Biology and Biochemistry, Rutgers, The State University of New Jersey
| | - Liping Liu
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey
- Department of Mathematics, Rutgers, The State University of New Jersey
| | - Hao Lin
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey
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6
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Kim S, Pochitaloff M, Stooke-Vaughan GA, Campàs O. Embryonic Tissues as Active Foams. NATURE PHYSICS 2021; 17:859-866. [PMID: 34367313 PMCID: PMC8336761 DOI: 10.1038/s41567-021-01215-1] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods, here we show that tissue fluidization in posterior zebrafish tissues is controlled by the stochastic dynamics of tensions at cell-cell contacts. We develop a computational framework that connects cell behavior to embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and cortical tension dynamics. We predict that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. By directly measuring strain and stress relaxation, as well as the dynamics of cell rearrangements, in elongating posterior zebrafish tissues, we show that tension fluctuations drive active cell rearrangements that fluidize the tissue. These results highlight a key role of non-equilibrium tension dynamics in developmental processes.
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Affiliation(s)
- Sangwoo Kim
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
| | - Marie Pochitaloff
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
| | | | - Otger Campàs
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
- Center for Bioengineering, University of California, Santa Barbara, CA 93106, USA
- Department of Molecular, Cellular and Developmental Biology, University of California, Santa Barbara, CA 93106, USA
- California NanoSystems Institute, University of California, Santa Barbara, CA 93106, USA
- Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany
- Correspondence should be addressed to Otger Camps ()
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7
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Devany J, Sussman DM, Yamamoto T, Manning ML, Gardel ML. Cell cycle-dependent active stress drives epithelia remodeling. Proc Natl Acad Sci U S A 2021; 118:e1917853118. [PMID: 33649197 PMCID: PMC7958291 DOI: 10.1073/pnas.1917853118] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Epithelia have distinct cellular architectures which are established in development, reestablished after wounding, and maintained during tissue homeostasis despite cell turnover and mechanical perturbations. In turn, cell shape also controls tissue function as a regulator of cell differentiation, proliferation, and motility. Here, we investigate cell shape changes in a model epithelial monolayer. After the onset of confluence, cells continue to proliferate and change shape over time, eventually leading to a final architecture characterized by arrested motion and more regular cell shapes. Such monolayer remodeling is robust, with qualitatively similar evolution in cell shape and dynamics observed across disparate perturbations. Here, we quantify differences in monolayer remodeling guided by the active vertex model to identify underlying order parameters controlling epithelial architecture. When monolayers are formed atop an extracellular matrix with varied stiffness, we find the cell density at which motion arrests varies significantly, but the cell shape remains constant, consistent with the onset of tissue rigidity. In contrast, pharmacological perturbations can significantly alter the cell shape at which tissue dynamics are arrested, consistent with varied amounts of active stress within the tissue. Across all experimental conditions, the final cell shape is well correlated to the cell proliferation rate, and cell cycle inhibition immediately arrests cell motility. Finally, we demonstrate cell cycle variation in junctional tension as a source of active stress within the monolayer. Thus, the architecture and mechanics of epithelial tissue can arise from an interplay between cell mechanics and stresses arising from cell cycle dynamics.
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Affiliation(s)
- John Devany
- Department of Physics, Institute for Biophysical Dynamics, James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Daniel M Sussman
- Department of Physics, BioInspired Institute, Syracuse University, Syracuse, NY 13244
- Department of Physics, Emory University, Atlanta, GA 30322
| | - Takaki Yamamoto
- Nonequilibrium Physics of Living Matter RIKEN Hakubi Research Team, RIKEN Center for Biosystems Dynamics Research, Kobe 650-0047, Japan
| | - M Lisa Manning
- Department of Physics, BioInspired Institute, Syracuse University, Syracuse, NY 13244
| | - Margaret L Gardel
- Department of Physics, Institute for Biophysical Dynamics, James Franck Institute, University of Chicago, Chicago, IL 60637;
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637
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8
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Singh AV, Maharjan RS, Kanase A, Siewert K, Rosenkranz D, Singh R, Laux P, Luch A. Machine-Learning-Based Approach to Decode the Influence of Nanomaterial Properties on Their Interaction with Cells. ACS APPLIED MATERIALS & INTERFACES 2021; 13:1943-1955. [PMID: 33373205 DOI: 10.1021/acsami.0c18470] [Citation(s) in RCA: 73] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In an in vitro nanotoxicity system, cell-nanoparticle (NP) interaction leads to the surface adsorption, uptake, and changes into nuclei/cell phenotype and chemistry, as an indicator of oxidative stress, genotoxicity, and carcinogenicity. Different types of nanomaterials and their chemical composition or "corona" have been widely studied in context with nanotoxicology. However, rare reports are available, which delineate the details of the cell shape index (CSI) and nuclear area factors (NAFs) as a descriptor of the type of nanomaterials. In this paper, we propose a machine-learning-based graph modeling and correlation-establishing approach using tight junction protein ZO-1-mediated alteration in the cell/nuclei phenotype to quantify and propose it as indices of cell-NP interactions. We believe that the phenotypic variation (CSI and NAF) in the epithelial cell is governed by the physicochemical descriptors (e.g., shape, size, zeta potential, concentration, diffusion coefficients, polydispersity, and so on) of the different classes of nanomaterials, which critically determines the intracellular uptake or cell membrane interactions when exposed to the epithelial cells at sub-lethal concentrations. The intrinsic and extrinsic physicochemical properties of the representative nanomaterials (NMs) were measured using optical (dynamic light scattering, NP tracking analysis) methods to create a set of nanodescriptors contributing to cell-NM interactions via phenotype adjustments. We used correlation function as a machine-learning algorithm to successfully predict cell and nuclei shapes and polarity functions as phenotypic markers for five different classes of nanomaterials studied herein this report. The CSI and NAF as nanodescriptors can be used as intuitive cell phenotypic parameters to define the safety of nanomaterials extensively used in consumer products and nanomedicine.
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Affiliation(s)
- Ajay Vikram Singh
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
| | - Romi-Singh Maharjan
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
| | - Anurag Kanase
- Department of Bioengineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Katherina Siewert
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
| | - Daniel Rosenkranz
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
| | - Rishabh Singh
- Rajarshi Shahu College of Engineering, 411007 Pune, India
| | - Peter Laux
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
| | - Andreas Luch
- Department of Chemical and Product Safety, German Federal Institute for Risk Assessment (BfR), Max-Dohrn-Straße 8-10, 10589 Berlin, Germany
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9
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Alaimo L, Luciano M, Mohammed D, Versaevel M, Bruyère C, Vercruysse E, Gabriele S. Engineering slit-like channels for studying the growth of epithelial tissues in 3D-confined spaces. Biotechnol Bioeng 2020; 117:2887-2896. [PMID: 32484903 DOI: 10.1002/bit.27446] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2020] [Revised: 05/25/2020] [Accepted: 05/31/2020] [Indexed: 01/02/2023]
Abstract
The development of epithelial lumens in ducts is essential to the functioning of various organs and in organogenesis. Ductal elongation requires the collective migration of cell cohorts in three-dimensional (3D) confined spaces, while maintaining their epithelial integrity. Epithelial lumens generally adopt circular morphologies, however abnormalities in complex physiological environments can lead to the narrowing of glandular spaces that adopt elongated and slit-like morphologies. Here, we describe a simple method to form epithelial tissues in microchannels of various widths (100-300 µm) with a constant height of 25 µm that mimic elongated geometries of glandular spaces. The significance of this biomimetic platform has been evidenced by studying the migration of epithelial cell sheets inside these narrow slits of varying dimensions. We show that the growth of epithelial tissues in 3D-confined slits leads to a gradient of cell density along the slit axis and that the migration cell velocity depends on the extent of the spatial confinement. Our findings indicate that nuclear orientation is higher for leader cells and depends on the slit width, whereas YAP protein was predominantly localized in the nucleus of leader cells. This method will pave the way to studies aiming at understanding how 3D-confined spaces, which are reminiscent of in vivo pathological conditions, can affect the growth and the homeostasis of epithelial tissues.
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Affiliation(s)
- Laura Alaimo
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Marine Luciano
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Danahe Mohammed
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Marie Versaevel
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Céline Bruyère
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Eléonore Vercruysse
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
| | - Sylvain Gabriele
- University of Mons, Laboratory for Complex Fluids and Interfaces, Mechanobiology and Soft Matter Group, CIRMAP, Research Institute for Biosciences, Place du Parc, Mons, Belgium
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10
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Lovrić J, Kaliman S, Barfuss W, Schröder-Turk GE, Smith AS. Geometric effects in random assemblies of ellipses. SOFT MATTER 2019; 15:8566-8577. [PMID: 31637393 DOI: 10.1039/c9sm01067j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize these effects, we perform an in-depth study of random assemblies generated by a slow compression of frictionless elliptical particles. The obtained configurations are then analysed using the Set Voronoi tessellation, which takes the particle shape into account. Not only do we analyse most scalar and vectorial morphological measures, which are commonly discussed in the literature or which have recently been addressed in experiments, but we also systematically explore the correlations between them. While in a limited range of parameters similarities with findings in 3D assemblies could be identified, important differences are found when a broad range of aspect ratios and packing fractions are considered. The data discussed in this study should thus provide a unique reference set such that geometric effects and differences from random assemblies could be clearly identified in more complex systems, including ones with soft and active particles that are typically found in biological systems.
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Affiliation(s)
- Jakov Lovrić
- Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia
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11
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Li X, Das A, Bi D. Mechanical Heterogeneity in Tissues Promotes Rigidity and Controls Cellular Invasion. PHYSICAL REVIEW LETTERS 2019; 123:058101. [PMID: 31491312 DOI: 10.1103/physrevlett.123.058101] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Revised: 06/05/2019] [Indexed: 06/10/2023]
Abstract
We study the influence of cell-level mechanical heterogeneity in epithelial tissues using a vertex-based model. Heterogeneity is introduced into the cell shape index (p_{0}) that tunes the stiffness at a single-cell level. The addition of heterogeneity can always enhance the mechanical rigidity of the epithelial layer by increasing its shear modulus, hence making it more rigid. There is an excellent scaling collapse of our data as a function of a single scaling variable f_{r}, which accounts for the overall fraction of rigid cells. We identify a universal threshold f_{r}^{*} that demarcates fluid versus solid tissues. Furthermore, this rigidity onset is far below the contact percolation threshold of rigid cells. These results give rise to a separation of rigidity and contact percolation processes that leads to distinct types of solid states. We also investigate the influence of heterogeneity on tumor invasion dynamics. There is an overall impedance of invasion as the tissue becomes more rigid. Invasion can also occur in an intermediate heterogeneous solid state that is characterized by significant spatial-temporal intermittency.
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Affiliation(s)
- Xinzhi Li
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Amit Das
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
| | - Dapeng Bi
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
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12
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Yu M, Mahtabfar A, Beelen P, Demiryurek Y, Shreiber DI, Zahn JD, Foty RA, Liu L, Lin H. Coherent Timescales and Mechanical Structure of Multicellular Aggregates. Biophys J 2019; 114:2703-2716. [PMID: 29874619 DOI: 10.1016/j.bpj.2018.04.025] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Revised: 03/29/2018] [Accepted: 04/09/2018] [Indexed: 02/06/2023] Open
Abstract
Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics in specifying multicellular reorganization during embryonic developments and malignant invasion. Tissue-like spheroids, when subjected to a compressive force, are known to exhibit liquid-like behaviors at long timescales (hours), largely because of cell rearrangements that serve to effectively dissipate the applied stress. At short timescales (seconds to minutes), before cell rearrangement, the mechanical behavior is strikingly different. The current work uses shape relaxation to investigate the structural characteristics of aggregates and discovers two coherent timescales: one on the order of seconds, the other tens of seconds. These timescales are universal, conserved across a variety of tested species, and persist despite great differences in other properties such as tissue surface tension and adhesion. A precise mathematical theory is used to correlate the timescales with mechanical properties and reveals that aggregates have a relatively strong envelope and an unusually "soft" interior (weak bulk elastic modulus). This characteristic is peculiar, considering that both layers consist of identical units (cells), but is consistent with the fact that this structure can engender both structural integrity and the flexibility required for remodeling. In addition, tissue surface tension, elastic modulus, and viscosity are proportional to each other. Considering that these tissue-level properties intrinsically derive from cellular-level properties, the proportionalities imply precise coregulation of the latter and in particular of the tension on the cell-medium and cell-cell interfaces.
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Affiliation(s)
- Miao Yu
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey
| | - Aria Mahtabfar
- Department of Surgery, Rutgers Robert Wood Johnson Medical School, New Brunswick, New Jersey
| | - Paul Beelen
- Department of Surgery, Rutgers Robert Wood Johnson Medical School, New Brunswick, New Jersey
| | - Yasir Demiryurek
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey
| | - David I Shreiber
- Department of Biomedical Engineering, The State University of New Jersey, Piscataway, New Jersey
| | - Jeffrey D Zahn
- Department of Biomedical Engineering, The State University of New Jersey, Piscataway, New Jersey
| | - Ramsey A Foty
- Department of Surgery, Rutgers Robert Wood Johnson Medical School, New Brunswick, New Jersey
| | - Liping Liu
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey; Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey
| | - Hao Lin
- Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey.
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13
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Kim S, Hilgenfeldt S. A simple landscape of metastable state energies for two-dimensional cellular matter. SOFT MATTER 2019; 15:237-242. [PMID: 30543253 DOI: 10.1039/c8sm01921e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The mechanical behavior of cellular matter in two dimensions can be inferred from geometric information near its energetic ground state. Here it is shown that the much larger set of all metastable state energies is universally described by a systematic expansion in moments of the joint probability distribution of size (area) and topology (number of neighbors). The approach captures bounds to the entire range of metastable state energies and quantitatively identifies any such state. The resulting energy landscape is invariant across different classes of energy functionals, across simulation techniques, and across system polydispersities. The theory also finds a threshold in tissue adhesion beyond which no metastable states are possible. Mechanical properties of cellular matter in biological and technological applications can thus be identified by visual information only.
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Affiliation(s)
- Sangwoo Kim
- Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, USA.
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14
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Koride S, Loza AJ, Sun SX. Epithelial vertex models with active biochemical regulation of contractility can explain organized collective cell motility. APL Bioeng 2018; 2:031906. [PMID: 31069315 PMCID: PMC6324211 DOI: 10.1063/1.5023410] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Accepted: 06/14/2018] [Indexed: 01/22/2023] Open
Abstract
Collective motions of groups of cells are observed in many biological settings such as embryo development, tissue formation, and cancer metastasis. To effectively model collective cell movement, it is important to incorporate cell specific features such as cell size, cell shape, and cell mechanics, as well as active behavior of cells such as protrusion and force generation, contractile forces, and active biochemical signaling mechanisms that regulate cell behavior. In this paper, we develop a comprehensive model of collective cell migration in confluent epithelia based on the vertex modeling approach. We develop a method to compute cell-cell viscous friction based on the vertex model and incorporate RhoGTPase regulation of cortical myosin contraction. Global features of collective cell migration are examined by computing the spatial velocity correlation function. As active cell force parameters are varied, we found rich dynamical behavior. Furthermore, we find that cells exhibit nonlinear phenomena such as contractile waves and vortex formation. Together our work highlights the importance of active behavior of cells in generating collective cell movement. The vertex modeling approach is an efficient and versatile approach to rigorously examine cell motion in the epithelium.
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Affiliation(s)
- Sarita Koride
- Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Andrew J Loza
- Department of Cell Biology, Washington University School of Medicine, St. Louis, Missouri 63110, USA
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15
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Kim S, Wang Y, Hilgenfeldt S. Universal Features of Metastable State Energies in Cellular Matter. PHYSICAL REVIEW LETTERS 2018; 120:248001. [PMID: 29957000 DOI: 10.1103/physrevlett.120.248001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Revised: 03/26/2018] [Indexed: 06/08/2023]
Abstract
Mechanical equilibrium states of cellular matter are overwhelmingly metastable and separated from each other by topology changes. Using theory and simulations, it is shown that for a wide class of energy functionals in 2D, including those describing tissue cell layers, local energy differences between neighboring metastable states as well as global energy differences between initial states and ground states are governed by simple, universal relations. Knowledge of instantaneous length of an edge undergoing a T1 transition is sufficient to predict local energy changes, while the initial edge length distribution yields a successful prediction for the global energy difference. An analytical understanding of the model parameters is provided.
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Affiliation(s)
- Sangwoo Kim
- Mechanical Sciences and Engineering, University of Illinois, Urbana-Champaign, Illinois 61801, USA
| | - Yiliang Wang
- Mechanical Sciences and Engineering, University of Illinois, Urbana-Champaign, Illinois 61801, USA
| | - Sascha Hilgenfeldt
- Mechanical Sciences and Engineering, University of Illinois, Urbana-Champaign, Illinois 61801, USA
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16
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Atia L, Bi D, Sharma Y, Mitchel JA, Gweon B, Koehler S, DeCamp SJ, Lan B, Kim JH, Hirsch R, Pegoraro AF, Lee KH, Starr JR, Weitz DA, Martin AC, Park JA, Butler JP, Fredberg JJ. Geometric constraints during epithelial jamming. NATURE PHYSICS 2018; 14:613-620. [PMID: 30151030 PMCID: PMC6108541 DOI: 10.1038/s41567-018-0089-9] [Citation(s) in RCA: 129] [Impact Index Per Article: 21.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively whereas variability of shape from cell-to-cell is regarded most often as biological noise. But where do cell shape and its variability come from? Here we report that cell shape and shape variability are mutually constrained through a relationship that is purely geometrical. That relationship is shown to govern processes as diverse as maturation of the pseudostratified bronchial epithelial layer cultured from non-asthmatic or asthmatic donors, and formation of the ventral furrow in the Drosophila embryo. Across these and other epithelial systems, shape variability collapses to a family of distributions that is common to all. That distribution, in turn, is accounted for by a mechanistic theory of cell-cell interaction showing that cell shape becomes progressively less elongated and less variable as the layer becomes progressively more jammed. These findings suggest a connection between jamming and geometry that spans living organisms and inert jammed systems, and thus transcends system details. Although molecular events are needed for any complete theory of cell shape and cell packing, observations point to the hypothesis that jamming behavior at larger scales of organization sets overriding geometrical constraints.
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Affiliation(s)
- Lior Atia
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Dapeng Bi
- Northeastern University, Department of Physics, Boston, Massachusetts 02115, USA
| | - Yasha Sharma
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Jennifer A Mitchel
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Bomi Gweon
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- Hanyang University, Department of Biomedical Engineering, Seoul 04763, Korea
| | - Stephan Koehler
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Stephen J DeCamp
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Bo Lan
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Jae Hun Kim
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Rebecca Hirsch
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Adrian F Pegoraro
- Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA
| | - Kyu Ha Lee
- The Forsyth Institute, Cambridge, Massachusetts 02142 USA
| | | | - David A Weitz
- Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA
| | - Adam C Martin
- Massachusetts Institute of Technology, Department of Biology, Cambridge, Massachusetts 02142, USA
| | - Jin-Ah Park
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - James P Butler
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- Dept. Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, Massachusetts, 02115, USA
| | - Jeffrey J Fredberg
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
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17
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Chen D, Aw WY, Devenport D, Torquato S. Structural Characterization and Statistical-Mechanical Model of Epidermal Patterns. Biophys J 2017; 111:2534-2545. [PMID: 27926854 DOI: 10.1016/j.bpj.2016.10.036] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Revised: 10/21/2016] [Accepted: 10/27/2016] [Indexed: 01/08/2023] Open
Abstract
In proliferating epithelia of mammalian skin, cells of irregular polygon-like shapes pack into complex, nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct space (correlation function) and Fourier space (structure factor) of the cell centroids in the early stages of embryonic development show structural directional dependence (statistical anisotropy), which is a reflection of the fact that cells are stretched, which promotes uniaxial growth along the epithelial plane. In the late stages, the patterns tend toward statistically isotropic states, as cells attain global polarization and epidermal growth shifts to produce the skin's outer stratified layers. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-range soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. In contrast with many vertex-based models, our statistical-mechanical model does not explicitly incorporate information about the cell shapes and interfacial energy between cells; nonetheless, our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments, as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. The array of structural descriptors that we deploy enable us to distinguish between normal, mechanically deformed, and pathological skin tissues. Our statistical-mechanical model enables one to generate tissue microstructure at will for further analysis. We also discuss ways in which our model might be extended to better understand morphogenesis (in particular the emergence of planar cell polarity), wound healing, and disease-progression processes in skin, and how it could be applied to the design of synthetic tissues.
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Affiliation(s)
- Duyu Chen
- Department of Chemistry, Princeton University, Princeton, New Jersey
| | - Wen Yih Aw
- Department of Molecular Biology, Princeton University, Princeton, New Jersey
| | - Danelle Devenport
- Department of Molecular Biology, Princeton University, Princeton, New Jersey
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey; Department of Physics, Princeton University, Princeton, New Jersey; Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey; Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey.
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18
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Kim S, Cassidy JJ, Yang B, Carthew RW, Hilgenfeldt S. Hexagonal Patterning of the Insect Compound Eye: Facet Area Variation, Defects, and Disorder. Biophys J 2017; 111:2735-2746. [PMID: 28002749 DOI: 10.1016/j.bpj.2016.11.004] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Revised: 11/04/2016] [Accepted: 11/07/2016] [Indexed: 11/25/2022] Open
Abstract
The regular hexagonal array morphology of facets (ommatidia) in the Drosophila compound eye is accomplished by regulation of cell differentiation and planar cell polarity during development. Mutations in certain genes disrupt regulation, causing a breakdown of this perfect symmetry, so that the ommatidial pattern shows onset of disorder in the form of packing defects. We analyze a variety of such mutants and compare them to normal (wild-type), finding that mutants show increased local variation in ommatidial area, which is sufficient to induce a significant number of defects. A model formalism based on Voronoi construction is developed to predict the observed correlation between ommatidium size variation and the number of defects, and to study the onset of disorder in this system with statistical tools. The model uncovers a previously unknown large-scale systematic size variation of the ommatidia across the eye of both wild-type and mutant animals. Such systematic variation of area, as well as its statistical fluctuations, are found to have distinct effects on eye disorder that can both be quantitatively modeled. Furthermore, the topological order is also influenced by the internal structure of the ommatidia, with cells of greater relative mechanical stiffness providing constraints to ommatidial deformation and thus to defect generation. Without free parameters, the simulation predicts the size-topology correlation for both wild-type and mutant eyes. This work develops formalisms of size-topology correlation that are very general and can be potentially applied to other cellular structures near the onset of disorder.
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Affiliation(s)
- Sangwoo Kim
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois.
| | - Justin J Cassidy
- Department of Molecular Biosciences, Northwestern University, Evanston, Illinois
| | - Boyuan Yang
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois
| | - Richard W Carthew
- Department of Molecular Biosciences, Northwestern University, Evanston, Illinois
| | - Sascha Hilgenfeldt
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois
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19
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Park JA, Atia L, Mitchel JA, Fredberg JJ, Butler JP. Collective migration and cell jamming in asthma, cancer and development. J Cell Sci 2016; 129:3375-83. [PMID: 27550520 PMCID: PMC5047682 DOI: 10.1242/jcs.187922] [Citation(s) in RCA: 77] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Collective cellular migration within the epithelial layer impacts upon development, wound healing and cancer invasion, but remains poorly understood. Prevailing conceptual frameworks tend to focus on the isolated role of each particular underlying factor - taken one at a time or at most a few at a time - and thus might not be tailored to describe a cellular collective that embodies a wide palette of physical and molecular interactions that are both strong and complex. To bridge this gap, we shift the spotlight to the emerging concept of cell jamming, which points to only a small set of parameters that govern when a cellular collective might jam and rigidify like a solid, or instead unjam and flow like a fluid. As gateways to cellular migration, the unjamming transition (UJT) and the epithelial-to-mesenchymal transition (EMT) share certain superficial similarities, but their congruence - or lack thereof - remains unclear. In this Commentary, we discuss aspects of cell jamming, its established role in human epithelial cell layers derived from the airways of non-asthmatic and asthmatic donors, and its speculative but emerging roles in development and cancer cell invasion.
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Affiliation(s)
- Jin-Ah Park
- Harvard T.H. Chan School of Public Health, Department of Environmental Health, Boston, MA 02115, USA
| | - Lior Atia
- Harvard T.H. Chan School of Public Health, Department of Environmental Health, Boston, MA 02115, USA
| | - Jennifer A Mitchel
- Harvard T.H. Chan School of Public Health, Department of Environmental Health, Boston, MA 02115, USA
| | - Jeffrey J Fredberg
- Harvard T.H. Chan School of Public Health, Department of Environmental Health, Boston, MA 02115, USA
| | - James P Butler
- Harvard T.H. Chan School of Public Health, Department of Environmental Health, Boston, MA 02115, USA Brigham and Women's Hospital, Harvard Medical School, Department of Medicine, Boston, MA 02115, USA
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