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Hohmann U, von Widdern JC, Ghadban C, Giudice MCL, Lemahieu G, Cavalcanti-Adam EA, Dehghani F, Hohmann T. Jamming Transitions in Astrocytes and Glioblastoma Are Induced by Cell Density and Tension. Cells 2022; 12:cells12010029. [PMID: 36611824 PMCID: PMC9818602 DOI: 10.3390/cells12010029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 12/07/2022] [Accepted: 12/17/2022] [Indexed: 12/24/2022] Open
Abstract
Collective behavior of cells emerges from coordination of cell-cell-interactions and is important to wound healing, embryonic and tumor development. Depending on cell density and cell-cell interactions, a transition from a migratory, fluid-like unjammed state to a more static and solid-like jammed state or vice versa can occur. Here, we analyze collective migration dynamics of astrocytes and glioblastoma cells using live cell imaging. Furthermore, atomic force microscopy, traction force microscopy and spheroid generation assays were used to study cell adhesion, traction and mechanics. Perturbations of traction and adhesion were induced via ROCK or myosin II inhibition. Whereas astrocytes resided within a non-migratory, jammed state, glioblastoma were migratory and unjammed. Furthermore, we demonstrated that a switch from an unjammed to a jammed state was induced upon alteration of the equilibrium between cell-cell-adhesion and tension from adhesion to tension dominated, via inhibition of ROCK or myosin II. Such behavior has implications for understanding the infiltration of the brain by glioblastoma cells and may help to identify new strategies to develop anti-migratory drugs and strategies for glioblastoma-treatment.
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Affiliation(s)
- Urszula Hohmann
- Department of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, 06108 Halle (Saale), Germany
| | - Julian Cardinal von Widdern
- Department of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, 06108 Halle (Saale), Germany
| | - Chalid Ghadban
- Department of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, 06108 Halle (Saale), Germany
| | - Maria Cristina Lo Giudice
- Department of Cellular Biophysics, Max Planck Institute for Medical Research, 69120 Heidelberg, Germany
| | - Grégoire Lemahieu
- Department of Cellular Biophysics, Max Planck Institute for Medical Research, 69120 Heidelberg, Germany
| | | | - Faramarz Dehghani
- Department of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, 06108 Halle (Saale), Germany
| | - Tim Hohmann
- Department of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, 06108 Halle (Saale), Germany
- Correspondence:
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Mary G, Mazuel F, Nier V, Fage F, Nagle I, Devaud L, Bacri JC, Asnacios S, Asnacios A, Gay C, Marcq P, Wilhelm C, Reffay M. All-in-one rheometry and nonlinear rheology of multicellular aggregates. Phys Rev E 2022; 105:054407. [PMID: 35706238 DOI: 10.1103/physreve.105.054407] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 03/24/2022] [Indexed: 06/15/2023]
Abstract
Tissues are generally subjected to external stresses, a potential stimulus for their differentiation or remodeling. While single-cell rheology has been extensively studied leading to controversial results about nonlinear response, mechanical tissue behavior under external stress is still poorly understood, in particular, the way individual cell properties translate at the tissue level. Herein, using magnetic cells we were able to form perfectly monitored cellular aggregates (magnetic molding) and to deform them under controlled applied stresses over a wide range of timescales and amplitudes (magnetic rheometer). We explore the rheology of these minimal tissue models using both standard assays (creep and oscillatory response) as well as an innovative broad spectrum solicitation coupled with inference analysis thus being able to determine in a single experiment the best rheological model. We find that multicellular aggregates exhibit a power-law response with nonlinearities leading to tissue stiffening at high stress. Moreover, we reveal the contribution of intracellular (actin network) and intercellular components (cell-cell adhesions) in this aggregate rheology.
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Affiliation(s)
- Gaëtan Mary
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - François Mazuel
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Vincent Nier
- Laboratoire Physico Chimie Curie, UMR 168, CNRS, Institut Curie, PSL University, Sorbonne Université, 75005 Paris, France
| | - Florian Fage
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Irène Nagle
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Louisiane Devaud
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Jean-Claude Bacri
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Sophie Asnacios
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
- Faculty of Science and Engineering, UFR 925 Physics, Sorbonne Université, Paris France
| | - Atef Asnacios
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Cyprien Gay
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
| | - Philippe Marcq
- Laboratoire Physico Chimie Curie, UMR 168, CNRS, Institut Curie, PSL University, Sorbonne Université, 75005 Paris, France
- Faculty of Science and Engineering, UFR 925 Physics, Sorbonne Université, Paris France
- Laboratoire Physique et Mécanique des Matériaux Hétérogènes, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris Cité, 75005 Paris, France
| | - Claire Wilhelm
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
- Laboratoire Physico Chimie Curie, UMR 168, CNRS, Institut Curie, PSL University, Sorbonne Université, 75005 Paris, France
| | - Myriam Reffay
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université de Paris Cité, 75205 Paris cedex 13, France
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3
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Livera POS, Anjos PHA, Miranda JA. Ferrofluid annulus in crossed magnetic fields. Phys Rev E 2022; 105:045106. [PMID: 35590587 DOI: 10.1103/physreve.105.045106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 04/06/2022] [Indexed: 06/15/2023]
Abstract
We study the dynamics and pattern formation of a ferrofluid annulus enveloped by two nonmagnetic fluids in a Hele-Shaw cell, subjected to an in-plane crossed magnetic field configuration involving the combination of radial and azimuthal magnetic fields. A perturbative, second-order mode-coupling analysis is employed to investigate how the ferrofluid annulus responds to variations in the relative strength of the radial and azimuthal magnetic field components, as well as in the thickness of magnetic fluid ring. By tuning the magnetic field components and the annulus' thickness, we have found the development of several stationary annular shapes, presenting polygon-shaped structures typically having skewed, peaked fingers. Such fingered structures may vary their skewness, sharpness, and number and arise on the inner, outer, or even both boundaries of the annulus. In addition to controlling the morphologies of the ferrofluid annuli, the external field can be used to put the annulus into a rotational motion, with an angular velocity having prescribed magnitude, and direction. Our second-order theory is utilized to obtain a correction to the linear stability analysis prediction of such angular velocity, usually resulting in a decreased weakly nonlinear value as compared with the magnitude predicted by purely linear theory. These theoretical results suggest the use of magnetic-field-controlled ferrofluid annuli in Hele-Shaw cells as a potential laboratory for microscale applications related to the manipulation of shape-programmable magnetic fluid objects and tunable fluidic-mixing devices in confined environments.
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Affiliation(s)
- Pedro O S Livera
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - Pedro H A Anjos
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
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Interaction of Glia Cells with Glioblastoma and Melanoma Cells under the Influence of Phytocannabinoids. Cells 2022; 11:cells11010147. [PMID: 35011711 PMCID: PMC8750637 DOI: 10.3390/cells11010147] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/10/2021] [Accepted: 12/31/2021] [Indexed: 01/27/2023] Open
Abstract
Brain tumor heterogeneity and progression are subject to complex interactions between tumor cells and their microenvironment. Glioblastoma and brain metastasis can contain 30–40% of tumor-associated macrophages, microglia, and astrocytes, affecting migration, proliferation, and apoptosis. Here, we analyzed interactions between glial cells and LN229 glioblastoma or A375 melanoma cells in the context of motility and cell–cell interactions in a 3D model. Furthermore, the effects of phytocannabinoids, cannabidiol (CBD), tetrahydrocannabidiol (THC), or their co-application were analyzed. Co-culture of tumor cells with glial cells had little effect on 3D spheroid formation, while treatment with cannabinoids led to significantly larger spheroids. The addition of astrocytes blocked cannabinoid-induced effects. None of the interventions affected cell death. Furthermore, glial cell-conditioned media led to a significant slowdown in collective, but not single-cell migration speed. Taken together, glial cells in glioblastoma and brain metastasis micromilieu impact the tumor spheroid formation, cell spreading, and motility. Since the size of spheroid remained unaffected in glial cell tumor co-cultures, phytocannabinoids increased the size of spheroids without any effects on migration. This aspect might be of relevance since phytocannabinoids are frequently used in tumor therapy for side effects.
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Perez JE, Nagle I, Wilhelm C. Magnetic molding of tumor spheroids: emerging model for cancer screening. Biofabrication 2020; 13. [PMID: 33126227 DOI: 10.1088/1758-5090/abc670] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 10/30/2020] [Indexed: 02/06/2023]
Abstract
Three-dimensional tissue culture, and particularly spheroid models, have recently been recognized as highly relevant in drug screening, toxicity assessment and tissue engineering due to their superior complexity and heterogeneity akin to the in vivo microenvironment. However, limitations in size control, shape reproducibility and long maturation times hinder their full applicability. Here, we report a spheroid formation technique based on the magnetic aggregation of cells with internalized magnetic nanoparticles. The method yields magnetic spheroids with high sphericity and allows fine-tuning the final spheroid diameter. Moreover, cohesive spheroids can be obtained in less than 24 hours. We show the proof of concept of the method using the CT26 murine colon carcinoma cell line and how different cell proliferation and invasion potentials can be attained by varying the spheroid size. Additionally, we show how the spheroid maturation impacts cell invasion and doxorubicin penetrability, highlighting the importance of this parameter in drug screening and therapeutic applications. Finally, we demonstrate the capability of the method to allow the measurement of the spheroid surface tension, a relevant output parameter in the context of cancer cell invasion and metastasis. The method can accommodate other cell lines able to be magnetically labeled, as we demonstrate using the U-87 MG human glioblastoma cell line, and shows promise in the therapeutic screening at early time points of tissue formation, as well as in studies of drug and nanoparticle tumor penetration.
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Affiliation(s)
- Jose Efrain Perez
- Laboratoire Matiere et Systemes Complexes UMR CNRS 7057, University of Paris, Paris, FRANCE
| | - Irène Nagle
- Laboratoire Matiere et Systemes Complexes UMR CNRS 7057, University of Paris, Paris, FRANCE
| | - Claire Wilhelm
- Laboratoire Matiere et Systemes Complexes UMR CNRS 7057, University of Paris, Batiment Condorcet, 10 rue Alice Domon et Leonie Duquet, 75025 Paris Cedax 13, Paris, 75013, FRANCE
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6
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Hohmann T, Hohmann U, Kolbe MR, Dahlmann M, Kobelt D, Stein U, Dehghani F. MACC1 driven alterations in cellular biomechanics facilitate cell motility in glioblastoma. Cell Commun Signal 2020; 18:85. [PMID: 32503676 PMCID: PMC7275321 DOI: 10.1186/s12964-020-00566-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2020] [Accepted: 03/23/2020] [Indexed: 12/31/2022] Open
Abstract
Background Metastasis-associated in colon cancer 1 (MACC1) is an established marker for metastasis and tumor cell migration in a multitude of tumor entities, including glioblastoma (GBM). Nevertheless, the mechanism underlying the increased migratory capacity in GBM is not comprehensively explored. Methods We performed live cell and atomic force microscopy measurements to assess cell migration and mechanical properties of MACC1 overexpressing GBM cells. We quantified MACC1 dependent dynamics of 3D aggregate formation. For mechanistic studies we measured the expression of key adhesion molecules using qRT-PCR, and MACC1 dependent changes in short term adhesion to fibronectin and laminin. We then determined changes in sub-cellular distribution of integrins and actin in dependence of MACC1, but also in microtubule and intermediate filament organization. Results MACC1 increased the migratory speed and elastic modulus of GBM cells, but decreased cell-cell adhesion and inhibited the formation of 3D aggregates. These effects were not associated with altered mRNA expression of several key adhesion molecules or altered short-term affinity to laminin and fibronectin. MACC1 did neither change the organization of the microtubule nor intermediate filament cytoskeleton, but resulted in increased amounts of protrusive actin on laminin. Conclusion MACC1 overexpression increases elastic modulus and migration and reduces adhesion of GBM cells thereby impeding 3D aggregate formation. The underlying molecular mechanism is independent on the organization of microtubules, intermediate filaments and several key adhesion molecules, but depends on adhesion to laminin. Thus, targeting re-organization of the cytoskeleton and cell motility via MACC1 may offer a treatment option to impede GBM spreading. Video Abstract
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Affiliation(s)
- Tim Hohmann
- Institute of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, Grosse Steinstrasse 52, 06108, Halle, Saale, Germany
| | - Urszula Hohmann
- Institute of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, Grosse Steinstrasse 52, 06108, Halle, Saale, Germany
| | - Marc R Kolbe
- Institute of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, Grosse Steinstrasse 52, 06108, Halle, Saale, Germany
| | - Mathias Dahlmann
- Experimental and Clinical Research Center, Charité Universitätsmedizin Berlin and Max-Delbrück-Center for Molecular Medicine in the Helmholtz Association, Robert-Rössle-Straße 10, 13125, Berlin, Germany.,German Cancer Consortium (DKTK), Im Neuenheimer Feld 280, 69120, Heidelberg, Germany
| | - Dennis Kobelt
- Experimental and Clinical Research Center, Charité Universitätsmedizin Berlin and Max-Delbrück-Center for Molecular Medicine in the Helmholtz Association, Robert-Rössle-Straße 10, 13125, Berlin, Germany.,German Cancer Consortium (DKTK), Im Neuenheimer Feld 280, 69120, Heidelberg, Germany
| | - Ulrike Stein
- Experimental and Clinical Research Center, Charité Universitätsmedizin Berlin and Max-Delbrück-Center for Molecular Medicine in the Helmholtz Association, Robert-Rössle-Straße 10, 13125, Berlin, Germany. .,German Cancer Consortium (DKTK), Im Neuenheimer Feld 280, 69120, Heidelberg, Germany.
| | - Faramarz Dehghani
- Institute of Anatomy and Cell Biology, Martin Luther University Halle-Wittenberg, Grosse Steinstrasse 52, 06108, Halle, Saale, Germany.
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7
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Cell membrane engineering with synthetic materials: Applications in cell spheroids, cellular glues and microtissue formation. Acta Biomater 2019; 90:21-36. [PMID: 30986529 DOI: 10.1016/j.actbio.2019.04.013] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Revised: 03/26/2019] [Accepted: 04/03/2019] [Indexed: 12/16/2022]
Abstract
Biologically inspired materials with tunable bio- and physicochemical properties provide an essential framework to actively control and support cellular behavior. Cell membrane remodeling approaches benefit from the advances in polymer science and bioconjugation methods, which allow for the installation of un-/natural molecules and particles on the cells' surface. Synthetically remodeled cells have superior properties and are under intense investigation in various therapeutic scenarios as cell delivery systems, bio-sensing platforms, injectable biomaterials and bioinks for 3D bioprinting applications. In this review article, recent advances in the field of cell surface remodeling via bio-chemical means and the potential biomedical applications of these emerging cell hybrids are discussed. STATEMENT OF SIGNIFICANCE: Recent advances in bioconjugation methods, controlled/living polymerizations, microfabrication techniques and 3D printing technologies have enabled researchers to probe specific cellular functions and cues for therapeutic and research purposes through the formation of cell spheroids and polymer-cell chimeras. This review article highlights recent non-genetic cell membrane engineering strategies towards the fabrication of cellular ensembles and microtissues with interest in 3D in vitro modeling, cell therapeutics and tissue engineering. From a wider perspective, these approaches may provide a roadmap for future advances in cell therapies which will expedite the clinical use of cells, thereby improving the quality and accessibility of disease treatments.
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8
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Ghosh S, Kumar SRP, Puri IK, Elankumaran S. Magnetic assembly of 3D cell clusters: visualizing the formation of an engineered tissue. Cell Prolif 2016; 49:134-44. [PMID: 26839975 DOI: 10.1111/cpr.12234] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2015] [Accepted: 09/12/2015] [Indexed: 01/05/2023] Open
Abstract
OBJECTIVES Contactless magnetic assembly of cells into 3D clusters has been proposed as a novel means for 3D tissue culture that eliminates the need for artificial scaffolds. However, thus far its efficacy has only been studied by comparing expression levels of generic proteins. Here, it has been evaluated by visualizing the evolution of cell clusters assembled by magnetic forces, to examine their resemblance to in vivo tissues. MATERIALS AND METHODS Cells were labeled with magnetic nanoparticles, then assembled into 3D clusters using magnetic force. Scanning electron microscopy was used to image intercellular interactions and morphological features of the clusters. RESULTS When cells were held together by magnetic forces for a single day, they formed intercellular contacts through extracellular fibers. These kept the clusters intact once the magnetic forces were removed, thus serving the primary function of scaffolds. The cells self-organized into constructs consistent with the corresponding tissues in vivo. Epithelial cells formed sheets while fibroblasts formed spheroids and exhibited position-dependent morphological heterogeneity. Cells on the periphery of a cluster were flattened while those within were spheroidal, a well-known characteristic of connective tissues in vivo. CONCLUSIONS Cells assembled by magnetic forces presented visual features representative of their in vivo states but largely absent in monolayers. This established the efficacy of contactless assembly as a means to fabricate in vitro tissue models.
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Affiliation(s)
- S Ghosh
- Department of Engineering Physics, McMaster University, Hamilton, ON, Canada
| | - S R P Kumar
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland Regional College of Veterinary Medicine, Virginia Tech, Blacksburg, VA, USA
| | - I K Puri
- Department of Engineering Physics, McMaster University, Hamilton, ON, Canada.,Department of Mechanical Engineering, McMaster University, Hamilton, ON, Canada
| | - S Elankumaran
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland Regional College of Veterinary Medicine, Virginia Tech, Blacksburg, VA, USA
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Du V, Fayol D, Reffay M, Luciani N, Bacri JC, Gay C, Wilhelm C. Magnetic engineering of stable rod-shaped stem cell aggregates: circumventing the pitfall of self-bending. Integr Biol (Camb) 2015; 7:170-7. [PMID: 25580701 DOI: 10.1039/c4ib00219a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
A current challenge for tissue engineering while restoring the function of diseased or damaged tissue is to customize the tissue according to the target area. Scaffold-free approaches usually yield spheroid shapes with the risk of necrosis at the center due to poor nutrient and oxygen diffusion. Here, we used magnetic forces developed at the cellular scale by miniaturized magnets to create rod-shaped aggregates of stem cells that subsequently matured into a tissue-like structure. However, during the maturation process, the tissue-rods spontaneously bent and coiled into sphere-like structures, triggered by the increasing cell-cell adhesion within the initially non-homogeneous tissue. Optimisation of the intra-tissular magnetic forces successfully hindered the transition, in order to produce stable rod-shaped stem cells aggregates.
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Affiliation(s)
- V Du
- Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université Paris 7, France.
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10
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Mazuel F, Reffay M, Du V, Bacri JC, Rieu JP, Wilhelm C. Magnetic flattening of stem-cell spheroids indicates a size-dependent elastocapillary transition. PHYSICAL REVIEW LETTERS 2015; 114:098105. [PMID: 25793856 DOI: 10.1103/physrevlett.114.098105] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Indexed: 06/04/2023]
Abstract
Cellular aggregates (spheroids) are widely used in biophysics and tissue engineering as model systems for biological tissues. In this Letter we propose novel methods for molding stem-cell spheroids, deforming them, and measuring their interfacial and elastic properties with a single method based on cell tagging with magnetic nanoparticles and application of a magnetic field gradient. Magnetic molding yields spheroids of unprecedented sizes (up to a few mm in diameter) and preserves tissue integrity. On subjecting these spheroids to magnetic flattening (over 150g), we observed a size-dependent elastocapillary transition with two modes of deformation: liquid-drop-like behavior for small spheroids, and elastic-sphere-like behavior for larger spheroids, followed by relaxation to a liquidlike drop.
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Affiliation(s)
- Francois Mazuel
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS, Université Paris Diderot, 75013 Paris, France
| | - Myriam Reffay
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS, Université Paris Diderot, 75013 Paris, France
| | - Vicard Du
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS, Université Paris Diderot, 75013 Paris, France
| | - Jean-Claude Bacri
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS, Université Paris Diderot, 75013 Paris, France
| | - Jean-Paul Rieu
- Institut Lumière Matière, UMR 5306, Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne cedex, France
| | - Claire Wilhelm
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS, Université Paris Diderot, 75013 Paris, France
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