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Ferraro R, Guido S, Caserta S, Tassieri M. i -Rheo-optical assay: Measuring the viscoelastic properties of multicellular spheroids. Mater Today Bio 2024; 26:101066. [PMID: 38693994 PMCID: PMC11061759 DOI: 10.1016/j.mtbio.2024.101066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Revised: 04/15/2024] [Accepted: 04/18/2024] [Indexed: 05/03/2024] Open
Abstract
This study introduces a novel mechanobiology assay, named "i-Rheo-optical assay", that integrates rheology with optical microscopy for analysing the viscoelastic properties of multicellular spheroids. These spheroids serve as three-dimensional models resembling tissue structures. The innovative technique enables real-time observation and quantification of morphological responses to applied stress using a cost-effective microscope coverslip for constant compression force application. By bridging a knowledge gap in biophysical research, which has predominantly focused on the elastic properties while only minimally exploring the viscoelastic nature in multicellular systems, the i-Rheo-optical assay emerges as an effective tool. It facilitates the measurement of broadband viscoelastic compressional moduli in spheroids, here derived from cancer (PANC-1) and non-tumoral (NIH/3T3) cell lines during compression tests. This approach plays a crucial role in elucidating the mechanical properties of spheroids and holds potential for identifying biomarkers to discriminate between healthy tissues and their pathological counterparts. Offering comprehensive insights into the biomechanical behaviour of biological systems, i-Rheo-optical assay marks a significant advancement in tissue engineering, cancer research, and therapeutic development.
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Affiliation(s)
- Rosalia Ferraro
- DICMaPI, Università di Napoli Federico II, P.le V. Tecchio 80, 80125, Napoli, Italy
- CEINGE Advanced Biotechnologies, Via Gaetano Salvatore, 486, 80131, Napoli, Italy
| | - Stefano Guido
- DICMaPI, Università di Napoli Federico II, P.le V. Tecchio 80, 80125, Napoli, Italy
- CEINGE Advanced Biotechnologies, Via Gaetano Salvatore, 486, 80131, Napoli, Italy
| | - Sergio Caserta
- DICMaPI, Università di Napoli Federico II, P.le V. Tecchio 80, 80125, Napoli, Italy
- CEINGE Advanced Biotechnologies, Via Gaetano Salvatore, 486, 80131, Napoli, Italy
| | - Manlio Tassieri
- Division of Biomedical Engineering, James Watt School of Engineering, Advanced Research Centre, University of Glasgow, Glasgow, G11 6EW, UK
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Rozman J, Yeomans JM, Sknepnek R. Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model. Phys Rev Lett 2023; 131:228301. [PMID: 38101347 DOI: 10.1103/physrevlett.131.228301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 06/26/2023] [Accepted: 10/20/2023] [Indexed: 12/17/2023]
Abstract
We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.
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Affiliation(s)
- Jan Rozman
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Rastko Sknepnek
- School of Science and Engineering, University of Dundee, Dundee DD1 4HN, United Kingdom
- School of Life Sciences, University of Dundee, Dundee DD1 5EH, United Kingdom
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Jensen OE, Revell CK. Couple stresses and discrete potentials in the vertex model of cellular monolayers. Biomech Model Mechanobiol 2023; 22:1465-1486. [PMID: 36201070 PMCID: PMC10511640 DOI: 10.1007/s10237-022-01620-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 07/26/2022] [Indexed: 11/25/2022]
Abstract
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here, we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformations. We develop discrete potential theory for localised monolayers having disordered internal structure and use this to derive the analogues of Airy and Mindlin stress functions. These scalar potentials typically have broad-banded spectra, highlighting the contributions of small-scale defects and boundary layers to global stress patterns. An affine approximation attributes couple stresses to pressure differences between cells sharing a trijunction, but simulations indicate an additional role for non-affine deformations.
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Affiliation(s)
- Oliver E. Jensen
- Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL UK
- Wellcome Trust Centre for Cell-Matrix Research, University of Manchester, Oxford Road, Manchester, M13 9PL UK
| | - Christopher K. Revell
- Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL UK
- Wellcome Trust Centre for Cell-Matrix Research, University of Manchester, Oxford Road, Manchester, M13 9PL UK
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Fielding SM, Cochran JO, Huang J, Bi D, Marchetti MC. Constitutive model for the rheology of biological tissue. Phys Rev E 2023; 108:L042602. [PMID: 37978678 DOI: 10.1103/physreve.108.l042602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
The rheology of biological tissue is key to processes such as embryo development, wound healing, and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquidlike tissue. Alongside this jamming/unjamming behavior, biological tissue also displays an inherent viscoelasticity, with a slow time and rate-dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.
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Affiliation(s)
- Suzanne M Fielding
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, UK
| | - James O Cochran
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, UK
| | - Junxiang Huang
- Department of Physics, Northeastern University, Massachusetts 02115, USA
| | - Dapeng Bi
- Department of Physics, Northeastern University, Massachusetts 02115, USA
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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6
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Staddon MF, Hernandez A, Bowick MJ, Moshe M, Marchetti MC. The role of non-affine deformations in the elastic behavior of the cellular vertex model. Soft Matter 2023; 19:3080-3091. [PMID: 37039037 DOI: 10.1039/d2sm01580c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The vertex model of epithelia describes the apical surface of a tissue as a tiling of polygonal cells, with a mechanical energy governed by deviations in cell shape from preferred, or target, area, A0, and perimeter, P0. The model exhibits a rigidity transition driven by geometric incompatibility as tuned by the target shape index, . For with p*(6) the perimeter of a regular hexagon of unit area, a cell can simultaneously attain both the preferred area and preferred perimeter. As a result, the tissue is in a mechanically soft compatible state, with zero shear and Young's moduli. For p0 < p*(6), it is geometrically impossible for any cell to realize the preferred area and perimeter simultaneously, and the tissue is in an incompatible rigid solid state. Using a mean-field approach, we present a complete analytical calculation of the linear elastic moduli of an ordered vertex model. We analyze a relaxation step that includes non-affine deformations, leading to a softer response than previously reported. The origin of the vanishing shear and Young's moduli in the compatible state is the presence of zero-energy deformations of cell shape. The bulk modulus exhibits a jump discontinuity at the transition and can be lower in the rigid state than in the fluid-like state. The Poisson's ratio can become negative which lowers the bulk and Young's moduli. Our work provides a unified treatment of linear elasticity for the vertex model and demonstrates that this linear response is protocol-dependent.
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Affiliation(s)
- Michael F Staddon
- Center for Systems Biology Dresden, Dresden, Germany.
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Arthur Hernandez
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
| | - Mark J Bowick
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
| | - Michael Moshe
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
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7
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Staddon MF, Murrell MP, Banerjee S. Interplay between substrate rigidity and tissue fluidity regulates cell monolayer spreading. Soft Matter 2022; 18:7877-7886. [PMID: 36205535 PMCID: PMC9700261 DOI: 10.1039/d2sm00757f] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Coordinated and cooperative motion of cells is essential for embryonic development, tissue morphogenesis, wound healing and cancer invasion. A predictive understanding of the emergent mechanical behaviors in collective cell motion is challenging due to the complex interplay between cell-cell interactions, cell-matrix adhesions and active cell behaviors. To overcome this challenge, we develop a predictive cellular vertex model that can delineate the relative roles of substrate rigidity, tissue mechanics and active cell properties on the movement of cell collectives. We apply the model to the specific case of collective motion in cell aggregates as they spread into a two-dimensional cell monolayer adherent to a soft elastic matrix. Consistent with recent experiments, we find that substrate stiffness regulates the driving forces for the spreading of cellular monolayer, which can be pressure-driven or crawling-based depending on substrate rigidity. On soft substrates, cell monolayer spreading is driven by an active pressure due to the influx of cells coming from the aggregate, whereas on stiff substrates, cell spreading is driven primarily by active crawling forces. Our model predicts that cooperation of cell crawling and tissue pressure drives faster spreading, while the spreading rate is sensitive to the mechanical properties of the tissue. We find that solid tissues spread faster on stiff substrates, with spreading rate increasing with tissue tension. By contrast, the spreading of fluid tissues is independent of substrate stiffness and is slower than solid tissues. We compare our theoretical results with experimental results on traction force generation and spreading kinetics of cell monolayers, and provide new predictions on the role of tissue fluidity and substrate rigidity on collective cell motion.
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Affiliation(s)
- Michael F Staddon
- Center for Systems Biology Dresden, Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Michael P Murrell
- Department of Biomedical Engineering and Department of Physics, Yale University, New Haven, CT, USA
- Systems Biology Institute, Yale University, West Haven, CT, USA
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Hopkins A, Chiang M, Loewe B, Marenduzzo D, Marchetti MC. Local Yield and Compliance in Active Cell Monolayers. Phys Rev Lett 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] [What about the content of this article? (0)] [Affiliation(s)] [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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9
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Moisdon É, Seez P, Molino F, Marcq P, Gay C. Mapping cell cortex rheology to tissue rheology and vice versa. Phys Rev E 2022; 106:034403. [PMID: 36266852 DOI: 10.1103/physreve.106.034403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 08/11/2022] [Indexed: 06/16/2023]
Abstract
The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.
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Affiliation(s)
- Étienne Moisdon
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université Paris Cité, 75205 Paris cedex 13, France
| | - Pierre Seez
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université Paris Cité, 75205 Paris cedex 13, France
| | - François Molino
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université de Montpellier, Place Eugène Bataillon, F-34095 Montpellier, France
| | - Philippe Marcq
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université Paris Cité, F-75005 Paris, France
| | - Cyprien Gay
- Laboratoire Matière et Systèmes Complexes, UMR 7057, CNRS and Université Paris Cité, 75205 Paris cedex 13, France
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Hernandez A, Staddon MF, Bowick MJ, Marchetti MC, Moshe M. Anomalous elasticity of a cellular tissue vertex model. Phys Rev E 2022; 105:064611. [PMID: 35854605 DOI: 10.1103/physreve.105.064611] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
Vertex models, such as those used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response. Here we provide a mean-field treatment of a highly simplified model: a uniform network of regular polygons with no topological rearrangements. Since all polygons deform in the same way, we only need to analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. We calculate and measure the mechanical resistance to various deformation protocols and discover that at the onset of rigidity, where a single zero-energy ground state exists, linear elasticity fails to describe the mechanical response to even infinitesimal deformations. In particular, we identify a breakdown of reciprocity expressed via different moduli for compressive and tensile loads, implying nonanalyticity of the energy functional. We give a pictorial representation in configuration space that reveals that the complex elastic response of the vertex model arises from the presence of two distinct sets of reference states (associated with target area and target perimeter). Our results on the critically compatible tissue provide a new route for the design of mechanical metamaterials that violate or extend classical elasticity.
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Affiliation(s)
- Arthur Hernandez
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael F Staddon
- Center for Systems Biology, Dresden 01307, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden 01307, Germany
- Max Planck Institute for the Physics of Complex Systems, Dresden 01187, Germany
| | - Mark J Bowick
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael Moshe
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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