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Li ZY, Chen YP, Liu HY, Li B. Three-Dimensional Chiral Morphogenesis of Active Fluids. PHYSICAL REVIEW LETTERS 2024; 132:138401. [PMID: 38613297 DOI: 10.1103/physrevlett.132.138401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 02/29/2024] [Indexed: 04/14/2024]
Abstract
Chirality is an essential nature of biological systems. However, it remains obscure how the handedness at the microscale is translated into chiral morphogenesis at the tissue level. Here, we investigate three-dimensional (3D) tissue morphogenesis using an active fluid theory invoking chirality. We show that the coordination of achiral and chiral stresses, arising from microscopic interactions and energy input of individual cells, can engender the self-organization of 3D papillary and helical structures. The achiral active stress drives the nucleation of asterlike topological defects, which initiate 3D out-of-plane budding, followed by rodlike elongation. The chiral active stress excites vortexlike topological defects, which favor the tip spheroidization and twisting of the elongated rod. These results unravel the chiral morphogenesis observed in our experiments of 3D organoids generated by human embryonic stem cells.
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Affiliation(s)
- Zhong-Yi Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Yun-Ping Chen
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Hao-Yu Liu
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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2
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Wang W, Ren H, Zhang R. Symmetry Breaking of Self-Propelled Topological Defects in Thin-Film Active Chiral Nematics. PHYSICAL REVIEW LETTERS 2024; 132:038301. [PMID: 38307071 DOI: 10.1103/physrevlett.132.038301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2023] [Revised: 10/09/2023] [Accepted: 11/28/2023] [Indexed: 02/04/2024]
Abstract
Active nematics represent a range of dense active matter systems which can engender spontaneous flows and self-propelled topological defects. Two-dimensional (2D) active nematic theory and simulation have been successful in explaining many quasi-2D experiments in which self-propelled +1/2 defects are observed to move along their symmetry axis. However, many active liquid crystals are essentially chiral nematic, but their twist mode becomes irrelevant under the 2D assumption. Here, we use theory and simulation to examine a three-dimensional active chiral nematic confined to a thin film, thus forming a quasi-2D system. We predict that the self-propelled +1/2 disclination in a curved thin film can break its mirror symmetry by moving circularly. Our prediction is confirmed by hydrodynamic simulations of thin spherical-shell and thin cylindrical-shell systems. In the spherical-shell confinement, the four emerged +1/2 disclinations exhibit rich dynamics as a function of activity and chirality. As such, we have proposed a new symmetry-breaking scenario in which self-propelled defects in quasi-2D active nematics can acquire an active angular velocity, greatly enriching their dynamics for finer control and emerging applications.
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Affiliation(s)
- Weiqiang Wang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Haijie Ren
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Rui Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
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Chattopadhyay J, Ramaswamy S, Dasgupta C, Maiti PK. Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium. Phys Rev E 2023; 107:024701. [PMID: 36932588 DOI: 10.1103/physreve.107.024701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 01/17/2023] [Indexed: 02/08/2023]
Abstract
In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.
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Affiliation(s)
- Jayeeta Chattopadhyay
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Ascione F, Caserta S, Esposito S, Villella VR, Maiuri L, Nejad MR, Doostmohammadi A, Yeomans JM, Guido S. Collective rotational motion of freely expanding T84 epithelial cell colonies. J R Soc Interface 2023; 20:20220719. [PMID: 36872917 PMCID: PMC9943890 DOI: 10.1098/rsif.2022.0719] [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] [Indexed: 02/25/2023] Open
Abstract
Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.
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Affiliation(s)
- Flora Ascione
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
| | - Sergio Caserta
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- CEINGE Biotecnologie Avanzate, Via Sergio Pansini 5, 80131 Naples, Italy
| | - Speranza Esposito
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Valeria Rachela Villella
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Luigi Maiuri
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Mehrana R. Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | | | - Julia M. Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Stefano Guido
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- CEINGE Biotecnologie Avanzate, Via Sergio Pansini 5, 80131 Naples, Italy
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Shimaya T, Takeuchi KA. Tilt-induced polar order and topological defects in growing bacterial populations. PNAS NEXUS 2022; 1:pgac269. [PMID: 36712383 PMCID: PMC9802490 DOI: 10.1093/pnasnexus/pgac269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 11/30/2022] [Indexed: 12/24/2022]
Abstract
Rod-shaped bacteria, such as Escherichia coli, commonly live forming mounded colonies. They initially grow two-dimensionally on a surface and finally achieve three-dimensional growth. While it was recently reported that three-dimensional growth is promoted by topological defects of winding number +1/2 in populations of motile bacteria, how cellular alignment plays a role in nonmotile cases is largely unknown. Here, we investigate the relevance of topological defects in colony formation processes of nonmotile E. coli populations, and found that both ±1/2 topological defects contribute to the three-dimensional growth. Analyzing the cell flow in the bottom layer of the colony, we observe that +1/2 defects attract cells and -1/2 defects repel cells, in agreement with previous studies on motile cells, in the initial stage of the colony growth. However, later, cells gradually flow toward -1/2 defects as well, exhibiting a sharp contrast to the existing knowledge. By investigating three-dimensional cell orientations by confocal microscopy, we find that vertical tilting of cells is promoted near the defects. Crucially, this leads to the emergence of a polar order in the otherwise nematic two-dimensional cell orientation. We extend the theory of active nematics by incorporating this polar order and the vertical tilting, which successfully explains the influx toward -1/2 defects in terms of a polarity-induced force. Our work reveals that three-dimensional cell orientations may result in qualitative changes in properties of active nematics, especially those of topological defects, which may be generically relevant in active matter systems driven by cellular growth instead of self-propulsion.
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Affiliation(s)
- Takuro Shimaya
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-0033 Tokyo, Japan
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Najma B, Varghese M, Tsidilkovski L, Lemma L, Baskaran A, Duclos G. Competing instabilities reveal how to rationally design and control active crosslinked gels. Nat Commun 2022; 13:6465. [PMID: 36309493 PMCID: PMC9617906 DOI: 10.1038/s41467-022-34089-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 10/13/2022] [Indexed: 12/25/2022] Open
Abstract
How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.
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Affiliation(s)
- Bibi Najma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Minu Varghese
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.214458.e0000000086837370Department of Physics, University of Michigan, Ann Arbor, MI 48109 USA
| | - Lev Tsidilkovski
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Linnea Lemma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.133342.40000 0004 1936 9676Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106 USA ,grid.16750.350000 0001 2097 5006Present Address: Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544 USA
| | - Aparna Baskaran
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Guillaume Duclos
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
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Li ZY, Zhang DQ, Lin SZ, Góźdź WT, Li B. Spontaneous organization and phase separation of skyrmions in chiral active matter. SOFT MATTER 2022; 18:7348-7359. [PMID: 36124977 DOI: 10.1039/d2sm00819j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Skyrmions are topologically protected vortex-like excitations that hold promise for applications such as information processing and electron manipulation. Here we combine theoretical analysis and numerical simulations to show that skyrmions can spontaneously emerge in chiral active matter without external confinements or regulation. Strikingly, these activity-driven skyrmions can either self-organize into a periodic, stable square lattice consisting of half Néel skyrmions and antiskyrmions, where the in-plane flows display an antiferromagnetic vortex array, or undergo phase separation between skyrmions with different topological numbers. We identify that the emerging skyrmion dynamics stems from the competition between the chiral and polar coherence length scales dictated by the interplay of intrinsic chirality, polarity, and elasticity in the system. Our results reveal unanticipated topological excitations, self-organization, and phase separation in non-equilibrium systems and also suggest a potential way towards engineering complicated bespoke skyrmionic structures through manipulating active matter.
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Affiliation(s)
- Zhong-Yi Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - De-Qing Zhang
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - Shao-Zhen Lin
- Aix Marseille Université, CNRS, Centre de Physique Théorique, Turing Center for Living Systems, 13009 Marseille, France
| | - Wojciech T Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
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Ruske LJ, Yeomans JM. Activity gradients in two- and three-dimensional active nematics. SOFT MATTER 2022; 18:5654-5661. [PMID: 35861255 DOI: 10.1039/d2sm00228k] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.
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Affiliation(s)
- Liam J Ruske
- Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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Brézin L, Risler T, Joanny JF. Spontaneous flow created by active topological defects. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:30. [PMID: 35389081 DOI: 10.1140/epje/s10189-022-00186-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.
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Affiliation(s)
- Louis Brézin
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France
- Collège de France, 75005, Paris, France
| | - Thomas Risler
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France.
| | - Jean-Francois Joanny
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France
- Collège de France, 75005, Paris, France
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