1
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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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3
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Haldar A, Sarkar A, Chatterjee S, Basu A. Active XY model on a substrate: Density fluctuations and phase ordering. Phys Rev E 2023; 108:034114. [PMID: 37849142 DOI: 10.1103/physreve.108.034114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 06/13/2023] [Indexed: 10/19/2023]
Abstract
We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.
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Affiliation(s)
- Astik Haldar
- Theory Division, Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India
| | - Apurba Sarkar
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, West Bengal, India
| | - Swarnajit Chatterjee
- Center for Biophysics & Department for Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Abhik Basu
- Theory Division, Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India
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4
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Rahman T, Peters F, Wan LQ. Cell jamming regulates epithelial chiral morphogenesis. J Biomech 2023; 147:111435. [PMID: 36641827 PMCID: PMC10020895 DOI: 10.1016/j.jbiomech.2023.111435] [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: 02/23/2022] [Revised: 08/24/2022] [Accepted: 01/03/2023] [Indexed: 01/07/2023]
Abstract
Internal organs such as the heart demonstrate apparent left-right (LR) asymmetric morphology and positioning. Cellular chirality and associated LR biased mechanical behavior such as cell migration have been attributed to LR symmetry breaking during embryonic development. Mathematical models have shown that chiral directional migration can be driven by cellular intrinsic torque. Tissue jamming state (i.e., solid-like vs fluid-like state) strongly regulates collective migratory behavior, but how it might affect chiral morphogenesis is still unknown. Here, we develop a cell vertex model to study the role of tissue rigidity or jamming state on chiral morphogenesis of the cells on a patterned ring-shaped tissue, simulating a previously reported experimental setup for measuring cell chirality. We simulate chirality as torsional forces acting on cell vertices. As expected, the cells undergo bidirectional migration at the opposing (inner and outer) boundaries of the ring-shaped tissue. We discover that more fluid-like tissues (unjammed) demonstrate a stronger chiral cell alignment and elongation than more solid-like (jammed) tissues and maintain a bigger difference in migration velocity between opposing tissue boundaries. Finally, we find that fluid-like tissues undergo more cell-neighbor exchange events. This study reveals that chiral torque is sufficient to achieve a biased cellular alignment as seen in vitro. It further sheds light on the mechanical regulation of chiral morphogenesis of tissues and reveals a role of cell density-independent tissue rigidity in this process.
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Affiliation(s)
- Tasnif Rahman
- Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
| | - Frank Peters
- Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
| | - Leo Q Wan
- Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA; Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA; Center for Biotechnology and Interdisciplinary Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA; Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
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5
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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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6
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Zhang DQ, Li ZY, Li B. Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics. Phys Rev E 2022; 105:064607. [PMID: 35854599 DOI: 10.1103/physreve.105.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 05/27/2022] [Indexed: 06/15/2023]
Abstract
Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.
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Affiliation(s)
- De-Qing Zhang
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Zhong-Yi Li
- 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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7
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Lier R, Armas J, Bo S, Duclut C, Jülicher F, Surówka P. Passive odd viscoelasticity. Phys Rev E 2022; 105:054607. [PMID: 35706288 DOI: 10.1103/physreve.105.054607] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2021] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that odd elasticity is not only present in active systems but also in broad classes of passive chiral viscoelastic fluids. In addition, we demonstrate that linear viscoelastic chiral solids require activity in order to manifest odd elastic responses. To model the phenomenon of passive odd viscoelasticity we propose a chiral extension of Jeffreys model. We apply our covariant formalism in order to derive the dispersion relations of hydrodynamic modes and obtain clear imprints of odd viscoelastic behavior.
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Affiliation(s)
- Ruben Lier
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, 01187 Dresden, Germany
| | - Jay Armas
- Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam, The Netherlands
- Dutch Institute for Emergent Phenomena (DIEP), University of Amsterdam, 1090 GL Amsterdam, The Netherlands
| | - Stefano Bo
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Charlie Duclut
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany
| | - Piotr Surówka
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam, The Netherlands
- Dutch Institute for Emergent Phenomena (DIEP), University of Amsterdam, 1090 GL Amsterdam, The Netherlands
- Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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8
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Kole SJ, Alexander GP, Ramaswamy S, Maitra A. Layered Chiral Active Matter: Beyond Odd Elasticity. PHYSICAL REVIEW LETTERS 2021; 126:248001. [PMID: 34213949 DOI: 10.1103/physrevlett.126.248001] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this Letter, starting from active model H^{*}, the general hydrodynamics of a pseudoscalar in a momentum-conserving fluid, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active "odder" elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with an antiferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state-an array of lines on an incompressible, freestanding film of chiral active fluid with a preferred normal direction-is generically unstable. However, this instability can be tuned in easily realizable experimental settings when the film is either on a substrate or in an ambient fluid.
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Affiliation(s)
- S J Kole
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Gareth P Alexander
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Ananyo Maitra
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005 Paris, France
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9
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CYK-1/Formin activation in cortical RhoA signaling centers promotes organismal left-right symmetry breaking. Proc Natl Acad Sci U S A 2021; 118:2021814118. [PMID: 33972425 PMCID: PMC8157923 DOI: 10.1073/pnas.2021814118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Proper left-right symmetry breaking is essential for animal development, and in many cases, this process is actomyosin-dependent. In Caenorhabditis elegans embryos active torque generation in the actomyosin layer promotes left-right symmetry breaking by driving chiral counterrotating cortical flows. While both Formins and Myosins have been implicated in left-right symmetry breaking and both can rotate actin filaments in vitro, it remains unclear whether active torques in the actomyosin cortex are generated by Formins, Myosins, or both. We combined the strength of C. elegans genetics with quantitative imaging and thin film, chiral active fluid theory to show that, while Non-Muscle Myosin II activity drives cortical actomyosin flows, it is permissive for chiral counterrotation and dispensable for chiral symmetry breaking of cortical flows. Instead, we find that CYK-1/Formin activation in RhoA foci is instructive for chiral counterrotation and promotes in-plane, active torque generation in the actomyosin cortex. Notably, we observe that artificially generated large active RhoA patches undergo rotations with consistent handedness in a CYK-1/Formin-dependent manner. Altogether, we conclude that CYK-1/Formin-dependent active torque generation facilitates chiral symmetry breaking of actomyosin flows and drives organismal left-right symmetry breaking in the nematode worm.
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10
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Banerjee D, Vitelli V, Jülicher F, Surówka P. Active Viscoelasticity of Odd Materials. PHYSICAL REVIEW LETTERS 2021; 126:138001. [PMID: 33861116 DOI: 10.1103/physrevlett.126.138001] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Revised: 02/17/2021] [Accepted: 02/19/2021] [Indexed: 06/12/2023]
Abstract
The mechanical response of active media ranging from biological gels to living tissues is governed by a subtle interplay between viscosity and elasticity. We generalize the canonical Kelvin-Voigt and Maxwell models to active viscoelastic media that break both parity and time-reversal symmetries. The resulting continuum theories exhibit viscous and elastic tensors that are both antisymmetric, or odd, under exchange of pairs of indices. We analyze how these parity violating viscoelastic coefficients determine the relaxation mechanisms and wave-propagation properties of odd materials.
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Affiliation(s)
- Debarghya Banerjee
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Vincenzo Vitelli
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
- Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany
| | - Piotr Surówka
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
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11
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The Actomyosin Cortex of Cells: A Thin Film of Active Matter. J Indian Inst Sci 2021. [DOI: 10.1007/s41745-020-00220-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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12
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Maitra A, Lenz M, Voituriez R. Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order. PHYSICAL REVIEW LETTERS 2020; 125:238005. [PMID: 33337208 DOI: 10.1103/physrevlett.125.238005] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 11/06/2020] [Indexed: 06/12/2023]
Abstract
Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.
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Affiliation(s)
- Ananyo Maitra
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005, Paris, France
| | - Martin Lenz
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005, Paris, France
| | - Raphael Voituriez
- Sorbonne Université and CNRS, Laboratoire Jean Perrin, F-75005, Paris, France
- Sorbonne Université and CNRS, Laboratoire de Physique Théorique de la Matière Condensée, F-75005, Paris, France
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13
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Huang ZF, Menzel AM, Löwen H. Dynamical Crystallites of Active Chiral Particles. PHYSICAL REVIEW LETTERS 2020; 125:218002. [PMID: 33274968 DOI: 10.1103/physrevlett.125.218002] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 10/02/2020] [Indexed: 06/12/2023]
Abstract
One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.
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Affiliation(s)
- Zhi-Feng Huang
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA
| | - Andreas M Menzel
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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14
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Li ZY, Zhang DQ, Lin SZ, Li B. Pattern Formation and Defect Ordering in Active Chiral Nematics. PHYSICAL REVIEW LETTERS 2020; 125:098002. [PMID: 32915620 DOI: 10.1103/physrevlett.125.098002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 08/04/2020] [Indexed: 06/11/2023]
Abstract
Many biological systems display intriguing chiral patterns and dynamics. Here, we present an active nematic theory accounting for individual spin to explore the collective handedness in chiral rod-shaped aggregations. We show that coordinated individual spin and motility can engender a vortex-array pattern with chirality and drive ordering of topological defects. During this chiral process, the stationary trefoil-like defects self-organize into a periodic, hexagon-dominated polygonal network, which segregates persistently rotating cometlike defects in pairs within each polygon, leading to a translation symmetry at the global scale while a broken reflection symmetry at the local scale. Such defect ordering agrees exactly with the Voronoi tiling of two-dimensional space and the emergence of the hexagonal symmetry is deciphered in analogy with topological charge neutralization. We calculate energy barriers to the topological transition of the defect ordering and explain the existing metastable states with nonhexagonal polygons. Our findings shed light on the chiral morphodynamics in life processes and also suggest a potential route towards tuning self-organization in active materials.
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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
- 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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15
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Pimpale LG, Middelkoop TC, Mietke A, Grill SW. Cell lineage-dependent chiral actomyosin flows drive cellular rearrangements in early Caenorhabditis elegans development. eLife 2020; 9:54930. [PMID: 32644039 PMCID: PMC7394549 DOI: 10.7554/elife.54930] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 07/05/2020] [Indexed: 12/15/2022] Open
Abstract
Proper positioning of cells is essential for many aspects of development. Daughter cell positions can be specified via orienting the cell division axis during cytokinesis. Rotatory actomyosin flows during division have been implied in specifying and reorienting the cell division axis, but how general such reorientation events are, and how they are controlled, remains unclear. We followed the first nine divisions of Caenorhabditis elegans embryo development and demonstrate that chiral counter-rotating flows arise systematically in early AB lineage, but not in early P/EMS lineage cell divisions. Combining our experiments with thin film active chiral fluid theory we identify a mechanism by which chiral counter-rotating actomyosin flows arise in the AB lineage only, and show that they drive lineage-specific spindle skew and cell reorientation events. In conclusion, our work sheds light on the physical processes that underlie chiral morphogenesis in early development.
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Affiliation(s)
- Lokesh G Pimpale
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
| | - Teije C Middelkoop
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
| | - Alexander Mietke
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.,Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, Dresden, Germany.,Center for Systems Biology Dresden, Dresden, Germany.,Department of Mathematics, Massachusetts Institute of Technology, Cambridge, United States
| | - Stephan W Grill
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,Biotechnology Center, TU Dresden, Dresden, Germany.,Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany
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16
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Epstein JM, Mandadapu KK. Time-reversal symmetry breaking in two-dimensional nonequilibrium viscous fluids. Phys Rev E 2020; 101:052614. [PMID: 32575182 DOI: 10.1103/physreve.101.052614] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Accepted: 05/05/2020] [Indexed: 06/11/2023]
Abstract
We study the rheological signatures of departure from equilibrium in two-dimensional viscous fluids with and without internal spin. Under the assumption of isotropy, we provide the most general linear constitutive relations for stress and couple stress in terms of the velocity and spin fields. Invoking Onsager's regression hypothesis for fluctuations about steady states, we derive the Green-Kubo formulas relating the transport coefficients to time-correlation functions of the fluctuating stress. In doing so, we show that one of the nonequilibrium transport coefficients, the odd viscosity, requires time-reversal symmetry breaking in the case of systems without internal spin. However, the Green-Kubo relations for systems with internal spin also show that there is a possibility for nonvanishing odd viscosity even when time-reversal symmetry is preserved. Furthermore, we find that breakdown of equipartition in nonequilibrium steady states results in the decoupling of the two rotational viscosities relating the vorticity and the internal spin.
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Affiliation(s)
- Jeffrey M Epstein
- Department of Physics, University of California, Berkeley, California, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA
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17
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Yang X, Ren C, Cheng K, Zhang HP. Robust boundary flow in chiral active fluid. Phys Rev E 2020; 101:022603. [PMID: 32168608 DOI: 10.1103/physreve.101.022603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 01/24/2020] [Indexed: 06/10/2023]
Abstract
We perform experiments on an active chiral fluid system of self-spinning rotors in a confining boundary. Along the boundary, actively rotating rotors collectively drive a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction ϕ); peak strength appears around a density ϕ=0.65. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary. Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions.
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Affiliation(s)
- Xiang Yang
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Chenyang Ren
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Kangjun Cheng
- Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China
| | - H P Zhang
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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18
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Hoffmann LA, Schakenraad K, Merks RMH, Giomi L. Chiral stresses in nematic cell monolayers. SOFT MATTER 2020; 16:764-774. [PMID: 31830190 DOI: 10.1039/c9sm01851d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation.
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Affiliation(s)
- Ludwig A Hoffmann
- Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
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19
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Markovich T, Tjhung E, Cates ME. Shear-Induced First-Order Transition in Polar Liquid Crystals. PHYSICAL REVIEW LETTERS 2019; 122:088004. [PMID: 30932571 DOI: 10.1103/physrevlett.122.088004] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Indexed: 06/09/2023]
Abstract
The hydrodynamic theory of polar liquid crystals is widely used to describe biological active fluids as well as passive molecular materials. Depending on the "shear-alignment parameter", in passive or weakly active polar fluids under external shear, the polar order parameter p is either inclined to the flow at a fixed (Leslie) angle, or rotates continuously. Here, we study the role of an additional "shear-elongation parameter" that has been neglected in the recent literature and causes |p| to change under flow. We show that this effect can give rise to a shear-induced first-order phase transition from isotropic to polar, and significantly change the rheological properties of both active and passive polar fluids.
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Affiliation(s)
- Tomer Markovich
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Elsen Tjhung
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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20
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Maitra A, Lenz M. Spontaneous rotation can stabilise ordered chiral active fluids. Nat Commun 2019; 10:920. [PMID: 30796222 PMCID: PMC6385212 DOI: 10.1038/s41467-019-08914-7] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Accepted: 02/06/2019] [Indexed: 12/05/2022] Open
Abstract
Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present a complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation-which drives chaotic flows in non-rotating active fluids-is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilisation in active systems, which could be key in interpreting the collective behaviors of some biological tissues, cytoskeletal systems and collections of bacteria.
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Affiliation(s)
- Ananyo Maitra
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France.
| | - Martin Lenz
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France.
- MultiScale Material Science for Energy and Environment, UMI 3466, CNRS-MIT, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA.
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21
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Naganathan SR, Fürthauer S, Rodriguez J, Fievet BT, Jülicher F, Ahringer J, Cannistraci CV, Grill SW. Morphogenetic degeneracies in the actomyosin cortex. eLife 2018; 7:37677. [PMID: 30346273 PMCID: PMC6226289 DOI: 10.7554/elife.37677] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Accepted: 10/16/2018] [Indexed: 01/07/2023] Open
Abstract
One of the great challenges in biology is to understand the mechanisms by which morphogenetic processes arise from molecular activities. We investigated this problem in the context of actomyosin-based cortical flow in C. elegans zygotes, where large-scale flows emerge from the collective action of actomyosin filaments and actin binding proteins (ABPs). Large-scale flow dynamics can be captured by active gel theory by considering force balances and conservation laws in the actomyosin cortex. However, which molecular activities contribute to flow dynamics and large-scale physical properties such as viscosity and active torque is largely unknown. By performing a candidate RNAi screen of ABPs and actomyosin regulators we demonstrate that perturbing distinct molecular processes can lead to similar flow phenotypes. This is indicative for a ‘morphogenetic degeneracy’ where multiple molecular processes contribute to the same large-scale physical property. We speculate that morphogenetic degeneracies contribute to the robustness of bulk biological matter in development.
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Affiliation(s)
| | - Sebastian Fürthauer
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.,Center for Computational Biology, Flatiron Institute, New York, United States
| | - Josana Rodriguez
- Institute for Cell and Molecular Biosciences, Newcastle University, Newcastle, United Kingdom.,Wellcome Trust/Cancer Research UK Gurdon Institute, Cambridge, United Kingdom
| | - Bruno Thomas Fievet
- Wellcome Trust/Cancer Research UK Gurdon Institute, Cambridge, United Kingdom
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Julie Ahringer
- Wellcome Trust/Cancer Research UK Gurdon Institute, Cambridge, United Kingdom
| | - Carlo Vittorio Cannistraci
- BIOTEC, Technische Universität Dresden, Dresden, Germany.,Brain Bio-Inspired Computing (BBC) Lab, IRCCS Centro Neurolesi "Bonino Pulejo", Messina, Italy
| | - Stephan W Grill
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.,BIOTEC, Technische Universität Dresden, Dresden, Germany
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22
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Dasbiswas K, Mandadapu KK, Vaikuntanathan S. Topological localization in out-of-equilibrium dissipative systems. Proc Natl Acad Sci U S A 2018; 115:E9031-E9040. [PMID: 30206153 PMCID: PMC6166820 DOI: 10.1073/pnas.1721096115] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this paper, we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We consider two physically disparate systems: stochastic networks governed by microscopic single-particle dynamics, and collections of driven interacting particles described by coarse-grained hydrodynamic theory. We derive our results by mapping to well-known electronic models and exploiting the resulting correspondence between a bulk topological number and the spectrum of dissipative modes localized at the boundary. For the Markov networks, we report a general procedure to uncover the topological properties in terms of the transition rates. For the active fluid on a substrate, we introduce a topological interpretation of fluid dissipative modes at the edge. In both cases, the presence of dissipative couplings to the environment that break time-reversal symmetry are crucial to ensuring topological protection. These examples constitute proof of principle that notions of topological protection do indeed extend to dissipative processes operating out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.
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Affiliation(s)
- Kinjal Dasbiswas
- The James Franck Institute, The University of Chicago, Chicago, IL 60637
- Department of Physics, University of California, Merced, CA 95343
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
| | - Suriyanarayanan Vaikuntanathan
- The James Franck Institute, The University of Chicago, Chicago, IL 60637;
- Department of Chemistry, The University of Chicago, Chicago, IL 60637
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23
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Jülicher F, Grill SW, Salbreux G. Hydrodynamic theory of active matter. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:076601. [PMID: 29542442 DOI: 10.1088/1361-6633/aab6bb] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2024]
Abstract
We review the general hydrodynamic theory of active soft materials that is motivated in particular by biological matter. We present basic concepts of irreversible thermodynamics of spatially extended multicomponent active systems. Starting from the rate of entropy production, we identify conjugate thermodynamic fluxes and forces and present generic constitutive equations of polar active fluids and active gels. We also discuss angular momentum conservation which plays a role in the the physics of active chiral gels. The irreversible thermodynamics of active gels provides a general framework to discuss the physics that underlies a wide variety of biological processes in cells and in multicellular tissues.
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Affiliation(s)
- Frank Jülicher
- Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany
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24
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Duclos G, Blanch-Mercader C, Yashunsky V, Salbreux G, Joanny JF, Prost J, Silberzan P. Spontaneous shear flow in confined cellular nematics. NATURE PHYSICS 2018; 14:728-732. [PMID: 30079095 PMCID: PMC6071846 DOI: 10.1038/s41567-018-0099-7] [Citation(s) in RCA: 93] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Accepted: 03/05/2018] [Indexed: 05/18/2023]
Abstract
In embryonic development or tumor evolution, cells often migrate collectively within confining tracks defined by their microenvironment 1,2. In some of these situations, the displacements within a cell strand are antiparallel 3, giving rise to shear flows. However, the mechanisms underlying these spontaneous flows remain poorly understood. Here, we show that an ensemble of spindle-shaped cells plated in a well-defined stripe spontaneously develop a shear flow whose characteristics depend on the width of the stripe. On wide stripes, the cells self-organize in a nematic phase with a director at a well-defined angle with the stripe's direction, and develop a shear flow close to the stripe's edges. However, on stripes narrower than a critical width, the cells perfectly align with the stripe's direction and the net flow vanishes. A hydrodynamic active gel theory provides an understanding of these observations and identifies the transition between the non-flowing phase oriented along the stripe and the tilted phase exhibiting shear flow as a Fréedericksz transition driven by the activity of the cells. This physical theory is grounded in the active nature of the cells and based on symmetries and conservation laws, providing a generic mechanism to interpret in vivo antiparallel cell displacements.
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Affiliation(s)
- G. Duclos
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
| | - C. Blanch-Mercader
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
| | - V. Yashunsky
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
| | | | - J.-F. Joanny
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
- ESPCI Paris, Paris, France
| | - J. Prost
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
- Mechanobiology Institute, National University of Singapore,
Singapore
| | - P. Silberzan
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research
University - Sorbonne Universités, UPMC – CNRS. Equipe
labellisée Ligue Contre le Cancer ; 75005, Paris, France
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25
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Nandi SK. Activity-dependent self-regulation of viscous length scales in biological systems. Phys Rev E 2018; 97:052404. [PMID: 29906984 DOI: 10.1103/physreve.97.052404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Indexed: 06/08/2023]
Abstract
The cellular cortex, which is a highly viscous thin cytoplasmic layer just below the cell membrane, controls the cell's mechanical properties, which can be characterized by a hydrodynamic length scale ℓ. Cells actively regulate ℓ via the activity of force-generating molecules, such as myosin II. Here we develop a general theory for such systems through a coarse-grained hydrodynamic approach including activity in the static description of the system providing an experimentally accessible parameter and elucidate the detailed mechanism of how a living system can actively self-regulate its hydrodynamic length scale, controlling the rigidity of the system. Remarkably, we find that ℓ, as a function of activity, behaves universally and roughly inversely proportional to the activity of the system. Our theory rationalizes a number of experimental findings on diverse systems, and comparison of our theory with existing experimental data shows good agreement.
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Affiliation(s)
- Saroj Kumar Nandi
- Max-Planck Institute für Physik Komplexer Systeme, 01187 Dresden, Germany
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26
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Abstract
We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or reconstituted active systems on surfaces. We introduce forces and torques acting on a surface, and derive the associated force balance conditions. We show that surfaces with in-plane rotational symmetry can have broken up-down, chiral, or planar-chiral symmetry. We discuss the rate of entropy production in the surface and write linear constitutive relations that satisfy the Onsager relations. We show that the bending modulus, the spontaneous curvature, and the surface tension of a passive surface are renormalized by active terms. Finally, we identify active terms which are not found in a passive theory and discuss examples of shape instabilities that are related to active processes in the surface.
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Affiliation(s)
- Guillaume Salbreux
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, United Kingdom
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
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27
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Banerjee T, Basu A. Active hydrodynamics of synchronization and ordering in moving oscillators. Phys Rev E 2017; 96:022201. [PMID: 28950575 DOI: 10.1103/physreve.96.022201] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Indexed: 11/07/2022]
Abstract
The nature of emergent collective behaviors of moving interacting physical agents is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and the degree of order in a collection of diffusively moving noisy oscillators. We address this by constructing a generic hydrodynamic theory for active phase fluctuations in a collection of a large number of nearly-phase-coherent moving oscillators in two dimensions. Our theory describes the general situation where phase fluctuations and oscillator mobility mutually affect each other. We show that the interplay between the active effects and the mobility of the oscillators leads to a variety of phenomena, ranging from synchronization with long-range, nearly-long-range, and quasi-long-range orders to instabilities and desynchronization with short-range order of the oscillator phases. We highlight the complex dependences of synchronization on the active effects. These should be testable in wide-ranging systems, e.g., oscillating chemical reactions in the presence of different reaction inhibitors and facilitators, live oriented cytoskeletal extracts, and vertebrate segmentation clocks.
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Affiliation(s)
- Tirthankar Banerjee
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India
| | - Abhik Basu
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India
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28
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Sato K. Direction‐dependent contraction forces on cell boundaries induce collective migration of epithelial cells within their sheet. Dev Growth Differ 2017. [DOI: 10.1111/dgd.12361] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Katsuhiko Sato
- Research Institute for Electronic Science Hokkaido University Sapporo 001‐0020 Japan
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29
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Gross P, Kumar KV, Grill SW. How Active Mechanics and Regulatory Biochemistry Combine to Form Patterns in Development. Annu Rev Biophys 2017; 46:337-356. [DOI: 10.1146/annurev-biophys-070816-033602] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Peter Gross
- BIOTEC, Technische Universität Dresden, 01307 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - K. Vijay Kumar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Stephan W. Grill
- BIOTEC, Technische Universität Dresden, 01307 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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30
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Whitfield CA, Adhyapak TC, Tiribocchi A, Alexander GP, Marenduzzo D, Ramaswamy S. Hydrodynamic instabilities in active cholesteric liquid crystals. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:50. [PMID: 28429181 DOI: 10.1140/epje/i2017-11536-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Accepted: 03/23/2017] [Indexed: 06/07/2023]
Abstract
We describe the basic properties and consequences of introducing active stresses, with principal direction along the local director, in cholesteric liquid crystals. The helical ground state is found to be linearly unstable to extensile stresses, without threshold in the limit of infinite system size, whereas contractile stresses are hydrodynamically screened by the cholesteric elasticity to give a finite threshold. This is confirmed numerically and the non-linear consequences of instability, in both extensile and contractile cases, are studied. We also consider the stresses associated to defects in the cholesteric pitch ([Formula: see text] lines) and show how the geometry near to the defect generates threshold-less flows reminiscent of those for defects in active nematics. At large extensile activity [Formula: see text] lines are spontaneously created and can form steady-state patterns sustained by constant active flows.
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Affiliation(s)
- Carl A Whitfield
- Department of Physics, University of Warwick, CV4 7AL, Coventry, UK
| | - Tapan Chandra Adhyapak
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128, Mainz, Germany
| | - Adriano Tiribocchi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, I-35131, Padova, Italy
| | - Gareth P Alexander
- Department of Physics, University of Warwick, CV4 7AL, Coventry, UK.
- Centre for Complexity Science, University of Warwick, CV4 7AL, Coventry, UK.
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, JCMB Kings Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK
| | - Sriram Ramaswamy
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, 500 075, Narsingi, Hyderabad, India
- Department of Physics, Indian Institute of Science, 560 012, Bangalore, India
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31
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Tao J, Li Y, Vig DK, Sun SX. Cell mechanics: a dialogue. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:036601. [PMID: 28129208 PMCID: PMC5518794 DOI: 10.1088/1361-6633/aa5282] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Under the microscope, eukaryotic animal cells can adopt a variety of different shapes and sizes. These cells also move and deform, and the physical mechanisms driving these movements and shape changes are important in fundamental cell biology, tissue mechanics, as well as disease biology. This article reviews some of the basic mechanical concepts in cells, emphasizing continuum mechanics description of cytoskeletal networks and hydrodynamic flows across the cell membrane. We discuss how cells can generate movement and shape changes by controlling mass fluxes at the cell boundary. These mass fluxes can come from polymerization/depolymerization of actin cytoskeleton, as well as osmotic and hydraulic pressure-driven flow of water across the cell membrane. By combining hydraulic pressure control with force balance conditions at the cell surface, we discuss a quantitative mechanism of cell shape and volume control. The broad consequences of this model on cell mechanosensation and tissue mechanics are outlined.
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Affiliation(s)
- Jiaxiang Tao
- Departments of Mechanical Engineering, Johns Hopkins University, Baltimore MD, United States of America
- Physical Sciences in Oncology Center, Johns Hopkins University, Baltimore MD, United States of America
| | - Yizeng Li
- Departments of Mechanical Engineering, Johns Hopkins University, Baltimore MD, United States of America
- Institute of NanoBioTechnology, Johns Hopkins University, Baltimore MD, United States of America
| | - Dhruv K Vig
- Departments of Mechanical Engineering, Johns Hopkins University, Baltimore MD, United States of America
- Institute of NanoBioTechnology, Johns Hopkins University, Baltimore MD, United States of America
| | - Sean X Sun
- Departments of Mechanical Engineering, Johns Hopkins University, Baltimore MD, United States of America
- Biomedical Engineering, Johns Hopkins University, Baltimore MD, United States of America
- Physical Sciences in Oncology Center, Johns Hopkins University, Baltimore MD, United States of America
- Institute of NanoBioTechnology, Johns Hopkins University, Baltimore MD, United States of America
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32
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Abstract
A new study reports that dynamic actin fibers in cells on circular islands self-organize into a swirling counter-clockwise pattern and describes a basic cytoskeletal mechanism for the establishment of left-right asymmetry that is based on myosin contraction and twisting of the formin-actin filament.
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Affiliation(s)
- Alex Mogilner
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; Department of Biology, New York University, 100 Washington Square East, 1009 Silver Center, New York, NY 10003, USA.
| | - Ben Fogelson
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
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33
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Spatiotemporal order and emergent edge currents in active spinner materials. Proc Natl Acad Sci U S A 2016; 113:12919-12924. [PMID: 27803323 DOI: 10.1073/pnas.1609572113] [Citation(s) in RCA: 90] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion (i.e., spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behavior of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-assemble into a triangular lattice with their orientations phase-locked into spatially periodic phases. The phase-locked patterns form dynamical analogs of the ground states of various spin models, transitioning from the three-state Potts antiferromagnet at low densities to the striped herringbone phase of planar quadrupoles at higher densities. As the density is raised further, the competition between active rotations and interactions leads to melting of the active spinner crystal. Emergent edge currents, whose direction is set by the chirality of the active spinning, arise as a nonequilibrium signature of the transition to the active spinner liquid and vanish when the system eventually undergoes kinetic arrest at very high densities. Our findings may be realized in systems ranging from liquid crystal and colloidal experiments to tabletop realizations using macroscopic chiral grains.
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Denk J, Huber L, Reithmann E, Frey E. Active Curved Polymers Form Vortex Patterns on Membranes. PHYSICAL REVIEW LETTERS 2016; 116:178301. [PMID: 27176542 DOI: 10.1103/physrevlett.116.178301] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Indexed: 06/05/2023]
Abstract
Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.
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Affiliation(s)
- Jonas Denk
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Lorenz Huber
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Emanuel Reithmann
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
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Naganathan SR, Middelkoop TC, Fürthauer S, Grill SW. Actomyosin-driven left-right asymmetry: from molecular torques to chiral self organization. Curr Opin Cell Biol 2016; 38:24-30. [DOI: 10.1016/j.ceb.2016.01.004] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Revised: 01/08/2016] [Accepted: 01/11/2016] [Indexed: 10/22/2022]
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Sato K, Hiraiwa T, Shibata T. Cell Chirality Induces Collective Cell Migration in Epithelial Sheets. PHYSICAL REVIEW LETTERS 2015; 115:188102. [PMID: 26565500 DOI: 10.1103/physrevlett.115.188102] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2014] [Indexed: 06/05/2023]
Abstract
During early development, epithelial cells form a monolayer sheet and migrate in a uniform direction. Here, we address how this collective migration can occur without breaking the cell-to-cell attachments. Repeated contraction and expansion of the cell-to-cell interfaces enables the cells to rearrange their positions autonomously within the sheet. We show that when the interface tension is strengthened in a direction that is tilted from the body axis, cell rearrangements occur in such a way that unidirectional movement is induced. We use a vertex model to demonstrate that such anisotropic tension can generate the unidirectional motion of cell sheets. Our results suggest that cell chirality facilitates collective cell migration during tissue morphogenesis.
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Affiliation(s)
- Katsuhiko Sato
- RIKEN Center for Developmental Biology, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe 650-0047, Japan
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0020, Japan
| | - Tetsuya Hiraiwa
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
- Department of Physics, Graduate School of Science, The University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Tatsuo Shibata
- RIKEN Center for Developmental Biology, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe 650-0047, Japan
- RIKEN Quantitative Biology Center, Kobe 650-0047, Japan
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37
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Yeo K, Lushi E, Vlahovska PM. Collective dynamics in a binary mixture of hydrodynamically coupled microrotors. PHYSICAL REVIEW LETTERS 2015; 114:188301. [PMID: 26001020 DOI: 10.1103/physrevlett.114.188301] [Citation(s) in RCA: 59] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2014] [Indexed: 06/04/2023]
Abstract
We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.
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Affiliation(s)
- Kyongmin Yeo
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
- Division of Applied Mathematics, Brown University, Rhode Island 02912, USA
| | - Enkeleida Lushi
- School of Engineering, Brown University, Rhode Island 02912, USA
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38
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Elgeti J, Winkler RG, Gompper G. Physics of microswimmers--single particle motion and collective behavior: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:056601. [PMID: 25919479 DOI: 10.1088/0034-4885/78/5/056601] [Citation(s) in RCA: 624] [Impact Index Per Article: 69.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
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Affiliation(s)
- J Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
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39
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Petroff AP, Wu XL, Libchaber A. Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells. PHYSICAL REVIEW LETTERS 2015; 114:158102. [PMID: 25933342 DOI: 10.1103/physrevlett.114.158102] [Citation(s) in RCA: 107] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/04/2023]
Abstract
We investigate a new form of collective dynamics displayed by Thiovulum majus, one of the fastest-swimming bacteria known. Cells spontaneously organize on a surface into a visually striking two-dimensional hexagonal lattice of rotating cells. As each constituent cell rotates its flagella, it creates a tornadolike flow that pulls neighboring cells towards and around it. As cells rotate against their neighbors, they exert forces on one another, causing the crystal to rotate and cells to reorganize. We show how these dynamics arise from hydrodynamic and steric interactions between cells. We derive the equations of motion for a crystal, show that this model explains several aspects of the observed dynamics, and discuss the stability of these active crystals.
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Affiliation(s)
- Alexander P Petroff
- Laboratory of Experimental Condensed Matter Physics, The Rockefeller University, New York, New York 10065, USA
| | - Xiao-Lun Wu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Albert Libchaber
- Laboratory of Experimental Condensed Matter Physics, The Rockefeller University, New York, New York 10065, USA
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40
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41
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Cellular chirality arising from the self-organization of the actin cytoskeleton. Nat Cell Biol 2015; 17:445-57. [DOI: 10.1038/ncb3137] [Citation(s) in RCA: 284] [Impact Index Per Article: 31.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Accepted: 02/13/2015] [Indexed: 12/12/2022]
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Naganathan SR, Fürthauer S, Nishikawa M, Jülicher F, Grill SW. Active torque generation by the actomyosin cell cortex drives left-right symmetry breaking. eLife 2014; 3:e04165. [PMID: 25517077 PMCID: PMC4269833 DOI: 10.7554/elife.04165] [Citation(s) in RCA: 154] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Accepted: 11/12/2014] [Indexed: 12/11/2022] Open
Abstract
Many developmental processes break left-right (LR) symmetry with a consistent handedness. LR asymmetry emerges early in development, and in many species the primary determinant of this asymmetry has been linked to the cytoskeleton. However, the nature of the underlying chirally asymmetric cytoskeletal processes has remained elusive. In this study, we combine thin-film active chiral fluid theory with experimental analysis of the C. elegans embryo to show that the actomyosin cortex generates active chiral torques to facilitate chiral symmetry breaking. Active torques drive chiral counter-rotating cortical flow in the zygote, depend on myosin activity, and can be altered through mild changes in Rho signaling. Notably, they also execute the chiral skew event at the 4-cell stage to establish the C. elegans LR body axis. Taken together, our results uncover a novel, large-scale physical activity of the actomyosin cytoskeleton that provides a fundamental mechanism for chiral morphogenesis in development.
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Affiliation(s)
- Sundar Ram Naganathan
- Biotechnology Center, Technical University 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
| | - Sebastian Fürthauer
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Masatoshi Nishikawa
- Biotechnology Center, Technical University 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
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Stephan W Grill
- Biotechnology Center, Technical University 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
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43
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Fürthauer S, Ramaswamy S. Phase-synchronized state of oriented active fluids. PHYSICAL REVIEW LETTERS 2013; 111:238102. [PMID: 24476307 DOI: 10.1103/physrevlett.111.238102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2013] [Indexed: 06/03/2023]
Abstract
We present a theory for self-driven fluids, such as motorized cytoskeletal extracts or microbial suspensions, that takes into account the underlying periodic duty cycle carried by the constituent active particles. We show that an orientationally ordered active fluid can undergo a transition to a state in which the particles synchronize their phases. This spontaneous breaking of time-translation invariance gives rise to flow instabilities distinct from those arising in phase-incoherent active matter. Our work is of relevance to the transport of fluids in living systems and makes predictions for concentrated active-particle suspensions and optically driven colloidal arrays.
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Affiliation(s)
- Sebastian Fürthauer
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 089, India
| | - Sriram Ramaswamy
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500 089, India
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Ledesma-Aguilar R, Yeomans JM. Enhanced motility of a microswimmer in rigid and elastic confinement. PHYSICAL REVIEW LETTERS 2013; 111:138101. [PMID: 24116818 DOI: 10.1103/physrevlett.111.138101] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Revised: 08/05/2013] [Indexed: 06/02/2023]
Abstract
We analyze the effect of confining rigid and elastic boundaries on the motility of a model dipolar microswimmer. Flexible boundaries are deformed by the velocity field of the swimmer in such a way that the motility of both extensile and contractile swimmers is enhanced. The magnitude of the increase in swimming velocity is controlled by the ratio of the swimmer-advection and elastic time scales, and the dipole moment of the swimmer. We explain our results by considering swimming between inclined rigid boundaries.
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Affiliation(s)
- Rodrigo Ledesma-Aguilar
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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