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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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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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Hoffmann LA, Carenza LN, Eckert J, Giomi L. Theory of defect-mediated morphogenesis. SCIENCE ADVANCES 2022; 8:eabk2712. [PMID: 35427161 PMCID: PMC9012457 DOI: 10.1126/sciadv.abk2712] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated by defects, and the renormalization of the system's surface tension by the active flow. The posttransitional regime is also characterized by several complex morphodynamical processes, such as oscillatory deformations, droplet nucleation, and active turbulence. Our findings offer an explanation of recent observations on tissue morphogenesis and shed light on the dynamics of active surfaces in general.
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Affiliation(s)
- Ludwig A. Hoffmann
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Livio Nicola Carenza
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Julia Eckert
- Physics of Life Processes, Leiden Institute of Physics, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
| | - Luca Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, Netherlands
- Corresponding author.
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Physics of liquid crystals in cell biology. Trends Cell Biol 2021; 32:140-150. [PMID: 34756501 DOI: 10.1016/j.tcb.2021.09.012] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 09/28/2021] [Accepted: 09/30/2021] [Indexed: 11/21/2022]
Abstract
The past decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result, an integrated view of cell biology is evolving, where genetic and molecular features are scrutinised hand in hand with physical and mechanical characteristics of cells. Physics of liquid crystals has emerged as a burgeoning new frontier in cell biology over the past few years, fuelled by an increasing identification of orientational order and topological defects in cell biology, spanning scales from subcellular filaments to individual cells and multicellular tissues. Here, we provide an account of the most recent findings and developments, together with future promises and challenges in this rapidly evolving interdisciplinary research direction.
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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: 7] [Impact Index Per Article: 2.3] [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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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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Blanch-Mercader C, Guillamat P, Roux A, Kruse K. Integer topological defects of cell monolayers: Mechanics and flows. Phys Rev E 2021; 103:012405. [PMID: 33601623 DOI: 10.1103/physreve.103.012405] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 12/10/2020] [Indexed: 12/13/2022]
Abstract
Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.
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Affiliation(s)
- Carles Blanch-Mercader
- Department of Biochemistry, University of Geneva, 1211 Geneva, Switzerland.,Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Pau Guillamat
- Department of Biochemistry, University of Geneva, 1211 Geneva, Switzerland
| | - Aurélien Roux
- Department of Biochemistry, University of Geneva, 1211 Geneva, Switzerland
| | - Karsten Kruse
- Department of Biochemistry, University of Geneva, 1211 Geneva, Switzerland.,Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland.,NCCR Chemical Biology, University of Geneva, 1211 Geneva, Switzerland
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Walton J, McKay G, Grinfeld M, Mottram NJ. Pressure-driven changes to spontaneous flow in active nematic liquid crystals. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:51. [PMID: 32743686 DOI: 10.1140/epje/i2020-11973-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We consider the effects of a pressure gradient on the spontaneous flow of an active nematic liquid crystal in a channel, subject to planar anchoring and no-slip conditions on the boundaries of the channel. We employ a model based on the Ericksen-Leslie theory of nematics, with an additional active stress accounting for the activity of the fluid. By directly solving the flow equation, we consider an asymptotic solution for the director angle equation for large activity parameter values and predict the possible values of the director angle in the bulk of the channel. Through a numerical solution of the full nonlinear equations, we examine the effects of pressure on the branches of stable and unstable equilibria, some of which are disconnected from the no-flow state. In the absence of a pressure gradient, solutions are either symmetric or antisymmetric about the channel midpoint; these symmetries are changed by the pressure gradient. Considering the activity-pressure state space allows us to predict qualitatively the extent of each solution type and to show, for large enough pressure gradients, that a branch of non-trivial director angle solutions exists for all activity values.
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Affiliation(s)
- Joshua Walton
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, G1 1XH, Glasgow, UK
| | - Geoffrey McKay
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, G1 1XH, Glasgow, UK.
| | - Michael Grinfeld
- Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, G1 1XH, Glasgow, UK
| | - Nigel J Mottram
- School of Mathematics and Statistics, University of Glasgow, University Place, G12 8SU, Glasgow, UK
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