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Xu H, Wu Y. Self-enhanced mobility enables vortex pattern formation in living matter. Nature 2024; 627:553-558. [PMID: 38480895 DOI: 10.1038/s41586-024-07114-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 01/24/2024] [Indexed: 03/22/2024]
Abstract
Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.
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Affiliation(s)
- Haoran Xu
- Department of Physics and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, P.R. China
| | - Yilin Wu
- Department of Physics and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, P.R. China.
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2
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Abstract
The trachea is a long tube that enables air passage between the larynx and the bronchi. C-shaped cartilage rings on the ventral side stabilise the structure. On its esophagus-facing dorsal side, deformable smooth muscle facilitates the passage of food in the esophagus. While the symmetry break along the dorsal-ventral axis is well understood, the molecular mechanism that results in the periodic Sox9 expression pattern that translates into the cartilage rings has remained elusive. Here, we review the molecular regulatory interactions that have been elucidated, and discuss possible patterning mechanisms. Understanding the principles of self-organisation is important, both to define biomedical interventions and to enable tissue engineering.
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Affiliation(s)
- Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
- *Correspondence: Dagmar Iber,
| | - Malte Mederacke
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
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3
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Worlitzer VM, Ariel G, Be'er A, Stark H, Bär M, Heidenreich S. Turbulence-induced clustering in compressible active fluids. SOFT MATTER 2021; 17:10447-10457. [PMID: 34762091 DOI: 10.1039/d1sm01276b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay between self-advection of the aligned swimmers and their defect topology. The typical cluster size is determined by the characteristic vortex size. Our results are obtained by investigating a continuum model of compressible polar active fluids, which incorporates typical experimental observations in bacterial suspensions, in particular a non-monotone dependence of speed on density.
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Affiliation(s)
- Vasco M Worlitzer
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
| | - Gil Ariel
- Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
| | - Avraham Be'er
- Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Midreshet Ben-Gurion, Israel
- Department of Physics, Ben-Gurion University of the Negev, 84105 Beer Sheva, Israel
| | - Holger Stark
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
| | - Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
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4
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James M, Suchla DA, Dunkel J, Wilczek M. Emergence and melting of active vortex crystals. Nat Commun 2021; 12:5630. [PMID: 34561437 PMCID: PMC8463610 DOI: 10.1038/s41467-021-25545-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/18/2021] [Indexed: 11/09/2022] Open
Abstract
Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.
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Affiliation(s)
- Martin James
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany
| | - Dominik Anton Suchla
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany.,Faculty of Physics, University of Göttingen, Göttingen, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany. .,Faculty of Physics, University of Göttingen, Göttingen, Germany.
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Linkmann M, Marchetti MC, Boffetta G, Eckhardt B. Condensate formation and multiscale dynamics in two-dimensional active suspensions. Phys Rev E 2020; 101:022609. [PMID: 32168685 DOI: 10.1103/physreve.101.022609] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Accepted: 02/05/2020] [Indexed: 11/07/2022]
Abstract
The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
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Linkmann M, Boffetta G, Marchetti MC, Eckhardt B. Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence. PHYSICAL REVIEW LETTERS 2019; 122:214503. [PMID: 31283308 DOI: 10.1103/physrevlett.122.214503] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Indexed: 06/09/2023]
Abstract
The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small-scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense suspension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2D bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
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7
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Continuation for Thin Film Hydrodynamics and Related Scalar Problems. COMPUTATIONAL METHODS IN APPLIED SCIENCES 2019. [DOI: 10.1007/978-3-319-91494-7_13] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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Norton MM, Baskaran A, Opathalage A, Langeslay B, Fraden S, Baskaran A, Hagan MF. Insensitivity of active nematic liquid crystal dynamics to topological constraints. Phys Rev E 2018; 97:012702. [PMID: 29448352 DOI: 10.1103/physreve.97.012702] [Citation(s) in RCA: 49] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Indexed: 11/07/2022]
Abstract
Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.
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Affiliation(s)
- Michael M Norton
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Arvind Baskaran
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Achini Opathalage
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Blake Langeslay
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Aparna Baskaran
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
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Blanch-Mercader C, Yashunsky V, Garcia S, Duclos G, Giomi L, Silberzan P. Turbulent Dynamics of Epithelial Cell Cultures. PHYSICAL REVIEW LETTERS 2018; 120:208101. [PMID: 29864293 DOI: 10.1103/physrevlett.120.208101] [Citation(s) in RCA: 67] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Revised: 02/12/2018] [Indexed: 05/23/2023]
Abstract
We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.
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Affiliation(s)
- C Blanch-Mercader
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - V Yashunsky
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - S Garcia
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - G Duclos
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - P Silberzan
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
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10
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Reinken H, Klapp SHL, Bär M, Heidenreich S. Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions. Phys Rev E 2018; 97:022613. [PMID: 29548118 DOI: 10.1103/physreve.97.022613] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
In this paper, we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [S. Heidenreich et al., Phys. Rev. E 94, 020601 (2016)2470-004510.1103/PhysRevE.94.020601], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.
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Affiliation(s)
- Henning Reinken
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
| | - Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
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