51
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Zhang R, Redford SA, Ruijgrok PV, Kumar N, Mozaffari A, Zemsky S, Dinner AR, Vitelli V, Bryant Z, Gardel ML, de Pablo JJ. Spatiotemporal control of liquid crystal structure and dynamics through activity patterning. NATURE MATERIALS 2021; 20:875-882. [PMID: 33603187 PMCID: PMC8404743 DOI: 10.1038/s41563-020-00901-4] [Citation(s) in RCA: 53] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 12/03/2020] [Indexed: 05/26/2023]
Abstract
Active materials are capable of converting free energy into mechanical work to produce autonomous motion, and exhibit striking collective dynamics that biology relies on for essential functions. Controlling those dynamics and transport in synthetic systems has been particularly challenging. Here, we introduce the concept of spatially structured activity as a means of controlling and manipulating transport in active nematic liquid crystals consisting of actin filaments and light-sensitive myosin motors. Simulations and experiments are used to demonstrate that topological defects can be generated at will and then constrained to move along specified trajectories by inducing local stresses in an otherwise passive material. These results provide a foundation for the design of autonomous and reconfigurable microfluidic systems where transport is controlled by modulating activity with light.
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Affiliation(s)
- Rui Zhang
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong SAR, China
| | - Steven A Redford
- The Graduate Program in Biophysical Sciences, The University of Chicago, Chicago, IL, USA
- James Franck Institute, The University of Chicago, Chicago, IL, USA
| | - Paul V Ruijgrok
- Department of Bioengineering, Stanford University, Stanford, CA, USA
| | - Nitin Kumar
- James Franck Institute, The University of Chicago, Chicago, IL, USA
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, India
| | - Ali Mozaffari
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA
| | - Sasha Zemsky
- Program in Biophysics, Stanford University, Stanford, CA, USA
| | - Aaron R Dinner
- James Franck Institute, The University of Chicago, Chicago, IL, USA
- Department of Chemistry, The University of Chicago, Chicago, IL, USA
| | - Vincenzo Vitelli
- James Franck Institute, The University of Chicago, Chicago, IL, USA
- Department of Physics, The University of Chicago, Chicago, IL, USA
| | - Zev Bryant
- Department of Bioengineering, Stanford University, Stanford, CA, USA
- Department of Structural Biology, Stanford University Medical Center, Stanford, CA, USA
| | - Margaret L Gardel
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA.
- James Franck Institute, The University of Chicago, Chicago, IL, USA.
- Department of Physics, The University of Chicago, Chicago, IL, USA.
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA.
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
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52
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Lavrentovich OD. Design of nematic liquid crystals to control microscale dynamics. LIQUID CRYSTALS REVIEWS 2021; 8:59-129. [PMID: 34956738 PMCID: PMC8698256 DOI: 10.1080/21680396.2021.1919576] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 04/11/2021] [Indexed: 05/25/2023]
Abstract
The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.
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Affiliation(s)
- Oleg D Lavrentovich
- Advanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH 44242, USA
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53
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Lamson AR, Moore JM, Fang F, Glaser MA, Shelley MJ, Betterton MD. Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:45. [PMID: 33779863 PMCID: PMC8220871 DOI: 10.1140/epje/s10189-021-00042-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 02/20/2021] [Indexed: 05/17/2023]
Abstract
In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.
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Affiliation(s)
- Adam R Lamson
- Department of Physics, University of Colorado Boulder, Boulder, USA.
| | - Jeffrey M Moore
- Department of Physics, University of Colorado Boulder, Boulder, USA
| | - Fang Fang
- Courant Institute, New York University, New York, USA
| | - Matthew A Glaser
- Department of Physics, University of Colorado Boulder, Boulder, USA
| | - Michael J Shelley
- Courant Institute, New York University, New York, USA
- Center for Computational Biology, Flatiron Institute, New York, USA
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54
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Vafa F, Bowick MJ, Shraiman BI, Marchetti MC. Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells. SOFT MATTER 2021; 17:3068-3073. [PMID: 33596291 DOI: 10.1039/d0sm02027c] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.
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Affiliation(s)
- Farzan Vafa
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
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55
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Tang X, Selinger JV. Alignment of a topological defect by an activity gradient. Phys Rev E 2021; 103:022703. [PMID: 33736015 DOI: 10.1103/physreve.103.022703] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2020] [Accepted: 01/21/2021] [Indexed: 01/10/2023]
Abstract
As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single defect of topological charge +1/2, moving in an activity gradient. This modeling uses three methods: (1) approximate analytic solution of hydrodynamic equations, (2) macroscopic, symmetry-based theory of the defect as an effective oriented particle, and (3) numerical simulation. All three methods show that an activity gradient aligns the defect orientation, and hence should be useful to control defect motion.
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Affiliation(s)
- Xingzhou Tang
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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56
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Nejad MR, Doostmohammadi A, Yeomans JM. Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics. SOFT MATTER 2021; 17:2500-2511. [PMID: 33503081 DOI: 10.1039/d0sm01794a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive limit, we show that, as the friction is increased, memory effects become more prominent and +1/2 topological defects leave increasingly persistent trails in the director field as they pass. The trails are preferential sites for defect formation and they tend to impose polar order on any new +1/2 defects. In the absence of noise and for high friction, it becomes very difficult to create defects, but trails formed by any defects present at the beginning of the simulations persist and organise into parallel arch-like patterns in the director field. We show aligned arches of equal width are approximate steady state solutions of the equations of motion which co-exist with the nematic state. We compare our results to other models in the literature, in particular dry systems with no hydrodynamics, where trails, arches and polar defect ordering have also been observed.
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Affiliation(s)
- Mehrana R Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | | | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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57
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Chardac A, Shankar S, Marchetti MC, Bartolo D. Emergence of dynamic vortex glasses in disordered polar active fluids. Proc Natl Acad Sci U S A 2021; 118:e2018218118. [PMID: 33658364 PMCID: PMC7958234 DOI: 10.1073/pnas.2018218118] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.
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Affiliation(s)
- Amélie Chardac
- Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Suraj Shankar
- Department of Physics, Harvard University, Cambridge, MA 02138
| | | | - Denis Bartolo
- Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France;
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58
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Colen J, Han M, Zhang R, Redford SA, Lemma LM, Morgan L, Ruijgrok PV, Adkins R, Bryant Z, Dogic Z, Gardel ML, de Pablo JJ, Vitelli V. Machine learning active-nematic hydrodynamics. Proc Natl Acad Sci U S A 2021; 118:e2016708118. [PMID: 33653956 PMCID: PMC7958379 DOI: 10.1073/pnas.2016708118] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.
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Affiliation(s)
- Jonathan Colen
- Department of Physics, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Ming Han
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637
| | - Rui Zhang
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637
- Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR, People's Republic of China
| | - Steven A Redford
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Graduate Program in Biophysical Sciences, University of Chicago, Chicago, IL 60637
| | - Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, MA 02454
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Link Morgan
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Paul V Ruijgrok
- Department of Bioengineering, Stanford University, Stanford, CA 94305
| | - Raymond Adkins
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Zev Bryant
- Department of Bioengineering, Stanford University, Stanford, CA 94305
- Department of Structural Biology, Stanford University Medical Center, Stanford, CA 94305
| | - Zvonimir Dogic
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Margaret L Gardel
- Department of Physics, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Juan J de Pablo
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637;
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL 60439
| | - Vincenzo Vitelli
- Department of Physics, University of Chicago, Chicago, IL 60637;
- James Franck Institute, University of Chicago, Chicago, IL 60637
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59
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Long C, Tang X, Selinger RLB, Selinger JV. Geometry and mechanics of disclination lines in 3D nematic liquid crystals. SOFT MATTER 2021; 17:2265-2278. [PMID: 33471022 DOI: 10.1039/d0sm01899f] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble +1/2 or -1/2 defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach-Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.
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Affiliation(s)
- Cheng Long
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Xingzhou Tang
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Robin L B Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Jonathan V Selinger
- Department of Physics, Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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60
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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] [MESH Headings] [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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61
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Kumar S, Mishra S. Active nematics with quenched disorder. Phys Rev E 2020; 102:052609. [PMID: 33327090 DOI: 10.1103/physreve.102.052609] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 11/02/2020] [Indexed: 11/07/2022]
Abstract
We introduce a two-dimensional active nematic with quenched disorder. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density and orientation. Disorder strength is tuned from zero to large values. Results from the numerical solution of equations of motion as well as the calculation of two-point orientation correlation function using linear approximation shows that the ordered steady state follows a disorder dependent crossover from quasi-long-range order to short-range order. Such crossover is due to the pinning of ±1/2 topological defects in the presence of finite disorder, which breaks the system in uncorrelated domains. Finite disorder slows the dynamics of +1/2 defect, and it leads to slower growth dynamics. The two-point correlation functions for the density and orientation fields show good dynamic scaling but no static scaling for the different disorder strengths. Our findings can motivate experimentalists to verify the results and find applications in living and artificial apolar systems in the presence of a quenched disorder.
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Affiliation(s)
- Sameer Kumar
- Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
| | - Shradha Mishra
- Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
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62
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Thijssen K, Nejad MR, Yeomans JM. Role of Friction in Multidefect Ordering. PHYSICAL REVIEW LETTERS 2020; 125:218004. [PMID: 33275020 DOI: 10.1103/physrevlett.125.218004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 07/30/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
We use continuum simulations to study the impact of friction on the ordering of defects in an active nematic. Even in a frictionless system, +1/2 defects tend to align side by side and orient antiparallel reflecting their propensity to form, and circulate with, flow vortices. Increasing friction enhances the effectiveness of the defect-defect interactions, and defects form dynamically evolving, large-scale, positionally, and orientationally ordered structures, which can be explained as a competition between hexagonal packing, preferred by the -1/2 defects, and rectangular packing, preferred by the +1/2 defects.
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Affiliation(s)
- Kristian Thijssen
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Mehrana R Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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63
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Hardoüin J, Laurent J, Lopez-Leon T, Ignés-Mullol J, Sagués F. Active microfluidic transport in two-dimensional handlebodies. SOFT MATTER 2020; 16:9230-9241. [PMID: 32926045 DOI: 10.1039/d0sm00610f] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.
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Affiliation(s)
- Jérôme Hardoüin
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
| | - Justine Laurent
- Laboratoire de Physique et Mécanique des Milieux hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, Paris, France and Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Teresa Lopez-Leon
- Laboratoire de Physique et Mécanique des Milieux hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, Paris, France and Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Jordi Ignés-Mullol
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
| | - Francesc Sagués
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
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64
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Chandragiri S, Doostmohammadi A, Yeomans JM, Thampi SP. Flow States and Transitions of an Active Nematic in a Three-Dimensional Channel. PHYSICAL REVIEW LETTERS 2020; 125:148002. [PMID: 33064508 DOI: 10.1103/physrevlett.125.148002] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 08/26/2020] [Indexed: 06/11/2023]
Abstract
We use active nematohydrodynamics to study the flow of an active fluid in a 3D microchannel, finding a transition between active turbulence and regimes where there is a net flow along the channel. We show that the net flow is only possible if the active nematic is flow aligning and that, in agreement with experiments, the appearance of the net flow depends on the aspect ratio of the channel cross section. We explain our results in terms of when the hydrodynamic screening due to the channel walls allows the emergence of vortex rolls across the channel.
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Affiliation(s)
- Santhan Chandragiri
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Amin Doostmohammadi
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Sumesh P Thampi
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
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65
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Strübing T, Khosravanizadeh A, Vilfan A, Bodenschatz E, Golestanian R, Guido I. Wrinkling Instability in 3D Active Nematics. NANO LETTERS 2020; 20:6281-6288. [PMID: 32786934 PMCID: PMC7496740 DOI: 10.1021/acs.nanolett.0c01546] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Revised: 08/04/2020] [Indexed: 05/13/2023]
Abstract
In nature, interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviors. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors, and depleting agent. It shows a rich behavior evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.
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Affiliation(s)
- Tobias Strübing
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Amir Khosravanizadeh
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Department
of Physics, Institute for Advanced Studies
in Basic Sciences, Zanjan 45137-66731, Iran
| | - Andrej Vilfan
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Jožef
Stefan Institute, 1000 Ljubljana, Slovenia
| | - Eberhard Bodenschatz
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Institute
for Dynamics of Complex Systems, Georg-August-University
Göttingen, 37073 Göttingen, Germany
- Laboratory
of Atomic and Solid-State Physics, Cornell
University, Ithaca, New York 14853, United
States
| | - Ramin Golestanian
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Rudolf
Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Isabella Guido
- Max
Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
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66
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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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67
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Zhang YH, Deserno M, Tu ZC. Dynamics of active nematic defects on the surface of a sphere. Phys Rev E 2020; 102:012607. [PMID: 32795046 DOI: 10.1103/physreve.102.012607] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 06/22/2020] [Indexed: 12/12/2022]
Abstract
A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge +2 due to the topological constraint. In equilibrium, the nematic field forms four +1/2 defects, located at the corners of a regular tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. If additionally the individual nematogens exhibit self-driven directional motion, the resulting active system creates large-scale flow that drives it out of equilibrium. In particular, the defects now follow complex dynamic trajectories which, depending on the strength of the active forcing, can be periodic (for weak forcing) or chaotic (for strong forcing). In this paper we derive an effective particle theory for this system, in which the topological defects are the degrees of freedom, whose exact equations of motion we subsequently determine. Numerical solutions of these equations confirm previously observed characteristics of their dynamics and clarify the role played by the time dependence of their global rotation. We also show that Onsager's variational principle offers an exceptionally transparent way to derive these dynamical equations, and we explain the defect mobility at the hydrodynamics level.
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Affiliation(s)
- Yi-Heng Zhang
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA
| | - Zhan-Chun Tu
- Department of Physics, Beijing Normal University, Beijing 100875, China
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68
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Soni H, Kumar N, Nambisan J, Gupta RK, Sood AK, Ramaswamy S. Phases and excitations of active rod-bead mixtures: simulations and experiments. SOFT MATTER 2020; 16:7210-7221. [PMID: 32393926 DOI: 10.1039/c9sm02552a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We present a large-scale numerical study, supplemented by experimental observations, on a quasi-two-dimensional active system of polar rods and spherical beads confined between two horizontal plates and energised by vertical vibration. For a low rod concentration Φr, our observations are consistent with a direct phase transition, as bead concentration Φb is increased, from the isotropic phase to a homogeneous flock. For Φr above a threshold value, an ordered band dense in both rods and beads occurs between the disordered phase and the homogeneous flock, in both experiments and simulations. Within the size ranges accessible, we observe only a single band, whose width increases with Φr. Deep in the ordered state, we observe broken-symmetry "sound" modes and giant number fluctuations. The direction-dependent sound speeds and the scaling of fluctuations are consistent with the predictions of field theories of flocking; sound damping rates show departures from such theories, but the range of wavenumbers explored is modest. At very high densities, we see phase separation into rod-rich and bead-rich regions, both of which move coherently.
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Affiliation(s)
- Harsh Soni
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
| | - Nitin Kumar
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Jyothishraj Nambisan
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and School of Physics, Georgia Institute of Technology, 770 State Street NW, Atlanta, GA 30332-0430, USA
| | - Rahul Kumar Gupta
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India.
| | - Sriram Ramaswamy
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
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69
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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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70
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Liverpool TB. Steady-state distributions and nonsteady dynamics in nonequilibrium systems. Phys Rev E 2020; 101:042107. [PMID: 32422705 DOI: 10.1103/physreve.101.042107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Accepted: 02/10/2020] [Indexed: 11/07/2022]
Abstract
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.
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71
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Turiv T, Krieger J, Babakhanova G, Yu H, Shiyanovskii SV, Wei QH, Kim MH, Lavrentovich OD. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. SCIENCE ADVANCES 2020; 6:eaaz6485. [PMID: 32426499 PMCID: PMC7220327 DOI: 10.1126/sciadv.aaz6485] [Citation(s) in RCA: 57] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 03/02/2020] [Indexed: 05/18/2023]
Abstract
Eukaryotic cells in living tissues form dynamic patterns with spatially varying orientational order that affects important physiological processes such as apoptosis and cell migration. The challenge is how to impart a predesigned map of orientational order onto a growing tissue. Here, we demonstrate an approach to produce cell monolayers of human dermal fibroblasts with predesigned orientational patterns and topological defects using a photoaligned liquid crystal elastomer (LCE) that swells anisotropically in an aqueous medium. The patterns inscribed into the LCE are replicated by the tissue monolayer and cause a strong spatial variation of cells phenotype, their surface density, and number density fluctuations. Unbinding dynamics of defect pairs intrinsic to active matter is suppressed by anisotropic surface anchoring allowing the estimation of the elastic characteristics of the tissues. The demonstrated patterned LCE approach has potential to control the collective behavior of cells in living tissues, cell differentiation, and tissue morphogenesis.
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Affiliation(s)
- Taras Turiv
- Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
- Corresponding author. (T.T.); (O.D.L.)
| | - Jess Krieger
- School of Biomedical Sciences, Kent State University, Kent, OH 44242, USA
| | - Greta Babakhanova
- Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
| | - Hao Yu
- Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
| | - Sergij V. Shiyanovskii
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
| | - Qi-Huo Wei
- Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
- Department of Physics, Kent State University, Kent, OH 44242, USA
| | - Min-Ho Kim
- School of Biomedical Sciences, Kent State University, Kent, OH 44242, USA
- Department of Biological Sciences, Kent State University, Kent, OH 44242, USA
| | - Oleg D. Lavrentovich
- Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242, USA
- Advanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA
- Department of Physics, Kent State University, Kent, OH 44242, USA
- Corresponding author. (T.T.); (O.D.L.)
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72
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Thijssen K, Metselaar L, Yeomans JM, Doostmohammadi A. Active nematics with anisotropic friction: the decisive role of the flow aligning parameter. SOFT MATTER 2020; 16:2065-2074. [PMID: 32003382 DOI: 10.1039/c9sm01963d] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.
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Affiliation(s)
- Kristian Thijssen
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Luuk Metselaar
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Amin Doostmohammadi
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.
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73
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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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74
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Čopar S, Kos Ž, Emeršič T, Tkalec U. Microfluidic control over topological states in channel-confined nematic flows. Nat Commun 2020; 11:59. [PMID: 31896755 PMCID: PMC6940393 DOI: 10.1038/s41467-019-13789-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2019] [Accepted: 11/28/2019] [Indexed: 12/02/2022] Open
Abstract
Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic channels with perpendicular surface alignment, nematics discontinuously transition from perpendicular structure at low flow rates to flow-aligned structure at high flow rates. Here we show how precise tuning of the driving pressure can be used to stabilize and manipulate a previously unresearched topologically protected chiral intermediate state which arises before the homeotropic to flow-aligned transition. We characterize the mechanisms underlying the transition and construct a phenomenological model to describe the critical behaviour and the phase diagram of the observed chiral flow state, and evaluate the effect of a forced symmetry breaking by introduction of a chiral dopant. Finally, we induce transitions on demand through channel geometry, application of laser tweezers, and careful control of the flow rate. It is interesting phenomenon that chiral order can emerge in intrinsically achiral liquid crystals. Here Čopar et al. demonstrate achiral-to-chiral transition of the nematic liquid crystals flow in microfluidic channels and their behaviour, stability, and dependence on geometric and material parameters.
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Affiliation(s)
- Simon Čopar
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
| | - Žiga Kos
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
| | - Tadej Emeršič
- Faculty of Medicine, Institute of Biophysics, University of Ljubljana, Vrazov trg 2, 1000, Ljubljana, Slovenia.,Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Uroš Tkalec
- Faculty of Medicine, Institute of Biophysics, University of Ljubljana, Vrazov trg 2, 1000, Ljubljana, Slovenia. .,Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia. .,Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000, Maribor, Slovenia.
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75
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Patelli A, Djafer-Cherif I, Aranson IS, Bertin E, Chaté H. Understanding Dense Active Nematics from Microscopic Models. PHYSICAL REVIEW LETTERS 2019; 123:258001. [PMID: 31922774 DOI: 10.1103/physrevlett.123.258001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 09/13/2019] [Indexed: 06/10/2023]
Abstract
We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smecticlike arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.
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Affiliation(s)
- Aurelio Patelli
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Ilyas Djafer-Cherif
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
| | - Igor S Aranson
- Department of Biomedical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Eric Bertin
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100094, China
- LPTMC, Sorbonne Université, CNRS, 75005 Paris, France
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76
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Kempf F, Mueller R, Frey E, Yeomans JM, Doostmohammadi A. Active matter invasion. SOFT MATTER 2019; 15:7538-7546. [PMID: 31451816 DOI: 10.1039/c9sm01210a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.
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Affiliation(s)
- Felix Kempf
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München - Theresienstr. 37, D-80333 Munich, Germany
| | - Romain Mueller
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München - Theresienstr. 37, D-80333 Munich, Germany
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
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77
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Foffano G, Lintuvuori JS, Stratford K, Cates ME, Marenduzzo D. Dynamic clustering and re-dispersion in concentrated colloid-active gel composites. SOFT MATTER 2019; 15:6896-6902. [PMID: 31423501 DOI: 10.1039/c9sm01249d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the dynamics of quasi-two-dimensional concentrated suspensions of colloidal particles in active gels by computer simulations. Remarkably, we find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites. Our quasi-two-dimensional "inverse" dispersions of passive particles in active fluids (as opposed to the more common "direct" suspensions of active particles in passive fluids) provide a promising route towards the self-assembly of new soft materials.
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Affiliation(s)
- G Foffano
- Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, UMR 8626, 91405 Orsay, France
| | - J S Lintuvuori
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | - K Stratford
- EPCC, School of Physics and Astronomy, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - M E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Gutherie Tait Road, Edinburgh EH9 3FD, UK.
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78
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Yang Q, Jiang Y, Fan D, Zheng K, Zhang J, Xu Z, Yao W, Zhang Q, Song Y, Zheng Q, Fan L, Gao W, Gao C. Nonsphere Drop Impact Assembly of Graphene Oxide Liquid Crystals. ACS NANO 2019; 13:8382-8391. [PMID: 31291085 DOI: 10.1021/acsnano.9b03926] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Creating long-lived topological textured liquid crystals (LCs) in confined nonspherical space is of significance in both generations of structures and fundamental studies of topological physics. However, it remains a great challenge due to the fluid character of LCs and the unstable tensional state of transient nonspheres. Here, we realize a rich series of topological textures confined in nonspherical geometries by drop impact assembly (DIA) of graphene oxide (GO) aqueous LCs. Various highly curved nonspherical morphologies of LCs were captured by gelator bath, generating distinct out-of-equilibrium yet long-lived macroscopic topological textures in 3D confinement. Our hydrodynamic investigations on DIA processes reveal that the shear-thinning fluid behavior of LCs and the arrested GO alignments mainly contribute to the topological richness in DIA. Utilizing the shaping behavior of GO LCs compared to other conventional linear polymers such as alginate, we further extend the DIA methodology to design more complex yet highly controllable functional composites and hybrids. This work thus reveals the potential to scale production of uniform yet anisotropic materials with rich topologic textures and tailored composition.
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Affiliation(s)
- Qiuyan Yang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Yanqiu Jiang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Dongyu Fan
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Kan Zheng
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Jiayi Zhang
- State Key Laboratory of Clean Energy Utilization , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Zhen Xu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Weiquan Yao
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Qingxu Zhang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Yihu Song
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Qiang Zheng
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Liwu Fan
- State Key Laboratory of Clean Energy Utilization , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Weiwei Gao
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
| | - Chao Gao
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province , Zhejiang University , 38 Zheda Road , Hangzhou 310027 , People's Republic of China
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79
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Carenza LN, Gonnella G, Lamura A, Negro G, Tiribocchi A. Lattice Boltzmann methods and active fluids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:81. [PMID: 31250142 DOI: 10.1140/epje/i2019-11843-6] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 05/24/2019] [Indexed: 05/24/2023]
Abstract
We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
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Affiliation(s)
- Livio Nicola Carenza
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy.
| | - Antonio Lamura
- Istituto Applicazioni Calcolo, CNR, Via Amendola 122/D, 70126, Bari, Italy
| | - Giuseppe Negro
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Adriano Tiribocchi
- Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, 00161, Roma, Italy
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80
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Pearce DJG. Activity Driven Orientational Order in Active Nematic Liquid Crystals on an Anisotropic Substrate. PHYSICAL REVIEW LETTERS 2019; 122:227801. [PMID: 31283272 DOI: 10.1103/physrevlett.122.227801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Indexed: 05/08/2023]
Abstract
We investigate the effect of an anisotropic substrate on the turbulent dynamics of a simulated two-dimensional active nematic. This is introduced as an anisotropic friction and an effective anisotropic viscosity, with the orientation of the anisotropy being defined by the substrate. In this system, we observe the emergence of global nematic order of topological defects that is controlled by the degree of anisotropy in the viscosity and the magnitude of the active stress. No global defect alignment is seen in passive liquid crystals with anisotropic viscosity or friction confirming that ordering is driven by the active stress. We then closely examine the active flow generated by a single defect to show that the net kinetic energy of the flow is dependent on the orientation of the defect relative to the substrate, resulting in a torque on the defect to align it with the anisotropy in the substrate.
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Affiliation(s)
- D J G Pearce
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland and Department of Biochemistry, University of Geneva, Geneva 1205, Switzerland
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81
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Abstract
We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop an analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stresses result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stresses and show that extensile active stress generates chaotic motion even under a simple model of the polarity field coupled with motion and deformation of the drop.
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Affiliation(s)
- Natsuhiko Yoshinaga
- WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan and MathAM-OIL, AIST, Sendai 980-8577, Japan
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82
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Zhao J, Gulan U, Horie T, Ohmura N, Han J, Yang C, Kong J, Wang S, Xu BB. Advances in Biological Liquid Crystals. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2019; 15:e1900019. [PMID: 30892830 DOI: 10.1002/smll.201900019] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Revised: 02/17/2019] [Indexed: 06/09/2023]
Abstract
Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.
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Affiliation(s)
- Jianguo Zhao
- Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Quanzhou, 362200, China
- Third Institute of Physics-Biophysics, University of Göttingen, 37077, Göttingen, Germany
| | - Utku Gulan
- Institute of Environmental Engineering, ETH Zurich, 8093, Zurich, Switzerland
| | - Takafumi Horie
- Department of Chemical Science and Engineering, Kobe University, Kobe, 657-8501, Japan
| | - Naoto Ohmura
- Department of Chemical Science and Engineering, Kobe University, Kobe, 657-8501, Japan
| | - Jun Han
- Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Quanzhou, 362200, China
| | - Chao Yang
- CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jie Kong
- Shaanxi Key Laboratory of Macromolecular Science and Technology, School of Science, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Steven Wang
- School of Engineering, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
| | - Ben Bin Xu
- Mechanical and Construction Engineering, Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK
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83
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Pearce DJG, Ellis PW, Fernandez-Nieves A, Giomi L. Geometrical Control of Active Turbulence in Curved Topographies. PHYSICAL REVIEW LETTERS 2019; 122:168002. [PMID: 31075037 DOI: 10.1103/physrevlett.122.168002] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Revised: 08/20/2018] [Indexed: 06/09/2023]
Abstract
We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.
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Affiliation(s)
- D J G Pearce
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - Perry W Ellis
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Alberto Fernandez-Nieves
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Department of Condensed Matter Physics, University of Barcelona, 08028 Barcelona, Spain
- ICREA-Institucio Catalana de Recerca i Estudis Avancats, 08010 Barcelona, Spain
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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84
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Lemma LM, DeCamp SJ, You Z, Giomi L, Dogic Z. Statistical properties of autonomous flows in 2D active nematics. SOFT MATTER 2019; 15:3264-3272. [PMID: 30920553 PMCID: PMC6924514 DOI: 10.1039/c8sm01877d] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs the motion of individual kinesin motors.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
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85
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Opathalage A, Norton MM, Juniper MPN, Langeslay B, Aghvami SA, Fraden S, Dogic Z. Self-organized dynamics and the transition to turbulence of confined active nematics. Proc Natl Acad Sci U S A 2019; 116:4788-4797. [PMID: 30804207 PMCID: PMC6421422 DOI: 10.1073/pnas.1816733116] [Citation(s) in RCA: 77] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.
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Affiliation(s)
| | | | | | - Blake Langeslay
- Department of Physics, Brandeis University, Waltham, MA 02453
| | - S Ali Aghvami
- Department of Physics, Brandeis University, Waltham, MA 02453
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, MA 02453;
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA 02453;
- Department of Physics, University of California, Santa Barbara, CA 93106
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86
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Miles CJ, Evans AA, Shelley MJ, Spagnolie SE. Active matter invasion of a viscous fluid: Unstable sheets and a no-flow theorem. PHYSICAL REVIEW LETTERS 2019; 122:098002. [PMID: 30932541 DOI: 10.1103/physrevlett.122.098002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Revised: 11/29/2018] [Indexed: 06/09/2023]
Abstract
We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities, governed at small times by an equation that also describes the Saffman-Taylor instability in a Hele-Shaw cell, or the Rayleigh-Taylor instability in a two-dimensional flow through a porous medium. Thin sheets of aligned pusher particles are always unstable, while sheets of aligned puller particles can either be stable (immotile particles), or unstable (motile particles) with a growth rate that is nonmonotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow everywhere and for all time.
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Affiliation(s)
- Christopher J Miles
- Department of Physics, University of Michigan, 450 Church St., Ann Arbor, Michigan 48109, USA
| | - Arthur A Evans
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, Wisconsin 53706, USA
| | - Michael J Shelley
- Flatiron Institute, Simons Foundation, New York, New York, USA; and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Saverio E Spagnolie
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, Wisconsin 53706, USA
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87
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Chandragiri S, Doostmohammadi A, Yeomans JM, Thampi SP. Active transport in a channel: stabilisation by flow or thermodynamics. SOFT MATTER 2019; 15:1597-1604. [PMID: 30672556 DOI: 10.1039/c8sm02103a] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to understand the behaviour of active systems confined to channels. Therefore here we use continuum simulations to investigate the behaviour of active fluids in a two-dimensional channel. Motivated by the fact that most experimental systems show no ordering in the absence of activity, we concentrate on temperatures where there is no nematic order in the passive system, so that any nematic order is induced by the active flow. We systematically analyze the results, identify several different stable flow states, provide a phase diagram and show that the key parameters controlling the flow are the ratio of channel width to the length scale of active flow vortices, and whether the system is flow aligning or flow tumbling.
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Affiliation(s)
- Santhan Chandragiri
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
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88
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Nemoto T, Fodor É, Cates ME, Jack RL, Tailleur J. Optimizing active work: Dynamical phase transitions, collective motion, and jamming. Phys Rev E 2019; 99:022605. [PMID: 30934223 DOI: 10.1103/physreve.99.022605] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 06/09/2023]
Abstract
Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.
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Affiliation(s)
- Takahiro Nemoto
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
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89
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Mueller R, Yeomans JM, Doostmohammadi A. Emergence of Active Nematic Behavior in Monolayers of Isotropic Cells. PHYSICAL REVIEW LETTERS 2019; 122:048004. [PMID: 30768306 DOI: 10.1103/physrevlett.122.048004] [Citation(s) in RCA: 63] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Indexed: 06/09/2023]
Abstract
There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle elongation emerge in monolayers of cells with isotropic shapes is an outstanding question. In this Letter, we present a minimal model of cellular monolayers based on cell deformation and force transmission at the cell-cell interface that explains the formation of topological defects and captures the flow-field and stress patterns around them. By including mechanical properties at the individual cell level, we further show that the instability that drives the formation of topological defects, and leads to active turbulence, emerges from a feedback between shape deformation and active driving. The model allows us to suggest new explanations for experimental observations in tissue mechanics, and to propose designs for future experiments.
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Affiliation(s)
- Romain Mueller
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, University of Oxford, Oxford OX1 3PU, United Kingdom
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90
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Tang X, Selinger JV. Theory of defect motion in 2D passive and active nematic liquid crystals. SOFT MATTER 2019; 15:587-601. [PMID: 30608104 DOI: 10.1039/c8sm01901k] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective "particles". For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows the coupling between translational and rotational motion. For active liquid crystals, the theory provides an alternative way to describe motion induced by the activity coefficient.
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Affiliation(s)
- Xingzhou Tang
- Department of Physics and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Jonathan V Selinger
- Department of Physics and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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91
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Cai LB, Chaté H, Ma YQ, Shi XQ. Dynamical subclasses of dry active nematics. Phys Rev E 2019; 99:010601. [PMID: 30780307 DOI: 10.1103/physreve.99.010601] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Indexed: 06/09/2023]
Abstract
We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.
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Affiliation(s)
- Li-Bing Cai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Hugues Chaté
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100094, China
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
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92
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Abstract
Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such "active nematics" systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here, we introduce an active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path toward more quantitative active matter research.
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93
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Joshi A, Putzig E, Baskaran A, Hagan MF. The interplay between activity and filament flexibility determines the emergent properties of active nematics. SOFT MATTER 2018; 15:94-101. [PMID: 30520495 DOI: 10.1039/c8sm02202j] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by differences between previous simulations of active nematics based on rigid rods and experimental realizations based on semiflexible biopolymer filaments, we describe a large-scale simulation study of a particle-based computational model that explicitly incorporates filament semiflexibility. We find that energy injected into the system at the particle scale preferentially excites bend deformations, reducing the apparent filament bend modulus. The emergent characteristics of the active nematic depend on activity and flexibility only through this activity-renormalized bend 'modulus', demonstrating that apparent values of material parameters, such as the Frank 'constants', depend on activity. Thus, phenomenological parameters within continuum hydrodynamic descriptions of active nematics must account for this dependence. Further, we present a systematic way to estimate these parameters from observations of deformation fields and defect shapes in experimental or simulation data.
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Affiliation(s)
- Abhijeet Joshi
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Elias Putzig
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
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94
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Abstract
Active matter is a wide class of nonequilibrium systems consisting of interacting self-propelled agents transducing the energy stored in the environment into mechanical motion. Numerous examples range from microscopic cytoskeletal filaments and swimming organisms (bacteria and unicellular algae), synthetic catalytic nanomotors, colloidal self-propelled Janus particles, to macroscopic bird flocks, fish schools, and even human crowds. Active matter demonstrates a remarkable tendency toward self-organization and development of collective states with the long-range spatial order. Furthermore, active materials exhibit properties that are not present in traditional materials like plastics or ceramics: self-repair, shape change, and adaptation. A suspension of microscopic swimmers, such as motile bacteria or self-propelled colloids (active suspensions), is possibly the simplest and the most explored realization of active matter. Recent studies of active suspensions revealed a wealth of unexpected behaviors, from a dramatic reduction of the effective viscosity, enhanced mixing and self-diffusion, rectification of chaotic motion, to artificial rheotaxis (drift against the imposed flow) and cross-stream migration. To date, most of the studies of active matter are performed in isotropic suspending medium, like water with the addition of some "fuel", e.g., nutrient for bacteria or H2O2 for catalytic bimetallic AuPt nanorods. A highly structured anisotropic suspending medium represented by lyotropic liquid crystal (water-soluble) opens enormous opportunities to control and manipulate active matter. Liquid crystals exhibit properties intermediate between solid and liquids; they may flow like a liquid but respond to deformations as a solid due to a crystal-like orientation of molecules. Liquid crystals doped by a small amount of active component represent a new class of composite materials (living liquid crystals or LLCs) with unusual mechanical and optical properties. LLCs demonstrate a variety of highly organized dynamic collective states, spontaneous formation of dynamic textures of topological defects (singularities of local molecular orientation), controlled and reconfigurable transport of cargo particles, manipulation of individual trajectories of microswimmers, and many others. Besides insights into fundamental mechanisms governing active materials, living liquid crystals may have intriguing applications, such as the design of new classes of soft adaptive bioinspired materials capable to respond to physical and chemical stimuli, such as light, magnetic, and electric fields, mechanical shear, airborne pollutants, and bacterial toxins. This Account details the most recent developments in the field of LLCs and discusses how the anisotropy of liquid crystals can be harnessed to control and manipulate active materials.
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Affiliation(s)
- Igor S. Aranson
- Departments of Biomedical Engineering, Chemistry and Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, United States
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95
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Dell'Arciprete D, Blow ML, Brown AT, Farrell FDC, Lintuvuori JS, McVey AF, Marenduzzo D, Poon WCK. A growing bacterial colony in two dimensions as an active nematic. Nat Commun 2018; 9:4190. [PMID: 30305618 PMCID: PMC6180060 DOI: 10.1038/s41467-018-06370-3] [Citation(s) in RCA: 78] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Accepted: 08/23/2018] [Indexed: 11/18/2022] Open
Abstract
How a single bacterium becomes a colony of many thousand cells is important in biomedicine and food safety. Much is known about the molecular and genetic bases of this process, but less about the underlying physical mechanisms. Here we study the growth of single-layer micro-colonies of rod-shaped Escherichiacoli bacteria confined to just under the surface of soft agarose by a glass slide. Analysing this system as a liquid crystal, we find that growth-induced activity fragments the colony into microdomains of well-defined size, whilst the associated flow orients it tangentially at the boundary. Topological defect pairs with charges \documentclass[12pt]{minimal}
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\begin{document}$$+ {\textstyle{1 \over 2}}$$\end{document}+12 defects being propelled to the periphery. Theoretical modelling suggests that these phenomena have different physical origins from similar observations in other extensile active nematics, and a growing bacterial colony belongs to a new universality class, with features reminiscent of the expanding universe. Rod-shaped bacteria are an example of active matter. Here the authors find that a growing bacterial colony harbours internal cellular flows affecting orientational ordering in its interior and at the boundary. Results suggest this system may belong to a new active matter universality class.
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Affiliation(s)
- D Dell'Arciprete
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.,Dipartimento di Fisica, Universita' di Roma La Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy
| | - M L Blow
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
| | - A T Brown
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
| | - F D C Farrell
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.,Life Sciences, University of Warwick, Coventry, CV4 7AL, UK
| | - J S Lintuvuori
- Université Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France
| | - A F McVey
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - W C K Poon
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
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96
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Kumar N, Zhang R, de Pablo JJ, Gardel ML. Tunable structure and dynamics of active liquid crystals. SCIENCE ADVANCES 2018; 4:eaat7779. [PMID: 30333990 PMCID: PMC6184751 DOI: 10.1126/sciadv.aat7779] [Citation(s) in RCA: 90] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2018] [Accepted: 08/31/2018] [Indexed: 05/21/2023]
Abstract
Active materials are capable of converting free energy into directional motion, giving rise to notable dynamical phenomena. Developing a general understanding of their structure in relation to the underlying nonequilibrium physics would provide a route toward control of their dynamic behavior and pave the way for potential applications. The active system considered here consists of a quasi-two-dimensional sheet of short (≈1 μm) actin filaments driven by myosin II motors. By adopting a concerted theoretical and experimental strategy, new insights are gained into the nonequilibrium properties of active nematics over a wide range of internal activity levels. In particular, it is shown that topological defect interactions can be led to transition from attractive to repulsive as a function of initial defect separation and relative orientation. Furthermore, by examining the +1/2 defect morphology as a function of activity, we found that the apparent elastic properties of the system (the ratio of bend-to-splay elastic moduli) are altered considerably by increased activity, leading to an effectively lower bend elasticity. At high levels of activity, the topological defects that decorate the material exhibit a liquid-like structure and adopt preferred orientations depending on their topological charge. Together, these results suggest that it should be possible to tune internal stresses in active nematic systems with the goal of designing out-of-equilibrium structures with engineered dynamic responses.
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Affiliation(s)
- Nitin Kumar
- James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
- Department of Physics, The University of Chicago, Chicago, IL 60637, USA
| | - Rui Zhang
- Institute for Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
| | - Juan J. de Pablo
- Institute for Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
- Institute for Molecular Engineering, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Margaret L. Gardel
- James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
- Department of Physics, The University of Chicago, Chicago, IL 60637, USA
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, IL 60637, USA
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97
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Bade ND, Kamien RD, Assoian RK, Stebe KJ. Edges impose planar alignment in nematic monolayers by directing cell elongation and enhancing migration. SOFT MATTER 2018; 14:6867-6874. [PMID: 30079410 PMCID: PMC7359601 DOI: 10.1039/c8sm00612a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Boundaries play an important role in the emergence of nematic order in classical liquid crystal systems; we explore their importance in adhesive cells that form active nematics. In particular, we study how cells are affected by an edge, which in our experiments is a boundary between adhesive and non-adhesive domains on a planar surface. We find that such edges induce elongation and direct the migration of isolated fibroblasts. In confluent monolayers, these elongated cells co-align and migrate to form an active, two-dimensional nematic structure in which edges enforce planar alignment and provide local slip to streams of cells that move along them. On an adhesive square island of dimensions 1 mm × 1 mm, cells near the edges in confluent nematic monolayers have enhanced alignment and velocity. The corners of the adhesive island seed defects with signs that depend on the direction of the motion of the streams of cells that meet there. Distortions emerge with rotations of -π/2 to form a -1/4 defect for streams that move clockwise or counterclockwise, and +π/2 to form a +1/4 defect for converging streams. We explore how cells transmit alignment information to each other in the absence of an edge by studying cell pairs and find that while such pairs do co-align, this alignment is only transient and short lived. These results shed light on the importance of edges in imposing nematic order in confluent monolayers and how edges can be used as tools to pattern the long-range organization of cells for tissue engineering applications.
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Affiliation(s)
- Nathan D Bade
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, USA.
| | - Randall D Kamien
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA
| | - Richard K Assoian
- Department of Systems Pharmacology and Translational Therapeutics, University of Pennsylvania, Philadelphia, PA, USA and Center for Engineering MechanoBiology, University of Pennsylvania, Philadelphia, PA, USA
| | - Kathleen J Stebe
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, USA.
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98
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Shankar S, Ramaswamy S, Marchetti MC, Bowick MJ. Defect Unbinding in Active Nematics. PHYSICAL REVIEW LETTERS 2018; 121:108002. [PMID: 30240234 DOI: 10.1103/physrevlett.121.108002] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2018] [Revised: 07/18/2018] [Indexed: 06/08/2023]
Abstract
We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the nonequilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a reentrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.
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Affiliation(s)
- Suraj Shankar
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Sriram Ramaswamy
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - M Cristina Marchetti
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Mark J Bowick
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
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99
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Copenhagen K, Malet-Engra G, Yu W, Scita G, Gov N, Gopinathan A. Frustration-induced phases in migrating cell clusters. SCIENCE ADVANCES 2018; 4:eaar8483. [PMID: 30214934 PMCID: PMC6135545 DOI: 10.1126/sciadv.aar8483] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Accepted: 07/27/2018] [Indexed: 05/21/2023]
Abstract
Certain malignant cancer cells form clusters in a chemoattractant gradient, which can spontaneously show three different phases of motion: translational, rotational, and random. Guided by our experiments on the motion of two-dimensional clusters in vitro, we developed an agent-based model in which the cells form a cohesive cluster due to attractive and alignment interactions. We find that when cells at the cluster rim are more motile, all three phases of motion coexist, in agreement with our observations. Using the model, we show that the transitions between different phases are driven by competition between an ordered rim and a disordered core accompanied by the creation and annihilation of topological defects in the velocity field. The model makes specific predictions, which we verify with our experimental data. Our results suggest that heterogeneous behavior of individuals, based on local environment, can lead to novel, experimentally observed phases of collective motion.
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Affiliation(s)
| | - Gema Malet-Engra
- Department of Oncology and Hemato-Oncology (DIPO), School of Medicine, University of Milan, Milan, Italy
- IFOM Foundation, Institute FIRC (Fondazione Italiana per la Ricerca sul Cancro) of Molecular Oncology, Milan, Italy
| | - Weimiao Yu
- Institute of Molecular and Cell Biology, National University of Singapore, Singapore, Singapore
| | - Giorgio Scita
- Department of Oncology and Hemato-Oncology (DIPO), School of Medicine, University of Milan, Milan, Italy
- IFOM Foundation, Institute FIRC (Fondazione Italiana per la Ricerca sul Cancro) of Molecular Oncology, Milan, Italy
| | - Nir Gov
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel
- Corresponding author. (N.G.); (A.G.)
| | - Ajay Gopinathan
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
- Corresponding author. (N.G.); (A.G.)
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100
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Doostmohammadi A, Ignés-Mullol J, Yeomans JM, Sagués F. Active nematics. Nat Commun 2018; 9:3246. [PMID: 30131558 PMCID: PMC6104062 DOI: 10.1038/s41467-018-05666-8] [Citation(s) in RCA: 263] [Impact Index Per Article: 43.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Revised: 06/28/2018] [Accepted: 07/19/2018] [Indexed: 11/09/2022] Open
Abstract
Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.
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Affiliation(s)
- Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Rd., Oxford, OX1 3PU, UK.
| | - Jordi Ignés-Mullol
- Departament de Ciència de Materials i Química Física and Institute of Nanoscience and Nanotechnology, Universitat de Barcelona, Martí I Franquès 1, 08028, Barcelona, Catalonia, Spain
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Rd., Oxford, OX1 3PU, UK
| | - Francesc Sagués
- Departament de Ciència de Materials i Química Física and Institute of Nanoscience and Nanotechnology, Universitat de Barcelona, Martí I Franquès 1, 08028, Barcelona, Catalonia, Spain
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