1
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Lemma B, Lemma LM, Ems-McClung SC, Walczak CE, Dogic Z, Needleman DJ. Structure and dynamics of motor-driven microtubule bundles. SOFT MATTER 2024. [PMID: 38872426 DOI: 10.1039/d3sm01336g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
Connecting the large-scale emergent behaviors of active cytoskeletal materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems. We approach this problem by studying the impact of depletion attraction on bundles of microtubules and kinesin-14 molecular motors. For all depletant concentrations, kinesin-14 bundles generate comparable extensile dynamics. However, this invariable mesoscopic behavior masks the transition in the microscopic motion of microtubules. Specifically, with increasing attraction, we observe a transition from bi-directional sliding with extension to pure extension with no sliding. Small-angle X-ray scattering shows that the transition in microtubule dynamics is concurrent with a structural rearrangement of microtubules from an open hexagonal to a compressed rectangular lattice. These results demonstrate that bundles of microtubules and molecular motors can display the same mesoscopic extensile behaviors despite having different internal structures and microscopic dynamics. They provide essential information for developing multiscale models of active matter.
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Affiliation(s)
- Bezia Lemma
- Physics Department, Harvard University, Cambridge, MA 02138, USA
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
| | - Linnea M Lemma
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
| | | | - Claire E Walczak
- Medical Sciences, Indiana University School of Medicine, Bloomington, IN 47405, USA
| | - Zvonimir Dogic
- Physics Department, Brandeis University, Waltham, MA 02453, USA.
- Physics Department, University of California, Santa Barbara, CA 93106, USA
- Biomolecular Science & Engineering Department, University of California, Santa Barbara, CA 93106, USA
| | - Daniel J Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Molecular & Cellular Biology Department, Harvard University, Cambridge, MA 02138, USA
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
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2
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Redford SA, Colen J, Shivers JL, Zemsky S, Molaei M, Floyd C, Ruijgrok PV, Vitelli V, Bryant Z, Dinner AR, Gardel ML. Motor crosslinking augments elasticity in active nematics. SOFT MATTER 2024; 20:2480-2490. [PMID: 38385209 PMCID: PMC10933839 DOI: 10.1039/d3sm01176c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Accepted: 01/12/2024] [Indexed: 02/23/2024]
Abstract
In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.
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Affiliation(s)
- Steven A Redford
- The Graduate Program in Biophysical Sciences, University of Chicago, Chicago, IL 60637, USA
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
| | - Jonathan Colen
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
| | - Jordan L Shivers
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Sasha Zemsky
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
- Program in Biophysics, Stanford University, Stanford, CA 94305, USA
| | - Mehdi Molaei
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
| | - Carlos Floyd
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Paul V Ruijgrok
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Vincenzo Vitelli
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
| | - Zev Bryant
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
- Department of Structural Biology, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Aaron R Dinner
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Margaret L Gardel
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
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3
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Najma B, Wei WS, Baskaran A, Foster PJ, Duclos G. Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors. Proc Natl Acad Sci U S A 2024; 121:e2300174121. [PMID: 38175870 PMCID: PMC10786313 DOI: 10.1073/pnas.2300174121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 10/07/2023] [Indexed: 01/06/2024] Open
Abstract
Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.
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Affiliation(s)
- Bibi Najma
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Wei-Shao Wei
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, MA02453
| | - Peter J. Foster
- Department of Physics, Brandeis University, Waltham, MA02453
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4
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Ray S, Zhang J, Dogic Z. Rectified Rotational Dynamics of Mobile Inclusions in Two-Dimensional Active Nematics. PHYSICAL REVIEW LETTERS 2023; 130:238301. [PMID: 37354394 DOI: 10.1103/physrevlett.130.238301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 04/14/2023] [Indexed: 06/26/2023]
Abstract
We investigate the dynamics of mobile inclusions embedded in 2D active nematics. The interplay between the inclusion shape, boundary-induced nematic order, and autonomous flows powers the inclusion motion. Disks and achiral gears exhibit unbiased rotational motion, but with distinct dynamics. In comparison, chiral gear-shaped inclusions exhibit long-term rectified rotation, which is correlated with dynamics and polarization of nearby +1/2 topological defects. The chirality of defect polarities and the active nematic texture around the inclusion correlate with the inclusion's instantaneous rotation rate. Inclusions provide a promising tool for probing the rheological properties of active nematics and extracting ordered motion from their inherently chaotic motion.
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Affiliation(s)
- Sattvic Ray
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Jie Zhang
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China (USTC), 230026 Hefei, China
- Department of Polymer Science and Engineering, CAS Key Laboratory of Soft Matter Chemistry, University of Science and Technology of China (USTC), 230026 Hefei, China
| | - Zvonimir Dogic
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
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5
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Lemma LM, Varghese M, Ross TD, Thomson M, Baskaran A, Dogic Z. Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids. PNAS NEXUS 2023; 2:pgad130. [PMID: 37168671 PMCID: PMC10165807 DOI: 10.1093/pnasnexus/pgad130] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/11/2022] [Revised: 02/27/2023] [Accepted: 04/03/2023] [Indexed: 05/13/2023]
Abstract
Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
- Department of Physics, University of California, Santa Barbara, 93106 CA, USA
| | - Minu Varghese
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
| | - Tyler D Ross
- Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd. Pasadena, 91125 CA, USA
| | - Matt Thomson
- Division of Biology and Biological Engineering, California Institute of Technology, 1200 E California Blvd., Pasadena, 91125 CA, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
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6
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Joshi C, Ray S, Lemma LM, Varghese M, Sharp G, Dogic Z, Baskaran A, Hagan MF. Data-Driven Discovery of Active Nematic Hydrodynamics. PHYSICAL REVIEW LETTERS 2022; 129:258001. [PMID: 36608242 DOI: 10.1103/physrevlett.129.258001] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.
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Affiliation(s)
- Chaitanya Joshi
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Sattvic Ray
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Minu Varghese
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 USA
| | - Graham Sharp
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Zvonimir Dogic
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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7
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Striebel M, Brauns F, Frey E. Length Regulation Drives Self-Organization in Filament-Motor Mixtures. PHYSICAL REVIEW LETTERS 2022; 129:238102. [PMID: 36563230 DOI: 10.1103/physrevlett.129.238102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 10/10/2022] [Indexed: 06/17/2023]
Abstract
Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.
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Affiliation(s)
- Moritz Striebel
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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8
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Spontaneous phase coordination and fluid pumping in model ciliary carpets. Proc Natl Acad Sci U S A 2022; 119:e2214413119. [PMID: 36322751 PMCID: PMC9659382 DOI: 10.1073/pnas.2214413119] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023] Open
Abstract
Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.
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9
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Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity. Nat Commun 2022; 13:6573. [PMID: 36323696 PMCID: PMC9630547 DOI: 10.1038/s41467-022-34396-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 10/24/2022] [Indexed: 11/06/2022] Open
Abstract
Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.
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10
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Najma B, Varghese M, Tsidilkovski L, Lemma L, Baskaran A, Duclos G. Competing instabilities reveal how to rationally design and control active crosslinked gels. Nat Commun 2022; 13:6465. [PMID: 36309493 PMCID: PMC9617906 DOI: 10.1038/s41467-022-34089-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 10/13/2022] [Indexed: 12/25/2022] Open
Abstract
How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.
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Affiliation(s)
- Bibi Najma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Minu Varghese
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.214458.e0000000086837370Department of Physics, University of Michigan, Ann Arbor, MI 48109 USA
| | - Lev Tsidilkovski
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Linnea Lemma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.133342.40000 0004 1936 9676Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106 USA ,grid.16750.350000 0001 2097 5006Present Address: Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544 USA
| | - Aparna Baskaran
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Guillaume Duclos
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
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11
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Lorenz C, Köster S. Multiscale architecture: Mechanics of composite cytoskeletal networks. BIOPHYSICS REVIEWS 2022; 3:031304. [PMID: 38505277 PMCID: PMC10903411 DOI: 10.1063/5.0099405] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 07/27/2022] [Indexed: 03/21/2024]
Abstract
Different types of biological cells respond differently to mechanical stresses, and these responses are mainly governed by the cytoskeleton. The main components of this biopolymer network are actin filaments, microtubules, and intermediate filaments, whose mechanical and dynamic properties are highly distinct, thus opening up a large mechanical parameter space. Aside from experiments on whole, living cells, "bottom-up" approaches, utilizing purified, reconstituted protein systems, tremendously help to shed light on the complex mechanics of cytoskeletal networks. Such experiments are relevant in at least three aspects: (i) from a fundamental point of view, cytoskeletal networks provide a perfect model system for polymer physics; (ii) in materials science and "synthetic cell" approaches, one goal is to fully understand properties of cellular materials and reconstitute them in synthetic systems; (iii) many diseases are associated with cell mechanics, so a thorough understanding of the underlying phenomena may help solving pressing biomedical questions. In this review, we discuss the work on networks consisting of one, two, or all three types of filaments, entangled or cross-linked, and consider active elements such as molecular motors and dynamically growing filaments. Interestingly, tuning the interactions among the different filament types results in emergent network properties. We discuss current experimental challenges, such as the comparability of different studies, and recent methodological advances concerning the quantification of attractive forces between filaments and their influence on network mechanics.
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Affiliation(s)
- C. Lorenz
- Institute for X-Ray Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - S. Köster
- Author to whom correspondence should be addressed:
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12
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Lepcha G, Singha T, Majumdar S, Pradhan AK, Das KS, Datta PK, Dey B. Adipic acid directed self-healable supramolecular metallogels of Co(II) and Ni(II): intriguing scaffolds for comparative optical-phenomenon in terms of third-order optical non-linearity. Dalton Trans 2022; 51:13435-13443. [PMID: 35993453 DOI: 10.1039/d2dt01983c] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Two brilliant outcomes of supramolecular self-assembly directed, low molecular weight organic gelator based self-healable Co(II) and Ni(II) metallogels were achieved. Adipic acid as the low molecular weight organic gelator and dimethylformamide (DMF) solvent are employed for the metallogelation process. Rheological analyses of both gel-scaffolds reveal mechanical toughness as well as visco-elasticity. Thixotropic behaviours of both the gels were scrutinized. Morphological variations due to the presence of two different metal ions with diverse metal-ligand coordinating interactions were established. The mechanistic pathways for forming stable metallogels of Co(II)-adipic acid (Co-AA) and Ni(II)-adipic acid (Ni-AA) were judiciously developed through infrared absorption spectral analysis. The nonlinear optical properties, such as the third-order process, of these synthesized metallogels were scrutinized by means of the Z-scan method at a beam excitation wavelength of 750 nm by a femtosecond laser with different excitation intensities ranging from 64 to 140 GW cm-2. The third-order nonlinear optical susceptibility (χ(3)) of the order of 10-14 esu was obtained from the measured Z-scan data. Both the metallogels exhibit positive nonlinear refraction and reverse saturable (RSA) absorption at high-intensity excitation. Co(II) and Ni(II) metallogels show nonlinear refractive indices (n2I) of (3.619 ± 0.146) × 10-6 cm2 GW-1 and (3.472 ± 0.102) × 10-6 cm2 GW-1, respectively, and two photon absorption coefficients (β) of (1.503 ± 0.045) × 10-1 cm GW-1 and (1.381 ± 0.029) × 10-1 cm GW-1 at an excitation intensity of 140 GW cm-2. We also studied the optical limiting properties with a limiting threshold of 9.57 mJ cm-2. Therefore, both metallogels can be considered promising materials for photonic devices: for instance, for optical switching and optical limiting.
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Affiliation(s)
- Gerald Lepcha
- Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India.
| | - Tara Singha
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India.
| | - Santanu Majumdar
- Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India.
| | - Amit Kumar Pradhan
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India.
| | - Krishna Sundar Das
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, West Bengal 700032, India
| | - Prasanta Kumar Datta
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India.
| | - Biswajit Dey
- Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India.
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13
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Lemma B, Mitchell NP, Subramanian R, Needleman DJ, Dogic Z. Active Microphase Separation in Mixtures of Microtubules and Tip-Accumulating Molecular Motors. PHYSICAL REVIEW. X 2022; 12:031006. [PMID: 36643940 PMCID: PMC9835929 DOI: 10.1103/physrevx.12.031006] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Mixtures of filaments and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. To develop a multiscale of these materials, we map the nonequilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulentlike extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous nonequilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D active foams. Finally, we describe intricate kinetic pathways that yield microphase separated structures and arise from the inherent frustration between the orientational order of filamentous microtubules and the positional order of tip-accumulating molecular motors. Our work reveals a range of novel active states. It also shows that the form of active stresses is not solely dictated by the properties of individual motors and filaments, but is also contingent on the constituent concentrations and spatial arrangement of motors on the filaments.
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Affiliation(s)
- Bezia Lemma
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
- Physics Department, University of California, Santa Barbara, California 93106, USA
| | - Noah P. Mitchell
- Physics Department, University of California, Santa Barbara, California 93106, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Radhika Subramanian
- Molecular Biology Department, Massachusetts General Hospital Boston, Massachusetts 02114, USA
- Genetics Department, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Daniel J. Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Molecular and Cellular Biology Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Zvonimir Dogic
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
- Physics Department, University of California, Santa Barbara, California 93106, USA
- Biomolecular Science and Engineering Department, University of California, Santa Barbara, California 93106, USA
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14
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Aranson IS. Bacterial active matter. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:076601. [PMID: 35605446 DOI: 10.1088/1361-6633/ac723d] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.
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Affiliation(s)
- Igor S Aranson
- Departments of Biomedical Engineering, Chemistry, and Mathematics, Pennsylvania State University, University Park, PA 16802, United States of America
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15
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Palmer B, Chen S, Govan P, Yan W, Gao T. Understanding topological defects in fluidized dry active nematics. SOFT MATTER 2022; 18:1013-1018. [PMID: 35018951 DOI: 10.1039/d1sm01405f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Dense assemblies of self-propelling rods (SPRs) may exhibit fascinating collective behaviors and anomalous physical properties that are far away from equilibrium. Using large-scale Brownian dynamics simulations, we investigate the dynamics of disclination defects in 2D fluidized swarming motions of dense dry SPRs (i.e., without hydrodynamic effects) that form notable local positional topological structures that are reminiscent of smectic order. We find the deformations of smectic-like rod layers can create unique polar structures that lead to slow translations and rotations of ±1/2-order defects, which are fundamentally different from the fast streaming defect motions observed in wet active matter. We measure and characterize the statistical properties of topological defects and reveal their connections with the coherent structures. Furthermore, we construct a bottom-up active-liquid-crystal model to analyze the instability of polar lanes, which effectively leads to defect formation between interlocked polar lanes and serves as the origin of the large-scale swarming motions.
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Affiliation(s)
- Bryce Palmer
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48864, USA.
| | - Sheng Chen
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48864, USA.
- Department of Biomedical Engineering, Yale University, West Haven, CT 06516, USA
| | - Patrick Govan
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48864, USA
| | - Wen Yan
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
| | - Tong Gao
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48864, USA.
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48864, USA
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16
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Yan W, Ansari S, Lamson A, Glaser MA, Blackwell R, Betterton MD, Shelley M. Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies. eLife 2022; 11:74160. [PMID: 35617115 PMCID: PMC9135453 DOI: 10.7554/elife.74160] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 04/24/2022] [Indexed: 11/17/2022] Open
Abstract
The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.
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Affiliation(s)
- Wen Yan
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
| | - Saad Ansari
- Department of Physics, University of Colorado BoulderBoulderUnited States
| | - Adam Lamson
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States,Department of Physics, University of Colorado BoulderBoulderUnited States
| | - Matthew A Glaser
- Department of Physics, University of Colorado BoulderBoulderUnited States
| | - Robert Blackwell
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
| | - Meredith D Betterton
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States,Department of Physics, University of Colorado BoulderBoulderUnited States,Department of Molecular, Cellular, and Developmental Biology, University of Colorado BoulderBoulderUnited States
| | - Michael Shelley
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States,Courant Institute, New York UniversityNew YorkUnited States
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17
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Mahajan A, Saintillan D. Self-induced hydrodynamic coil-stretch transition of active polymers. Phys Rev E 2022; 105:014608. [PMID: 35193223 DOI: 10.1103/physreve.105.014608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
We analyze the conformational dynamics and statistical properties of an active polymer model. The polymer is described as a freely jointed bead-rod chain subject to stochastic active force dipoles that act on the suspending solvent where they drive long-ranged fluid flows. Using Langevin simulations of isolated chains in unconfined domains, we show how the coupling of active flows with polymer conformations leads to emergent dynamics. Systems with contractile dipoles behave similarly to passive Brownian chains with enhanced fluctuations due to dipolar flows. In systems with extensile dipoles, however, our simulations uncover an active coil-stretch transition whereby the polymer spontaneously unfolds and stretches out in its own self-induced hydrodynamic flow, and we characterize this transition in terms of a dimensionless activity parameter comparing active dipolar forces to thermal fluctuations. We discuss our findings in the context of the classic coil-stretch transition of passive polymers in extensional flows and complement our simulations with a simple kinetic model for an active trimer.
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Affiliation(s)
- Achal Mahajan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA
| | - David Saintillan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA
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18
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Lemma LM, Norton MM, Tayar AM, DeCamp SJ, Aghvami SA, Fraden S, Hagan MF, Dogic Z. Multiscale Microtubule Dynamics in Active Nematics. PHYSICAL REVIEW LETTERS 2021; 127:148001. [PMID: 34652175 DOI: 10.1103/physrevlett.127.148001] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 06/14/2021] [Accepted: 08/12/2021] [Indexed: 05/12/2023]
Abstract
In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael M Norton
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Alexandra M Tayar
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Stephen J DeCamp
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - S Ali Aghvami
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
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19
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Fiorenza SA, Steckhahn DG, Betterton MD. Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:105. [PMID: 34406510 PMCID: PMC10202044 DOI: 10.1140/epje/s10189-021-00097-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 06/21/2021] [Indexed: 05/24/2023]
Abstract
Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.
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Affiliation(s)
- Shane A Fiorenza
- Department of Physics, University of Colorado Boulder, Boulder, USA
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20
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Abstract
Cytoskeletal active nematics exhibit striking nonequilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold, the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale nonequilibrium dynamics of active nematics.
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21
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Chen YC, Jolicoeur B, Chueh CC, Wu KT. Flow coupling between active and passive fluids across water-oil interfaces. Sci Rep 2021; 11:13965. [PMID: 34234195 PMCID: PMC8263611 DOI: 10.1038/s41598-021-93310-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 06/23/2021] [Indexed: 01/17/2023] Open
Abstract
Active fluid droplets surrounded by oil can spontaneously develop circulatory flows. However, the dynamics of the surrounding oil and their influence on the active fluid remain poorly understood. To investigate interactions between the active fluid and the passive oil across their interface, kinesin-driven microtubule-based active fluid droplets were immersed in oil and compressed into a cylinder-like shape. The droplet geometry supported intradroplet circulatory flows, but the circulation was suppressed when the thickness of the oil layer surrounding the droplet decreased. Experiments with tracers and network structure analyses and continuum models based on the dynamics of self-elongating rods demonstrated that the flow transition resulted from flow coupling across the interface between active fluid and oil, with a millimeter-scale coupling length. In addition, two novel millifluidic devices were developed that could trigger and suppress intradroplet circulatory flows in real time: one by changing the thickness of the surrounding oil layer and the other by locally deforming the droplet. This work highlights the role of interfacial dynamics in the active fluid droplet system and shows that circulatory flows within droplets can be affected by millimeter-scale flow coupling across the interface between the active fluid and the oil.
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Affiliation(s)
- Yen-Chen Chen
- Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
| | - Brock Jolicoeur
- Department of Physics, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
| | - Chih-Che Chueh
- Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, 701, Taiwan
| | - Kun-Ta Wu
- Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, 01609, USA.
- Department of Physics, Worcester Polytechnic Institute, Worcester, MA, 01609, USA.
- The Martin Fisher School of Physics, Brandeis University, Waltham, MA, 02454, USA.
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22
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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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23
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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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24
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Chandrakar P, Varghese M, Aghvami SA, Baskaran A, Dogic Z, Duclos G. Confinement Controls the Bend Instability of Three-Dimensional Active Liquid Crystals. PHYSICAL REVIEW LETTERS 2020; 125:257801. [PMID: 33416339 DOI: 10.1103/physrevlett.125.257801] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 10/15/2020] [Accepted: 11/11/2020] [Indexed: 06/12/2023]
Abstract
Spontaneous growth of long-wavelength deformations is a defining feature of active liquid crystals. We investigate the effect of confinement on the instability of 3D active liquid crystals in the isotropic phase composed of extensile microtubule bundles and kinesin molecular motors. When shear aligned, such fluids exhibit finite-wavelength self-amplifying bend deformations. By systematically changing the channel size we elucidate how the instability wavelength and its growth rate depend on the channel dimensions. Experimental findings are qualitatively consistent with a minimal hydrodynamic model, where the fastest growing deformation is set by a balance of active driving and elastic relaxation. Our results demonstrate that confinement determines the structure and dynamics of active fluids on all experimentally accessible length scales.
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Affiliation(s)
- Pooja Chandrakar
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Minu Varghese
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - S Ali Aghvami
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Guillaume Duclos
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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25
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Moore JM, Thompson TN, Glaser MA, Betterton MD. Collective motion of driven semiflexible filaments tuned by soft repulsion and stiffness. SOFT MATTER 2020; 16:9436-9442. [PMID: 32959862 DOI: 10.1039/d0sm01036g] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins form complex structures important for cell mechanics, motility, and division. Collective dynamics of cytoskeletal systems can be reconstituted using filament gliding experiments, in which cytoskeletal filaments are propelled by surface-bound motor proteins. These experiments have observed diverse dynamical states, including flocks, polar streams, swirling vortices, and single-filament spirals. Recent experiments with microtubules and kinesin motor proteins found that the collective behavior of gliding filaments can be tuned by altering the concentration of the crowding macromolecule methylcellulose in solution. Increasing the methylcellulose concentration reduced filament crossing, promoted alignment, and led to a transition from active, isotropically oriented filaments to locally aligned polar streams. This emergence of collective motion is typically explained as an increase in alignment interactions by Vicsek-type models of active polar particles. However, it is not yet understood how steric interactions and bending stiffness modify the collective behavior of active semiflexible filaments. Here we use simulations of driven filaments with tunable soft repulsion and rigidity in order to better understand how the interplay between filament flexibility and steric effects can lead to different active dynamic states. We find that increasing filament stiffness decreases the probability of filament alignment, yet increases collective motion and long-range order, in contrast to the assumptions of a Vicsek-type model. We identify swirling flocks, polar streams, buckling bands, and spirals, and describe the physics that govern transitions between these states. In addition to repulsion and driving, tuning filament stiffness can promote collective behavior, and controls the transition between active isotropic filaments, locally aligned flocks, and polar streams.
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Affiliation(s)
- Jeffrey M Moore
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Tyler N Thompson
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Matthew A Glaser
- Department of Physics, University of Colorado, Boulder, CO 80309, USA.
| | - Meredith D Betterton
- Department of Physics, University of Colorado, Boulder, CO 80309, USA. and Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, CO 80309, USA
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26
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Gagnon DA, Dessi C, Berezney JP, Boros R, Chen DTN, Dogic Z, Blair DL. Shear-Induced Gelation of Self-Yielding Active Networks. PHYSICAL REVIEW LETTERS 2020; 125:178003. [PMID: 33156652 DOI: 10.1103/physrevlett.125.178003] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Accepted: 09/14/2020] [Indexed: 06/11/2023]
Abstract
An enticing feature of active materials is the possibility of controlling macroscale rheological properties through the activity of the microscopic constituents. Using a unique combination of microscopy and rheology we study three dimensional microtubule-based active materials whose autonomous flows are powered by a continually rearranging connected network. We quantify the relationship between the microscopic dynamics and the bulk mechanical properties of these nonequilibrium networks. Experiments reveal a surprising nonmonotonic viscosity that strongly depends on the relative magnitude of the rate of internally generated activity and the externally applied shear. A simple two-state mechanical model that accounts for both the solidlike and yielded fluidlike elements of the network accurately describes the rheological measurements.
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Affiliation(s)
- David A Gagnon
- Department of Physics and Institute for Soft Matter Synthesis & Metrology, Georgetown University, 3700 O Street NW, Washington, D.C. 20057, USA
| | - Claudia Dessi
- Department of Physics and Institute for Soft Matter Synthesis & Metrology, Georgetown University, 3700 O Street NW, Washington, D.C. 20057, USA
| | - John P Berezney
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Remi Boros
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Daniel T-N Chen
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Zvonimir Dogic
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Daniel L Blair
- Department of Physics and Institute for Soft Matter Synthesis & Metrology, Georgetown University, 3700 O Street NW, Washington, D.C. 20057, USA
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27
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Chen S, Yan W, Gao T. Scaling law of Brownian rotation in dense hard-rod suspensions. Phys Rev E 2020; 102:012608. [PMID: 32794925 DOI: 10.1103/physreve.102.012608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 07/02/2020] [Indexed: 11/07/2022]
Abstract
Self-diffusion in dense rod suspensions are subject to strong geometric constraints because of steric interactions. This topological effect is essentially anisotropic when rods are nematically aligned with their neighbors, raising considerable challenges in understanding and analyzing their impacts on the bulk physical properties. Via a classical Doi-Onsager kinetic model with the Maier-Saupe potential, we characterize the long-time rotational Brownian diffusivity for dense suspensions of hard rods of finite aspect ratios, based on quadratic orientation autocorrelation functions. Furthermore, we show that the computed nonmonotonic scalings of the diffusivity as a function of volume fraction can be accurately predicted by an alternative tube model in the nematic phase.
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Affiliation(s)
- Sheng Chen
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48864, USA
| | - Wen Yan
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
| | - Tong Gao
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48864, USA.,Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48864, USA
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28
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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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29
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Vliegenthart GA, Ravichandran A, Ripoll M, Auth T, Gompper G. Filamentous active matter: Band formation, bending, buckling, and defects. SCIENCE ADVANCES 2020; 6:eaaw9975. [PMID: 32832652 PMCID: PMC7439626 DOI: 10.1126/sciadv.aaw9975] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2019] [Accepted: 06/05/2020] [Indexed: 06/01/2023]
Abstract
Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.
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30
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Duclos G, Adkins R, Banerjee D, Peterson MSE, Varghese M, Kolvin I, Baskaran A, Pelcovits RA, Powers TR, Baskaran A, Toschi F, Hagan MF, Streichan SJ, Vitelli V, Beller DA, Dogic Z. Topological structure and dynamics of three-dimensional active nematics. Science 2020; 367:1120-1124. [PMID: 32139540 DOI: 10.1126/science.aaz4547] [Citation(s) in RCA: 83] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Accepted: 02/07/2020] [Indexed: 12/30/2022]
Abstract
Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms.
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Affiliation(s)
- Guillaume Duclos
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Raymond Adkins
- Department of Physics, University of California, Santa Barbara, CA 93111, USA
| | - Debarghya Banerjee
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.,Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, Netherlands
| | | | - Minu Varghese
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Itamar Kolvin
- Department of Physics, University of California, Santa Barbara, CA 93111, USA
| | - Arvind Baskaran
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | | | - Thomas R Powers
- School of Engineering, Brown University, Providence, RI 02912, USA.,Department of Physics, Brown University, Providence, RI 02912, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands.,Instituto per le Applicazioni del Calcolo CNR, 00185 Rome, Italy
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | | | - Vincenzo Vitelli
- James Frank Institute and Department of Physics, The University of Chicago, Chicago, IL 60637, USA
| | - Daniel A Beller
- Department of Physics, University of California, Merced, CA 95343, USA.
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA 02453, USA. .,Department of Physics, University of California, Santa Barbara, CA 93111, USA
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31
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Lenz M. Reversal of contractility as a signature of self-organization in cytoskeletal bundles. eLife 2020; 9:51751. [PMID: 32149609 PMCID: PMC7082124 DOI: 10.7554/elife.51751] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Accepted: 03/05/2020] [Indexed: 12/13/2022] Open
Abstract
Bundles of cytoskeletal filaments and molecular motors generate motion in living cells, and have internal structures ranging from very organized to apparently disordered. The mechanisms powering the disordered structures are debated, and existing models predominantly predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay between three well-characterized internal dynamical processes in cytoskeletal bundles: filament assembly and disassembly, the attachement-detachment dynamics of motors and that of crosslinking proteins. The resulting self-organization is easily understood in terms of motor and crosslink localization, and allows for an extensive control of the active bundle mechanics, including reversals of the filaments’ apparent velocities and the possibility of generating extension instead of contraction. This reversal mirrors some recent experimental observations, and provides a robust criterion to experimentally elucidate the underpinnings of both actomyosin activity and the dynamics of microtubule/motor assemblies in vitro as well as in diverse intracellular structures ranging from contractile bundles to the mitotic spindle.
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Affiliation(s)
- Martin Lenz
- Université Paris-Saclay, CNRS, LPTMS, Orsay, France.,PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, Paris, France
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32
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Edelmaier C, Lamson AR, Gergely ZR, Ansari S, Blackwell R, McIntosh JR, Glaser MA, Betterton MD. Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling. eLife 2020; 9:48787. [PMID: 32053104 PMCID: PMC7311174 DOI: 10.7554/elife.48787] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 02/12/2020] [Indexed: 01/19/2023] Open
Abstract
The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle. Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle. Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know. Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle – including its length, structure and position – imaged from dividing yeast cells. Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly. Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.
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Affiliation(s)
| | - Adam R Lamson
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Zachary R Gergely
- Department of Physics, University of Colorado Boulder, Boulder, United States.,Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
| | - Saad Ansari
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Robert Blackwell
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - J Richard McIntosh
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
| | - Matthew A Glaser
- Department of Physics, University of Colorado Boulder, Boulder, United States
| | - Meredith D Betterton
- Department of Physics, University of Colorado Boulder, Boulder, United States.,Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Boulder, United States
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33
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Fürthauer S, Lemma B, Foster PJ, Ems-McClung SC, Yu CH, Walczak CE, Dogic Z, Needleman DJ, Shelley MJ. Self-straining of actively crosslinked microtubule networks. NATURE PHYSICS 2019; 15:1295-1300. [PMID: 32322291 PMCID: PMC7176317 DOI: 10.1038/s41567-019-0642-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 07/17/2019] [Indexed: 05/26/2023]
Abstract
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and densely crosslinked. Relating their large-scale dynamics to the properties of their constituents remains an unsolved problem. Here, we study an in vitro active gel made from aligned microtubules and XCTK2 kinesin motors. Using photobleaching, we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local microtubule polarity and motor concentration. This phenomenon is also observed, and remains unexplained, in spindles. We derive a general framework for coarse graining microtubule gels crosslinked by molecular motors from microscopic considerations. Using microtubule-microtubule coupling through a force-velocity relationship for kinesin, this theory naturally explains the experimental results: motors generate an active strain rate in regions of changing polarity, which allows microtubules of opposite polarities to slide past each other without stressing the material.
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Affiliation(s)
| | - Bezia Lemma
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics, Brandeis University, Waltham, MA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Peter J Foster
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | | | - Che-Hang Yu
- Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA
| | | | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Daniel J Needleman
- Paulson School of Engineering & Applied Science and Department of Molecular & Cellular Biology, Harvard University, Cambridge, MA, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
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34
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Striebel M, Graf IR, Frey E. A Mechanistic View of Collective Filament Motion in Active Nematic Networks. Biophys J 2019; 118:313-324. [PMID: 31843261 DOI: 10.1016/j.bpj.2019.11.3387] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2019] [Revised: 11/18/2019] [Accepted: 11/21/2019] [Indexed: 01/05/2023] Open
Abstract
Protein filament networks are structures crucial for force generation and cell shape. A central open question is how collective filament dynamics emerges from interactions between individual network constituents. To address this question, we study a minimal but generic model for a nematic network in which filament sliding is driven by the action of motor proteins. Our theoretical analysis shows how the interplay between viscous drag on filaments and motor-induced forces governs force propagation through such interconnected filament networks. We find that the ratio between these antagonistic forces establishes the range of filament interaction, which determines how the local filament velocity depends on the polarity of the surrounding network. This force-propagation mechanism implies that the polarity-independent sliding observed in Xenopus egg extracts and in vitro experiments with purified components is a consequence of a large force-propagation length. We suggest how our predictions can be tested by tangible in vitro experiments whose feasibility is assessed with the help of simulations and an accompanying theoretical analysis.
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Affiliation(s)
- Moritz Striebel
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Isabella R Graf
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany.
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35
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Redemann S, Fürthauer S, Shelley M, Müller-Reichert T. Current approaches for the analysis of spindle organization. Curr Opin Struct Biol 2019; 58:269-277. [DOI: 10.1016/j.sbi.2019.05.023] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Revised: 05/28/2019] [Accepted: 05/29/2019] [Indexed: 01/06/2023]
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36
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Lin Z, Gao T. Direct-forcing fictitious domain method for simulating non-Brownian active particles. Phys Rev E 2019; 100:013304. [PMID: 31499789 DOI: 10.1103/physreve.100.013304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Indexed: 11/07/2022]
Abstract
We present a direct-forcing fictitious domain method for simulating non-Brownian squirmer particles with both the hydrodynamic interactions and collisions being fully resolved. In this method, we solve the particle motion by distributing collocation points inside the particle interior domain that overlay upon a fixed Eulerian mesh. The fluid motions, including those of the "fictitious fluids" being extended into the particle, are solved on the entire computation domain. Pseudo-body forces are used to enforce the fictitious fluids to follow the particle movement. A direct-forcing approach is employed to map physical variables between the overlaid meshes, which does not require additional iterations to achieve convergence. We perform a series of numerical studies at both small and finite Reynolds numbers. First, accuracy of the algorithm is examined in studying benchmark problems of a free-swimming squirmer and two side-by-side squirmers. Then we investigate statistic properties of the quasi-two-dimensional collective dynamics for a monolayer of squirmer particles that are confined on a surface immersed in a bulk flow. Finally, we explore the physical mechanisms of how a freely moving short cylinder interacts with a monolayer of active particles, and find out that the cylinder movement is dominated by collision. We demonstrate that a more directional migration of cylinder can be resultant from an inhomogeneous distribution of active particles around the cylinder that has an anisotropic shape.
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Affiliation(s)
- Zhaowu Lin
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Tong Gao
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA.,Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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37
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Maryshev I, Goryachev AB, Marenduzzo D, Morozov A. Dry active turbulence in a model for microtubule-motor mixtures. SOFT MATTER 2019; 15:6038-6043. [PMID: 31298679 DOI: 10.1039/c9sm00558g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the dynamics and phase behaviour of a dry suspension of microtubules and molecular motors. We obtain a set of continuum equations by rigorously coarse graining a microscopic model where motor-induced interactions lead to parallel or antiparallel ordering. Through numerical simulations, we show that this model generically creates either stable stripes, or a never-settling pattern where stripes periodically form, rotate and then split up. We derive a minimal model which displays the same instability as the full model, and clarifies the underlying physical mechanism. The necessary ingredients are an extensile flux arising from microtubule sliding and an interfacial torque favouring ordering along density gradients. We argue that our minimal model unifies various previous observations of chaotic behaviour in dry active matter into a general universality class.
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Affiliation(s)
- Ivan Maryshev
- Centre for Synthetic and Systems Biology, Institute of Cell Biology, School of Biological Sciences, The University of Edinburgh, Max Born Crescent, Edinburgh EH9 3BF, UK.
| | - Andrew B Goryachev
- Centre for Synthetic and Systems Biology, Institute of Cell Biology, School of Biological Sciences, The University of Edinburgh, Max Born Crescent, Edinburgh EH9 3BF, UK.
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Alexander Morozov
- 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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38
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Man Y, Kanso E. Morphological transitions of axially-driven microfilaments. SOFT MATTER 2019; 15:5163-5173. [PMID: 31215548 DOI: 10.1039/c8sm02397b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The interactions of microtubules with motor proteins are ubiquitous in cellular and sub-cellular processes that involve motility and cargo transport. In vitro motility assays have demonstrated that motor-driven microtubules exhibit rich dynamical behaviors from straight to curved configurations. Here, we theoretically investigate the dynamic instabilities of elastic filaments, with free-ends, driven by single follower forces that emulate the action of molecular motors. Using the resistive force theory at low Reynolds number, and a combination of numerical techniques with linear stability analysis, we show the existence of four distinct regimes of filament behavior, including a novel buckled state with locked curvature. These successive instabilities recapitulate the full range of experimentally-observed microtubule behavior, implying that neither structural nor actuation asymmetry are needed to elicit this rich repertoire of motion.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical engineering, University of Southern California, CA 90007, USA.
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39
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Abstract
The assembly of the mitotic spindle and the subsequent segregation of sister chromatids are based on the self-organized action of microtubule filaments, motor proteins, and other microtubule-associated proteins, which constitute the fundamental force-generating elements in the system. Many of the components in the spindle have been identified, but until recently it remained unclear how their collective behaviors resulted in such a robust bipolar structure. Here, we review the current understanding of the physics of the metaphase spindle that is only now starting to emerge.
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Affiliation(s)
- David Oriola
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307, Dresden, Germany; .,Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany.,Center for Systems Biology Dresden, 01307, Dresden, Germany
| | - Daniel J Needleman
- School of Engineering and Applied Sciences, Department of Molecular and Cellular Biology, and FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts 021382, USA
| | - Jan Brugués
- Max Planck Institute of Molecular Cell Biology and Genetics, 01307, Dresden, Germany; .,Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany.,Center for Systems Biology Dresden, 01307, Dresden, Germany
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40
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Rickman J, Nédélec F, Surrey T. Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization. Phys Biol 2019; 16:046004. [PMID: 31013252 PMCID: PMC7655122 DOI: 10.1088/1478-3975/ab0fb1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Active networks composed of filaments and motor proteins can self-organize into a
variety of architectures. Computer simulations in two or three spatial
dimensions and including or omitting steric interactions between filaments can
be used to model active networks. Here we examine how these modelling choices
affect the state space of network self-organization. We compare the networks
generated by different models of a system of dynamic microtubules and
microtubule-crosslinking motors. We find that a thin 3D model that includes
steric interactions between filaments is the most versatile, capturing a variety
of network states observed in recent experiments. In contrast, 2D models either
with or without steric interactions which prohibit microtubule crossings can
produce some, but not all, observed network states. Our results provide
guidelines for the most appropriate choice of model for the study of different
network types and elucidate mechanisms of active network organization.
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Affiliation(s)
- Jamie Rickman
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, United Kingdom. Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, London WC1 6BT, United Kingdom
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41
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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: 45] [Impact Index Per Article: 9.0] [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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42
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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: 74] [Impact Index Per Article: 14.8] [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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43
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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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44
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Bonelli F, Carenza LN, Gonnella G, Marenduzzo D, Orlandini E, Tiribocchi A. Lamellar ordering, droplet formation and phase inversion in exotic active emulsions. Sci Rep 2019; 9:2801. [PMID: 30808917 PMCID: PMC6391428 DOI: 10.1038/s41598-019-39190-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Accepted: 12/10/2018] [Indexed: 11/26/2022] Open
Abstract
We study numerically the behaviour of a two-dimensional mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the lamellar phase in the passive limit, we show that the interplay between nonequilibrium and thermodynamic forces creates a range of multifarious exotic emulsions. When the active component is contractile (e.g., an actomyosin solution), moderate activity enhances the efficiency of lamellar ordering, whereas strong activity favours the creation of passive droplets within an active matrix. For extensile activity (occurring, e.g., in microtubule-motor suspensions), instead, we observe an emulsion of spontaneously rotating droplets of different size. By tuning the overall composition, we can create high internal phase emulsions, which undergo sudden phase inversion when activity is switched off. Therefore, we find that activity provides a single control parameter to design composite materials with a strikingly rich range of morphologies.
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Affiliation(s)
- F Bonelli
- Dipartimento di Meccanica, Matematica e Management, DMMM, Politecnico di Bari, 70125, Bari, Italy
| | - L N Carenza
- Dipartimento di Fisica, Universitá degli Srudi di Bari and INFN, Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - G Gonnella
- Dipartimento di Fisica, Universitá degli Srudi di Bari and INFN, Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ, United Kingdom
| | - E Orlandini
- Dipartimento di Fisica e Astronomia, Universitá di Padova, 35131, Padova, Italy
| | - A Tiribocchi
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, Viale Regina Elena, 295, I-00161, Roma, Italy.
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Ravichandran A, Duman Ö, Hoore M, Saggiorato G, Vliegenthart GA, Auth T, Gompper G. Chronology of motor-mediated microtubule streaming. eLife 2019; 8:e39694. [PMID: 30601119 PMCID: PMC6338466 DOI: 10.7554/elife.39694] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 12/28/2018] [Indexed: 12/19/2022] Open
Abstract
We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.
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Affiliation(s)
- Arvind Ravichandran
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Özer Duman
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Masoud Hoore
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Guglielmo Saggiorato
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Gerard A Vliegenthart
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Thorsten Auth
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced SimulationForschungszentrum JülichJülichGermany
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Arango-Restrepo A, Barragán D, Rubi JM. Self-assembling outside equilibrium: emergence of structures mediated by dissipation. Phys Chem Chem Phys 2019; 21:17475-17493. [DOI: 10.1039/c9cp01088b] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.
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Affiliation(s)
- A. Arango-Restrepo
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
| | - D. Barragán
- Escuela de Química
- Facultad de Ciencias
- Universidad Nacional de Colombia
- Medellín
- Colombia
| | - J. M. Rubi
- Departament de Física de la Matéria Condensada
- Facultat de Física
- Universitat de Barcelona
- 08028 Barcelona
- Spain
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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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48
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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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Foster PJ, Fürthauer S, Shelley MJ, Needleman DJ. From cytoskeletal assemblies to living materials. Curr Opin Cell Biol 2018; 56:109-114. [PMID: 30500745 DOI: 10.1016/j.ceb.2018.10.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Revised: 09/21/2018] [Accepted: 10/31/2018] [Indexed: 11/29/2022]
Abstract
Many subcellular structures contain large numbers of cytoskeletal filaments. Such assemblies underlie much of cell division, motility, signaling, metabolism, and growth. Thus, understanding cell biology requires understanding the properties of networks of cytoskeletal filaments. While there are well established disciplines in biology dedicated to studying isolated proteins - their structure (Structural Biology) and behaviors (Biochemistry) - it is much less clear how to investigate, or even just describe, the structure and behaviors of collections of cytoskeletal filaments. One approach is to use methodologies from Mechanics and Soft Condensed Matter Physics, which have been phenomenally successful in the domains where they have been traditionally applied. From this perspective, collections of cytoskeletal filaments are viewed as materials, albeit very complex, 'active' materials, composed of molecules which use chemical energy to perform mechanical work. A major challenge is to relate these material level properties to the behaviors of the molecular constituents. Here we discuss this materials perspective and review recent work bridging molecular and network scale properties of the cytoskeleton, focusing on the organization of microtubules by dynein as an illustrative example.
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Affiliation(s)
- Peter J Foster
- Physics of Livings Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Sebastian Fürthauer
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA; Courant Institute, New York University, New York, NY 10012, USA
| | - Daniel J Needleman
- John A. Paulson School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA; Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA
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50
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Extensile motor activity drives coherent motions in a model of interphase chromatin. Proc Natl Acad Sci U S A 2018; 115:11442-11447. [PMID: 30348795 DOI: 10.1073/pnas.1807073115] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The 3D spatiotemporal organization of the human genome inside the cell nucleus remains a major open question in cellular biology. In the time between two cell divisions, chromatin-the functional form of DNA in cells-fills the nucleus in its uncondensed polymeric form. Recent in vivo imaging experiments reveal that the chromatin moves coherently, having displacements with long-ranged correlations on the scale of micrometers and lasting for seconds. To elucidate the mechanism(s) behind these motions, we develop a coarse-grained active polymer model where chromatin is represented as a confined flexible chain acted upon by molecular motors that drive fluid flows by exerting dipolar forces on the system. Numerical simulations of this model account for steric and hydrodynamic interactions as well as internal chain mechanics. These demonstrate that coherent motions emerge in systems involving extensile dipoles and are accompanied by large-scale chain reconfigurations and nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that self-organizing long-ranged hydrodynamic couplings between chromatin-associated active motor proteins are responsible for the observed coherent dynamics.
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