1
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Anjur-Dietrich MI, Hererra VG, Farhadifar R, Wu H, Merta H, Bahmanyar S, Shelley MJ, Needleman DJ. Clustering of cortical dynein regulates the mechanics of spindle orientation in human mitotic cells. bioRxiv 2023:2023.09.11.557210. [PMID: 37745442 PMCID: PMC10515834 DOI: 10.1101/2023.09.11.557210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2023]
Abstract
The forces which orient the spindle in human cells remain poorly understood due to a lack of direct mechanical measurements in mammalian systems. We use magnetic tweezers to measure the force on human mitotic spindles. Combining the spindle's measured resistance to rotation, the speed it rotates after laser ablating astral microtubules, and estimates of the number of ablated microtubules reveals that each microtubule contacting the cell cortex is subject to ~1 pN of pulling force, suggesting that each is pulled on by an individual dynein motor. We find that the concentration of dynein at the cell cortex and extent of dynein clustering are key determinants of the spindle's resistance to rotation, with little contribution from cytoplasmic viscosity, which we explain using a biophysically based mathematical model. This work reveals how pulling forces on astral microtubules determine the mechanics of spindle orientation and demonstrates the central role of cortical dynein clustering.
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Affiliation(s)
- Maya I. Anjur-Dietrich
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Vicente Gomez Hererra
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
| | - Reza Farhadifar
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
| | - Haiyin Wu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA
| | - Holly Merta
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, CT 06520, USA
| | - Shirin Bahmanyar
- Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, CT 06520, USA
| | - Michael J. Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
| | - Daniel J. Needleman
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Department of Molecular and Cellular Biology, 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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Stone HA, Shelley MJ, Boyko E. A note about convected time derivatives for flows of complex fluids. Soft Matter 2023. [PMID: 37404018 DOI: 10.1039/d3sm00497j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Subscribe] [Scholar Register] [Indexed: 07/06/2023]
Abstract
We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.
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Affiliation(s)
- Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, New Jersey 08544, USA.
| | - Michael J Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY 10010, USA
| | - Evgeniy Boyko
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, 3200003, Israel.
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3
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Dutta S, Farhadifar R, Lu W, Kabacaoğlu G, Blackwell R, Stein DB, Lakonishok M, Gelfand VI, Shvartsman SY, Shelley MJ. Self-organized intracellular twisters. ArXiv 2023:arXiv:2304.02112v2. [PMID: 37064529 PMCID: PMC10104197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 04/18/2023]
Abstract
Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.
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Affiliation(s)
- Sayantan Dutta
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Reza Farhadifar
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Wen Lu
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | | | - Robert Blackwell
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - David B Stein
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Margot Lakonishok
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | - Vladimir I Gelfand
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | - Stanislav Y Shvartsman
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
- Center of Computational Biology, Flatiron Institute, New York, NY
- Department of Molecular Biology and Lewis Sigler Institute of Integrative Genomics, Princeton University, Princeton, NJ
| | - Michael J Shelley
- Center of Computational Biology, Flatiron Institute, New York, NY
- Courant Institute of Mathematical Sciences, New York University, New York, NY
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4
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Dutta S, Farhadifar R, Lu W, Kabacaoğlu G, Blackwell R, Stein DB, Lakonishok M, Gelfand VI, Shvartsman SY, Shelley MJ. Self-organized intracellular twisters. bioRxiv 2023:2023.04.04.534476. [PMID: 37066165 PMCID: PMC10104069 DOI: 10.1101/2023.04.04.534476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/18/2023]
Abstract
Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.
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Affiliation(s)
- Sayantan Dutta
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Reza Farhadifar
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Wen Lu
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | | | - Robert Blackwell
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - David B Stein
- Center of Computational Biology, Flatiron Institute, New York, NY
| | - Margot Lakonishok
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | - Vladimir I Gelfand
- Department of Cell and Developmental Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL
| | - Stanislav Y Shvartsman
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
- Center of Computational Biology, Flatiron Institute, New York, NY
- Department of Molecular Biology and Lewis Sigler Institute of Integrative Genomics, Princeton University, Princeton, NJ
| | - Michael J Shelley
- Center of Computational Biology, Flatiron Institute, New York, NY
- Courant Institute of Mathematical Sciences, New York University, New York, NY
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5
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Chakrabarti B, Shelley MJ, Fürthauer S. Collective Motion and Pattern Formation in Phase-Synchronizing Active Fluids. Phys Rev Lett 2023; 130:128202. [PMID: 37027863 DOI: 10.1103/physrevlett.130.128202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2022] [Revised: 11/21/2022] [Accepted: 02/22/2023] [Indexed: 06/19/2023]
Abstract
Many active particles, such as swimming micro-organisms or motor proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to synchronization of their duty cycles. Here, we study the collective dynamics of a suspension of active particles coupled through hydrodynamics. We find that at high enough density the system transitions to a state of collective motion by a mechanism that is distinct from other instabilities in active matter systems. Second, we demonstrate that the emergent nonequilibrium states feature stationary chimera patterns in which synchronized and phase-isotropic regions coexist. Third, we show that in confinement, oscillatory flows and robust unidirectional pumping states exist, and can be selected by choice of alignment boundary conditions. These results point toward a new route to collective motion and pattern formation and could guide the design of new active materials.
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Affiliation(s)
- Brato Chakrabarti
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
- Courant Institute, New York University, New York, New York 10012, USA
| | - Sebastian Fürthauer
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
- Institute of Applied Physics, TU Wien, A-1040 Wien, Austria
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6
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Ansari S, Yan W, Lamson A, Shelley MJ, Glaser MA, Betterton MD. Active condensation of filaments under spatial confinement. Front Phys 2022; 10:897255. [PMID: 38116396 PMCID: PMC10730113 DOI: 10.3389/fphy.2022.897255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles.
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Affiliation(s)
- Saad Ansari
- Department of Physics, University of Colorado Boulder, Colorado, USA
| | - Wen Yan
- Center for Computational Biology, Flatiron Institute, New York, USA
| | - Adam Lamson
- Center for Computational Biology, Flatiron Institute, New York, USA
| | - Michael J. Shelley
- Center for Computational Biology, Flatiron Institute, New York, USA
- Courant Institute, New York University, New York, USA
| | - Matthew A. Glaser
- Department of Physics, University of Colorado Boulder, Colorado, USA
- Center for Computational Biology, Flatiron Institute, New York, USA
| | - Meredith D. Betterton
- Department of Physics, University of Colorado Boulder, Colorado, USA
- Center for Computational Biology, Flatiron Institute, New York, USA
- Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, Colorado, USA
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7
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Hu S, Zhang J, Shelley MJ. Enhanced clamshell swimming with asymmetric beating at low Reynolds number. Soft Matter 2022; 18:3605-3612. [PMID: 35481832 DOI: 10.1039/d2sm00292b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A single flexible filament can be actuated to escape from the scallop theorem and generate net propulsion at low Reynolds number. In this work, we study the dynamics of a simple boundary-driven multi-filament swimmer, a two-arm clamshell actuated at the hinged point, using a nonlocal slender body approximation with hydrodynamic interactions. We first consider an elastic clamshell consisted of flexible filaments with intrinsic curvature, and then build segmental models consisted of rigid segments connected by different mechanical joints with different forms of response torques. The simplicity of the system allows us to fully explore the effect of various parameters on the swimming performance. Optimal included angles and elastoviscous numbers are identified. The segmental models capture the characteristic dynamics of the elastic clamshell. We further demonstrate how the swimming performance can be significantly enhanced by the asymmetric beating patterns induced by biased torques.
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Affiliation(s)
- Shiyuan Hu
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
- Department of Physics, New York University, New York, NY 10003, USA
- NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai 200062, China
| | - Jun Zhang
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
- Department of Physics, New York University, New York, NY 10003, USA
- NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai 200062, China
| | - Michael J Shelley
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA.
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8
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Chakrabarti B, Fürthauer S, Shelley MJ. A multiscale biophysical model gives quantized metachronal waves in a lattice of beating cilia. Proc Natl Acad Sci U S A 2022; 119:e2113539119. [PMID: 35046031 PMCID: PMC8795537 DOI: 10.1073/pnas.2113539119] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 12/02/2021] [Indexed: 11/18/2022] Open
Abstract
Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer-scale motor activity inside individual cilia. Our study of a one-dimensional lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that, in homogeneous beds of cilia, these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that, in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves.
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Affiliation(s)
- Brato Chakrabarti
- Center for Computational Biology, Flatiron Institute, New York, NY 10010
| | - Sebastian Fürthauer
- Center for Computational Biology, Flatiron Institute, New York, NY 10010;
- Institute of Applied Physics, TU Wien, Vienna 1040, Austria
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, NY 10010;
- Courant Institute, New York University, New York, NY 10012
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9
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Founounou N, Farhadifar R, Collu GM, Weber U, Shelley MJ, Mlodzik M. Tissue fluidity mediated by adherens junction dynamics promotes planar cell polarity-driven ommatidial rotation. Nat Commun 2021; 12:6974. [PMID: 34848713 PMCID: PMC8632910 DOI: 10.1038/s41467-021-27253-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 11/08/2021] [Indexed: 12/02/2022] Open
Abstract
The phenomenon of tissue fluidity-cells' ability to rearrange relative to each other in confluent tissues-has been linked to several morphogenetic processes and diseases, yet few molecular regulators of tissue fluidity are known. Ommatidial rotation (OR), directed by planar cell polarity signaling, occurs during Drosophila eye morphogenesis and shares many features with polarized cellular migration in vertebrates. We utilize in vivo live imaging analysis tools to quantify dynamic cellular morphologies during OR, revealing that OR is driven autonomously by ommatidial cell clusters rotating in successive pulses within a permissive substrate. Through analysis of a rotation-specific nemo mutant, we demonstrate that precise regulation of junctional E-cadherin levels is critical for modulating the mechanical properties of the tissue to allow rotation to progress. Our study defines Nemo as a molecular tool to induce a transition from solid-like tissues to more viscoelastic tissues broadening our molecular understanding of tissue fluidity.
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Affiliation(s)
- Nabila Founounou
- grid.59734.3c0000 0001 0670 2351Dept. of Cell, Developmental, & Regenerative Biology, Graduate School of Biomedical Sciences, Icahn School of Medicine at Mount Sinai, One Gustave L Levy Place, New York, NY 10029 USA
| | - Reza Farhadifar
- grid.430264.7Center for Computational Biology, Flatiron Institute, Simons Foundation, 162 5th Ave, New York, NY 10010 USA ,grid.38142.3c000000041936754XDepartment of Molecular and Cellular Biology, Harvard University, 52 Oxford St, Cambridge, MA 02138 USA
| | - Giovanna M. Collu
- grid.59734.3c0000 0001 0670 2351Dept. of Cell, Developmental, & Regenerative Biology, Graduate School of Biomedical Sciences, Icahn School of Medicine at Mount Sinai, One Gustave L Levy Place, New York, NY 10029 USA
| | - Ursula Weber
- grid.59734.3c0000 0001 0670 2351Dept. of Cell, Developmental, & Regenerative Biology, Graduate School of Biomedical Sciences, Icahn School of Medicine at Mount Sinai, One Gustave L Levy Place, New York, NY 10029 USA
| | - Michael J. Shelley
- grid.430264.7Center for Computational Biology, Flatiron Institute, Simons Foundation, 162 5th Ave, New York, NY 10010 USA ,grid.137628.90000 0004 1936 8753Courant Institute, New York University, 251 Mercer St, New York, NY 10012 USA
| | - Marek Mlodzik
- Dept. of Cell, Developmental, & Regenerative Biology, Graduate School of Biomedical Sciences, Icahn School of Medicine at Mount Sinai, One Gustave L Levy Place, New York, NY, 10029, USA.
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10
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Gallagher N, Collyer J, Shelley MJ, Sneddon KJ, Bowe CM. Football-related maxillofacial injuries. Br J Oral Maxillofac Surg 2021; 60:584-588. [PMID: 35027217 DOI: 10.1016/j.bjoms.2021.10.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Accepted: 10/02/2021] [Indexed: 11/29/2022]
Abstract
Maxillofacial injuries sustained playing sports are becoming increasingly common, and in the UK where football is the most popular team sport, associated maxillofacial injuries are a regular occurrence. This study retrospectively examined data on patients who were referred with facial injuries sustained playing football between 2007 and 2019 (n = 265). Demographics, mechanism of injury, diagnosis, and treatment received were analysed. The mean (SD) age was 25 (11.0) years (range 3-85) and there was a strong male predominance (n = 256, 97% male). Facial fractures were diagnosed in 143 (54%) patients. The most common injury was a midface fracture and the most common mechanism of injury was a clash of heads. Patients with a facial fracture were significantly more likely to have sustained a concurrent head injury (p = 0.006). Those who were elbowed or punched were significantly more likely to have a facial fracture than a soft tissue or dentoalveolar injury (p ≤ 0.05). Players who clashed heads were significantly more likely to have a midface fracture (p ≤ 0.001). In conclusion, football-related maxillofacial injuries predominantly affect young adult males following a clash of heads. An elbow or punch to the face carries a significant risk of facial fracture and concurrent head injury. Therefore, to reduce the percentage of maxillofacial injuries seen in this sport, observed intentional contact between players, using an elbow or fist to the face in particular, must continue to carry the highest sanction.
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Affiliation(s)
- N Gallagher
- Department of Oral & Maxillofacial Surgery, Queen Victoria Hospital Foundation Trust, East Grinstead, United Kingdom
| | - J Collyer
- Department of Oral & Maxillofacial Surgery, Queen Victoria Hospital Foundation Trust, East Grinstead, United Kingdom
| | - M J Shelley
- Department of Oral & Maxillofacial Surgery, Queen Victoria Hospital Foundation Trust, East Grinstead, United Kingdom
| | - K J Sneddon
- Department of Oral & Maxillofacial Surgery, Queen Victoria Hospital Foundation Trust, East Grinstead, United Kingdom
| | - C M Bowe
- Department of Oral & Maxillofacial Surgery, Queen Victoria Hospital Foundation Trust, East Grinstead, United Kingdom.
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11
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Hu SY, Chu JJ, Shelley MJ, Zhang J. Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows. Phys Rev Lett 2021; 127:074503. [PMID: 34459633 DOI: 10.1103/physrevlett.127.074503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 03/19/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior-random walks, ballistic transport, and trapping-depending upon the filament's relative length and effective flexibility. Moreover, we find that filaments execute Lévy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of "conveyor belts." Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon.
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Affiliation(s)
- Shi-Yuan Hu
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
- Department of Physics, New York University, New York, New York 10003, USA
| | - Jun-Jun Chu
- School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Michael J Shelley
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Jun Zhang
- Applied Mathematics Lab, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
- Department of Physics, New York University, New York, New York 10003, USA
- NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai 200062, China
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12
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Brosseau Q, Usabiaga FB, Lushi E, Wu Y, Ristroph L, Ward MD, Shelley MJ, Zhang J. Metallic microswimmers driven up the wall by gravity. Soft Matter 2021; 17:6597-6602. [PMID: 34259695 DOI: 10.1039/d1sm00554e] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show that tail-heavy swimmers preferentially orient upwards and ascend along inclined planes. We show that such gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even ultraheavy microswimmers to climb nearly vertical surfaces. Theory and simulations show that the buoyancy or gravitational torque that tends to align the rods is reinforced by a fore-aft drag asymmetry induced by hydrodynamic interactions with the wall.
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Affiliation(s)
- Quentin Brosseau
- Applied Mathematics Laboratory, Courant Institute, New York University, NY, NY 10012, USA
| | | | - Enkeleida Lushi
- Department of Math. Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
| | - Yang Wu
- Department of Chemistry, New York University, NY, NY 10012, USA
| | - Leif Ristroph
- Applied Mathematics Laboratory, Courant Institute, New York University, NY, NY 10012, USA
| | - Michael D Ward
- Department of Chemistry, New York University, NY, NY 10012, USA
| | - Michael J Shelley
- Applied Mathematics Laboratory, Courant Institute, New York University, NY, NY 10012, USA and Flatiron Institute, Simons Foundation, NY, NY 10010, USA
| | - Jun Zhang
- Applied Mathematics Laboratory, Courant Institute, New York University, NY, NY 10012, USA and Department of Physics, New York University, NY, NY 10003, USA and NYU-ECNU Physics and Mathematics Research Institutes, New York University Shanghai, Shanghai 200062, China
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13
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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. Eur Phys J 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] [What about the content of this article? (0)] [Affiliation(s)] [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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14
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Abstract
Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.
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Affiliation(s)
- Y -N Young
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
- Courant Institute, New York University, New York, New York 10012, USA
| | - David B Stein
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
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15
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Stein DB, De Canio G, Lauga E, Shelley MJ, Goldstein RE. Swirling Instability of the Microtubule Cytoskeleton. Phys Rev Lett 2021; 126:028103. [PMID: 33512217 DOI: 10.1103/physrevlett.126.028103] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 11/29/2020] [Indexed: 05/12/2023]
Abstract
In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly Drosophila melanogaster have shown a transition from a spatially disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions, we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.
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Affiliation(s)
- David B Stein
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Gabriele De Canio
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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16
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Farhadifar R, Yu CH, Fabig G, Wu HY, Stein DB, Rockman M, Müller-Reichert T, Shelley MJ, Needleman DJ. Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution. eLife 2020; 9:e55877. [PMID: 32966209 PMCID: PMC7511230 DOI: 10.7554/elife.55877] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Accepted: 08/31/2020] [Indexed: 01/17/2023] Open
Abstract
The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.
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Affiliation(s)
- Reza Farhadifar
- Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard UniversityCambridgeUnited States
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
| | - Che-Hang Yu
- Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard UniversityCambridgeUnited States
| | - Gunar Fabig
- Experimental Center, Faculty of Medicine Carl Gustav CarusDresdenGermany
| | - Hai-Yin Wu
- Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard UniversityCambridgeUnited States
| | - David B Stein
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
| | - Matthew Rockman
- Department of Biology and Center for Genomics & Systems Biology, New York UniversityNew YorkUnited States
| | | | - Michael J Shelley
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
- Courant Institute, New York UniversityNew YorkUnited States
| | - Daniel J Needleman
- Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard UniversityCambridgeUnited States
- Center for Computational Biology, Flatiron InstituteNew YorkUnited States
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17
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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. Nat Phys 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] [What about the content of this article? (0)] [Affiliation(s)] [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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18
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Brosseau Q, Usabiaga FB, Lushi E, Wu Y, Ristroph L, Zhang J, Ward M, Shelley MJ. Relating Rheotaxis and Hydrodynamic Actuation using Asymmetric Gold-Platinum Phoretic Rods. Phys Rev Lett 2019; 123:178004. [PMID: 31702241 DOI: 10.1103/physrevlett.123.178004] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 08/20/2019] [Indexed: 06/10/2023]
Abstract
We explore the behavior of micron-scale autophoretic Janus (Au/Pt) rods, having various Au/Pt length ratios, swimming near a wall in an imposed background flow. We find that their ability to robustly orient and move upstream, i.e., to rheotax, depends strongly on the Au/Pt ratio, which is easily tunable in synthesis. Numerical simulations of swimming rods actuated by a surface slip show a similar rheotactic tunability when varying the location of the surface slip versus surface drag. The slip location determines whether swimmers are pushers (rear actuated), pullers (front actuated), or in between. Our simulations and modeling show that pullers rheotax most robustly due to their larger tilt angle to the wall, which makes them responsive to flow gradients. Thus, rheotactic response infers the nature of difficult to measure flow fields of an active particle, establishes its dependence on swimmer type, and shows how Janus rods can be tuned for flow responsiveness.
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Affiliation(s)
- Quentin Brosseau
- Courant Institute, New York University, New York, New York 10012, USA
| | | | - Enkeleida Lushi
- Department of Mathematics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
| | - Yang Wu
- Department of Chemistry, New York University, New York, New York 10012, USA
| | - Leif Ristroph
- Courant Institute, New York University, New York, New York 10012, USA
| | - Jun Zhang
- Courant Institute, New York University, New York, New York 10012, USA
- Department of Physics, New York University, New York, New York 10003, USA
- New York University-East China Normal University Institute of Physics, New York University Shanghai, Shanghai 200062, China
| | - Michael Ward
- Department of Chemistry, New York University, New York, New York 10012, USA
| | - Michael J Shelley
- Courant Institute, New York University, New York, New York 10012, USA
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
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19
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Oppenheimer N, Stein DB, Shelley MJ. Rotating Membrane Inclusions Crystallize Through Hydrodynamic and Steric Interactions. Phys Rev Lett 2019; 123:148101. [PMID: 31702169 DOI: 10.1103/physrevlett.123.148101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 06/10/2023]
Abstract
We show that rotating membrane inclusions can crystallize due to combined hydrodynamic and steric interactions. Alone, steric repulsion of unconfined particles, even with thermal fluctuations, does not lead to crystallization, nor do rotational hydrodynamic interactions which allow only a marginally stable lattice. Hydrodynamic interactions enable particles to explore states inaccessible to a nonrotational system, yet, unlike Brownian motion, Hamiltonian conservation confines the ensemble which, when combined with steric interactions, anneals into a stable crystal state.
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Affiliation(s)
- Naomi Oppenheimer
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - David B Stein
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
- Courant Institute, New York University, New York, New York 10012, USA
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20
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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. Phys Rev Lett 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] [What about the content of this article? (0)] [Affiliation(s)] [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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21
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Yan W, Zhang H, Shelley MJ. Computing collision stress in assemblies of active spherocylinders: Applications of a fast and generic geometric method. J Chem Phys 2019; 150:064109. [DOI: 10.1063/1.5080433] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wen Yan
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Huan Zhang
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
- Zhiyuan College and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
| | - Michael J. Shelley
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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22
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Barrett AW, Boyapati RP, Bisase BS, Norris PM, Shelley MJ, Collyer J, Sneddon KJ, Gulati A. Verruciform Xanthoma of the Oral Mucosa: A Series of Eight Typical and Three Anomalous Cases. Int J Surg Pathol 2019; 27:492-498. [PMID: 30727785 DOI: 10.1177/1066896919827374] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this series, there are 8 typical verruciform xanthomas of the oral mucosa and 3 anomalies, 1 polypoid, 1 florid, and 1 carcinomatous. All were characterized by infiltrates of CD68-positive xanthomatous histiocytes in the lamina propria. The 11 patients comprised 6 men and 5 women (mean age = 54.5 years, range = 40-69). Both keratinized and nonkeratinized sites were affected. A history of lichenoid inflammation was recorded in 5 patients. The polypoid xanthoma presented in a woman aged 54 years as a polyp of the labial commissure. The florid lesion affected the dorsum of the tongue of a man aged 54 years and at 20 mm was the largest of the 11 lesions, but the only one with candidal infection. The squamous cell carcinoma manifested as a papilloverrucous hyperkeratosis of the palatal gingiva in a man aged 69 years. The latter 2 (and 1 "typical" verruciform xanthoma) required re-excision, but none has since recurred.
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Affiliation(s)
- A W Barrett
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - R P Boyapati
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - B S Bisase
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - P M Norris
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - M J Shelley
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - J Collyer
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - K J Sneddon
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - A Gulati
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
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23
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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24
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Abstract
One-dimensional crystals of passively-driven particles in microfluidic channels exhibit collective vibrational modes reminiscent of acoustic 'phonons'. These phonons are induced by the long-range hydrodynamic interactions among the particles and are neutrally stable at the linear level. Here, we analyze the effect of particle activity - self-propulsion - on the emergence and stability of these phonons. We show that the direction of wave propagation in active crystals is sensitive to the intensity of the background flow. We also show that activity couples, at the linear level, transverse waves to the particles' rotational motion, inducing a new mode of instability that persists in the limit of large background flow, or, equivalently, vanishingly small activity. We then report a new phenomenon of phonons switching back and forth between two adjacent crystals in both passively-driven and active systems, similar in nature to the wave switching observed in quantum mechanics, optical communication, and density stratified fluids. These findings could have implications for the design of commercial microfluidic systems and the self-assembly of passive and active micro-particles into one-dimensional structures.
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Affiliation(s)
- Alan Cheng Hou Tsang
- Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA. and Bioengineering, Stanford University, Stanford, California 94305, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Eva Kanso
- Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA. and Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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25
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Davies Wykes MS, Zhong X, Tong J, Adachi T, Liu Y, Ristroph L, Ward MD, Shelley MJ, Zhang J. Guiding microscale swimmers using teardrop-shaped posts. Soft Matter 2017; 13:4681-4688. [PMID: 28466943 DOI: 10.1039/c7sm00203c] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardrop-shaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardrop-shaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations.
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Affiliation(s)
| | - Xiao Zhong
- Molecular Design Institute, Department of Chemistry, New York University, USA
| | - Jiajun Tong
- Applied Mathematics Laboratory, Courant Institute, New York University, USA.
| | - Takuji Adachi
- Molecular Design Institute, Department of Chemistry, New York University, USA
| | - Yanpeng Liu
- Applied Mathematics Laboratory, Courant Institute, New York University, USA. and Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, China
| | - Leif Ristroph
- Applied Mathematics Laboratory, Courant Institute, New York University, USA.
| | - Michael D Ward
- Molecular Design Institute, Department of Chemistry, New York University, USA
| | - Michael J Shelley
- Applied Mathematics Laboratory, Courant Institute, New York University, USA. and Flatiron Institute, Simons Foundation, USA
| | - Jun Zhang
- Applied Mathematics Laboratory, Courant Institute, New York University, USA. and Department of Physics, New York University, USA and NYU-ECNU Joint Physics, Mathematics Research Institutes, NYU Shanghai, China
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26
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Abstract
The position of the spindle determines the position of the cleavage plane, and is thus crucial for cell division. Although spindle positioning has been extensively studied, the underlying forces ultimately responsible for moving the spindle remain poorly understood. A recent pioneering study by Garzon-Coral et al. uses magnetic tweezers to perform the first direct measurements of the forces involved in positioning the mitotic spindle. Combining this with molecular perturbations and geometrical effects, they use their data to argue that the forces that keep the spindle in its proper position for cell division arise from astral microtubules growing and pushing against the cell's cortex. Here, we review these ground-breaking experiments, the various biomechanical models for spindle positioning that they seek to differentiate, and discuss new questions raised by these measurements.
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Affiliation(s)
- Hai-Yin Wu
- Department of Physics, Harvard University, Cambridge, MA, USA
- Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, MA, USA
| | - Ehssan Nazockdast
- Center for Computational Biology, Simons Foundation, New York, NY, USA
| | - Michael J Shelley
- Center for Computational Biology, Simons Foundation, New York, NY, USA
- Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
| | - Daniel J Needleman
- Faculty of Arts and Sciences Center for Systems Biology, Harvard University, Cambridge, MA, USA
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA
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27
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Barrett AW, Sneddon KJ, Tighe JV, Gulati A, Newman L, Collyer J, Norris PM, Coombes DM, Shelley MJ, Bisase BS, Liebmann RD. Dentigerous Cyst and Ameloblastoma of the Jaws. Int J Surg Pathol 2016; 25:141-147. [PMID: 27621276 DOI: 10.1177/1066896916666319] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
AIM To determine how many ameloblastomas were misdiagnosed as dentigerous cysts (DCs) by correlating the radiological and histopathological features of a series of both entities. METHODS AND RESULTS Histopathology reports and radiological imaging of 135 DCs and 43 ameloblastomas were reviewed. Any clinical or radiological feature that suggested that the diagnosis of DC was wrong-for example, absence of an unerupted tooth-prompted review of the original histology. A total of 34 cases coded as DC at diagnosis were excluded; in the remaining 101 patients, the clinicoradiological and histopathological features were consistent with DC in 96 (95.0%). Review of the histology revealed that 4 patients had actually had odontogenic keratocysts (OKCs) and one a luminal/simple unicystic ameloblastoma (UA). One other OKC and 3 other ameloblastomas (1 luminal UA, 2 solid/multicystic) had originally been diagnosed as DC; these had been identified prior to the study. Of the 9 misdiagnosed patients, 6 were ≤20 years old. Clinically, DC had been the only, or one of the differential, diagnoses in 7 patients; in the other 2, the clinical diagnosis was radicular cyst. In none of the 4 misdiagnosed ameloblastomas was the radiology compatible with a diagnosis of DC. Incorrect terminology had been used on the histopathology request form in 5 of the 34 excluded cases where the clinical diagnosis was DC, despite the cyst being periapical to an erupted carious or root-filled tooth. CONCLUSIONS The entire clinical team must ensure that a histopathological diagnosis of DC is consistent with the clinicoradiological scenario, particularly in younger patients.
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Affiliation(s)
- Andrew W Barrett
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Kenneth J Sneddon
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - John V Tighe
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Aakshay Gulati
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Laurence Newman
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Jeremy Collyer
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Paul M Norris
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Darryl M Coombes
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Michael J Shelley
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
| | - Brian S Bisase
- 1 Queen Victoria Hospital NHSF Trust, East Grinstead, West Sussex, UK
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28
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Davies Wykes MS, Palacci J, Adachi T, Ristroph L, Zhong X, Ward MD, Zhang J, Shelley MJ. Dynamic self-assembly of microscale rotors and swimmers. Soft Matter 2016; 12:4584-4589. [PMID: 27121100 DOI: 10.1039/c5sm03127c] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Biological systems often involve the self-assembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a well-controlled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components self-assemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micron-scale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial run-and-tumble motion.
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Affiliation(s)
- Megan S Davies Wykes
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA.
| | - Jérémie Palacci
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA. and Department of Physics, University of California, San Diego, Mayer Hall 4222, 9500 Gilman Dr., La Jolla, CA 92093, USA.
| | - Takuji Adachi
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA.
| | - Leif Ristroph
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA.
| | - Xiao Zhong
- Molecular Design Institute, Department of Chemistry, New York University, 29 Washington Square Place, Brown Building, 5th Fl, New York, NY 10003, USA
| | - Michael D Ward
- Molecular Design Institute, Department of Chemistry, New York University, 29 Washington Square Place, Brown Building, 5th Fl, New York, NY 10003, USA
| | - Jun Zhang
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA. and Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA and NYU-ECNU Institutes of Mathematical Sciences and Physics Research, NYU-Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China
| | - Michael J Shelley
- Applied Mathematics Laboratory, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1110, USA.
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Abstract
Many cellular processes are driven by cytoskeletal assemblies. It remains unclear how cytoskeletal filaments and motor proteins organize into cellular scale structures and how molecular properties of cytoskeletal components affect the large-scale behaviors of these systems. Here, we investigate the self-organization of stabilized microtubules in Xenopus oocyte extracts and find that they can form macroscopic networks that spontaneously contract. We propose that these contractions are driven by the clustering of microtubule minus ends by dynein. Based on this idea, we construct an active fluid theory of network contractions, which predicts a dependence of the timescale of contraction on initial network geometry, a development of density inhomogeneities during contraction, a constant final network density, and a strong influence of dynein inhibition on the rate of contraction, all in quantitative agreement with experiments. These results demonstrate that the motor-driven clustering of filament ends is a generic mechanism leading to contraction.
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Affiliation(s)
- Peter J Foster
- John A. Paulson School of Engineering and Applied Sciences, FAS Center for Systems Biology, Harvard University, Cambridge, United States
| | - Sebastian Fürthauer
- Courant Institute of Mathematical Science, New York University, New York, United States.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
| | - Michael J Shelley
- Courant Institute of Mathematical Science, New York University, New York, United States
| | - Daniel J Needleman
- John A. Paulson School of Engineering and Applied Sciences, FAS Center for Systems Biology, Harvard University, Cambridge, United States.,Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
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Gao T, Blackwell R, Glaser MA, Betterton MD, Shelley MJ. Multiscale modeling and simulation of microtubule-motor-protein assemblies. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:062709. [PMID: 26764729 PMCID: PMC5082993 DOI: 10.1103/physreve.92.062709] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 05/10/2023]
Abstract
Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.
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Affiliation(s)
- Tong Gao
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Robert Blackwell
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Matthew A Glaser
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - M D Betterton
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael J Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Gao T, Blackwell R, Glaser MA, Betterton MD, Shelley MJ. Multiscale polar theory of microtubule and motor-protein assemblies. Phys Rev Lett 2015; 114:048101. [PMID: 25679909 PMCID: PMC4425281 DOI: 10.1103/physrevlett.114.048101] [Citation(s) in RCA: 79] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Indexed: 05/20/2023]
Abstract
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new "bioactive" liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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Affiliation(s)
- Tong Gao
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Robert Blackwell
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - Matthew A. Glaser
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - M. D. Betterton
- Department of Physics and Liquid Crystal Materials Research Center and Biofrontiers Institute, University of Colorado, Boulder, Colorado 80309, USA
| | - Michael J. Shelley
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Villarroel Dorrego M, Papp Y, Shelley MJ, Barrett AW. Chondroid lipoma of the tongue: a report of two cases. Oral Maxillofac Surg 2014; 18:219-222. [PMID: 23900485 DOI: 10.1007/s10006-013-0426-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2013] [Accepted: 07/09/2013] [Indexed: 06/02/2023]
Abstract
BACKGROUND Chondroid lipoma affecting the oral cavity is rare and usually presents as a polyp of benign clinical appearance which is easily excised. However, the histopathological features of chondroid lipoma resemble liposarcoma due to the presence of lipoblasts and lack of mature cartilage. CASE REPORTS The clinicopathological features of two cases of chondroid lipoma of the dorsum of the tongue, one in a 66-year-old woman and the other in a 43-year-old man, are described. CONCLUSION Once the diagnosis had been established, no treatment other than surgical excision was necessary and in neither case has there been recurrence in two years of follow-up.
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Abstract
We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.
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Affiliation(s)
- Hassan Masoud
- Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Michael J Shelley
- Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Takagi D, Palacci J, Braunschweig AB, Shelley MJ, Zhang J. Hydrodynamic capture of microswimmers into sphere-bound orbits. Soft Matter 2014; 10:1784-9. [PMID: 24800268 DOI: 10.1039/c3sm52815d] [Citation(s) in RCA: 115] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Self-propelled particles can exhibit surprising non-equilibrium behaviors, and how they interact with obstacles or boundaries remains an important open problem. Here we show that chemically propelled micro-rods can be captured, with little change in their speed, into close orbits around solid spheres resting on or near a horizontal plane. We show that this interaction between sphere and particle is short-range, occurring even for spheres smaller than the particle length, and for a variety of sphere materials. We consider a simple model, based on lubrication theory, of a force- and torque-free swimmer driven by a surface slip (the phoretic propulsion mechanism) and moving near a solid surface. The model demonstrates capture, or movement towards the surface, and yields speeds independent of distance. This study reveals the crucial aspects of activity–driven interactions of self-propelled particles with passive objects, and brings into question the use of colloidal tracers as probes of active matter.
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Abstract
Recent advances in micro- and nanoscale fabrication techniques allow for the construction of rigid, helically shaped microswimmers that can be actuated using applied magnetic fields. These swimmers represent the first steps toward the development of microrobots for targeted drug delivery and minimally invasive surgical procedures. To assess the performance of these devices and improve on their design, we perform shape optimization computations to determine swimmer geometries that maximize speed in the direction of a given applied magnetic torque. We directly assess aspects of swimmer shapes that have been developed in previous experimental studies, including helical propellers with elongated cross sections and attached payloads. From these optimizations, we identify key improvements to existing designs that result in swimming speeds that are 70-470% of their original values.
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Affiliation(s)
- Eric E Keaveny
- Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom.
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Takagi D, Braunschweig AB, Zhang J, Shelley MJ. Dispersion of self-propelled rods undergoing fluctuation-driven flips. Phys Rev Lett 2013; 110:038301. [PMID: 23373955 DOI: 10.1103/physrevlett.110.038301] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2012] [Indexed: 06/01/2023]
Abstract
Synthetic microswimmers may someday perform medical and technological tasks, but predicting their motion and dispersion is challenging. Here we show that chemically propelled rods tend to move on a surface along large circles but curiously show stochastic changes in the sign of the orbit curvature. By accounting for fluctuation-driven flipping of slightly curved rods, we obtain analytical predictions for the ensemble behavior in good agreement with our experiments. This shows that minor defects in swimmer shape can yield major long-term effects on macroscopic dispersion.
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Affiliation(s)
- Daisuke Takagi
- Applied Math Lab, Courant Institute, New York University, New York, New York 10012, USA
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38
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Lushi E, Goldstein RE, Shelley MJ. Collective chemotactic dynamics in the presence of self-generated fluid flows. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 86:040902. [PMID: 23214522 DOI: 10.1103/physreve.86.040902] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2011] [Indexed: 05/12/2023]
Abstract
In microswimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers." Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually repelling due to the nontrivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.
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Affiliation(s)
- Enkeleida Lushi
- Courant Institute of Mathematical Sciences, New York University, New York 10012, USA.
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39
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Abstract
Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics.
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Affiliation(s)
- Trushant Majmudar
- Courant Institute of Mathematical Sciences, 251 Mercer Street, New York University, New York, NY 10012, USA.
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40
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Abstract
The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.
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Affiliation(s)
- David Saintillan
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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41
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Shinar T, Mana M, Piano F, Shelley MJ. A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo. Proc Natl Acad Sci U S A 2011; 108:10508-13. [PMID: 21670261 PMCID: PMC3127902 DOI: 10.1073/pnas.1017369108] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We present a model of cytoplasmically driven microtubule-based pronuclear motion in the single-celled Caenorhabditis elegans embryo. In this model, a centrosome pair at the male pronucleus initiates stochastic microtubule (MT) growth. These MTs encounter motor proteins, distributed throughout the cytoplasm, that attach and exert a pulling force. The consequent MT-length-dependent pulling forces drag the pronucleus through the cytoplasm. On physical grounds, we assume that the motor proteins also exert equal and opposite forces on the surrounding viscous cytoplasm, here modeled as an incompressible Newtonian fluid constrained within an ellipsoidal eggshell. This naturally leads to streaming flows along the MTs. Our computational method is based on an immersed boundary formulation that allows for the simultaneous treatment of fluid flow and the dynamics of structures immersed within. Our simulations demonstrate that the balance of MT pulling forces and viscous nuclear drag is sufficient to move the pronucleus, while simultaneously generating minus-end directed flows along MTs that are similar to the observed movement of yolk granules toward the center of asters. Our simulations show pronuclear migration, and moreover, a robust pronuclear centration and rotation very similar to that observed in vivo. We find also that the confinement provided by the eggshell significantly affects the internal dynamics of the cytoplasm, increasing by an order of magnitude the forces necessary to translocate and center the pronucleus.
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Affiliation(s)
- Tamar Shinar
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
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42
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Hohenegger C, Shelley MJ. Stability of active suspensions. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 81:046311. [PMID: 20481831 DOI: 10.1103/physreve.81.046311] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2009] [Revised: 01/25/2010] [Indexed: 05/29/2023]
Abstract
We study theoretically the stability of "active suspensions," modeled here as a Stokesian fluid in which are suspended motile particles. The basis of our study is a kinetic model recently posed by Saintillan and Shelley [D. Saintillan and M. J. Shelley, Phys. Rev. Lett. 100, 178103 (2008); D. Saintillan and M. J. Shelley, Phys. Fluids 20, 123304 (2008)] where the motile particles are either "pushers" or "pullers." General considerations suggest that, in the absence of diffusional processes, perturbations from uniform isotropy will decay for pullers, but grow unboundedly for pushers, suggesting a possible ill-posedness. Hence, we investigate the structure of this system linearized near a state of uniform isotropy. The linearized system is nonnormal and variable coefficient, and not wholly described by an eigenvalue problem, in particular at small length scales. Using a high wave-number asymptotic analysis, we show that while long-wave stability depends on the particular swimming mechanism, short-wave stability does not and that the growth of perturbations for pusher suspensions is associated not with concentration fluctuations, as we show these generally decay, but with a proliferation of oscillations in swimmer orientation. These results are also confirmed through numerical simulation and suggest that the basic model is well-posed, even in the absence of translational and rotational diffusion effects. We also consider the influence of diffusional effects in the case where the rotational and translational diffusion coefficients are proportional and inversely proportional, respectively, to the volume concentration and predict the existence of a critical volume concentration or system size for the onset of the long-wave instability in a pusher suspension. We find reasonable agreement between the predictions of our theory and numerical simulations of rodlike swimmers by Saintillan and Shelley [D. Saintillan and M. J. Shelley, Phys. Rev. Lett. 99, 058102 (2007)].
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Affiliation(s)
- Christel Hohenegger
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
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43
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Ramsey RA, Shelley MJ. Re: root fragment in the ostium of the maxillary sinus [Br. J. Oral Maxillfac. Surg. 47 (2009) 572-573]. Br J Oral Maxillofac Surg 2009; 48:154-5. [PMID: 19910089 DOI: 10.1016/j.bjoms.2009.10.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2009] [Accepted: 10/01/2009] [Indexed: 10/20/2022]
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Keaveny EE, Shelley MJ. Hydrodynamic mobility of chiral colloidal aggregates. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:051405. [PMID: 19518454 DOI: 10.1103/physreve.79.051405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2009] [Indexed: 05/27/2023]
Abstract
A recent advance in colloidal technology [Zerrouki, Nature (London) 455, 380 (2008)] uses magnetic aggregation to enable the formation of micron-scale particle clusters with helical symmetry. The basic building blocks of these aggregates are doublets composed of two micron-scale beads of different radii bonded together by a magnetic cement. Such self-assembled structures offer potential for controllable transport and separation in a low Reynolds number environment using externally applied magnetic or electric fields. Establishing the hydrodynamic properties of the aggregates, in particular the coupling between rotation and translation afforded by the cluster geometry, is an essential initial step toward the design of microfluidic devices employing these aggregates. To quantify this coupling, we first determine parametrized expressions that describe the positions of the beads in an aggregate as a function of size ratio of the two beads composing the doublets. With the geometry of the structure known, we perform hydrodynamic calculations to ascertain entries of the mobility matrix for the aggregate and establish the relationship between the applied torque about the helical axis and translations parallel to this direction. We find that for larger values of the particle radius ratio the coupling between rotations and translations changes sign as the number of doublets in the aggregate increases. This feature indicates that the clusters possess a more complex superhelical structure.
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Affiliation(s)
- Eric E Keaveny
- Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
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45
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Saintillan D, Shelley MJ. Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys Rev Lett 2008; 100:178103. [PMID: 18518342 DOI: 10.1103/physrevlett.100.178103] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2007] [Indexed: 05/26/2023]
Abstract
We use kinetic theory and nonlinear continuum simulations to study the collective dynamics in suspensions of self-propelled particles. The stability of aligned suspensions is first analyzed, and we demonstrate that such suspensions are always unstable to fluctuations, a result that generalizes previous predictions by Simha and Ramaswamy. Isotropic suspensions are also considered, and it is shown that an instability for the particle stress occurs in that case. Using simulations, nonlinear effects are investigated, and the long-time behavior of the suspensions is observed to be characterized by the formation of strong density fluctuations, resulting in efficient fluid mixing.
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Affiliation(s)
- David Saintillan
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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46
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Alben S, Shelley MJ. Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. Phys Rev Lett 2008; 100:074301. [PMID: 18352554 DOI: 10.1103/physrevlett.100.074301] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2007] [Indexed: 05/26/2023]
Abstract
We investigate the "flapping flag" instability through a model for an inextensible flexible sheet in an inviscid 2D flow with a free vortex sheet. We solve the fully-nonlinear dynamics numerically and find a transition from a power spectrum dominated by discrete frequencies to an apparently continuous spectrum of frequencies. We compute the linear stability domain which agrees with previous approximate models in scaling but differs by large multiplicative factors. We also find hysteresis, in agreement with previous experiments.
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Affiliation(s)
- Silas Alben
- School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, USA.
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Abstract
UNLABELLED Fixation of the maxillofacial skeleton following trauma or osteotomy surgery has been achieved by the use of titanium plates and screws for the past two decades. Advances in materials science has enabled the development of biodegradable or resorbable plates and screws for internal fixation of the maxillofacial skeleton. This paper presents the biochemistry of resorbable materials and our early experiences in their clinical applications. CLINICAL RELEVANCE This manuscript illustrates the use of a resorbable material to fix the maxillofacial skeleton following osteotomies and trauma.
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Abstract
It is shown that a slender elastic fiber moving in a Stokesian fluid can be susceptible to a buckling instability--termed the "stretch-coil" instability--when moving in the neighborhood of a hyperbolic stagnation point of the flow. When the stagnation point is part of an extended cellular flow, it is found that immersed fibers can move as random walkers across time-independent closed-streamline flow. It is also found that the flow is segregated into transport regions around hyperbolic stagnation points and their manifolds, and closed entrapment regions around elliptic points.
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Affiliation(s)
- Y-N Young
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
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49
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Saintillan D, Shelley MJ. Orientational order and instabilities in suspensions of self-locomoting rods. Phys Rev Lett 2007; 99:058102. [PMID: 17930796 DOI: 10.1103/physrevlett.99.058102] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2007] [Indexed: 05/25/2023]
Abstract
The orientational order and dynamics in suspensions of self-locomoting slender rods are investigated numerically. In agreement with previous theoretical predictions, nematic suspensions of swimming particles are found to be unstable at long wavelengths as a result of hydrodynamic fluctuations. Nevertheless, a local nematic ordering is shown to persist over short length scales and to have a significant impact on the mean swimming speed. The consequences of the large-scale orientational disorder for particle dispersion are also discussed.
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Affiliation(s)
- David Saintillan
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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Abstract
PURPOSE To present a surgical technique for the early maintenance of the severely contracted socket following reconstruction. METHODS Two patients with severely contracted sockets following multiple procedures and recurrent failure were identified over a 1 year period. Following fornix and eyelid reconstruction, silicone fixative was injected into the fornix through a standard conformer. The silicone fixed around a pre-placed K-wire passed from the lateral orbital rim to the posterior lacrimal crest. Both silicone and wire were removed at 3 months. RESULTS Both patients were able to wear and maintain an acceptable prosthesis following the surgical procedure. CONCLUSION This is a safe and effective method for the early maintenance of a severely contracted socket. This technique minimizes cheesewiring or extrusion and avoids damage to superior and inferior muscles and structures.
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