1
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Ni Q, Ge Z, Li Y, Shatkin G, Fu J, Bera K, Yang Y, Wang Y, Sen A, Wu Y, Vasconcelos ACN, Feinberg AP, Konstantopoulos K, Sun SX. Cytoskeletal activation of NHE1 regulates mechanosensitive cell volume adaptation and proliferation. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.08.31.555808. [PMID: 37693593 PMCID: PMC10491192 DOI: 10.1101/2023.08.31.555808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
Mammalian cells can rapidly respond to osmotic and hydrostatic pressure imbalances during an environmental change, generating large fluxes of water and ions that alter cell volume within minutes. While the role of ion pump and leak in cell volume regulation has been well-established, the potential contribution of the actomyosin cytoskeleton and its interplay with ion transporters is unclear. We discovered a cell volume regulation system that is controlled by cytoskeletal activation of ion transporters. After a hypotonic shock, normal-like cells (NIH-3T3, MCF-10A, and others) display a slow secondary volume increase (SVI) following the immediate regulatory volume decrease. We show that SVI is initiated by hypotonic stress induced Ca 2+ influx through stretch activated channel Piezo1, which subsequently triggers actomyosin remodeling. The actomyosin network further activates NHE1 through their synergistic linker ezrin, inducing SVI after the initial volume recovery. We find that SVI is absent in cancer cell lines such as HT1080 and MDA-MB-231, where volume regulation is dominated by intrinsic response of ion transporters. A similar cytoskeletal activation of NHE1 can also be achieved by mechanical stretching. On compliant substrates where cytoskeletal contractility is attenuated, SVI generation is abolished. Moreover, cytoskeletal activation of NHE1 during SVI triggers nuclear deformation, leading to a significant, immediate transcriptomic change in 3T3 cells, a phenomenon that is again absent in HT1080 cells. While hypotonic shock hinders ERK-dependent cell growth, cells deficient in SVI are unresponsive to such inhibitory effects. Overall, our findings reveal the critical role of Ca 2+ and actomyosin-mediated mechanosensation in the regulation of ion transport, cell volume, transcriptomics, and cell proliferation.
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Yadav SA, Khatri D, Soni A, Khetan N, Athale CA. Wave-like oscillations of clamped microtubules driven by collective dynein transport. Biophys J 2024; 123:509-524. [PMID: 38258292 PMCID: PMC10912927 DOI: 10.1016/j.bpj.2024.01.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Revised: 12/05/2023] [Accepted: 01/17/2024] [Indexed: 01/24/2024] Open
Abstract
Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a "gliding-assay" geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective "order parameter" based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.
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Affiliation(s)
| | | | - Aman Soni
- Division of Biology, IISER Pune, Pune, India
| | - Neha Khetan
- Division of Biology, IISER Pune, Pune, India
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3
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Bondoc-Naumovitz KG, Laeverenz-Schlogelhofer H, Poon RN, Boggon AK, Bentley SA, Cortese D, Wan KY. Methods and Measures for Investigating Microscale Motility. Integr Comp Biol 2023; 63:1485-1508. [PMID: 37336589 PMCID: PMC10755196 DOI: 10.1093/icb/icad075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 05/31/2023] [Accepted: 06/06/2023] [Indexed: 06/21/2023] Open
Abstract
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.
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Affiliation(s)
| | | | - Rebecca N Poon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Alexander K Boggon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Samuel A Bentley
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Dario Cortese
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, Exeter, UK
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4
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Wan KY. Active oscillations in microscale navigation. Anim Cogn 2023; 26:1837-1850. [PMID: 37665482 PMCID: PMC10769930 DOI: 10.1007/s10071-023-01819-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Revised: 07/27/2023] [Accepted: 08/12/2023] [Indexed: 09/05/2023]
Abstract
Living organisms routinely navigate their surroundings in search of better conditions, more food, or to avoid predators. Typically, animals do so by integrating sensory cues from the environment with their locomotor apparatuses. For single cells or small organisms that possess motility, fundamental physical constraints imposed by their small size have led to alternative navigation strategies that are specific to the microscopic world. Intriguingly, underlying these myriad exploratory behaviours or sensory functions is the onset of periodic activity at multiple scales, such as the undulations of cilia and flagella, the vibrations of hair cells, or the oscillatory shape modes of migrating neutrophils. Here, I explore oscillatory dynamics in basal microeukaryotes and hypothesize that these active oscillations play a critical role in enhancing the fidelity of adaptive sensorimotor integration.
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Affiliation(s)
- Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, Exeter, EX4 4QD, UK.
- Department of Mathematics and Statistics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
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5
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Zaferani M, Abbaspourrad A. Biphasic Chemokinesis of Mammalian Sperm. PHYSICAL REVIEW LETTERS 2023; 130:248401. [PMID: 37390449 DOI: 10.1103/physrevlett.130.248401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 04/03/2023] [Indexed: 07/02/2023]
Abstract
The female reproductive tract (FRT) continuously modulates mammalian sperm motion by releasing various clues as sperm migrate toward the fertilization site. An existing gap in our understanding of sperm migration within the FRT is a quantitative picture of how sperm respond to and navigate the biochemical clues within the FRT. In this experimental study, we have found that in response to biochemical clues, mammalian sperm display two distinct chemokinetic behaviors which are dependent upon the rheological properties of the media: chiral, characterized by swimming in circles; and hyperactive, characterized by random reorientation events. We used minimal theoretical modeling, along with statistical characterization of the chiral and hyperactive trajectories, to show that the effective diffusivity of these motion phases decreases with increasing concentration of chemical stimulant. In the context of navigation this concentration dependent chemokinesis suggests that the chiral or hyperactive motion refines the sperm search area within different FRT functional regions. Further, the ability to switch between phases indicates that sperm may use various stochastic navigational strategies, such as run and tumble or intermittent search, within the fluctuating and spatially heterogeneous environment of the FRT.
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Affiliation(s)
- Meisam Zaferani
- Department of Food Science, Cornell University, Ithaca 14850, New York, USA
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6
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Quillen AC. Robust formation of metachronal waves in directional chains of phase oscillators. Phys Rev E 2023; 107:034401. [PMID: 37073033 DOI: 10.1103/physreve.107.034401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 02/16/2023] [Indexed: 04/20/2023]
Abstract
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest-neighbor interactions, connected in a loop and with rotational symmetry, so each oscillator resembles every other oscillator in the chain. Numerical integrations of the discrete phase oscillator systems and a continuum approximation show that directional models (those that do not obey reversal symmetry), can exhibit instability to short wavelength perturbations but only in regions where the slope in phase has a particular sign. This causes short wavelength perturbations to develop that can vary the winding number that describes the sum of phase differences across the loop and the resulting metachronal wave speed. Numerical integrations of stochastic directional phase oscillator models show that even a weak level of noise can seed instabilities that resolve into metachronal wave states.
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Affiliation(s)
- A C Quillen
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
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7
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Ringers C, Bialonski S, Ege M, Solovev A, Hansen JN, Jeong I, Friedrich BM, Jurisch-Yaksi N. Novel analytical tools reveal that local synchronization of cilia coincides with tissue-scale metachronal waves in zebrafish multiciliated epithelia. eLife 2023; 12:77701. [PMID: 36700548 PMCID: PMC9940908 DOI: 10.7554/elife.77701] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 01/25/2023] [Indexed: 01/27/2023] Open
Abstract
Motile cilia are hair-like cell extensions that beat periodically to generate fluid flow along various epithelial tissues within the body. In dense multiciliated carpets, cilia were shown to exhibit a remarkable coordination of their beat in the form of traveling metachronal waves, a phenomenon which supposedly enhances fluid transport. Yet, how cilia coordinate their regular beat in multiciliated epithelia to move fluids remains insufficiently understood, particularly due to lack of rigorous quantification. We combine experiments, novel analysis tools, and theory to address this knowledge gap. To investigate collective dynamics of cilia, we studied zebrafish multiciliated epithelia in the nose and the brain. We focused mainly on the zebrafish nose, due to its conserved properties with other ciliated tissues and its superior accessibility for non-invasive imaging. We revealed that cilia are synchronized only locally and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Even though synchronization is local only, we observed global patterns of traveling metachronal waves across the zebrafish multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right noses, unveiling a chiral asymmetry of metachronal coordination. To understand the implications of synchronization for fluid pumping, we used a computational model of a regular array of cilia. We found that local metachronal synchronization prevents steric collisions, i.e., cilia colliding with each other, and improves fluid pumping in dense cilia carpets, but hardly affects the direction of fluid flow. In conclusion, we show that local synchronization together with tissue-scale cilia alignment coincide and generate metachronal wave patterns in multiciliated epithelia, which enhance their physiological function of fluid pumping.
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Affiliation(s)
- Christa Ringers
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
- Department of Pharmaceutical Biosciences and Science for Life Laboratory, Uppsala UniversityUppsalaSweden
| | - Stephan Bialonski
- Institute for Data-Driven Technologies, Aachen University of Applied SciencesJülichGermany
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
| | - Mert Ege
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
| | - Anton Solovev
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
- Cluster of Excellence 'Physics of Life', Technical University DresdenDresdenGermany
| | - Jan Niklas Hansen
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
| | - Inyoung Jeong
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
| | - Benjamin M Friedrich
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
- Cluster of Excellence 'Physics of Life', Technical University DresdenDresdenGermany
| | - Nathalie Jurisch-Yaksi
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
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8
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Pochitaloff M, Miranda M, Richard M, Chaiyasitdhi A, Takagi Y, Cao W, De La Cruz EM, Sellers JR, Joanny JF, Jülicher F, Blanchoin L, Martin P. Flagella-like beating of actin bundles driven by self-organized myosin waves. NATURE PHYSICS 2022; 18:1240-1247. [PMID: 37396880 PMCID: PMC10312380 DOI: 10.1038/s41567-022-01688-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 06/23/2022] [Indexed: 07/04/2023]
Abstract
Wave-like beating of eukaryotic cilia and flagella-threadlike protrusions found in many cells and microorganisms-is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending. Here we show that in the presence of myosin motors, polymerizing actin filaments self-assemble into polar bundles that exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin-bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin bundle shape, providing a feedback mechanism between the myosin activity and filament deformations for the self-organization of large motor filament assemblies.
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Affiliation(s)
- Marie Pochitaloff
- Laboratoire Physico-Chimie Curie, Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Paris, France
- Present address: Department of Mechanical Engineering, UC Santa Barbara, Santa Barbara, CA, USA
| | - Martin Miranda
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Mathieu Richard
- Laboratoire Physico-Chimie Curie, Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Paris, France
| | - Atitheb Chaiyasitdhi
- Laboratoire Physico-Chimie Curie, Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Paris, France
| | - Yasuharu Takagi
- Laboratory of Molecular Physiology, National Heart, Lung and Blood Institute, NIH, Bethesda, MD, USA
| | - Wenxiang Cao
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA
| | - Enrique M. De La Cruz
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA
| | - James R. Sellers
- Laboratory of Molecular Physiology, National Heart, Lung and Blood Institute, NIH, Bethesda, MD, USA
| | - Jean-François Joanny
- Laboratoire Physico-Chimie Curie, Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Paris, France
- Collège de France, Paris, France
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany
| | - Laurent Blanchoin
- CytomorphoLab, Biosciences and Biotechnology Institute of Grenoble, Laboratoire de Physiologie Cellulaire & Végétale, Université Grenoble-Alpes/CEA/CNRS/INRA, Grenoble, France
- CytomorphoLab, Hôpital Saint Louis, Institut Universitaire d’Hématologie, UMRS1160, INSERM/AP-HP/Université Paris Diderot, Paris, France
| | - Pascal Martin
- Laboratoire Physico-Chimie Curie, Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Paris, France
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9
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Ishimoto K, Moreau C, Yasuda K. Self-organized swimming with odd elasticity. Phys Rev E 2022; 105:064603. [PMID: 35854482 DOI: 10.1103/physreve.105.064603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a nonsymmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.
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Affiliation(s)
- Kenta Ishimoto
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Clément Moreau
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Kento Yasuda
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
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10
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Pérez-Cervera A, Lindner B, Thomas PJ. Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators. BIOLOGICAL CYBERNETICS 2022; 116:219-234. [PMID: 35320405 PMCID: PMC9068686 DOI: 10.1007/s00422-022-00929-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 02/16/2022] [Indexed: 05/10/2023]
Abstract
Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.
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Affiliation(s)
- Alberto Pérez-Cervera
- National Research University Higher School of Economics, Moscow, Russia
- Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Institute of Physics, Humboldt University, Berlin, Germany
| | - Peter J. Thomas
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH USA
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11
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Holzhausen K, Thomas PJ, Lindner B. Analytical approach to the mean-return-time phase of isotropic stochastic oscillators. Phys Rev E 2022; 105:024202. [PMID: 35291171 DOI: 10.1103/physreve.105.024202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT isochrons.
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Affiliation(s)
- Konstantin Holzhausen
- Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
| | - Peter J Thomas
- Department of Mathematics, Applied Mathematics and Statistics, 212 Yost Hall, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio, USA
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
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12
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Solovev A, Friedrich BM. Synchronization in cilia carpets and the Kuramoto model with local coupling: Breakup of global synchronization in the presence of noise. CHAOS (WOODBURY, N.Y.) 2022; 32:013124. [PMID: 35105113 DOI: 10.1063/5.0075095] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
Carpets of beating cilia represent a paradigmatic example of self-organized synchronization of noisy biological oscillators, characterized by traveling waves of cilia phase. We present a multi-scale model of a cilia carpet that comprises realistic hydrodynamic interactions between cilia computed for a chiral cilia beat pattern from unicellular Paramecium and active noise of the cilia beat. We demonstrate an abrupt loss of global synchronization beyond a characteristic noise strength. We characterize stochastic transitions between synchronized and disordered dynamics, which generalize the notion of phase slips in pairs of coupled noisy phase oscillators. Our theoretical work establishes a link between the two-dimensional Kuramoto model of phase oscillators with mirror-symmetric oscillator coupling and detailed models of biological oscillators with asymmetric, chiral interactions.
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13
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Mammalian sperm hyperactivation regulates navigation via physical boundaries and promotes pseudo-chemotaxis. Proc Natl Acad Sci U S A 2021; 118:2107500118. [PMID: 34716265 DOI: 10.1073/pnas.2107500118] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 09/27/2021] [Indexed: 11/18/2022] Open
Abstract
Mammalian sperm migration within the complex and dynamic environment of the female reproductive tract toward the fertilization site requires navigational mechanisms, through which sperm respond to the tract environment and maintain the appropriate swimming behavior. In the oviduct (fallopian tube), sperm undergo a process called "hyperactivation," which involves switching from a nearly symmetrical, low-amplitude, and flagellar beating pattern to an asymmetrical, high-amplitude beating pattern that is required for fertilization in vivo. Here, exploring bovine sperm motion in high-aspect ratio microfluidic reservoirs as well as theoretical and computational modeling, we demonstrate that sperm hyperactivation, in response to pharmacological agonists, modulates sperm-sidewall interactions and thus navigation via physical boundaries. Prior to hyperactivation, sperm remained swimming along the sidewalls of the reservoirs; however, once hyperactivation caused the intrinsic curvature of sperm to exceed a critical value, swimming along the sidewalls was reduced. We further studied the effect of noise in the intrinsic curvature near the critical value and found that these nonthermal fluctuations yielded an interesting "Run-Stop" motion on the sidewall. Finally, we observed that hyperactivation produced a "pseudo-chemotaxis" behavior, in that sperm stayed longer within microfluidic chambers containing higher concentrations of hyperactivation agonists.
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14
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Gaikwad AS, Nandagiri A, Potter DL, Nosrati R, O'Connor AE, Jadhav S, Soria J, Prabhakar R, O'Bryan MK. CRISPs Function to Boost Sperm Power Output and Motility. Front Cell Dev Biol 2021; 9:693258. [PMID: 34422816 PMCID: PMC8374954 DOI: 10.3389/fcell.2021.693258] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Accepted: 07/20/2021] [Indexed: 12/17/2022] Open
Abstract
Fertilization requires sperm to travel long distances through the complex environment of the female reproductive tract. Despite the strong association between poor motility and infertility, the kinetics of sperm tail movement and the role individual proteins play in this process is poorly understood. Here, we use a high spatiotemporal sperm imaging system and an analysis protocol to define the role of CRISPs in the mechanobiology of sperm function. Each of CRISP1, CRISP2, and CRISP4 is required to optimize sperm flagellum waveform. Each plays an autonomous role in defining beat frequency, flexibility, and power dissipation. We thus posit that the expansion of the CRISP family from one member in basal vertebrates, to three in most mammals, and four in numerous rodents, represents an example of neofunctionalization wherein proteins with a common core function, boosting power output, have evolved to optimize different aspects of sperm tail performance.
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Affiliation(s)
- Avinash S Gaikwad
- School of Biological Sciences, Monash University, Clayton, VIC, Australia.,School of BioSciences and Bio21 Institute, The Faculty of Science, The University of Melbourne, Parkville, VIC, Australia
| | - Ashwin Nandagiri
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India.,Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, Australia
| | - David L Potter
- Monash Micro Imaging - Advanced Optical Microscopy, Monash University, Clayton, VIC, Australia
| | - Reza Nosrati
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, Australia
| | - Anne E O'Connor
- School of Biological Sciences, Monash University, Clayton, VIC, Australia.,School of BioSciences and Bio21 Institute, The Faculty of Science, The University of Melbourne, Parkville, VIC, Australia
| | - Sameer Jadhav
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India
| | - Julio Soria
- Laboratory for Turbulence Research in Aerospace & Combustion (LTRAC), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, Australia
| | - Ranganathan Prabhakar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, Australia
| | - Moira K O'Bryan
- School of BioSciences and Bio21 Institute, The Faculty of Science, The University of Melbourne, Parkville, VIC, Australia
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15
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Abstract
Motile cilia can coordinate with each other to beat in the form of a metachronal wave, which can facilitate the self-propulsion of microorganisms such as Paramecium and can also be used for fluid transport such as mucus removal in trachea. How can we predict the collective behavior of arrays of many cilia coordinated by hydrodynamic interactions, and in particular, the properties of the emerging metachronal waves, from the single-cilium characteristics? We address this question using a bottom-up coarse-graining approach and present results that contribute to understanding how the dynamical self-organization of ciliary arrays can be controlled, which can have significant biological, medical, and engineering implications. On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.
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16
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Zaferani M, Javi F, Mokhtare A, Li P, Abbaspourrad A. Rolling controls sperm navigation in response to the dynamic rheological properties of the environment. eLife 2021; 10:68693. [PMID: 34346314 PMCID: PMC8387022 DOI: 10.7554/elife.68693] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 08/03/2021] [Indexed: 01/02/2023] Open
Abstract
Mammalian sperm rolling around their longitudinal axes is a long-observed component of motility, but its function in the fertilization process, and more specifically in sperm migration within the female reproductive tract, remains elusive. While investigating bovine sperm motion under simple shear flow and in a quiescent microfluidic reservoir and developing theoretical and computational models, we found that rolling regulates sperm navigation in response to the rheological properties of the sperm environment. In other words, rolling enables a sperm to swim progressively even if the flagellum beats asymmetrically. Therefore, a rolling sperm swims stably along the nearby walls (wall-dependent navigation) and efficiently upstream under an external fluid flow (rheotaxis). By contrast, an increase in ambient viscosity and viscoelasticity suppresses rolling, consequently, non-rolling sperm are less susceptible to nearby walls and external fluid flow and swim in two-dimensional diffusive circular paths (surface exploration). This surface exploration mode of swimming is caused by the intrinsic asymmetry in flagellar beating such that the curvature of a sperm's circular path is proportional to the level of asymmetry. We found that the suppression of rolling is reversible and occurs in sperm with lower asymmetry in their beating pattern at higher ambient viscosity and viscoelasticity. Consequently, the rolling component of motility may function as a regulatory tool allowing sperm to navigate according to the rheological properties of the functional region within the female reproductive tract.
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Affiliation(s)
- Meisam Zaferani
- Department of Food Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, United States
| | - Farhad Javi
- Department of Food Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, United States
| | - Amir Mokhtare
- Department of Food Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, United States
| | - Peilong Li
- Department of Food Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, United States
| | - Alireza Abbaspourrad
- Department of Food Science, College of Agriculture and Life Sciences, Cornell University, Ithaca, United States
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17
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Nandagiri A, Gaikwad AS, Potter DL, Nosrati R, Soria J, O'Bryan MK, Jadhav S, Prabhakar R. Flagellar energetics from high-resolution imaging of beating patterns in tethered mouse sperm. eLife 2021; 10:62524. [PMID: 33929317 PMCID: PMC8159377 DOI: 10.7554/elife.62524] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 04/29/2021] [Indexed: 01/07/2023] Open
Abstract
We demonstrate a technique for investigating the energetics of flagella or cilia. We record the planar beating of tethered mouse sperm at high resolution. Beating waveforms are reconstructed using proper orthogonal decomposition of the centerline tangent-angle profiles. Energy conservation is employed to obtain the mechanical power exerted by the dynein motors from the observed kinematics. A large proportion of the mechanical power exerted by the dynein motors is dissipated internally by the motors themselves. There could also be significant dissipation within the passive structures of the flagellum. The total internal dissipation is considerably greater than the hydrodynamic dissipation in the aqueous medium outside. The net power input from the dynein motors in sperm from Crisp2-knockout mice is significantly smaller than in wildtype samples, indicating that ion-channel regulation by cysteine-rich secretory proteins controls energy flows powering the axoneme.
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Affiliation(s)
- Ashwin Nandagiri
- IITB-Monash Research Academy, Mumbai, India.,Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India.,Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia
| | | | - David L Potter
- Monash Micro-Imaging, Monash University, Clayton, Australia
| | - Reza Nosrati
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia
| | - Julio Soria
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia
| | - Moira K O'Bryan
- School of BioSciences, University of Melbourne, Parkville, Australia
| | - Sameer Jadhav
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India
| | - Ranganathan Prabhakar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia
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18
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Circular swimming motility and disordered hyperuniform state in an algae system. Proc Natl Acad Sci U S A 2021; 118:2100493118. [PMID: 33931505 DOI: 10.1073/pnas.2100493118] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae ([Formula: see text]), which swim in circles at the air-liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.
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19
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Solovev A, Friedrich BM. Lagrangian mechanics of active systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:49. [PMID: 33834308 PMCID: PMC8032648 DOI: 10.1140/epje/s10189-021-00016-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 01/12/2021] [Indexed: 05/26/2023]
Abstract
We present a multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics of shape-changing immersed objects, e.g., biological microswimmers and active surfaces. The key idea is to consider principal shape changes as generalized coordinates and define conjugate generalized hydrodynamic friction forces. Conveniently, the corresponding generalized friction coefficients can be pre-computed and subsequently reused to solve dynamic equations of motion fast. This framework extends Lagrangian mechanics of dissipative systems to active surfaces and active microswimmers, whose shape dynamics is driven by internal forces. As an application case, we predict in-phase and anti-phase synchronization in pairs of cilia for an experimentally measured cilia beat pattern.
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20
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Hamilton E, Cicuta P. Changes in geometrical aspects of a simple model of cilia synchronization control the dynamical state, a possible mechanism for switching of swimming gaits in microswimmers. PLoS One 2021; 16:e0249060. [PMID: 33831025 PMCID: PMC8031381 DOI: 10.1371/journal.pone.0249060] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2020] [Accepted: 03/10/2021] [Indexed: 12/23/2022] Open
Abstract
Active oscillators, with purely hydrodynamic coupling, are useful simple models to understand various aspects of motile cilia synchronization. Motile cilia are used by microorganisms to swim and to control the flow fields in their surroundings; the patterns observed in cilia carpets can be remarkably complex, and can be changed over time by the organism. It is often not known to what extent the coupling between cilia is due to just hydrodynamic forces, and neither is it known if it is biological or physical triggers that can change the dynamical collective state. Here we treat this question from a very simplified point of view. We describe three possible mechanisms that enable a switch in the dynamical state, in a simple scenario of a chain of oscillators. We find that shape-change provides the most consistent strategy to control collective dynamics, but also imposing small changes in frequency produces some unique stable states. Demonstrating these effects in the abstract minimal model proves that these could be possible explanations for gait switching seen in ciliated micro organisms like Paramecium and others. Microorganisms with many cilia could in principle be taking advantage of hydrodynamic coupling, to switch their swimming gait through either a shape change that manifests in decreased coupling between groups of cilia, or alterations to the beat style of a small subset of the cilia.
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Affiliation(s)
- Evelyn Hamilton
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
| | - Pietro Cicuta
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
- * E-mail:
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21
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Gnesotto FS, Gradziuk G, Ronceray P, Broedersz CP. Learning the non-equilibrium dynamics of Brownian movies. Nat Commun 2020; 11:5378. [PMID: 33097699 PMCID: PMC7585442 DOI: 10.1038/s41467-020-18796-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 09/10/2020] [Indexed: 01/30/2023] Open
Abstract
Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.
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Affiliation(s)
- Federico S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany
| | - Pierre Ronceray
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, 08544, USA.
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333, München, Germany.
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, HV, 1081, The Netherlands.
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22
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Li K, Guo F, Zhou X, Wang X, He L, Zhang L. An attraction-repulsion transition of force on two asymmetric wedges induced by active particles. Sci Rep 2020; 10:11702. [PMID: 32678189 PMCID: PMC7367348 DOI: 10.1038/s41598-020-68677-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2019] [Accepted: 05/21/2020] [Indexed: 02/04/2023] Open
Abstract
Effective interaction between two asymmetric wedges immersed in a two-dimensional active bath is investigated by computer simulations. The attraction–repulsion transition of effective force between two asymmetric wedges is subjected to the relative position of two wedges, the wedge-to-wedge distance, the active particle density, as well as the apex angle of two wedges. By exchanging the position of the two asymmetric wedges in an active bath, firstly a simple attraction–repulsion transition of effective force occurs, completely different from passive Brownian particles. Secondly the transition of effective force is symmetric for the long-range distance between two asymmetric wedges, while it is asymmetric for the short-range case. Our investigations may provide new possibilities to govern the motion and assembly of microscopic objects by taking advantage of the self-driven behaviour of active particles.
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Affiliation(s)
- Ke Li
- Department of Physics, Zhejiang University, Hangzhou, 310027, Zhejiang, China
| | - Fuchen Guo
- Department of Physics, Zhejiang University, Hangzhou, 310027, Zhejiang, China
| | - Xiaolin Zhou
- Department of Physics, Zhejiang University, Hangzhou, 310027, Zhejiang, China
| | - Xianghong Wang
- Department of Physics, Wenzhou University, Wenzhou, 325035, Zhejiang, China
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou, 325035, Zhejiang, China.
| | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou, 310027, Zhejiang, China.
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23
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Walker BJ, Phuyal S, Ishimoto K, Tung CK, Gaffney EA. Computer-assisted beat-pattern analysis and the flagellar waveforms of bovine spermatozoa. ROYAL SOCIETY OPEN SCIENCE 2020; 7:200769. [PMID: 32742702 PMCID: PMC7353979 DOI: 10.1098/rsos.200769] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 05/18/2020] [Indexed: 05/28/2023]
Abstract
Obstructed by hurdles in information extraction, handling and processing, computer-assisted sperm analysis systems have typically not considered in detail the complex flagellar waveforms of spermatozoa, despite their defining role in cell motility. Recent developments in imaging techniques and data processing have produced significantly improved methods of waveform digitization. Here, we use these improvements to demonstrate that near-complete flagellar capture is realizable on the scale of hundreds of cells, and, further, that meaningful statistical comparisons of flagellar waveforms may be readily performed with widely available tools. Representing the advent of high-fidelity computer-assisted beat-pattern analysis, we show how such a statistical approach can distinguish between samples using complex flagellar beating patterns rather than crude summary statistics. Dimensionality-reduction techniques applied to entire samples also reveal qualitatively distinct components of the beat, and a novel data-driven methodology for the generation of representative synthetic waveform data is proposed.
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Affiliation(s)
- Benjamin J. Walker
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Shiva Phuyal
- Department of Physics, North Carolina A&T State University, Greensboro, NC 27411, USA
| | - Kenta Ishimoto
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan
| | - Chih-Kuan Tung
- Department of Physics, North Carolina A&T State University, Greensboro, NC 27411, USA
| | - Eamonn A. Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
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24
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Anand SK, Chelakkot R, Singh SP. Beating to rotational transition of a clamped active ribbon-like filament. SOFT MATTER 2019; 15:7926-7933. [PMID: 31538995 DOI: 10.1039/c9sm01386e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We present a detailed study of a clamped ribbon-like filament under a compressive active force using Brownian dynamics simulations. We show that a clamped ribbon-like filament is able to capture beating as well as rotational motion under the compressive force. The nature of oscillation is governed by the torsional rigidity of the filament. The frequency of oscillation is almost independent of the torsional rigidity. The beating of the filament gives a butterfly-shaped trajectory of the free-end monomer, whereas rotational motion yields a circular trajectory on a plane. The binormal correlation and the principal component analysis reveal the butterfly, elliptical, and circular trajectories of the free end monomer. We present a phase diagram for different kinds of motion in the parameter regime of compressive force and torsional rigidity.
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Affiliation(s)
- Shalabh K Anand
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India.
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25
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SpermQ⁻A Simple Analysis Software to Comprehensively Study Flagellar Beating and Sperm Steering. Cells 2018; 8:cells8010010. [PMID: 30587820 PMCID: PMC6357160 DOI: 10.3390/cells8010010] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2018] [Revised: 12/14/2018] [Accepted: 12/20/2018] [Indexed: 11/16/2022] Open
Abstract
Motile cilia, also called flagella, are found across a broad range of species; some cilia propel prokaryotes and eukaryotic cells like sperm, while cilia on epithelial surfaces create complex fluid patterns e.g., in the brain or lung. For sperm, the picture has emerged that the flagellum is not only a motor but also a sensor that detects stimuli from the environment, computing the beat pattern according to the sensory input. Thereby, the flagellum navigates sperm through the complex environment in the female genital tract. However, we know very little about how environmental signals change the flagellar beat and, thereby, the swimming behavior of sperm. It has been proposed that distinct signaling domains in the flagellum control the flagellar beat. However, a detailed analysis has been mainly hampered by the fact that current comprehensive analysis approaches rely on complex microscopy and analysis systems. Thus, knowledge on sperm signaling regulating the flagellar beat is based on custom quantification approaches that are limited to only a few aspects of the beat pattern, do not resolve the kinetics of the entire flagellum, rely on manual, qualitative descriptions, and are only a little comparable among each other. Here, we present SpermQ, a ready-to-use and comprehensive analysis software to quantify sperm motility. SpermQ provides a detailed quantification of the flagellar beat based on common time-lapse images acquired by dark-field or epi-fluorescence microscopy, making SpermQ widely applicable. We envision SpermQ becoming a standard tool in flagellar and motile cilia research that allows to readily link studies on individual signaling components in sperm and distinct flagellar beat patterns.
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26
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Boundary behaviours of Leishmania mexicana: A hydrodynamic simulation study. J Theor Biol 2018; 462:311-320. [PMID: 30465777 PMCID: PMC6333917 DOI: 10.1016/j.jtbi.2018.11.016] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Revised: 11/13/2018] [Accepted: 11/15/2018] [Indexed: 01/08/2023]
Abstract
It is well established that the parasites of the genus Leishmania exhibit complex surface interactions with the sandfly vector midgut epithelium, but no prior study has considered the details of their hydrodynamics. Here, the boundary behaviours of motile Leishmania mexicana promastigotes are explored in a computational study using the boundary element method, with a model flagellar beating pattern that has been identified from digital videomicroscopy. In particular a simple flagellar kinematics is observed and quantified using image processing and mode identification techniques, suggesting a simple mechanical driver for the Leishmania beat. Phase plane analysis and long-time simulation of a range of Leishmania swimming scenarios demonstrate an absence of stable boundary motility for an idealised model promastigote, with behaviours ranging from boundary capture to deflection into the bulk both with and without surface forces between the swimmer and the boundary. Indeed, the inclusion of a short-range repulsive surface force results in the deflection of all surface-bound promastigotes, suggesting that the documented surface detachment of infective metacyclic promastigotes may be the result of their particular morphology and simple hydrodynamics. Further, simulation elucidates a remarkable morphology-dependent hydrodynamic mechanism of boundary approach, hypothesised to be the cause of the well-established phenomenon of tip-first epithelial attachment of Leishmania promastigotes to the sandfly vector midgut.
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27
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Dey S, Massiera G, Pitard E. Role of spatial heterogeneity in the collective dynamics of cilia beating in a minimal one-dimensional model. Phys Rev E 2018; 97:012403. [PMID: 29448350 DOI: 10.1103/physreve.97.012403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Indexed: 11/07/2022]
Abstract
Cilia are elastic hairlike protuberances of the cell membrane found in various unicellular organisms and in several tissues of most living organisms. In some tissues such as the airway tissues of the lung, the coordinated beating of cilia induces a fluid flow of crucial importance as it allows the continuous cleaning of our bronchia, known as mucociliary clearance. While most of the models addressing the question of collective dynamics and metachronal wave consider homogeneous carpets of cilia, experimental observations rather show that cilia clusters are heterogeneously distributed over the tissue surface. The purpose of this paper is to investigate the role of spatial heterogeneity on the coherent beating of cilia using a very simple one-dimensional model for cilia known as the rower model. We systematically study systems consisting of a few rowers to hundreds of rowers and we investigate the conditions for the emergence of collective beating. When considering a small number of rowers, a phase drift occurs, hence, a bifurcation in beating frequency is observed as the distance between rower clusters is changed. In the case of many rowers, a distribution of frequencies is observed. We found in particular the pattern of the patchy structure that shows the best robustness in collective beating behavior, as the density of cilia is varied over a wide range.
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Affiliation(s)
- Supravat Dey
- L2C, Univ Montpellier, CNRS, 34095 Montpellier, France
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28
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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29
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Ishimoto K, Gadêlha H, Gaffney EA, Smith DJ, Kirkman-Brown J. Human sperm swimming in a high viscosity mucus analogue. J Theor Biol 2018; 446:1-10. [PMID: 29462624 DOI: 10.1016/j.jtbi.2018.02.013] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Revised: 02/12/2018] [Accepted: 02/13/2018] [Indexed: 12/16/2022]
Abstract
Remarkably, mammalian sperm maintain a substantive proportion of their progressive swimming speed within highly viscous fluids, including those of the female reproductive tract. Here, we analyse the digital microscopy of a human sperm swimming in a highly viscous, weakly elastic mucus analogue. We exploit principal component analysis to simplify its flagellar beat pattern, from which boundary element calculations are used to determine the time-dependent flow field around the sperm cell. The sperm flow field is further approximated in terms of regularised point forces, and estimates of the mechanical power consumption are determined, for comparison with analogous low viscosity media studies. This highlights extensive differences in the structure of the flows surrounding human sperm in different media, indicating how the cell-cell and cell-boundary hydrodynamic interactions significantly differ with the physical microenvironment. The regularised point force decomposition also provides cell-level information that may ultimately be incorporated into sperm population models. We further observe indications that the core feature in explaining the effectiveness of sperm swimming in high viscosity media is the loss of cell yawing, which is related with a greater density of regularised point force singularities along the axis of symmetry of the flagellar beat to represent the flow field. In turn this implicates a reduction of the wavelength of the distal beat pattern - and hence dynamical wavelength selection of the flagellar beat - as the dominant feature governing the effectiveness of sperm swimming in highly viscous media.
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Affiliation(s)
- Kenta Ishimoto
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK; The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8501, Japan; Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan.
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, UK; Centre for Human Reproductive Science, Birmingham Women's and Children's NHS Foundation Trust, Birmingham B15 2TG, UK
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - David J Smith
- School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK; Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, UK; Centre for Human Reproductive Science, Birmingham Women's and Children's NHS Foundation Trust, Birmingham B15 2TG, UK
| | - Jackson Kirkman-Brown
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, UK; Centre for Human Reproductive Science, Birmingham Women's and Children's NHS Foundation Trust, Birmingham B15 2TG, UK
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30
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Saggiorato G, Alvarez L, Jikeli JF, Kaupp UB, Gompper G, Elgeti J. Human sperm steer with second harmonics of the flagellar beat. Nat Commun 2017; 8:1415. [PMID: 29123094 PMCID: PMC5680276 DOI: 10.1038/s41467-017-01462-y] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 09/20/2017] [Indexed: 12/21/2022] Open
Abstract
Sperm are propelled by bending waves traveling along their flagellum. For steering in gradients of sensory cues, sperm adjust the flagellar waveform. Symmetric and asymmetric waveforms result in straight and curved swimming paths, respectively. Two mechanisms causing spatially asymmetric waveforms have been proposed: an average flagellar curvature and buckling. We image flagella of human sperm tethered with the head to a surface. The waveform is characterized by a fundamental beat frequency and its second harmonic. The superposition of harmonics breaks the beat symmetry temporally rather than spatially. As a result, sperm rotate around the tethering point. The rotation velocity is determined by the second-harmonic amplitude and phase. Stimulation with the female sex hormone progesterone enhances the second-harmonic contribution and, thereby, modulates sperm rotation. Higher beat frequency components exist in other flagellated cells; therefore, this steering mechanism might be widespread and could inspire the design of synthetic microswimmers.
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Affiliation(s)
- Guglielmo Saggiorato
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany
| | - Luis Alvarez
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany.
| | - Jan F Jikeli
- Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Biophysical Imaging, Institute of Innate Immunity, University Hospital Bonn, 53127, Bonn, Germany
| | - U Benjamin Kaupp
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany
| | - Gerhard Gompper
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany
| | - Jens Elgeti
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany.
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31
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Ishimoto K, Gadêlha H, Gaffney EA, Smith DJ, Kirkman-Brown J. Coarse-Graining the Fluid Flow around a Human Sperm. PHYSICAL REVIEW LETTERS 2017; 118:124501. [PMID: 28388208 DOI: 10.1103/physrevlett.118.124501] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Indexed: 06/07/2023]
Abstract
The flagellar beat is extracted from human sperm digital imaging microscopy and used to determine the flow around the cell and its trajectory, via boundary element simulation. Comparison of the predicted cell trajectory with observation demonstrates that simulation can predict fine-scale sperm dynamics at the qualitative level. The flow field is also observed to reduce to a time-dependent summation of regularized Stokes flow singularities, approximated at leading order by a blinking force triplet. Such regularized singularity decompositions may be used to upscale cell level detail into population models of human sperm motility.
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Affiliation(s)
- Kenta Ishimoto
- The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8501, Japan
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, United Kingdom
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - David J Smith
- School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
| | - Jackson Kirkman-Brown
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
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32
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Oriola D, Gadêlha H, Casademunt J. Nonlinear amplitude dynamics in flagellar beating. ROYAL SOCIETY OPEN SCIENCE 2017; 4:160698. [PMID: 28405357 PMCID: PMC5383814 DOI: 10.1098/rsos.160698] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2016] [Accepted: 02/02/2017] [Indexed: 05/30/2023]
Abstract
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
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Affiliation(s)
- David Oriola
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, UK
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Jaume Casademunt
- Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
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33
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Oriola D, Gadêlha H, Casademunt J. Nonlinear amplitude dynamics in flagellar beating. ROYAL SOCIETY OPEN SCIENCE 2017. [PMID: 28405357 DOI: 10.5061/dryad.qs65q] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
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Affiliation(s)
- David Oriola
- Departament de Física de la Matèria Condensada, Facultat de Física , Universitat de Barcelona , Avinguda Diagonal 647, 08028 Barcelona, Spain
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, UK; Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Jaume Casademunt
- Departament de Física de la Matèria Condensada, Facultat de Física , Universitat de Barcelona , Avinguda Diagonal 647, 08028 Barcelona, Spain
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34
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Izumida Y, Kori H, Seifert U. Energetics of synchronization in coupled oscillators rotating on circular trajectories. Phys Rev E 2016; 94:052221. [PMID: 27967039 DOI: 10.1103/physreve.94.052221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2016] [Indexed: 06/06/2023]
Abstract
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
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Affiliation(s)
- Yuki Izumida
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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35
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Mathijssen AJTM, Doostmohammadi A, Yeomans JM, Shendruk TN. Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films. J R Soc Interface 2016; 13:20150936. [PMID: 26841796 DOI: 10.1098/rsif.2015.0936] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Biological flows over surfaces and interfaces can result in accumulation hotspots or depleted voids of microorganisms in natural environments. Apprehending the mechanisms that lead to such distributions is essential for understanding biofilm initiation. Using a systematic framework, we resolve the dynamics and statistics of swimming microbes within flowing films, considering the impact of confinement through steric and hydrodynamic interactions, flow and motility, along with Brownian and run-tumble fluctuations. Micro-swimmers can be peeled off the solid wall above a critical flow strength. However, the interplay of flow and fluctuations causes organisms to migrate back towards the wall above a secondary critical value. Hence, faster flows may not always be the most efficacious strategy to discourage biofilm initiation. Moreover, we find run-tumble dynamics commonly used by flagellated microbes to be an intrinsically more successful strategy to escape from boundaries than equivalent levels of enhanced Brownian noise in ciliated organisms.
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Affiliation(s)
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
| | - Tyler N Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
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36
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Ilse SE, Holm C, de Graaf J. Surface roughness stabilizes the clustering of self-propelled triangles. J Chem Phys 2016; 145:134904. [PMID: 27782450 DOI: 10.1063/1.4963804] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sven Erik Ilse
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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37
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Wan KY, Goldstein RE. Coordinated beating of algal flagella is mediated by basal coupling. Proc Natl Acad Sci U S A 2016; 113:E2784-93. [PMID: 27140605 PMCID: PMC4878519 DOI: 10.1073/pnas.1518527113] [Citation(s) in RCA: 74] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Cilia and flagella often exhibit synchronized behavior; this includes phase locking, as seen in Chlamydomonas, and metachronal wave formation in the respiratory cilia of higher organisms. Since the observations by Gray and Rothschild of phase synchrony of nearby swimming spermatozoa, it has been a working hypothesis that synchrony arises from hydrodynamic interactions between beating filaments. Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga Volvox has shown that hydrodynamic coupling alone is sufficient to produce synchrony. However, the situation is more complex in unicellular organisms bearing few flagella. We show that flagella of Chlamydomonas mutants deficient in filamentary connections between basal bodies display markedly different synchronization from the wild type. We perform micromanipulation on configurations of flagella and conclude that a mechanism, internal to the cell, must provide an additional flagellar coupling. In naturally occurring species with 4, 8, or even 16 flagella, we find diverse symmetries of basal body positioning and of the flagellar apparatus that are coincident with specific gaits of flagellar actuation, suggesting that it is a competition between intracellular coupling and hydrodynamic interactions that ultimately determines the precise form of flagellar coordination in unicellular algae.
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Affiliation(s)
- Kirsty Y Wan
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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38
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Battle C, Broedersz CP, Fakhri N, Geyer VF, Howard J, Schmidt CF, MacKintosh FC. Broken detailed balance at mesoscopic scales in active biological systems. Science 2016; 352:604-7. [PMID: 27126047 DOI: 10.1126/science.aac8167] [Citation(s) in RCA: 164] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 01/26/2016] [Indexed: 12/28/2022]
Abstract
Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.
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Affiliation(s)
- Christopher Battle
- Drittes Physikalisches Institut, Georg-August-Universität, 37077 Göttingen, Germany. The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
| | - Chase P Broedersz
- The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA. Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany. Lewis-Sigler Institute for Integrative Genomics and Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA
| | - Nikta Fakhri
- Drittes Physikalisches Institut, Georg-August-Universität, 37077 Göttingen, Germany. The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Veikko F Geyer
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA
| | - Jonathon Howard
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA
| | - Christoph F Schmidt
- Drittes Physikalisches Institut, Georg-August-Universität, 37077 Göttingen, Germany. The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA.
| | - Fred C MacKintosh
- The Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA. Department of Physics and Astronomy, Vrije Universiteit, Amsterdam, Netherlands.
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39
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de Graaf J, Menke H, Mathijssen AJTM, Fabritius M, Holm C, Shendruk TN. Lattice-Boltzmann hydrodynamics of anisotropic active matter. J Chem Phys 2016; 144:134106. [DOI: 10.1063/1.4944962] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Henri Menke
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | | | - Marc Fabritius
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Tyler N. Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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40
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Kaiser A, Babel S, ten Hagen B, von Ferber C, Löwen H. How does a flexible chain of active particles swell? J Chem Phys 2016; 142:124905. [PMID: 25833607 DOI: 10.1063/1.4916134] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.
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Affiliation(s)
- Andreas Kaiser
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Sonja Babel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Christian von Ferber
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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41
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Kirkegaard JB, Marron AO, Goldstein RE. Motility of Colonial Choanoflagellates and the Statistics of Aggregate Random Walkers. PHYSICAL REVIEW LETTERS 2016; 116:038102. [PMID: 26849616 PMCID: PMC7616083 DOI: 10.1103/physrevlett.116.038102] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2015] [Indexed: 06/05/2023]
Abstract
We illuminate the nature of the three-dimensional random walks of microorganisms composed of individual organisms adhered together. Such aggregate random walkers are typified by choanoflagellates, eukaryotes that are the closest living relatives of animals. In the colony-forming species Salpingoeca rosetta we show that the beating of each flagellum is stochastic and uncorrelated with others, and the vectorial sum of the flagellar propulsion manifests as stochastic helical swimming. A quantitative theory for these results is presented and species variability discussed.
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Affiliation(s)
- Julius B Kirkegaard
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Alan O Marron
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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42
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Quaranta G, Aubin-Tam ME, Tam D. Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella. PHYSICAL REVIEW LETTERS 2015; 115:238101. [PMID: 26684142 DOI: 10.1103/physrevlett.115.238101] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 05/27/2023]
Abstract
The influence of hydrodynamic forces on eukaryotic flagella synchronization is investigated by triggering phase locking between a controlled external flow and the flagella of C. reinhardtii. Hydrodynamic forces required for synchronization are over an order of magnitude larger than hydrodynamic forces experienced in physiological conditions. Our results suggest that synchronization is due instead to coupling through cell internal fibers connecting the flagella. This conclusion is confirmed by observations of the vfl3 mutant, with impaired mechanical connection between the flagella.
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Affiliation(s)
- Greta Quaranta
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Daniel Tam
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
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43
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Klindt GS, Friedrich BM. Flagellar swimmers oscillate between pusher- and puller-type swimming. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:063019. [PMID: 26764816 DOI: 10.1103/physreve.92.063019] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2015] [Indexed: 06/05/2023]
Abstract
Self-propulsion of cellular microswimmers generates flow signatures, commonly classified as pusher and puller type, which characterize hydrodynamic interactions with other cells or boundaries. Using experimentally measured beat patterns, we compute that the flagellated green alga Chlamydomonas oscillates between pusher and puller, rendering it an approximately neutral swimmer, when averaging over its full beat cycle. Beyond a typical distance of 100μm from the cell, inertia attenuates oscillatory microflows. We show that hydrodynamic interactions between cells oscillate in time and are of similar magnitude as stochastic swimming fluctuations. From our analysis, we also find that the rate of hydrodynamic dissipation varies in time, which implies that flagellar beat patterns are not optimized with respect to this measure.
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Affiliation(s)
- Gary S Klindt
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
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44
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Gravish N, Peters JM, Combes SA, Wood RJ. Collective Flow Enhancement by Tandem Flapping Wings. PHYSICAL REVIEW LETTERS 2015; 115:188101. [PMID: 26565499 DOI: 10.1103/physrevlett.115.188101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2015] [Indexed: 06/05/2023]
Abstract
We examine the fluid-mechanical interactions that occur between arrays of flapping wings when operating in close proximity at a moderate Reynolds number (Re≈100-1000). Pairs of flapping wings are oscillated sinusoidally at frequency f, amplitude θ_{M}, phase offset ϕ, and wing separation distance D^{*}, and outflow speed v^{*} is measured. At a fixed separation distance, v^{*} is sensitive to both f and ϕ, and we observe both constructive and destructive interference in airspeed. v^{*} is maximized at an optimum phase offset, ϕ_{max}, which varies with wing separation distance, D^{*}. We propose a model of collective flow interactions between flapping wings based on vortex advection, which reproduces our experimental data.
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Affiliation(s)
- Nick Gravish
- SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
- OEB, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jacob M Peters
- OEB, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Stacey A Combes
- NPB, University of California Davis, Davis, California 95616, USA
| | - Robert J Wood
- SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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45
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Riley EE, Lauga E. Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J Theor Biol 2015; 382:345-55. [DOI: 10.1016/j.jtbi.2015.06.045] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Revised: 06/24/2015] [Accepted: 06/28/2015] [Indexed: 01/19/2023]
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46
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Kaiser A, Sokolov A, Aranson IS, Lowen H. Mechanisms of Carrier Transport Induced by a Microswimmer Bath. IEEE Trans Nanobioscience 2015; 14:260-6. [DOI: 10.1109/tnb.2014.2361652] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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47
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de Graaf J, Rempfer G, Holm C. Diffusiophoretic Self-Propulsion for Partially Catalytic Spherical Colloids. IEEE Trans Nanobioscience 2015; 14:272-88. [DOI: 10.1109/tnb.2015.2403255] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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48
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Wan KY, Goldstein RE. Rhythmicity, recurrence, and recovery of flagellar beating. PHYSICAL REVIEW LETTERS 2014; 113:238103. [PMID: 25526162 PMCID: PMC7616081 DOI: 10.1103/physrevlett.113.238103] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2014] [Indexed: 06/04/2023]
Abstract
The eukaryotic flagellum beats with apparently unfailing periodicity, yet responds rapidly to stimuli. Like the human heartbeat, flagellar oscillations are now known to be noisy. Using the alga C. reinhardtii, we explore three aspects of nonuniform flagellar beating. We report the existence of rhythmicity, waveform noise peaking at transitions between power and recovery strokes, and fluctuations of interbeat intervals that are correlated and even recurrent, with memory extending to hundreds of beats. These features are altered qualitatively by physiological perturbations. Further, we quantify the recovery of periodic breaststroke beating from transient hydrodynamic forcing. These results will help constrain microscopic theories on the origins and regulation of flagellar beating.
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Affiliation(s)
- Kirsty Y Wan
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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49
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Werner S, Rink JC, Riedel-Kruse IH, Friedrich BM. Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies. PLoS One 2014; 9:e113083. [PMID: 25426857 PMCID: PMC4245084 DOI: 10.1371/journal.pone.0113083] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Accepted: 10/19/2014] [Indexed: 12/21/2022] Open
Abstract
We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.
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Affiliation(s)
- Steffen Werner
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Jochen C. Rink
- Max Planck Institute for Cell Biology and Genetics, Dresden, Germany
| | - Ingmar H. Riedel-Kruse
- Department of Bioengineering, Stanford University, Stanford, California, United States of America
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Jabbarzadeh M, Hyon Y, Fu HC. Swimming fluctuations of micro-organisms due to heterogeneous microstructure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:043021. [PMID: 25375607 DOI: 10.1103/physreve.90.043021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2014] [Indexed: 06/04/2023]
Abstract
Swimming microorganisms in biological complex fluids may be greatly influenced by heterogeneous media and microstructure with length scales comparable to the organisms. A fundamental effect of swimming in a heterogeneous rather than homogeneous medium is that variations in local environments lead to swimming velocity fluctuations. Here we examine long-range hydrodynamic contributions to these fluctuations using a Najafi-Golestanian swimmer near spherical and filamentous obstacles. We find that forces on microstructures determine changes in swimming speed. For macroscopically isotropic networks, we also show how the variance of the fluctuations in swimming speeds are related to density and orientational correlations in the medium.
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Affiliation(s)
- Mehdi Jabbarzadeh
- Department of Mechanical Engineering, University of Nevada at Reno, Reno, Nevada 89557 USA
| | - YunKyong Hyon
- Division of Computational Sciences in Mathematics, National Institute for Mathematical Sciences, Daejeon, Republic of Korea 305-811
| | - Henry C Fu
- Department of Mechanical Engineering, University of Nevada at Reno, Reno, Nevada 89557 USA
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