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Xia Y, Hu Z, Wei D, Chen K, Peng Y, Yang M. Biomimetic Synchronization in Biciliated Robots. PHYSICAL REVIEW LETTERS 2024; 133:048302. [PMID: 39121428 DOI: 10.1103/physrevlett.133.048302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Revised: 04/15/2024] [Accepted: 06/10/2024] [Indexed: 08/11/2024]
Abstract
Direct mechanical coupling is known to be critical for establishing synchronization among cilia. However, the actual role of the connections is still elusive-partly because controlled experiments in living samples are challenging. Here, we employ an artificial ciliary system to address this issue. Two cilia are formed by chains of self-propelling robots and anchored to a shared base so that they are purely mechanically coupled. The system mimics biological ciliary beating but allows fine control over the beating dynamics. With different schemes of mechanical coupling, artificial cilia exhibit rich motility patterns. Particularly, their synchronous beating display two distinct modes-analogous to those observed in C. reinhardtii, the biciliated model organism for studying synchronization. Close examination suggests that the system evolves towards the most dissipative mode. Using this guideline in both simulations and experiments, we are able to direct the system into a desired state by altering the modes' respective dissipation. Our results have significant implications in understanding the synchronization of cilia.
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Affiliation(s)
| | | | - Da Wei
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Ke Chen
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | | | - Mingcheng Yang
- Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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2
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Hu S, Meng F. Multiflagellate Swimming Controlled by Hydrodynamic Interactions. PHYSICAL REVIEW LETTERS 2024; 132:204002. [PMID: 38829103 DOI: 10.1103/physrevlett.132.204002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Revised: 02/18/2024] [Accepted: 04/16/2024] [Indexed: 06/05/2024]
Abstract
Many eukaryotic microorganisms propelled by multiple flagella can swim very rapidly with distinct gaits. Here, we model a three-dimensional mutiflagellate swimmer, resembling the microalgae. When the flagella are actuated synchronously, the swimming efficiency can be enhanced or reduced by interflagella hydrodynamic interactions (HIs), determined by the intrinsic tilting angle of the flagella. The asynchronous gait with a phase difference between neighboring flagella can reduce oscillatory motion via the basal mechanical coupling. In the presence of a spherical body, simulations taking into account the flagella-body interactions reveal the advantage of anterior configuration compared with posterior configuration, where in the latter case an optimal flagella number arises. Apart from understanding the role of HIs in the multiflagellate microorganisms, this work could also guide laboratory fabrications of novel microswimmers.
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Affiliation(s)
- Shiyuan Hu
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Fanlong Meng
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
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3
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Wei D, Quaranta G, Aubin-Tam ME, Tam DSW. The younger flagellum sets the beat for Chlamydomonas reinhardtii. eLife 2024; 13:e86102. [PMID: 38752724 PMCID: PMC11098555 DOI: 10.7554/elife.86102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 04/03/2024] [Indexed: 05/18/2024] Open
Abstract
Eukaryotes swim with coordinated flagellar (ciliary) beating and steer by fine-tuning the coordination. The model organism for studying flagellate motility, Chlamydomonas reinhardtii, employs synchronous, breaststroke-like flagellar beating to swim, and it modulates the beating amplitudes differentially to steer. This strategy hinges on both inherent flagellar asymmetries (e.g. different response to chemical messengers) and such asymmetries being effectively coordinated in the synchronous beating. In C. reinhardtii, the synchrony of beating is known to be supported by a mechanical connection between flagella; however, how flagellar asymmetries persist in the synchrony remains elusive. For example, it has been speculated for decades that one flagellum leads the beating, as its dynamic properties (i.e. frequency, waveform, etc.) appear to be copied by the other one. In this study, we combine experiments, computations, and modeling efforts to elucidate the roles played by each flagellum in synchronous beating. With a non-invasive technique to selectively load each flagellum, we show that the coordinated beating essentially only responds to load exerted on the cis flagellum; and that such asymmetry in response derives from a unilateral coupling between the two flagella. Our results highlight a distinct role for each flagellum in coordination and have implication for biflagellates' tactic behaviors.
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Affiliation(s)
- Da Wei
- Department of Bionanoscience, Delft University of TechnologyDelftNetherlands
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of SciencesBeijingChina
| | - Greta Quaranta
- Laboratory for Aero and Hydrodynamics, Delft University of TechnologyDelftNetherlands
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Delft University of TechnologyDelftNetherlands
| | - Daniel SW Tam
- Laboratory for Aero and Hydrodynamics, Delft University of TechnologyDelftNetherlands
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4
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von Kenne A, Bär M, Niedermayer T. Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves. Phys Rev E 2024; 109:054407. [PMID: 38907471 DOI: 10.1103/physreve.109.054407] [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: 10/18/2023] [Accepted: 01/11/2024] [Indexed: 06/24/2024]
Abstract
Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.
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Affiliation(s)
- Albert von Kenne
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
| | - Thomas Niedermayer
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
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5
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Ling F, Essock-Burns T, McFall-Ngai M, Katija K, Nawroth JC, Kanso E. Flow Physics Explains Morphological Diversity of Ciliated Organs. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.02.12.528181. [PMID: 38168341 PMCID: PMC10760039 DOI: 10.1101/2023.02.12.528181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Organs that pump fluids by the coordinated beat of motile cilia through the lumen are integral to animal physiology. Such organs include the human airways, brain ventricles, and reproductive tracts. Although cilia organization and duct morphology vary drastically in the animal kingdom, ducts are typically classified as either carpet or flame designs. The reason behind this dichotomy and how duct design relates to fluid pumping remain unclear. Here, we demonstrate that two structural parameters -- lumen diameter and cilia-to-lumen ratio -- organize the observed duct diversity into a continuous spectrum that connects carpets to flames across all animal phyla. Using a unified fluid model, we show that carpet and flame designs maximize flow rate and pressure generation, respectively. We propose that convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance, along with universal design rules for ciliary pumps.
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6
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Wan KY, Poon RN. Mechanisms and functions of multiciliary coordination. Curr Opin Cell Biol 2024; 86:102286. [PMID: 38035649 DOI: 10.1016/j.ceb.2023.102286] [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: 09/11/2023] [Revised: 10/20/2023] [Accepted: 11/02/2023] [Indexed: 12/02/2023]
Abstract
Ciliated organisms are present in virtually every branch of the eukaryotic tree of life. In diverse systems, cilia operate in a coordinated manner to drive fluid flows, or even propel entire organisms. How do groups of motile cilia coordinate their activity within a cell or across a tissue to fulfil essential functions of life? In this review, we highlight the latest developments in our understanding of the mechanisms and functions of multiciliary coordination in diverse systems. We explore new and emerging trends in bioimaging, analytical, and computational methods, which together with their application in new model systems, have conspired to deliver important insights into one of the most fundamental questions in cellular dynamics.
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Affiliation(s)
- Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, UK.
| | - Rebecca N Poon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, UK
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7
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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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8
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Cass JF, Bloomfield-Gadêlha H. The reaction-diffusion basis of animated patterns in eukaryotic flagella. Nat Commun 2023; 14:5638. [PMID: 37758714 PMCID: PMC10533521 DOI: 10.1038/s41467-023-40338-2] [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: 05/25/2023] [Accepted: 07/20/2023] [Indexed: 09/29/2023] Open
Abstract
The flagellar beat of bull spermatozoa and C. Reinhardtii are modelled by a minimal, geometrically exact, reaction-diffusion system. Spatio-temporal animated patterns describe flagellar waves, analogous to chemical-patterns from classical reaction-diffusion systems, with sliding-controlled molecular motor reaction-kinetics. The reaction-diffusion system is derived from first principles as a consequence of the high-internal dissipation by the flagellum relative to the external hydrodynamic dissipation. Quantitative comparison with nonlinear, large-amplitude simulations shows that animated reaction-diffusion patterns account for the experimental beating of both bull sperm and C. Reinhardtii. Our results suggest that a unified mechanism may exist for motors controlled by sliding, without requiring curvature-sensing, and uninfluenced by hydrodynamics. High-internal dissipation instigates autonomous travelling waves independently of the external fluid, enabling progressive swimming, otherwise not possible, in low viscosity environments, potentially critical for external fertilizers and aquatic microorganisms. The reaction-diffusion system may prove a powerful tool for studying pattern formation of movement on animated structures.
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Affiliation(s)
- James F Cass
- School of Engineering Mathematics and Technology, and Bristol Robotics Laboratory, University of Bristol, Bristol, UK
| | - Hermes Bloomfield-Gadêlha
- School of Engineering Mathematics and Technology, and Bristol Robotics Laboratory, University of Bristol, Bristol, UK.
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9
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Bentley SA, Laeverenz-Schlogelhofer H, Anagnostidis V, Cammann J, Mazza MG, Gielen F, Wan KY. Phenotyping single-cell motility in microfluidic confinement. eLife 2022; 11:e76519. [PMID: 36416411 PMCID: PMC9683786 DOI: 10.7554/elife.76519] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 10/13/2022] [Indexed: 11/24/2022] Open
Abstract
The movement trajectories of organisms serve as dynamic read-outs of their behaviour and physiology. For microorganisms this can be difficult to resolve due to their small size and fast movement. Here, we devise a novel droplet microfluidics assay to encapsulate single micron-sized algae inside closed arenas, enabling ultralong high-speed tracking of the same cell. Comparing two model species - Chlamydomonas reinhardtii (freshwater, 2 cilia), and Pyramimonas octopus (marine, 8 cilia), we detail their highly-stereotyped yet contrasting swimming behaviours and environmental interactions. By measuring the rates and probabilities with which cells transition between a trio of motility states (smooth-forward swimming, quiescence, tumbling or excitable backward swimming), we reconstruct the control network that underlies this gait switching dynamics. A simplified model of cell-roaming in circular confinement reproduces the observed long-term behaviours and spatial fluxes, including novel boundary circulation behaviour. Finally, we establish an assay in which pairs of droplets are fused on demand, one containing a trapped cell with another containing a chemical that perturbs cellular excitability, to reveal how aneural microorganisms adapt their locomotor patterns in real-time.
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Affiliation(s)
- Samuel A Bentley
- Living Systems Institute, University of ExeterExeterUnited Kingdom
- Mathematics and Statistics, University of ExeterExeterUnited Kingdom
- Biosciences, University of ExeterExeterUnited Kingdom
| | - Hannah Laeverenz-Schlogelhofer
- Living Systems Institute, University of ExeterExeterUnited Kingdom
- Mathematics and Statistics, University of ExeterExeterUnited Kingdom
| | - Vasileios Anagnostidis
- Living Systems Institute, University of ExeterExeterUnited Kingdom
- Biosciences, University of ExeterExeterUnited Kingdom
- Physics and Astronomy, University of ExeterExeterUnited Kingdom
| | - Jan Cammann
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough UniversityLoughboroughUnited Kingdom
| | - Marco G Mazza
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough UniversityLoughboroughUnited Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS)GöttingenGermany
| | - Fabrice Gielen
- Living Systems Institute, University of ExeterExeterUnited Kingdom
- Physics and Astronomy, University of ExeterExeterUnited Kingdom
| | - Kirsty Y Wan
- Living Systems Institute, University of ExeterExeterUnited Kingdom
- Mathematics and Statistics, University of ExeterExeterUnited Kingdom
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10
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Junker AD, Woodhams LG, Soh AWJ, O’Toole ET, Bayly PV, Pearson CG. Basal bodies bend in response to ciliary forces. Mol Biol Cell 2022; 33:ar146. [PMID: 36287828 PMCID: PMC9727800 DOI: 10.1091/mbc.e22-10-0468-t] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Motile cilia beat with an asymmetric waveform consisting of a power stroke that generates a propulsive force and a recovery stroke that returns the cilium back to the start. Cilia are anchored to the cell cortex by basal bodies (BBs) that are directly coupled to the ciliary doublet microtubules (MTs). We find that, consistent with ciliary forces imposing on BBs, bending patterns in BB triplet MTs are responsive to ciliary beating. BB bending varies as environmental conditions change the ciliary waveform. Bending occurs where striated fibers (SFs) attach to BBs and mutants with short SFs that fail to connect to adjacent BBs exhibit abnormal BB bending, supporting a model in which SFs couple ciliary forces between BBs. Finally, loss of the BB stability protein Poc1, which helps interconnect BB triplet MTs, prevents the normal distributed BB and ciliary bending patterns. Collectively, BBs experience ciliary forces and manage mechanical coupling of these forces to their surrounding cellular architecture for normal ciliary beating.
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Affiliation(s)
- Anthony D. Junker
- Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045
| | - Louis G. Woodhams
- Department of Mechanical Engineering and Material Science, Washington University in St. Louis, St. Louis, MO 63130
| | - Adam W. J. Soh
- Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045
| | - Eileen T. O’Toole
- Department of Molecular, Cellular and Developmental Biology, University of Colorado, Boulder, CO 80302
| | - Philip V. Bayly
- Department of Mechanical Engineering and Material Science, Washington University in St. Louis, St. Louis, MO 63130
| | - Chad G. Pearson
- Department of Cell and Developmental Biology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045,*Address correspondence to: Chad G. Pearson ()
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11
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Spontaneous phase coordination and fluid pumping in model ciliary carpets. Proc Natl Acad Sci U S A 2022; 119:e2214413119. [PMID: 36322751 PMCID: PMC9659382 DOI: 10.1073/pnas.2214413119] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023] Open
Abstract
Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.
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12
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Soh AWJ, Pearson CG. Ciliate cortical organization and dynamics for cell motility: Comparing ciliates and vertebrates. J Eukaryot Microbiol 2022; 69:e12880. [PMID: 34897878 PMCID: PMC9188629 DOI: 10.1111/jeu.12880] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The generation of efficient fluid flow is crucial for organismal development and homeostasis, sexual reproduction, and motility. Multi-ciliated cells possess fields of motile cilia that beat in synchrony to propel fluid. Ciliary arrays are remarkably conserved in their organization and function. Ciliates have polarized multi-ciliary arrays (MCAs) to promote fluid flow for cell motility. The ciliate cortex is decorated with hundreds of basal bodies (BB) forming linear rows along the cell's anterior-posterior axis. BBs scaffold and position cilia to form the organized ciliary array. Nascent BBs assemble at the base of BBs. As nascent BBs mature, they integrate into the cortical BB and cytoskeletal network and nucleate their own cilium. The organization of MCAs is balanced between cortical stability and cortical dynamism. The cortical cytoskeletal network both establishes and maintains a stable organization of the MCA in the face of mechanical forces exerted by ciliary beating. At the same time, MCA organization is plastic, such that it remodels for optimal ciliary mobility during development and in response to environmental conditions. Such plasticity promotes effective feeding and ecological behavior required for these organisms. Together, these properties allow an organism to effectively sense, adapt to, and move through its environment.
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Affiliation(s)
- Adam W. J. Soh
- Anschutz Medical Campus, Department of Cell and Developmental Biology, University of Colorado, Aurora, CO 80045
| | - Chad G. Pearson
- Anschutz Medical Campus, Department of Cell and Developmental Biology, University of Colorado, Aurora, CO 80045
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13
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Tătulea-Codrean M, Lauga E. Elastohydrodynamic Synchronization of Rotating Bacterial Flagella. PHYSICAL REVIEW LETTERS 2022; 128:208101. [PMID: 35657856 DOI: 10.1103/physrevlett.128.208101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Revised: 02/03/2022] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
To rotate continuously without jamming, the flagellar filaments of bacteria need to be locked in phase. While several models have been proposed for eukaryotic flagella, the synchronization of bacterial flagella is less well understood. Starting from a reduced model of flexible and hydrodynamically coupled bacterial flagella, we rigorously coarse grain the equations of motion using the method of multiple scales, and hence show that bacterial flagella generically synchronize to zero phase difference via an elastohydrodynamic mechanism. Remarkably, the far-field rate of synchronization is maximized at an intermediate value of elastic compliance, with surprising implications for bacteria.
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Affiliation(s)
- Maria Tătulea-Codrean
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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14
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Diaz K, Robinson TL, Aydin YO, Aydin E, Goldman DI, Wan KY. A minimal robophysical model of quadriflagellate self-propulsion. BIOINSPIRATION & BIOMIMETICS 2021; 16:066001. [PMID: 34359055 DOI: 10.1088/1748-3190/ac1b6e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
Locomotion at the microscale is remarkably sophisticated. Microorganisms have evolved diverse strategies to move within highly viscous environments, using deformable, propulsion-generating appendages such as cilia and flagella to drive helical or undulatory motion. In single-celled algae, these appendages can be arranged in different ways around an approximately 10 μm long cell body, and coordinated in distinct temporal patterns. Inspired by the observation that some quadriflagellates (bearing four flagella) have an outwardly similar morphology and flagellar beat pattern, yet swim at different speeds, this study seeks to determine whether variations in swimming performance could arise solely from differences in swimming gait. Robotics approaches are particularly suited to such investigations, where the phase relationships between appendages can be readily manipulated. Here, we developed autonomous, algae-inspired robophysical models that can self-propel in a viscous fluid. These macroscopic robots (length and width = 8.5 cm, height = 2 cm) have four independently actuated 'flagella' (length = 13 cm) that oscillate under low-Reynolds number conditions (Re∼O(10-1)). We tested the swimming performance of these robot models with appendages arranged two distinct configurations, and coordinated in three distinct gaits. The gaits, namely the pronk, the trot, and the gallop, correspond to gaits adopted by distinct microalgal species. When the appendages are inserted perpendicularly around a central 'body', the robot achieved a net performance of 0.15-0.63 body lengths per cycle, with the trot gait being the fastest. Robotic swimming performance was found to be comparable to that of the algal microswimmers across all gaits. By creating a minimal robot that can successfully reproduce cilia-inspired drag-based swimming, our work paves the way for the design of next-generation devices that have the capacity to autonomously navigate aqueous environments.
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Affiliation(s)
- Kelimar Diaz
- Interdisciplinary Graduate Program in Quantitative Biosciences, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
| | - Tommie L Robinson
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
| | - Yasemin Ozkan Aydin
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
- Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, United States of America
| | - Enes Aydin
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
| | - Daniel I Goldman
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America
| | - Kirsty Y Wan
- Living Systems Institute & College of Engineering, Mathematics, and Physical Sciences, University of Exeter, EX4 4QD, United Kingdom
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15
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Abstract
To gain a holistic understanding of cellular function, we must understand not just the role of individual organelles, but also how multiple macromolecular assemblies function collectively. Centrioles produce fundamental cellular processes through their ability to organise cytoskeletal fibres. In addition to nucleating microtubules, centrioles form lesser-known polymers, termed rootlets. Rootlets were identified over a 100 years ago and have been documented morphologically since by electron microscopy in different eukaryotic organisms. Rootlet-knockout animals have been created in various systems, providing insight into their physiological functions. However, the precise structure and function of rootlets is still enigmatic. Here, I consider common themes of rootlet function and assembly across diverse cellular systems. I suggest that the capability of rootlets to form physical links from centrioles to other cellular structures is a general principle unifying their functions in diverse cells and serves as an example of how cellular function arises from collective organellar activity.
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Affiliation(s)
- Robert Mahen
- The Medical Research Council Cancer Unit, University of Cambridge, Hills Road, Cambridge CB2 0XZ, UK
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16
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Rode S, Elgeti J, Gompper G. Multi-ciliated microswimmers-metachronal coordination and helical swimming. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:76. [PMID: 34101070 PMCID: PMC8187229 DOI: 10.1140/epje/s10189-021-00078-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Accepted: 05/07/2021] [Indexed: 05/05/2023]
Abstract
The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with [Formula: see text]) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.
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Affiliation(s)
- Sebastian Rode
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Jens Elgeti
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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Byron ML, Murphy DW, Katija K, Hoover AP, Daniels J, Garayev K, Takagi D, Kanso E, Gemmell BJ, Ruszczyk M, Santhanakrishnan A. Metachronal motion across scales: current challenges and future directions. Integr Comp Biol 2021; 61:1674-1688. [PMID: 34048537 DOI: 10.1093/icb/icab105] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.
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Affiliation(s)
| | - David W Murphy
- University of South Florida, 4202 E. Fowler Ave, Tampa, FL, 33620, USA
| | - Kakani Katija
- Monterey Bay Aquarium Research Institute, 7700 Sandholdt Rd, Moss Landing, CA, 95039, USA
| | | | - Joost Daniels
- Monterey Bay Aquarium Research Institute, 7700 Sandholdt Rd, Moss Landing, CA, 95039, USA
| | - Kuvvat Garayev
- University of South Florida, 4202 E. Fowler Ave, Tampa, FL, 33620, USA
| | - Daisuke Takagi
- University of Hawaii at Manoa, 2500 Campus Rd, Honolulu, HI, 96822
| | - Eva Kanso
- University of Southern California, University Park, Los Angeles, CA, 90007
| | | | - Melissa Ruszczyk
- Georgia Institute of Technology, 310 Ferst Dr, Atlanta, GA, 30332, USA
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Jones C, Gomez M, Muoio RM, Vidal A, Mcknight RA, Brubaker ND, Ahmed WW. Stochastic force dynamics of the model microswimmer Chlamydomonas reinhardtii: Active forces and energetics. Phys Rev E 2021; 103:032403. [PMID: 33862745 DOI: 10.1103/physreve.103.032403] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 02/03/2021] [Indexed: 01/26/2023]
Abstract
We study the stochastic force dynamics of a model microswimmer (Chlamydomonas reinhardtii), using a combined experimental, theoretical, and numerical approach. While swimming dynamics have been extensively studied using hydrodynamic approaches, which infer forces from the viscous flow field, we directly measure the stochastic forces generated by the microswimmer using an optical trap via the photon momentum method. We analyze the force dynamics by modeling the microswimmer as a self-propelled particle, à la active matter, and analyze its energetics using methods from stochastic thermodynamics. We find complex oscillatory force dynamics and power dissipation on the order of 10^{6}k_{B}T/s(∼fW).
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Affiliation(s)
- Corbyn Jones
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Mauricio Gomez
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Ryan M Muoio
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Alex Vidal
- Department of Computer Science, California State University Fullerton, California 92831, USA
| | - R Anthony Mcknight
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Nicholas D Brubaker
- Department of Mathematics, California State University Fullerton, California 92831, USA
| | - Wylie W Ahmed
- Department of Physics, California State University Fullerton, California 92831, USA
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