1
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Lindemann CB, Lesich KA. The mechanics of cilia and flagella: What we know and what we need to know. Cytoskeleton (Hoboken) 2024. [PMID: 38780123 DOI: 10.1002/cm.21879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Revised: 05/04/2024] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
In this review, we provide a condensed overview of what is currently known about the mechanical functioning of the flagellar/ciliary axoneme. We also present a list of 10 specific areas where our current knowledge is incomplete and explain the benefits of further experimental investigation. Many of the physical parameters of the axoneme and its component parts have not been determined. This limits our ability to understand how the axoneme structure contributes to its functioning in several regards. It restricts our ability to understand how the mechanics of the structure contribute to the regulation of motor function. It also confines our ability to understand the three-dimensional workings of the axoneme and how various beating modes are accomplished. Lastly, it prevents accurate computational modeling of the axoneme in three-dimensions.
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Affiliation(s)
- Charles B Lindemann
- Department of Biological Sciences, Oakland University, Rochester, Michigan, USA
| | - Kathleen A Lesich
- Department of Biological Sciences, Oakland University, Rochester, Michigan, USA
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2
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Liu Z, Chao Y, Zheng Z, Zhu L. Spontaneous oscillation of an active filament under viscosity gradients. SOFT MATTER 2024; 20:3845-3853. [PMID: 38651457 DOI: 10.1039/d4sm00095a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We investigate the effects of uniform viscosity gradients on the spontaneous oscillations of an elastic, active filament in viscous fluids. Combining numerical simulations and linear stability analysis, we demonstrate that a viscosity gradient increasing from the filament's base to tip destabilises the system, facilitating its self-oscillation. This effect is elucidated through a reduced-order model, highlighting the delicate balance between destabilising active forces and stabilising viscous forces. Additionally, we reveal that while a perpendicular viscosity gradient to the filament's orientation minimally affects instability, it induces asymmetric ciliary beating, thus generating a net flow along the gradient. Our findings offer new insights into the complex behaviours of biological and artificial filaments in complex fluid environments, contributing to the broader understanding of filament dynamics in heterogeneous viscous media.
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Affiliation(s)
- Zhaorong Liu
- Department of Mechanical Engineering, National University of Singapore, 117575, Singapore.
| | - Youchuang Chao
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
| | - Zhijun Zheng
- CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China
| | - Lailai Zhu
- Department of Mechanical Engineering, National University of Singapore, 117575, Singapore.
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3
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Link KG, Guy RD, Thomases B, Arratia PE. Effect of fluid elasticity on the emergence of oscillations in an active elastic filament. J R Soc Interface 2024; 21:20240046. [PMID: 38774961 DOI: 10.1098/rsif.2024.0046] [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: 06/02/2023] [Accepted: 03/20/2024] [Indexed: 07/31/2024] Open
Abstract
Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.
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Affiliation(s)
- Kathryn G Link
- Department of Mathematics, University of California , Davis, CA 95616, USA
| | - Robert D Guy
- Department of Mathematics, University of California , Davis, CA 95616, USA
| | - Becca Thomases
- Department of Mathematical Sciences, Smith College , Northampton, MA 01063, USA
| | - Paulo E Arratia
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania , Philadelphia, PA 19104, USA
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4
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Nassir M, Levi M, Wiser A, Shaked NT. Evaluation of women's aging influence on sperm passage inside the fallopian tube using 3D dynamic mechanical modeling. Front Bioeng Biotechnol 2024; 12:1324802. [PMID: 38712332 PMCID: PMC11070836 DOI: 10.3389/fbioe.2024.1324802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 02/27/2024] [Indexed: 05/08/2024] Open
Abstract
The fallopian tubes play an important role in human fertility by facilitating the spermatozoa passage to the oocyte as well as later actively facilitating the fertilized oocyte transportation to the uterus cavity. The fallopian tubes undergo changes involving biological, physical, and morphological processes due to women aging, which may impair fertility. Here, we have modelled fallopian tubes of women at different ages and evaluated the chances of normal and pathological sperm cells reaching the fertilization site, the ampulla. By utilizing a unique combination of simulative tools, we implemented dynamic three-dimensional (3D) detailed geometrical models of many normal and pathological sperm cells swimming together in 3D geometrical models of three fallopian tubes associated with different women's age groups. By tracking the sperm cell swim, we found that for all age groups, the number of normal sperm cells in the ampulla is the largest, compared with the pathological sperm cells. On the other hand, the number of normal sperm cells in the fertilization site decreases due to the morphological and mechanical changes that occur in the fallopian tube with age. Moreover, in older ages, the normal sperm cells swim with lower velocities and for shorter distances inside the ampulla toward the ovary. Thus, the changes that the human fallopian tube undergoes due to women's aging have a significant influence on the human sperm cell motility. Our model of sperm cell motility through the fallopian tube in relation to the woman's age morphological changes provides a new scope for the investigation and treatment of diseases and infertility cases associated with aging, as well as a potential personalized medicine tool for evaluating the chances of a natural fertilization per specific features of a man's sperm and a woman's reproductive system.
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Affiliation(s)
- Mayssam Nassir
- Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Mattan Levi
- Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Amir Wiser
- Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Natan T. Shaked
- Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
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5
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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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6
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Corkidi G, Montoya F, González-Cota AL, Hernández-Herrera P, Bruce NC, Bloomfield-Gadêlha H, Darszon A. Human sperm rotate with a conserved direction during free swimming in four dimensions. J Cell Sci 2023; 136:jcs261306. [PMID: 37902031 PMCID: PMC10729817 DOI: 10.1242/jcs.261306] [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: 05/11/2023] [Accepted: 10/23/2023] [Indexed: 10/31/2023] Open
Abstract
Head rotation in human spermatozoa is essential for different swimming modes and fertilisation, as it links the molecular workings of the flagellar beat with sperm motion in three-dimensional (3D) space over time. Determining the direction of head rotation has been hindered by the symmetry and translucent nature of the sperm head, and by the fast 3D motion driven by the helical flagellar beat. Analysis has been mostly restricted to two-dimensional (2D) single focal plane image analysis, which enables tracking of head centre position but not tracking of head rotation. Despite the conserved helical beating of the human sperm flagellum, human sperm head rotation has been reported to be uni- or bi-directional, and even to intermittently change direction in a given cell. Here, we directly measure the head rotation of freely swimming human sperm using multi-plane 4D (3D+t) microscopy and show that: (1) 2D microscopy is unable to distinguish head rotation direction in human spermatozoa; (2) head rotation direction in non-capacitating and capacitating solutions, for both aqueous and viscous media, is counterclockwise (CCW), as seen from head to tail, in all rotating spermatozoa, regardless of the experimental conditions; and (3) head rotation is suppressed in 36% of spermatozoa swimming in non-capacitating viscous medium, although CCW rotation is recovered after incubation in capacitating conditions within the same viscous medium, possibly unveiling an unexplored aspect of the essential need of capacitation for fertilisation. Our observations show that the CCW head rotation in human sperm is conserved. It constitutes a robust and persistent helical driving mechanism that influences sperm navigation in 3D space over time, and thus is of critical importance in cell motility, propulsion of flagellated microorganisms, sperm motility assessments, human reproduction research, and self-organisation of flagellar beating patterns and swimming in 3D space.
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Affiliation(s)
- Gabriel Corkidi
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Fernando Montoya
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Ana L. González-Cota
- Departamento de Genética del Desarrollo y Fisiología Molecular and Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Paul Hernández-Herrera
- Laboratorio Nacional de Microscopía Avanzada, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Neil C. Bruce
- Instituto de Ciencias Aplicadas y Tecnología, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Ciudad Universitaria, 04510 Ciudad de México, México
| | - Hermes Bloomfield-Gadêlha
- School of Engineering Mathematics and Technology & Bristol Robotics Laboratory, University of Bristol, Bristol BS8 1TW, UK
| | - Alberto Darszon
- Departamento de Genética del Desarrollo y Fisiología Molecular and Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
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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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Dynamic 3D Modeling for Human Sperm Motility through the Female Cervical Canal and Uterine Cavity to Predict Sperm Chance of Reaching the Oocyte. Cells 2023; 12:cells12010203. [PMID: 36611996 PMCID: PMC9818231 DOI: 10.3390/cells12010203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2022] [Revised: 12/12/2022] [Accepted: 12/14/2022] [Indexed: 01/05/2023] Open
Abstract
Sperm motility in the female genital tract is a key factor in the natural selection of competent cells that will produce a healthy offspring. We created a dynamic three-dimensional (3D) mechanical model of human sperm cells swimming inside cervical canal and uterine cavity dynamic 3D models, all generated based on experimental studies. Using these simulations, we described the sperm cells' behaviors during swimming inside the 3D tract model as a function of 3D displacement and time. We evaluated normal- and abnormal-morphology sperm cells according to their chances of reaching the oocyte site. As expected, we verified that the number of normal sperm cells that succeeded in reaching the fallopian tube sites is greater than the number of abnormal sperm cells. However, interestingly, after inspecting various abnormal sperm cells, we found out that their scores changed compared to swimming in an infinite medium, as is the case with in vitro fertilization. Thus, the interactions of abnormal sperm cells and the complicated geometry and dynamics of the uterus are significant factors in the filtering of abnormal sperm cells until they reach the oocyte site. Our study provides an advanced tool for sperm analysis and selection criteria for fertility treatments.
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10
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Howard J, Chasteen A, Ouyang X, Geyer VF, Sartori P. Predicting the locations of force-generating dyneins in beating cilia and flagella. Front Cell Dev Biol 2022; 10:995847. [PMID: 36303602 PMCID: PMC9592896 DOI: 10.3389/fcell.2022.995847] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 09/13/2022] [Indexed: 11/18/2022] Open
Abstract
Cilia and flagella are slender cylindrical organelles whose bending waves propel cells through fluids and drive fluids across epithelia. The bending waves are generated by dynein motor proteins, ATPases whose force-generating activity changes over time and with position along the axoneme, the motile structure within the cilium. A key question is: where, in an actively beating axoneme, are the force-generating dyneins located? Answering this question is crucial for determining which of the conformational states adopted by the dynein motors generate the forces that bend the axoneme. The question is difficult to answer because the flagellum contains a large number of dyneins in a complex three-dimensional architecture. To circumvent this complexity, we used a molecular-mechanics approach to show how the bending moments produced by single pairs of dynein motors work against elastic and hydrodynamic forces. By integrating the individual motor activities over the length of the axoneme, we predict the locations of the force-generating dyneins in a beating axoneme. The predicted location depends on the beat frequency, the wavelength, and the elastic and hydrodynamic properties of the axoneme. To test these predictions using cryogenic electron microscopy, cilia with shorter wavelengths, such as found in Chlamydomonas, are more suitable than sperm flagella with longer wavelengths because, in the former, the lag between force and curvature is less dependent on the specific mechanical properties and experimental preparation.
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Affiliation(s)
- Jonathon Howard
- Department of Molecular Biophysics & Biochemistry, Yale University, New Haven, United States
- Instituto Gulbenkian de Ciência, Oeiras, Portugal
- Department of Physics, Yale University, New Haven, United States
- Yale Quantitative Biology Institute, New Haven, United States
- *Correspondence: Jonathon Howard,
| | - Alexander Chasteen
- Department of Molecular Biophysics & Biochemistry, Yale University, New Haven, United States
| | - Xiaoyi Ouyang
- Department of Physics, Yale University, New Haven, United States
| | - Veikko F. Geyer
- Center for Molecular and Cellular Bioengineering (CMCB), Technische Universität Dresden, Dresden, Germany
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11
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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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12
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Prior C, Panter J, Kusumaatmaja H. A minimal model of elastic instabilities in biological filament bundles. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220287. [PMID: 36128703 PMCID: PMC9490347 DOI: 10.1098/rsif.2022.0287] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
We present a model of a system of elastic fibres which exhibits complex, coupled, nonlinear deformations via a connecting elastic spring network. This model can capture physically observed deformations such as global buckling, pinching and internal collapse. We explore the transitions between these deformation modes numerically, using an energy minimization approach, highlighting how supported environments, or stiff outer sheath structures, favour internal structural collapse over global deformation. We then derive a novel analytic buckling criterion for the internal collapse of the system, a mode of structural collapse pertinent in many biological filament bundles such as the optic nerve bundle and microtubule bundles involved in cell abscission.
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Affiliation(s)
- Chris Prior
- Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
| | - Jack Panter
- Department of Physics, Durham University, Durham DH1 3LE, UK
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13
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Guido I, Vilfan A, Ishibashi K, Sakakibara H, Shiraga M, Bodenschatz E, Golestanian R, Oiwa K. A Synthetic Minimal Beating Axoneme. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2022; 18:e2107854. [PMID: 35815940 DOI: 10.1002/smll.202107854] [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: 12/17/2021] [Revised: 06/03/2022] [Indexed: 06/15/2023]
Abstract
Cilia and flagella are beating rod-like organelles that enable the directional movement of microorganisms in fluids and fluid transport along the surface of biological organisms or inside organs. The molecular motor axonemal dynein drives their beating by interacting with microtubules. Constructing synthetic beating systems with axonemal dynein capable of mimicking ciliary beating still represents a major challenge. Here, the bottom-up engineering of a sustained beating synthoneme consisting of a pair of microtubules connected by a series of periodic arrays of approximately eight axonemal dyneins is reported. A model leads to the understanding of the motion through the cooperative, cyclic association-dissociation of the molecular motor from the microtubules. The synthoneme represents a bottom-up self-organized bio-molecular machine at the nanoscale with cilia-like properties.
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Affiliation(s)
- Isabella Guido
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany
- Jožef Stefan Institute, Ljubljana, 1000, Slovenia
| | - Kenta Ishibashi
- Graduate School of Frontier Biosciences, Osaka University, Osaka, 5650871, Japan
- Center for Information and Neural Networks (CiNet), National Institute of Information and Communications Technology, Osaka, 565-0871, Japan
| | - Hitoshi Sakakibara
- Advanced ICT Research Institute, National Institute of Information and Communications Technology, Kobe, 651-2492, Japan
| | - Misaki Shiraga
- Graduate School of Life Science, University of Hyogo, Hyogo, 678-1297, Japan
| | - Eberhard Bodenschatz
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany
- Institute for Dynamics of Complex Systems, Georg-August-University Göttingen, 37073, Göttingen, Germany
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY, 14853, USA
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, UK
| | - Kazuhiro Oiwa
- Advanced ICT Research Institute, National Institute of Information and Communications Technology, Kobe, 651-2492, Japan
- Graduate School of Life Science, University of Hyogo, Hyogo, 678-1297, Japan
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14
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Rallabandi B, Wang Q, Potomkin M. Self-sustained three-dimensional beating of a model eukaryotic flagellum. SOFT MATTER 2022; 18:5312-5322. [PMID: 35792826 DOI: 10.1039/d2sm00514j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Flagella and cilia are common features of a wide variety of biological cells and play important roles in locomotion and feeding at the microscale. The beating of flagella is controlled by molecular motors that exert forces along the length of the flagellum and are regulated by a feedback mechanism coupled to the flagella deformation. We develop a three-dimensional (3D) flagellum beating model based on sliding-controlled motor feedback, accounting for both bending and twist, as well as differential bending resistances along and orthogonal to the major bending plane of the flagellum. We show that beating is generated and sustained spontaneously for a sufficiently high motor activity through an instability mechanism. Isotropic bending rigidities in the flagellum lead to 3D helical beating patterns. By contrast, anisotropic flagella present a rich variety of wave-like beating dynamics, including both 3D beating patterns as well as planar beating patterns. We show that the ability to generate nearly planar beating despite the 3D beating machinery requires only a modest degree of bending anisotropy, and is a feature observed in many eukaryotic flagella such as mammalian spermatozoa.
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Affiliation(s)
- Bhargav Rallabandi
- Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA.
| | - Qixuan Wang
- Department of Mathematics, University of California, Riverside, CA 92521, USA.
| | - Mykhailo Potomkin
- Department of Mathematics, University of California, Riverside, CA 92521, USA.
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15
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Woodhams LG, Shen Y, Bayly PV. Generation of ciliary beating by steady dynein activity: the effects of inter-filament coupling in multi-filament models. J R Soc Interface 2022; 19:20220264. [PMID: 35857924 PMCID: PMC9257587 DOI: 10.1098/rsif.2022.0264] [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: 04/03/2022] [Accepted: 06/20/2022] [Indexed: 09/05/2023] Open
Abstract
The structure of the axoneme in motile cilia and flagella is emerging with increasing detail from high-resolution imaging, but the mechanism by which the axoneme creates oscillatory, propulsive motion remains mysterious. It has recently been proposed that this motion may be caused by a dynamic 'flutter' instability that can occur under steady dynein loading, and not by switching or modulation of dynein motor activity (as commonly assumed). In the current work, we have built an improved multi-filament mathematical model of the axoneme and implemented it as a system of discrete equations using the finite-element method. The eigenvalues and eigenvectors of this model predict the emergence of oscillatory, wave-like solutions in the absence of dynein regulation and specify the associated frequencies and waveforms of beating. Time-domain simulations with this model illustrate the behaviour predicted by the system's eigenvalues. This model and analysis allow us to efficiently explore the potential effects of difficult to measure biophysical parameters, such as elasticity of radial spokes and inter-doublet links, on the ciliary waveform. These results support the idea that dynamic instability without dynamic dynein regulation is a plausible and robust mechanism for generating ciliary beating.
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Affiliation(s)
- Louis G. Woodhams
- Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130-4899, USA
| | - Yenan Shen
- Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Philip V. Bayly
- Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130-4899, USA
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16
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Omori T, Munakata S, Ishikawa T. Self-sustaining oscillation of two axonemal microtubules based on a stochastic bonding model between microtubules and dynein. Phys Rev E 2022; 106:014402. [PMID: 35974562 DOI: 10.1103/physreve.106.014402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 06/17/2022] [Indexed: 06/15/2023]
Abstract
The motility of cilia and flagella plays important physiological roles, and there has been a great deal of research on the mechanisms underlying the motility of molecular motors. Although recent molecular structural analyses have revealed the components of the ciliary axoneme, the mechanisms involved in the regulation of dynein activity are still unknown, and how multiple dyneins coordinate their movements remains unclear. In particular, the mode of binding for axonemal dynein has not been elucidated. In this study, we constructed a thermodynamic stochastic model of microtubule-dynein coupling and reproduced the experiments of Aoyama and Kamiya on the minimal component of axonemal microtubule-dynein. We then identified the binding mode of axonemal dynein and clarified the relationship between dynein activity distribution and axonemal movement. Based on our numerical results, the slip-bond mechanism agrees quantitatively with the experimental results in terms of amplitude, frequency, and propagation velocity, implying that axial microtubule-dynein coupling may follow a slip-bond mechanism. Moreover, the frequency and propagation velocity decayed in proportion to the fourth power of microtubule length, and the critical load of the trigger for the oscillation agreed well with Euler's critical load.
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Affiliation(s)
- T Omori
- Department of Finemechanics, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
| | - S Munakata
- Department of Biomedical Engineering, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
| | - T Ishikawa
- Department of Finemechanics, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
- Department of Biomedical Engineering, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
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17
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Ahmad R, Bae AJ, Su YJ, Pozveh SG, Bodenschatz E, Pumir A, Gholami A. Bio-hybrid micro-swimmers propelled by flagella isolated from C. reinhardtii. SOFT MATTER 2022; 18:4767-4777. [PMID: 35703562 DOI: 10.1039/d2sm00574c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Bio-hybrid micro-swimmers, composed of biological entities integrated with synthetic constructs, actively transport cargo by converting chemical energy into mechanical work. Here, using isolated and demembranated flagella from green algae Chlamydomonas reinhardtii (C. reinhardtii), we build efficient axonemally-driven micro-swimmers that consume ATP to propel micron-sized beads. Depending on the calcium concentration, we observed two main classes of motion: whereas beads move along curved trajectories at calcium concentrations below 0.03 mM, they are propelled along straight paths when the calcium concentration increases. In this regime, they reached velocities of approximately 20 μm s-1, comparable to human sperm velocity in vivo. We relate this transition to the properties of beating axonemes, in particular the reduced static curvature with increasing calcium concentration. Our designed system has potential applications in the fabrication of synthetic micro-swimmers, and in particular, bio-actuated medical micro-robots for targeted drug delivery.
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Affiliation(s)
- Raheel Ahmad
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
| | - Albert J Bae
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
- Lewis & Clark College, Portland, Oregon, USA
| | - Yu-Jung Su
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
| | - Samira Goli Pozveh
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
| | - Eberhard Bodenschatz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
- Institute for Dynamics of Complex Systems, University of Göttingen, Göttingen 37077, Germany
- Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Alain Pumir
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
- Univ Lyon, Ecole Normale Superieure de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Azam Gholami
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
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18
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Wang C, Tang H, Zhang X. Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics. BIOINSPIRATION & BIOMIMETICS 2022; 17:041002. [PMID: 35443232 DOI: 10.1088/1748-3190/ac68ba] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 04/20/2022] [Indexed: 06/14/2023]
Abstract
Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.
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Affiliation(s)
- Chenglei Wang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Hui Tang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Xing Zhang
- The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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19
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Nassir M, Levi M, Dardikman-Yoffe G, Mirsky SK, Shaked NT. Prediction of Sperm Progression in Three Dimensions Using Rapid Optical Imaging and Dynamic Mechanical Modeling. Cells 2022; 11:cells11081319. [PMID: 35455999 PMCID: PMC9030059 DOI: 10.3390/cells11081319] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2022] [Revised: 03/29/2022] [Accepted: 03/29/2022] [Indexed: 11/16/2022] Open
Abstract
We present a multidisciplinary approach for predicting how sperm cells with various morphologies swim in three-dimensions (3D), from milliseconds to much longer time scales at spatial resolutions of less than half a micron. We created the sperm 3D geometry and built a numerical mechanical model using the experimentally acquired dynamic 3D refractive-index profiles of sperm cells swimming in vitro as imaged by high-resolution optical diffraction tomography. By controlling parameters in the model, such as the size and shape of the sperm head and tail, we can then predict how different sperm cells, normal or abnormal, would swim in 3D, in the short or long term. We quantified various 3D structural factor effects on the sperm long-term motility. We found that some abnormal sperm cells swim faster than normal sperm cells, in contrast to the commonly used sperm selection assumption during in vitro fertilization (IVF), according to which sperm cells should mainly be chosen based on their progressive motion. We thus establish a new tool for sperm analysis and male-infertility diagnosis, as well as sperm selection criteria for fertility treatments.
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20
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Powar S, Parast FY, Nandagiri A, Gaikwad AS, Potter DL, O'Bryan MK, Prabhakar R, Soria J, Nosrati R. Unraveling the Kinematics of Sperm Motion by Reconstructing the Flagellar Wave Motion in 3D. SMALL METHODS 2022; 6:e2101089. [PMID: 35138044 DOI: 10.1002/smtd.202101089] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Revised: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Sperm swim through the female reproductive tract by propagating a 3D flagellar wave that is self-regulatory in nature and driven by dynein motors. Traditional microscopy methods fail to capture the full dynamics of sperm flagellar activity as they only image and analyze sperm motility in 2D. Here, an automated platform to analyze sperm swimming behavior in 3D by using thin-lens approximation and high-speed dark field microscopy to reconstruct the flagellar waveform in 3D is presented. It is found that head-tethered mouse sperm exhibit a rolling beating behavior in 3D with the beating frequency of 6.2 Hz using spectral analysis. The flagellar waveform bends in 3D, particularly in the distal regions, but is only weakly nonplanar and ambidextrous in nature, with the local helicity along the flagellum fluctuating between clockwise and counterclockwise handedness. These findings suggest a nonpersistent flagellar helicity. This method provides new opportunities for the accurate measurement of the full motion of eukaryotic flagella and cilia which is essential for a biophysical understanding of their activation by dynein motors.
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Affiliation(s)
- Sushant Powar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
| | - Farin Yazdan Parast
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
| | - Ashwin Nandagiri
- IITB-Monash Research Academy, Indian Institute of Technology Bombay, Mumbai, 400076, India
| | - Avinash S Gaikwad
- School of BioSciences, Faculty of Science, University of Melbourne, Parkville, Victoria, 3010, Australia
- School of Biological Sciences, Monash University, Clayton, Victoria, 3800, Australia
| | - David L Potter
- Monash Micro-Imaging, Monash University, Clayton, Victoria, 3800, Australia
| | - Moira K O'Bryan
- School of BioSciences, Faculty of Science, University of Melbourne, Parkville, Victoria, 3010, Australia
- School of Biological Sciences, Monash University, Clayton, Victoria, 3800, Australia
| | - Ranganathan Prabhakar
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
| | - Julio Soria
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
- Laboratory for Turbulence Research in Aerospace & Combustion (LTRAC), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
| | - Reza Nosrati
- Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia
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21
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Abstract
Place a drop of pond water under the microscope, and you will likely find an ocean of extraordinary and diverse single-celled organisms called ciliates. This remarkable group of single-celled organisms wield microtubules, active systems, electrical signaling, and chemical sensors to build intricate geometrical structures and perform complex behaviors that can appear indistinguishable from those of macroscopic animals. Advances in computer vision and machine learning are making it possible to completely digitize and track the dynamics of complex ciliates and mine these data for the hidden structure, patterns, and motifs that are responsible for their behaviors. By deconstructing the diversity of ciliate behaviors in the natural world, themes for organizing and controlling matter at the microscale are beginning to take hold, suggesting new modular approaches for the design of autonomous molecular machines that emulate nature’s finest examples.
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Affiliation(s)
- Scott M Coyle
- Department of Biochemistry, University of Wisconsin, Madison, Madison, Wisconsin 53706
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22
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Striggow F, Nadporozhskaia L, Friedrich BM, Schmidt OG, Medina-Sánchez M. Micromotor-mediated sperm constrictions for improved swimming performance. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:67. [PMID: 33974155 PMCID: PMC8113191 DOI: 10.1140/epje/s10189-021-00050-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2020] [Accepted: 03/03/2021] [Indexed: 05/26/2023]
Abstract
Sperm-driven micromotors, consisting of a single sperm cell captured in a microcap, utilize the strong propulsion generated by the flagellar beat of motile spermatozoa for locomotion. It enables the movement of such micromotors in biological media, while being steered remotely by means of an external magnetic field. The substantial decrease in swimming speed, caused by the additional hydrodynamic load of the microcap, limits the applicability of sperm-based micromotors. Therefore, to improve the performance of such micromotors, we first investigate the effects of additional cargo on the flagellar beat of spermatozoa. We designed two different kinds of microcaps, which each result in different load responses of the flagellar beat. As an additional design feature, we constrain rotational degrees of freedom of the cell's motion by modifying the inner cavity of the cap. Particularly, cell rolling is substantially reduced by tightly locking the sperm head inside the microcap. Likewise, cell yawing is decreased by aligning the micromotors under an external static magnetic field. The observed differences in swimming speed of different micromotors are not so much a direct consequence of hydrodynamic effects, but rather stem from changes in flagellar bending waves, hence are an indirect effect. Our work serves as proof-of-principle that the optimal design of microcaps is key for the development of efficient sperm-driven micromotors.
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Affiliation(s)
- Friedrich Striggow
- Institute for Integrative Nanosciences, Leibniz IFW Dresden e.V., Helmholtzstraße 20, 01069, Dresden, Germany
| | | | - Benjamin M Friedrich
- Center for Advancing Electronics Dresden, TU Dresden, 01069, Dresden, Germany.
- Cluster of Excellence 'Physics of Life', TU Dresden, 01307, Dresden, Germany.
- School of Science, TU Dresden, 01062, Dresden, Germany.
| | - Oliver G Schmidt
- Institute for Integrative Nanosciences, Leibniz IFW Dresden e.V., Helmholtzstraße 20, 01069, Dresden, Germany
- School of Science, TU Dresden, 01062, Dresden, Germany
- Research Center for Materials, Architectures and Integration of Nanomembranes (MAIN), TU Chemnitz, Rosenbergstraße 6, 09126, Chemnitz, Germany
| | - Mariana Medina-Sánchez
- Institute for Integrative Nanosciences, Leibniz IFW Dresden e.V., Helmholtzstraße 20, 01069, Dresden, Germany.
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23
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Brette R. Integrative Neuroscience of Paramecium, a "Swimming Neuron". eNeuro 2021; 8:ENEURO.0018-21.2021. [PMID: 33952615 PMCID: PMC8208649 DOI: 10.1523/eneuro.0018-21.2021] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Revised: 03/17/2021] [Accepted: 03/18/2021] [Indexed: 11/28/2022] Open
Abstract
Paramecium is a unicellular organism that swims in fresh water by beating thousands of cilia. When it is stimulated (mechanically, chemically, optically, thermally…), it often swims backward then turns and swims forward again. This "avoiding reaction" is triggered by a calcium-based action potential. For this reason, some authors have called Paramecium a "swimming neuron." This review summarizes current knowledge about the physiological basis of behavior of Paramecium.
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Affiliation(s)
- Romain Brette
- Sorbonne Université, Institut National de la Santé et de la Recherche Médicale, Centre National de la Recherche Scientifique, Institut de la Vision, Paris 75012, France
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24
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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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25
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Cicconofri G, Noselli G, DeSimone A. The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis. eLife 2021; 10:58610. [PMID: 33899736 PMCID: PMC8075587 DOI: 10.7554/elife.58610] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 02/12/2021] [Indexed: 01/01/2023] Open
Abstract
We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.
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Affiliation(s)
| | - Giovanni Noselli
- SISSA - International School for Advanced Studies, Trieste, Italy
| | - Antonio DeSimone
- SISSA - International School for Advanced Studies, Trieste, Italy.,The BioRobotics Institute, Scuola Superiore Sant'Anna, Trieste, Italy
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26
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Qin K, Peng Z, Chen Y, Nganguia H, Zhu L, Pak OS. Propulsion of an elastic filament in a shear-thinning fluid. SOFT MATTER 2021; 17:3829-3839. [PMID: 33885447 DOI: 10.1039/d0sm02130j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Some micro-organisms and artificial micro-swimmers propel at low Reynolds numbers (Re) via the interaction of their flexible appendages with the surrounding fluid. While their locomotion has been extensively studied with a Newtonian fluid assumption, in realistic biological environments these micro-swimmers invariably encounter rheologically complex fluids. In particular, many biological fluids such as blood and different types of mucus have shear-thinning viscosities. The influence of this ubiquitous non-Newtonian rheology on the performance of flexible swimmers remains largely unknown. Here, we present a first study to examine how shear-thinning rheology alters the fluid-structure interaction and hence the propulsion performance of elastic swimmers at low Re. Via a simple elastic swimmer actuated magnetically, we demonstrate that shear-thinning rheology can either enhance or hinder elastohydrodynamic propulsion, depending on the intricate interplay between elastic and viscous forces as well as the magnetic actuation. We also use a reduced-order model to elucidate the mechanisms underlying the enhanced and hindered propulsion observed in different physical regimes. These results and improved understanding could guide the design of flexible micro-swimmers in non-Newtonian fluids.
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Affiliation(s)
- Ke Qin
- Department of Mechanical Engineering, Santa Clara University, Santa Clara, California, 95053, USA.
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27
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Liao W, Lauga E. Energetics of synchronization for model flagella and cilia. Phys Rev E 2021; 103:042419. [PMID: 34005959 DOI: 10.1103/physreve.103.042419] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2020] [Accepted: 02/16/2021] [Indexed: 11/07/2022]
Abstract
Synchronization is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronize their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of coswimming spermatozoa was consistent with minimization of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella, (2) spheres orbiting above a no-slip surface to model interacting flexible cilia, and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimized in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics, (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres, and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronization in these setups.
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Affiliation(s)
- Weida Liao
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom
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28
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Cortese D, Wan KY. Control of Helical Navigation by Three-Dimensional Flagellar Beating. PHYSICAL REVIEW LETTERS 2021; 126:088003. [PMID: 33709750 DOI: 10.1103/physrevlett.126.088003] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2020] [Revised: 12/10/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
Helical swimming is a ubiquitous strategy for motile cells to generate self-gradients for environmental sensing. The model biflagellate Chlamydomonas reinhardtii rotates at a constant 1-2 Hz as it swims, but the mechanism is unclear. Here, we show unequivocally that the rolling motion derives from a persistent, nonplanar flagellar beat pattern. This is revealed by high-speed imaging and micromanipulation of live cells. We construct a fully 3D model to relate flagellar beating directly to the free-swimming trajectories. For realistic geometries, the model reproduces both the sense and magnitude of the axial rotation of live cells. We show that helical swimming requires further symmetry breaking between the two flagella. These functional differences underlie all tactic responses, particularly phototaxis. We propose a control strategy by which cells steer toward or away from light by modulating the sign of biflagellar dominance.
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Affiliation(s)
- Dario Cortese
- Living Systems Institute and College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QD, United Kingdom
| | - Kirsty Y Wan
- Living Systems Institute and College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QD, United Kingdom
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29
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Goli Pozveh S, Bae AJ, Gholami A. Resistive force theory and wave dynamics in swimming flagellar apparatus isolated from C. reinhardtii. SOFT MATTER 2021; 17:1601-1613. [PMID: 33355581 PMCID: PMC8323821 DOI: 10.1039/d0sm01969k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
Cilia-driven motility and fluid transport are ubiquitous in nature and essential for many biological processes, including swimming of eukaryotic unicellular organisms, mucus transport in airway apparatus or fluid flow in the brain. The-biflagellated micro-swimmer Chlamydomonas reinhardtii is a model organism to study the dynamics of flagellar synchronization. Hydrodynamic interactions, intracellular mechanical coupling or cell body rocking is believed to play a crucial role in the synchronization of flagellar beating in green algae. Here, we use freely swimming intact flagellar apparatus isolated from a wall-less strain of Chlamydomonas to investigate wave dynamics. Our analysis on phase coordinates shows that when the frequency difference between the flagella is high (10-41% of the mean), neither mechanical coupling via basal body nor hydrodynamics interactions are strong enough to synchronize two flagella, indicating that the beating frequency is perhaps controlled internally by the cell. We also examined the validity of resistive force theory for a flagellar apparatus swimming freely in the vicinity of a substrate and found quantitative agreement between the experimental data and simulations with a drag anisotropy of ratio 2. Finally, using a simplified wave form, we investigated the influence of phase and frequency differences, intrinsic curvature and wave amplitude on the swimming trajectory of flagellar apparatus. Our analysis shows that by controlling the phase or frequency differences between two flagella, steering can occur.
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Affiliation(s)
- Samira Goli Pozveh
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
| | - Albert J Bae
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
| | - Azam Gholami
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.
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Guo H, Man Y, Wan KY, Kanso E. Intracellular coupling modulates biflagellar synchrony. J R Soc Interface 2021; 18:20200660. [PMID: 33435844 DOI: 10.1098/rsif.2020.0660] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate Chlamydomonas reinhardtii using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.
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Affiliation(s)
- Hanliang Guo
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA.,Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Yi Man
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Exeter EX4 4QD, UK
| | - Eva Kanso
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
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31
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Calcium signaling modulates the dynamics of cilia and flagella. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2020; 49:619-631. [PMID: 33105487 DOI: 10.1007/s00249-020-01471-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2020] [Accepted: 10/12/2020] [Indexed: 10/23/2022]
Abstract
To adapt to changing environments cells must signal and signaling requires messengers whose concentration varies with time in space. We here consider the messenger role of calcium ions implicated in regulation of the wave-like bending dynamics of cilia and flagella. The emphasis is on microtubules as polyelectrolytes serving as transmission lines for the flow of Ca2+ signals in the axoneme. This signaling is superimposed with a geometric clutch mechanism for the regulation of flagella bending dynamics and our modeling produces results in agreement with experimental data.
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32
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Satarić MV, Nemeš T, Satarić B, Sekulić D, Zdravković S. Calcium ions tune the beats of cilia and flagella. Biosystems 2020; 196:104172. [DOI: 10.1016/j.biosystems.2020.104172] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 05/13/2020] [Accepted: 05/13/2020] [Indexed: 01/19/2023]
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Mondal D, Adhikari R, Sharma P. Internal friction controls active ciliary oscillations near the instability threshold. SCIENCE ADVANCES 2020; 6:eabb0503. [PMID: 32851170 PMCID: PMC7423358 DOI: 10.1126/sciadv.abb0503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 07/02/2020] [Indexed: 06/11/2023]
Abstract
Ciliary oscillations driven by molecular motors cause fluid motion at micron scale. Stable oscillations require a substantial source of dissipation to balance the energy input of motors. Conventionally, it stems from external fluid. We show, in contrast, that external fluid friction is negligible compared to internal elastic stress through a simultaneous measurement of motion and flow field of an isolated and active Chlamydomonas cilium beating near the instability threshold. Consequently, internal friction emerges as the sole source of dissipation for ciliary oscillations. We combine these experimental insights with theoretical modeling of active filaments to show that an instability to oscillations takes place when active stresses are strain softening and shear thinning. Together, our results reveal a counterintuitive mechanism of ciliary beating and provide a general experimental and theoretical methodology to analyze other active filaments, both biological and synthetic ones.
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Affiliation(s)
- Debasmita Mondal
- Department of Physics, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | - Ronojoy Adhikari
- The Institute of Mathematical Sciences–Homi Bhabha National Institute, Chennai 600113, India
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK
| | - Prerna Sharma
- Department of Physics, Indian Institute of Science, Bangalore, Karnataka 560012, India
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Gadêlha H, Hernández-Herrera P, Montoya F, Darszon A, Corkidi G. Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering. SCIENCE ADVANCES 2020; 6:eaba5168. [PMID: 32789171 PMCID: PMC7399739 DOI: 10.1126/sciadv.aba5168] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 06/18/2020] [Indexed: 05/21/2023]
Abstract
Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.
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Affiliation(s)
- Hermes Gadêlha
- Department of Engineering Mathematics, University of Bristol, BS8 1UB Bristol, UK
| | - Paul Hernández-Herrera
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Fernando Montoya
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Alberto Darszon
- Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Gabriel Corkidi
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
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35
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Amador GJ, Wei D, Tam D, Aubin-Tam ME. Fibrous Flagellar Hairs of Chlamydomonas reinhardtii Do Not Enhance Swimming. Biophys J 2020; 118:2914-2925. [PMID: 32502384 PMCID: PMC7300311 DOI: 10.1016/j.bpj.2020.05.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Revised: 04/06/2020] [Accepted: 04/27/2020] [Indexed: 01/18/2023] Open
Abstract
The flagella of Chlamydomonas reinhardtii possess fibrous ultrastructures of a nanometer-scale thickness known as mastigonemes. These structures have been widely hypothesized to enhance flagellar thrust; however, detailed hydrodynamic analysis supporting this claim is lacking. In this study, we present a comprehensive investigation into the hydrodynamic effects of mastigonemes using a genetically modified mutant lacking the fibrous structures. Through high-speed observations of freely swimming cells, we found the average and maximum swimming speeds to be unaffected by the presence of mastigonemes. In addition to swimming speeds, no significant difference was found for flagellar gait kinematics. After our observations of swimming kinematics, we present direct measurements of the hydrodynamic forces generated by flagella with and without mastigonemes. These measurements were conducted using optical tweezers, which enabled high temporal and spatial resolution of hydrodynamic forces. Through our measurements, we found no significant difference in propulsive flows due to the presence of mastigonemes. Direct comparison between measurements and fluid mechanical modeling revealed that swimming hydrodynamics were accurately captured without including mastigonemes on the modeled swimmer's flagella. Therefore, mastigonemes do not appear to increase the flagella's effective area while swimming, as previously thought. Our results refute the longstanding claim that mastigonemes enhance flagellar thrust in C. reinhardtii, and so, their function still remains enigmatic.
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Affiliation(s)
- Guillermo J Amador
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, Delft, the Netherlands; Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, the Netherlands
| | - Da Wei
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, the Netherlands
| | - Daniel Tam
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, Delft, the Netherlands.
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, the Netherlands.
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36
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Cicuta P. The use of biophysical approaches to understand ciliary beating. Biochem Soc Trans 2020; 48:221-229. [PMID: 31922188 PMCID: PMC7054749 DOI: 10.1042/bst20190571] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2019] [Revised: 11/27/2019] [Accepted: 12/09/2019] [Indexed: 11/25/2022]
Abstract
Motile cilia are a striking example of the functional cellular organelle, conserved across all the eukaryotic species. Motile cilia allow the swimming of cells and small organisms and transport of liquids across epithelial tissues. Whilst the molecular structure is now very well understood, the dynamics of cilia is not well established either at the single cilium level nor at the level of collective beating. Indeed, a full understanding of this requires connecting together behaviour across various lengthscales, from the molecular to the organelle, then at the cellular level and up to the tissue scale. Aside from the fundamental interest in this system, understanding beating is important to elucidate aspects of embryonic development and a variety of health conditions from fertility to genetic and infectious diseases of the airways.
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Affiliation(s)
- Pietro Cicuta
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, U.K
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37
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Gong A, Rode S, Kaupp UB, Gompper G, Elgeti J, Friedrich BM, Alvarez L. The steering gaits of sperm. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190149. [PMID: 31884910 PMCID: PMC7017342 DOI: 10.1098/rstb.2019.0149] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/24/2019] [Indexed: 11/25/2022] Open
Abstract
Sperm are highly specialized cells, which have been subject to substantial evolutionary pressure. Whereas some sperm features are highly conserved, others have undergone major modifications. Some of these variations are driven by adaptation to mating behaviours or fitness at the organismic level. Others represent alternative solutions to the same task. Sperm must find the egg for fertilization. During this task, sperm rely on long slender appendages termed flagella that serve as sensory antennas, propellers and steering rudders. The beat of the flagellum is periodic. The resulting travelling wave generates the necessary thrust for propulsion in the fluid. Recent studies reveal that, for steering, different species rely on different fundamental features of the beat wave. Here, we discuss some examples of unity and diversity across sperm from different species with a particular emphasis on the steering mechanisms. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
- A. Gong
- Center of Advanced European Studies and Research (CAESAR), Molecular Sensory Systems, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany
| | - S. Rode
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - U. B. Kaupp
- Center of Advanced European Studies and Research (CAESAR), Molecular Sensory Systems, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany
| | - G. Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - J. Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - B. M. Friedrich
- Biological Algorithms Group, TU Dresden, Biological Systems Path of the Center for Advancing Electronics Dresden (CFAED), Helmholtzstrasse 18, 01069 Dresden, Germany
| | - L. Alvarez
- Center of Advanced European Studies and Research (CAESAR), Molecular Sensory Systems, Ludwig-Erhard-Allee 2, 53175 Bonn, Germany
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38
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Wan KY. Synchrony and symmetry-breaking in active flagellar coordination. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190393. [PMID: 31884920 PMCID: PMC7017343 DOI: 10.1098/rstb.2019.0393] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/02/2019] [Indexed: 12/12/2022] Open
Abstract
Living creatures exhibit a remarkable diversity of locomotion mechanisms, evolving structures specialized for interacting with their environment. In the vast majority of cases, locomotor behaviours such as flying, crawling and running are orchestrated by nervous systems. Surprisingly, microorganisms can enact analogous movement gaits for swimming using multiple, fast-moving cellular protrusions called cilia and flagella. Here, I demonstrate intermittency, reversible rhythmogenesis and gait mechanosensitivity in algal flagella, to reveal the active nature of locomotor patterning. In addition to maintaining free-swimming gaits, I show that the algal flagellar apparatus functions as a central pattern generator that encodes the beating of each flagellum in a network in a distinguishable manner. The latter provides a novel symmetry-breaking mechanism for cell reorientation. These findings imply that the capacity to generate and coordinate complex locomotor patterns does not require neural circuitry but rather the minimal ingredients are present in simple unicellular organisms. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
- Kirsty Y. Wan
- Living Systems Institute, University of Exeter, Exeter EX4 4QD, UK
- College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Exeter EX4 4QD, UK
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39
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Abstract
Cilia are specialized cellular organelles that are united in structure and implicated in diverse key life processes across eukaryotes. In both unicellular and multicellular organisms, variations on the same ancestral form mediate sensing, locomotion and the production of physiological flows. As we usher in a new, more interdisciplinary era, the way we study cilia is changing. This special theme issue brings together biologists, biophysicists and mathematicians to highlight the remarkable range of systems in which motile cilia fulfil vital functions, and to inspire and define novel strategies for future research. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
- Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
| | - Gáspár Jékely
- Living Systems Institute, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
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40
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Abstract
Cilia, or eukaryotic flagella, are microscopic active filaments expressed on the surface of many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces. Cilia are characterized by a highly conserved and intricate internal structure in which molecular motors exert forces on microtubule doublets causing cilia oscillations. The spatial and temporal regulations of this molecular machinery are not well understood. Several theories suggest that geometric feedback control from cilium deformations to molecular activity is needed. Here, we implement a recent sliding control model, where the unbinding of molecular motors is dictated by the sliding motion between microtubule doublets. We investigate the waveforms exhibited by the model cilium, as well as the associated molecular motor dynamics, for hinged and clamped boundary conditions. Hinged filaments exhibit base-to-tip oscillations while clamped filaments exhibit both base-to-tip and tip-to-base oscillations. We report the change in oscillation frequencies and amplitudes as a function of motor activity and sperm number, and we discuss the validity of these results in the context of experimental observations of cilia behaviour. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Feng Ling
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Eva Kanso
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
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41
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Chakrabarti B, Saintillan D. Hydrodynamic Synchronization of Spontaneously Beating Filaments. PHYSICAL REVIEW LETTERS 2019; 123:208101. [PMID: 31809101 DOI: 10.1103/physrevlett.123.208101] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2019] [Revised: 09/12/2019] [Indexed: 06/10/2023]
Abstract
Using a geometric feedback model of the flagellar axoneme accounting for dynein motor kinetics, we study elastohydrodynamic phase synchronization in a pair of spontaneously beating filaments with waveforms ranging from sperm to cilia and Chlamydomonas. Our computations reveal that both in-phase and antiphase synchrony can emerge for asymmetric beats while symmetric waveforms go in phase, and elucidate the mechanism for phase slips due to biochemical noise. Model predictions agree with recent experiments and illuminate the crucial roles of hydrodynamics and mechanochemical feedback in synchronization.
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Affiliation(s)
- Brato Chakrabarti
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
| | - David Saintillan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
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42
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Ling F, Guo H, Kanso E. Instability-driven oscillations of elastic microfilaments. J R Soc Interface 2019; 15:20180594. [PMID: 30958229 DOI: 10.1098/rsif.2018.0594] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory and low-order bead-spring models. Our results show that, away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.
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Affiliation(s)
- Feng Ling
- Department of Aerospace and Mechanical Engineering, University of Southern California , Los Angeles, CA 90089 , USA
| | - Hanliang Guo
- Department of Aerospace and Mechanical Engineering, University of Southern California , Los Angeles, CA 90089 , USA
| | - Eva Kanso
- Department of Aerospace and Mechanical Engineering, University of Southern California , Los Angeles, CA 90089 , USA
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43
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Moreau C, Giraldi L, Gadêlha H. The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella. J R Soc Interface 2019; 15:rsif.2018.0235. [PMID: 29973402 DOI: 10.1098/rsif.2018.0235] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2018] [Accepted: 06/06/2018] [Indexed: 11/12/2022] Open
Abstract
The inertialess fluid-structure interactions of active and passive inextensible filaments and slender-rods are ubiquitous in nature, from the dynamics of semi-flexible polymers and cytoskeletal filaments to cellular mechanics and flagella. The coupling between the geometry of deformation and the physical interaction governing the dynamics of bio-filaments is complex. Governing equations negotiate elastohydrodynamical interactions with non-holonomic constraints arising from the filament inextensibility. Such elastohydrodynamic systems are structurally convoluted, prone to numerical errors, thus requiring penalization methods and high-order spatio-temporal propagators. The asymptotic coarse-graining formulation presented here exploits the momentum balance in the asymptotic limit of small rod-like elements which are integrated semi-analytically. This greatly simplifies the elastohydrodynamic interactions and overcomes previous numerical instability. The resulting matricial system is straightforward and intuitive to implement, and allows for a fast and efficient computation, more than a hundred times faster than previous schemes. Only basic knowledge of systems of linear equations is required, and implementation achieved with any solver of choice. Generalizations for complex interaction of multiple rods, Brownian polymer dynamics, active filaments and non-local hydrodynamics are also straightforward. We demonstrate these in four examples commonly found in biological systems, including the dynamics of filaments and flagella. Three of these systems are novel in the literature. We additionally provide a Matlab code that can be used as a basis for further generalizations.
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Affiliation(s)
- Clément Moreau
- Université Côte d'Azur, Inria, CNRS, LJAD, McTAO team, Sophia Antipolis, France
| | - Laetitia Giraldi
- Université Côte d'Azur, Inria, CNRS, LJAD, McTAO team, Sophia Antipolis, France
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, UK
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Feofilova M, Mahamdeh M, Howard J. The Kinetics of Nucleotide Binding to Isolated Chlamydomonas Axonemes Using UV-TIRF Microscopy. Biophys J 2019; 117:679-687. [PMID: 31400919 PMCID: PMC6712413 DOI: 10.1016/j.bpj.2019.07.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Revised: 06/19/2019] [Accepted: 07/01/2019] [Indexed: 11/13/2022] Open
Abstract
Cilia and flagella are long, slender organelles found in many eukaryotic cells, where they have sensory, developmental, and motile functions. All cilia and flagella contain a microtubule-based structure called the axoneme. In motile cilia and flagella, which drive cell locomotion and fluid transport, the axoneme contains, along most of its length, motor proteins from the axonemal dynein family. These motor proteins drive motility by using energy derived from the hydrolysis of ATP to generate a bending wave, which travels down the axoneme. As a first step toward visualizing the ATPase activity of the axonemal dyneins during bending, we have investigated the kinetics of nucleotide binding to axonemes. Using a specially built ultraviolet total internal reflection fluorescence microscope, we found that the fluorescent ATP analog methylanthraniloyl ATP (mantATP), which has been shown to support axonemal motility, binds all along isolated, immobilized axonemes. By studying the recovery of fluorescence after photobleaching, we found that there are three mantATP binding sites: one that bleaches rapidly (time constant ≈ 1.7 s) and recovers slowly (time constant ≈ 44 s), one that bleaches with the same time constant but does not recover, and one that does not bleach. By reducing the dynein content in the axoneme using mutants and salt extraction, we provide evidence that the slow-recovering component, but not the other components, corresponds to axonemal dyneins. The recovery rate of this component, however, is too slow to be consistent with the activation of beating observed at higher mantATP concentrations; this indicates that the dyneins may be inhibited due to their immobilization at the surface. The development of this method is a first step toward direct observation of the traveling wave of dynein activity.
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45
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Andorfer R, Alper JD. From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures. WILEY INTERDISCIPLINARY REVIEWS. NANOMEDICINE AND NANOBIOTECHNOLOGY 2019; 11:e1553. [PMID: 30740918 PMCID: PMC6881777 DOI: 10.1002/wnan.1553] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Revised: 12/27/2018] [Accepted: 12/28/2018] [Indexed: 11/06/2022]
Abstract
As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.
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Affiliation(s)
- Rachel Andorfer
- Department of Bioengineering, Clemson University, Clemson, South Carolina
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina
| | - Joshua D. Alper
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina
- Department of Biological Sciences, Clemson University, Clemson, South Carolina
- Eukaryotic Pathogen Innovations Center, Clemson University, Clemson, South Carolina
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Man Y, Kanso E. Morphological transitions of axially-driven microfilaments. SOFT MATTER 2019; 15:5163-5173. [PMID: 31215548 DOI: 10.1039/c8sm02397b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The interactions of microtubules with motor proteins are ubiquitous in cellular and sub-cellular processes that involve motility and cargo transport. In vitro motility assays have demonstrated that motor-driven microtubules exhibit rich dynamical behaviors from straight to curved configurations. Here, we theoretically investigate the dynamic instabilities of elastic filaments, with free-ends, driven by single follower forces that emulate the action of molecular motors. Using the resistive force theory at low Reynolds number, and a combination of numerical techniques with linear stability analysis, we show the existence of four distinct regimes of filament behavior, including a novel buckled state with locked curvature. These successive instabilities recapitulate the full range of experimentally-observed microtubule behavior, implying that neither structural nor actuation asymmetry are needed to elicit this rich repertoire of motion.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical engineering, University of Southern California, CA 90007, USA.
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47
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Satarić MV, Nemeš T, Sekulić D, Tuszynski JA. How signals of calcium ions initiate the beats of cilia and flagella. Biosystems 2019; 182:42-51. [PMID: 31202860 DOI: 10.1016/j.biosystems.2019.103981] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Revised: 06/03/2019] [Accepted: 06/04/2019] [Indexed: 11/17/2022]
Abstract
Cilia and flagella are cell organelles serving basic roles in cellular motility. Ciliary movement is performed by a sweeping-like repeated bending motion, which gives rise to a self-propagating "ciliary beat". The hallmark structure in cilia is the axoneme, a stable architecture of microtubule doublets. The motion of axoneme is powered by the axonemal dynein motor family powered by ATP hydrolysis. It is still unclear how the organized beat of cilium and flagella emerges from the combined action of hundreds of dynein molecules. It has been hypothesized that such coordination is mediated by mechanical stress due to transverse, radial or sliding deformations. The beating asymmetry is crucial for airway ciliary function and it requires tubulin glutamination a unique posttranslational modification of C-termini of constituent microtubules that is highly abundant in cilia and flagella. The exact role of tubulin glutamination in ciliary or flagellar function is still unclear. In this paper we analyze the role of calcium (Ca2+) ions based on the experimental evidence that the flagellar asymmetry can be increased due to the entry of extracellular Ca2+ through, for example, the nimodipine-sensitive pathway located in the flagella. We propose a new scenario based on the polyelectrolyte properties of cellular microtubules (MTs) such that dynamic influx of Ca2+ ions provides the initiation and synchronization of dynein sliding along microtubules. We also point out the possible interplay between tubulin polyglutaminated C-termini and localized pulses of Ca2+ ions along microtubules.
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Affiliation(s)
- Miljko V Satarić
- Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
| | - Tomas Nemeš
- Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
| | - Dalibor Sekulić
- Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia
| | - Jack A Tuszynski
- Department of Physics, University of Alberta, Edmonton, Alberta, Canada; DIMEAS, Politecnico di Torino, Turin, Italy
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Szatkowski L, Merz DR, Jiang N, Ejikeme I, Belonogov L, Ross JL, Dima RI. Mechanics of the Microtubule Seam Interface Probed by Molecular Simulations and in Vitro Severing Experiments. J Phys Chem B 2019; 123:4888-4900. [PMID: 31117616 DOI: 10.1021/acs.jpcb.9b03059] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Microtubules (MTs) are structural components essential for cell morphology and organization. It has recently been shown that defects in the filament's lattice structure can be healed to create stronger filaments in a local area and ultimately cause global changes in MT organization and cell mobility. The ability to break, causing a defect, and heal appears to be a physiologically relevant and important feature of the MT structure. Defects can be created by MT severing enzymes and are target sites for complete severing or for healing by newly incorporated dimers. One particular lattice defect, the MT lattice ''seam" interface, is a location often speculated to be a weak site, a site of disassembly, or a target site for MT binding proteins. Despite seams existing in many MT structures, very little is known about the seam's role in MT function and dynamics. In this study, we probed the mechanical stability of the seam interface by applying coarse-grained indenting molecular dynamics. We found that the seam interface is as structurally robust as the typical lattice structure of MTs. Our results suggest that, unlike prior results that claim the seam is a weak site, it is just as strong as any other location on the MT, corroborating recent mechanical measurements.
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Affiliation(s)
- Lukasz Szatkowski
- Department of Chemistry , University of Cincinnati , Cincinnati , Ohio 45221 , United States
| | - Dale R Merz
- Department of Chemistry , University of Cincinnati , Cincinnati , Ohio 45221 , United States
| | - Nan Jiang
- Department of Chemistry , University of Cincinnati , Cincinnati , Ohio 45221 , United States
| | - Ifunanya Ejikeme
- Department of Chemistry , University of Cincinnati , Cincinnati , Ohio 45221 , United States
| | - Liudmila Belonogov
- Department of Physics , University of Massachusetts , Amherst , Massachusetts 01003 , United States
| | - Jennifer L Ross
- Department of Physics , University of Massachusetts , Amherst , Massachusetts 01003 , United States
| | - Ruxandra I Dima
- Department of Chemistry , University of Cincinnati , Cincinnati , Ohio 45221 , United States
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Bottier M, Thomas KA, Dutcher SK, Bayly PV. How Does Cilium Length Affect Beating? Biophys J 2019; 116:1292-1304. [PMID: 30878201 PMCID: PMC6451027 DOI: 10.1016/j.bpj.2019.02.012] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Revised: 01/23/2019] [Accepted: 02/13/2019] [Indexed: 12/21/2022] Open
Abstract
The effects of cilium length on the dynamics of cilia motion were investigated by high-speed video microscopy of uniciliated mutants of the swimming alga, Chlamydomonas reinhardtii. Cells with short cilia were obtained by deciliating cells via pH shock and allowing cilia to reassemble for limited times. The frequency of cilia beating was estimated from the motion of the cell body and of the cilium. Key features of the ciliary waveform were quantified from polynomial curves fitted to the cilium in each image frame. Most notably, periodic beating did not emerge until the cilium reached a critical length between 2 and 4 μm. Surprisingly, in cells that exhibited periodic beating, the frequency of beating was similar for all lengths with only a slight decrease in frequency as length increased from 4 μm to the normal length of 10-12 μm. The waveform average curvature (rad/μm) was also conserved as the cilium grew. The mechanical metrics of ciliary propulsion (force, torque, and power) all increased in proportion to length. The mechanical efficiency of beating appeared to be maximal at the normal wild-type length of 10-12 μm. These quantitative features of ciliary behavior illuminate the biophysics of cilia motion and, in future studies, may help distinguish competing hypotheses of the underlying mechanism of oscillation.
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Affiliation(s)
- Mathieu Bottier
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri; Department of Genetics, Washington University in St. Louis, St. Louis, Missouri
| | - Kyle A Thomas
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri
| | - Susan K Dutcher
- Department of Genetics, Washington University in St. Louis, St. Louis, Missouri
| | - Philip V Bayly
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri.
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50
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Abstract
Motility of cilia (also known as flagella in some eukaryotes) is based on axonemal doublet microtubule sliding that is driven by the dynein molecular motors. Dyneins are organized into intricately patterned inner and outer rows of arms, whose collective activity is to produce inter-microtubule movement. However, to generate a ciliary bend, not all dyneins can be active simultaneously. The switch point model accounts, in part, for how dynein motors are regulated during ciliary movement. On the basis of this model, supported by key direct experimental observations as well as more recent theoretical and structural studies, we are now poised to understand the mechanics of how ciliary dynein coordination controls axonemal bend formation and propagation.
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Affiliation(s)
- Stephen M King
- Department of Molecular Biology and Biophysics, University of Connecticut Health Center, Farmington, CT 06030-3305
| | - Winfield S Sale
- Department of Cell Biology, Emory University, Atlanta, GA 30322
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