1
|
Narayanasamy N, Bingham E, Fadero T, Ozan Bozdag G, Ratcliff WC, Yunker P, Thutupalli S. Metabolically-driven flows enable exponential growth in macroscopic multicellular yeast. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.19.599734. [PMID: 38948761 PMCID: PMC11213004 DOI: 10.1101/2024.06.19.599734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/02/2024]
Abstract
The ecological and evolutionary success of multicellular lineages is due in no small part to their increased size relative to unicellular ancestors. However, large size also poses biophysical challenges, especially regarding the transport of nutrients to all cells; these constraints are typically overcome through multicellular innovations (e.g., a circulatory system). Here we show that an emergent biophysical mechanism - spontaneous fluid flows arising from metabolically-generated density gradients - can alleviate constraints on nutrient transport, enabling exponential growth in nascent multicellular clusters of yeast lacking any multicellular adaptations for nutrient transport or fluid flow. Surprisingly, beyond a threshold size, the metabolic activity of experimentally-evolved snowflake yeast clusters drives large-scale fluid flows that transport nutrients throughout the cluster at speeds comparable to those generated by the cilia of extant multicellular organisms. These flows support exponential growth at macroscopic sizes that theory predicts should be diffusion limited. This work demonstrates how simple physical mechanisms can act as a 'biophysical scaffold' to support the evolution of multicellularity by opening up phenotypic possibilities prior to genetically-encoded innovations. More broadly, our findings highlight how co-option of conserved physical processes is a crucial but underappreciated facet of evolutionary innovation across scales.
Collapse
Affiliation(s)
- Nishant Narayanasamy
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore, India
| | - Emma Bingham
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
- Interdisciplinary Graduate Program in Quantitative Biosciences, Georgia Institute of Technology, Atlanta, GA, USA
| | | | - G Ozan Bozdag
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA
| | - William C Ratcliff
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA
| | - Peter Yunker
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
| | - Shashi Thutupalli
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore, India
- International Centre for Theoretical Sciences (TIFR), Bangalore, India
| |
Collapse
|
2
|
Hu S, Meng F. Multiflagellate Swimming Controlled by Hydrodynamic Interactions. PHYSICAL REVIEW LETTERS 2024; 132:204002. [PMID: 38829103 DOI: 10.1103/physrevlett.132.204002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Revised: 02/18/2024] [Accepted: 04/16/2024] [Indexed: 06/05/2024]
Abstract
Many eukaryotic microorganisms propelled by multiple flagella can swim very rapidly with distinct gaits. Here, we model a three-dimensional mutiflagellate swimmer, resembling the microalgae. When the flagella are actuated synchronously, the swimming efficiency can be enhanced or reduced by interflagella hydrodynamic interactions (HIs), determined by the intrinsic tilting angle of the flagella. The asynchronous gait with a phase difference between neighboring flagella can reduce oscillatory motion via the basal mechanical coupling. In the presence of a spherical body, simulations taking into account the flagella-body interactions reveal the advantage of anterior configuration compared with posterior configuration, where in the latter case an optimal flagella number arises. Apart from understanding the role of HIs in the multiflagellate microorganisms, this work could also guide laboratory fabrications of novel microswimmers.
Collapse
Affiliation(s)
- Shiyuan Hu
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Fanlong Meng
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
| |
Collapse
|
3
|
Wei D, Quaranta G, Aubin-Tam ME, Tam DSW. The younger flagellum sets the beat for Chlamydomonas reinhardtii. eLife 2024; 13:e86102. [PMID: 38752724 PMCID: PMC11098555 DOI: 10.7554/elife.86102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 04/03/2024] [Indexed: 05/18/2024] Open
Abstract
Eukaryotes swim with coordinated flagellar (ciliary) beating and steer by fine-tuning the coordination. The model organism for studying flagellate motility, Chlamydomonas reinhardtii, employs synchronous, breaststroke-like flagellar beating to swim, and it modulates the beating amplitudes differentially to steer. This strategy hinges on both inherent flagellar asymmetries (e.g. different response to chemical messengers) and such asymmetries being effectively coordinated in the synchronous beating. In C. reinhardtii, the synchrony of beating is known to be supported by a mechanical connection between flagella; however, how flagellar asymmetries persist in the synchrony remains elusive. For example, it has been speculated for decades that one flagellum leads the beating, as its dynamic properties (i.e. frequency, waveform, etc.) appear to be copied by the other one. In this study, we combine experiments, computations, and modeling efforts to elucidate the roles played by each flagellum in synchronous beating. With a non-invasive technique to selectively load each flagellum, we show that the coordinated beating essentially only responds to load exerted on the cis flagellum; and that such asymmetry in response derives from a unilateral coupling between the two flagella. Our results highlight a distinct role for each flagellum in coordination and have implication for biflagellates' tactic behaviors.
Collapse
Affiliation(s)
- Da Wei
- Department of Bionanoscience, Delft University of TechnologyDelftNetherlands
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of SciencesBeijingChina
| | - Greta Quaranta
- Laboratory for Aero and Hydrodynamics, Delft University of TechnologyDelftNetherlands
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Delft University of TechnologyDelftNetherlands
| | - Daniel SW Tam
- Laboratory for Aero and Hydrodynamics, Delft University of TechnologyDelftNetherlands
| |
Collapse
|
4
|
von Kenne A, Bär M, Niedermayer T. Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves. Phys Rev E 2024; 109:054407. [PMID: 38907471 DOI: 10.1103/physreve.109.054407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 01/11/2024] [Indexed: 06/24/2024]
Abstract
Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.
Collapse
Affiliation(s)
- Albert von Kenne
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
| | - Thomas Niedermayer
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Berlin 10587, Germany
| |
Collapse
|
5
|
Laeverenz-Schlogelhofer H, Wan KY. Bioelectric control of locomotor gaits in the walking ciliate Euplotes. Curr Biol 2024; 34:697-709.e6. [PMID: 38237598 DOI: 10.1016/j.cub.2023.12.051] [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: 09/01/2023] [Revised: 11/20/2023] [Accepted: 12/18/2023] [Indexed: 02/29/2024]
Abstract
Diverse animal species exhibit highly stereotyped behavioral actions and locomotor sequences as they explore their natural environments. In many such cases, the neural basis of behavior is well established, where dedicated neural circuitry contributes to the initiation and regulation of certain response sequences. At the microscopic scale, single-celled eukaryotes (protists) also exhibit remarkably complex behaviors and yet are completely devoid of nervous systems. Here, to address the question of how single cells control behavior, we study locomotor patterning in the exemplary hypotrich ciliate Euplotes, a highly polarized cell, which actuates a large number of leg-like appendages called cirri (each a bundle of ∼25-50 cilia) to swim in fluids or walk on surfaces. As it navigates its surroundings, a walking Euplotes cell is routinely observed to perform side-stepping reactions, one of the most sophisticated maneuvers ever observed in a single-celled organism. These are spontaneous and stereotyped reorientation events involving a transient and fast backward motion followed by a turn. Combining high-speed imaging with simultaneous time-resolved electrophysiological recordings, we show that this complex coordinated motion sequence is tightly regulated by rapid membrane depolarization events, which orchestrate the activity of different cirri on the cell. Using machine learning and computer vision methods, we map detailed measurements of cirri dynamics to the cell's membrane bioelectrical activity, revealing a differential response in the front and back cirri. We integrate these measurements with a minimal model to understand how Euplotes-a unicellular organism-manipulates its membrane potential to achieve real-time control over its motor apparatus.
Collapse
Affiliation(s)
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, Exeter EX4 4QD, UK.
| |
Collapse
|
6
|
Wan KY, Poon RN. Mechanisms and functions of multiciliary coordination. Curr Opin Cell Biol 2024; 86:102286. [PMID: 38035649 DOI: 10.1016/j.ceb.2023.102286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Revised: 10/20/2023] [Accepted: 11/02/2023] [Indexed: 12/02/2023]
Abstract
Ciliated organisms are present in virtually every branch of the eukaryotic tree of life. In diverse systems, cilia operate in a coordinated manner to drive fluid flows, or even propel entire organisms. How do groups of motile cilia coordinate their activity within a cell or across a tissue to fulfil essential functions of life? In this review, we highlight the latest developments in our understanding of the mechanisms and functions of multiciliary coordination in diverse systems. We explore new and emerging trends in bioimaging, analytical, and computational methods, which together with their application in new model systems, have conspired to deliver important insights into one of the most fundamental questions in cellular dynamics.
Collapse
Affiliation(s)
- Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, UK.
| | - Rebecca N Poon
- Living Systems Institute, University of Exeter, Stocker Road, EX4 4QD, UK
| |
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
Rombouts J, Elliott J, Erzberger A. Forceful patterning: theoretical principles of mechanochemical pattern formation. EMBO Rep 2023; 24:e57739. [PMID: 37916772 DOI: 10.15252/embr.202357739] [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: 06/30/2023] [Revised: 09/21/2023] [Accepted: 09/27/2023] [Indexed: 11/03/2023] Open
Abstract
Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.
Collapse
Affiliation(s)
- Jan Rombouts
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Developmental Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Jenna Elliott
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Anna Erzberger
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| |
Collapse
|
9
|
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.
Collapse
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.
| |
Collapse
|
10
|
Hickey DJ, Golestanian R, Vilfan A. Nonreciprocal interactions give rise to fast cilium synchronization in finite systems. Proc Natl Acad Sci U S A 2023; 120:e2307279120. [PMID: 37756336 PMCID: PMC10556628 DOI: 10.1073/pnas.2307279120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 08/14/2023] [Indexed: 09/29/2023] Open
Abstract
Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.
Collapse
Affiliation(s)
- David J. Hickey
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
| | - Ramin Golestanian
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OxfordOX1 3PU, United Kingdom
| | - Andrej Vilfan
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
- Department of Condensed Matter Physics, Jožef Stefan Institute, 1000Ljubljana, Slovenia
| |
Collapse
|
11
|
Cui M, Dutcher S, Bayly P, Meacham J. Robust acoustic trapping and perturbation of single-cell microswimmers illuminate three-dimensional swimming and ciliary coordination. Proc Natl Acad Sci U S A 2023; 120:e2218951120. [PMID: 37307440 PMCID: PMC10290211 DOI: 10.1073/pnas.2218951120] [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: 11/05/2022] [Accepted: 04/18/2023] [Indexed: 06/14/2023] Open
Abstract
We report a label-free acoustic microfluidic method to confine single, cilia-driven swimming cells in space without limiting their rotational degrees of freedom. Our platform integrates a surface acoustic wave (SAW) actuator and bulk acoustic wave (BAW) trapping array to enable multiplexed analysis with high spatial resolution and trapping forces that are strong enough to hold individual microswimmers. The hybrid BAW/SAW acoustic tweezers employ high-efficiency mode conversion to achieve submicron image resolution while compensating for parasitic system losses to immersion oil in contact with the microfluidic chip. We use the platform to quantify cilia and cell body motion for wildtype biciliate cells, investigating effects of environmental variables like temperature and viscosity on ciliary beating, synchronization, and three-dimensional helical swimming. We confirm and expand upon the existing understanding of these phenomena, for example determining that increasing viscosity promotes asynchronous beating. Motile cilia are subcellular organelles that propel microorganisms or direct fluid and particulate flow. Thus, cilia are critical to cell survival and human health. The unicellular alga Chlamydomonas reinhardtii is widely used to investigate the mechanisms underlying ciliary beating and coordination. However, freely swimming cells are difficult to image with sufficient resolution to capture cilia motion, necessitating that the cell body be held during experiments. Acoustic confinement is a compelling alternative to use of a micropipette, or to magnetic, electrical, and optical trapping that may modify the cells and affect their behavior. Beyond establishing our approach to studying microswimmers, we demonstrate a unique ability to mechanically perturb cells via rapid acoustic positioning.
Collapse
Affiliation(s)
- Mingyang Cui
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO63130
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Susan K. Dutcher
- Department of Genetics, Washington University School of Medicine in St. Louis, St. Louis, MO63110
| | - Philip V. Bayly
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO63130
| | - J. Mark Meacham
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO63130
| |
Collapse
|
12
|
Zheng E, Brandenbourger M, Robinet L, Schall P, Lerner E, Coulais C. Self-Oscillation and Synchronization Transitions in Elastoactive Structures. PHYSICAL REVIEW LETTERS 2023; 130:178202. [PMID: 37172256 DOI: 10.1103/physrevlett.130.178202] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Revised: 02/23/2023] [Accepted: 04/05/2023] [Indexed: 05/14/2023]
Abstract
The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Among these, spontaneous self-oscillations of mechanical structures is perhaps the simplest and most widespread type of nonequilibrium phenomenon. Yet, we lack experimental model systems to investigate the various dynamical phenomena that may appear. Here, we introduce a centimeter-sized model system for one-dimensional elastoactive structures. We show that such structures exhibit flagellar motion when pinned at one end, self-snapping when pinned at two ends, and synchronization when coupled together with a sufficiently stiff link. We further demonstrate that these transitions can be described quantitatively by simple models of coupled pendula with follower forces. Beyond the canonical case considered here, we anticipate our work to open avenues for the understanding and design of the self-organization and response of active biological and synthetic solids, e.g., in higher dimensions and for more intricate geometries.
Collapse
Affiliation(s)
- Ellen Zheng
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Martin Brandenbourger
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Louis Robinet
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Peter Schall
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Edan Lerner
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Corentin Coulais
- Institute of Physics, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| |
Collapse
|
13
|
Mo C, Fedosov DA. Hydrodynamic clustering of two finite-length flagellated swimmers in viscoelastic fluids. J R Soc Interface 2023; 20:20220667. [PMID: 36751932 PMCID: PMC9905986 DOI: 10.1098/rsif.2022.0667] [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: 09/10/2022] [Accepted: 01/09/2023] [Indexed: 02/09/2023] Open
Abstract
Clustering of flagellated microswimmers such as sperm is often mediated by hydrodynamic interactions between them. To better understand the interaction of microswimmers in viscoelastic fluids, we perform two-dimensional simulations of two swimming sheets, using a viscoelastic version of the smoothed dissipative particle dynamics method that implements the Oldroyd-B fluid model. Elasticity of sheets (stiff versus soft) defines two qualitatively different regimes of clustering, where stiff sheets exhibit a much more robust clustering than soft sheets. A formed doublet of soft sheets generally swims faster than a single swimmer, while a pair of two stiff sheets normally shows no speed enhancement after clustering. A pair of two identical swimmers is stable for most conditions, while differences in the beating amplitudes and/or frequencies between the two sheets can destroy the doublet stability. Clustering of two distinct swimmers is most stable at Deborah numbers of De = τω ≈ 1 (τ is the relaxation time of a viscoelastic fluid and ω is the beating frequency), in agreement with experimental observations. Therefore, the clustering of two swimmers depends non-monotonically on De. Our results suggest that the cluster stability is likely a dominant factor which determines the cluster size of collectively moving flagellated swimmers.
Collapse
Affiliation(s)
- Chaojie Mo
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
- Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315100, People’s Republic of China
| | - Dmitry A. Fedosov
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| |
Collapse
|
14
|
Ringers C, Bialonski S, Ege M, Solovev A, Hansen JN, Jeong I, Friedrich BM, Jurisch-Yaksi N. Novel analytical tools reveal that local synchronization of cilia coincides with tissue-scale metachronal waves in zebrafish multiciliated epithelia. eLife 2023; 12:77701. [PMID: 36700548 PMCID: PMC9940908 DOI: 10.7554/elife.77701] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 01/25/2023] [Indexed: 01/27/2023] Open
Abstract
Motile cilia are hair-like cell extensions that beat periodically to generate fluid flow along various epithelial tissues within the body. In dense multiciliated carpets, cilia were shown to exhibit a remarkable coordination of their beat in the form of traveling metachronal waves, a phenomenon which supposedly enhances fluid transport. Yet, how cilia coordinate their regular beat in multiciliated epithelia to move fluids remains insufficiently understood, particularly due to lack of rigorous quantification. We combine experiments, novel analysis tools, and theory to address this knowledge gap. To investigate collective dynamics of cilia, we studied zebrafish multiciliated epithelia in the nose and the brain. We focused mainly on the zebrafish nose, due to its conserved properties with other ciliated tissues and its superior accessibility for non-invasive imaging. We revealed that cilia are synchronized only locally and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Even though synchronization is local only, we observed global patterns of traveling metachronal waves across the zebrafish multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right noses, unveiling a chiral asymmetry of metachronal coordination. To understand the implications of synchronization for fluid pumping, we used a computational model of a regular array of cilia. We found that local metachronal synchronization prevents steric collisions, i.e., cilia colliding with each other, and improves fluid pumping in dense cilia carpets, but hardly affects the direction of fluid flow. In conclusion, we show that local synchronization together with tissue-scale cilia alignment coincide and generate metachronal wave patterns in multiciliated epithelia, which enhance their physiological function of fluid pumping.
Collapse
Affiliation(s)
- Christa Ringers
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
- Department of Pharmaceutical Biosciences and Science for Life Laboratory, Uppsala UniversityUppsalaSweden
| | - Stephan Bialonski
- Institute for Data-Driven Technologies, Aachen University of Applied SciencesJülichGermany
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
| | - Mert Ege
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
| | - Anton Solovev
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
- Cluster of Excellence 'Physics of Life', Technical University DresdenDresdenGermany
| | - Jan Niklas Hansen
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
| | - Inyoung Jeong
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
| | - Benjamin M Friedrich
- Center for Advancing Electronics, Technical University DresdenDresdenGermany
- Cluster of Excellence 'Physics of Life', Technical University DresdenDresdenGermany
| | - Nathalie Jurisch-Yaksi
- Department of Clinical and Molecular Medicine, Norwegian University of Science and TechnologyTrondheimNorway
- Kavli Institute for Systems, Neuroscience and Centre for Neural Computation, Norwegian University of Science and TechnologyTrondheimNorway
| |
Collapse
|
15
|
Locomotion of bovine spermatozoa during the transition from individual cells to bundles. Proc Natl Acad Sci U S A 2023; 120:e2211911120. [PMID: 36638212 PMCID: PMC9934168 DOI: 10.1073/pnas.2211911120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
Various locomotion strategies employed by microorganisms are observed in complex biological environments. Spermatozoa assemble into bundles to improve their swimming efficiency compared to individual cells. However, the dynamic mechanisms for the formation of sperm bundles have not been fully characterized. In this study, we numerically and experimentally investigate the locomotion of spermatozoa during the transition from individual cells to bundles of two cells. Three consecutive dynamic behaviors are found across the course of the transition: hydrodynamic attraction/repulsion, alignment, and synchronization. The hydrodynamic attraction/repulsion depends on the relative orientation and distance between spermatozoa as well as their flagellar wave patterns and phase shift. Once the heads are attached, we find a stable equilibrium of the rotational hydrodynamics resulting in the alignment of the heads. The synchronization results from the combined influence of hydrodynamic and mechanical cell-to-cell interactions. Additionally, we find that the flagellar beat is regulated by the interactions during the bundle formation, whereby spermatozoa can synchronize their beats to enhance their swimming velocity.
Collapse
|
16
|
Leptos KC, Chioccioli M, Furlan S, Pesci AI, Goldstein RE. Phototaxis of Chlamydomonas arises from a tuned adaptive photoresponse shared with multicellular Volvocine green algae. Phys Rev E 2023; 107:014404. [PMID: 36797913 PMCID: PMC7616094 DOI: 10.1103/physreve.107.014404] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 12/16/2022] [Indexed: 06/18/2023]
Abstract
A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.
Collapse
Affiliation(s)
- Kyriacos C. Leptos
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | | | | | | | | |
Collapse
|
17
|
Spontaneous phase coordination and fluid pumping in model ciliary carpets. Proc Natl Acad Sci U S A 2022; 119:e2214413119. [PMID: 36322751 PMCID: PMC9659382 DOI: 10.1073/pnas.2214413119] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023] Open
Abstract
Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.
Collapse
|
18
|
Soh AWJ, Woodhams LG, Junker AD, Enloe CM, Noren BE, Harned A, Westlake CJ, Narayan K, Oakey JS, Bayly PV, Pearson CG. Intracellular connections between basal bodies promote the coordinated behavior of motile cilia. Mol Biol Cell 2022; 33:br18. [PMID: 35767367 DOI: 10.1091/mbc.e22-05-0150] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Hydrodynamic flow produced by multiciliated cells is critical for fluid circulation and cell motility. Hundreds of cilia beat with metachronal synchrony for fluid flow. Cilia-driven fluid flow produces extracellular hydrodynamic forces that cause neighboring cilia to beat in a synchronized manner. However, hydrodynamic coupling between neighboring cilia is not the sole mechanism that drives cilia synchrony. Cilia are nucleated by basal bodies (BBs) that link to each other and to the cell's cortex via BB-associated appendages. The intracellular BB and cortical network is hypothesized to synchronize ciliary beating by transmitting cilia coordination cues. The extent of intracellular ciliary connections and the nature of these stimuli remain unclear. Moreover, how BB connections influence the dynamics of individual cilia has not been established. We show by focused ion beam scanning electron microscopy imaging that cilia are coupled both longitudinally and laterally in the ciliate Tetrahymena thermophila by the underlying BB and cortical cytoskeletal network. To visualize the behavior of individual cilia in live, immobilized Tetrahymena cells, we developed Delivered Iron Particle Ubiety Live Light (DIPULL) microscopy. Quantitative and computer analyses of ciliary dynamics reveal that BB connections control ciliary waveform and coordinate ciliary beating. Loss of BB connections reduces cilia-dependent fluid flow forces.
Collapse
Affiliation(s)
- Adam W J Soh
- Department of Cell and Developmental Biology, Anschutz Medical Campus, University of Colorado, Aurora, CO 80045
| | - Louis G Woodhams
- Department of Mechanical Engineering and Material Science, Washington University in St. Louis, St. Louis, MO 63130
| | - Anthony D Junker
- Department of Cell and Developmental Biology, Anschutz Medical Campus, University of Colorado, Aurora, CO 80045
| | - Cassidy M Enloe
- Department of Chemical Engineering, College of Engineering and Applied Science, University of Wyoming, Laramie, WY 82071
| | - Benjamin E Noren
- Department of Chemical Engineering, College of Engineering and Applied Science, University of Wyoming, Laramie, WY 82071
| | - Adam Harned
- Center for Molecular Microscopy and Center for Cancer Research, National Cancer Institute, National Institutes of Health, Bethesda, MD 20892.,Cancer Research Technology Program, Frederick National Laboratory for Cancer Research, and
| | - Christopher J Westlake
- Laboratory of Cell and Developmental Signaling, Center for Cancer Research, National Cancer Institute, National Institutes of Health, Frederick, MD 21702
| | - Kedar Narayan
- Center for Molecular Microscopy and Center for Cancer Research, National Cancer Institute, National Institutes of Health, Bethesda, MD 20892.,Cancer Research Technology Program, Frederick National Laboratory for Cancer Research, and
| | - John S Oakey
- Department of Chemical Engineering, College of Engineering and Applied Science, University of Wyoming, Laramie, WY 82071
| | - Philip V Bayly
- Department of Mechanical Engineering and Material Science, Washington University in St. Louis, St. Louis, MO 63130
| | - Chad G Pearson
- Department of Cell and Developmental Biology, Anschutz Medical Campus, University of Colorado, Aurora, CO 80045
| |
Collapse
|
19
|
Soh AWJ, Pearson CG. Ciliate cortical organization and dynamics for cell motility: Comparing ciliates and vertebrates. J Eukaryot Microbiol 2022; 69:e12880. [PMID: 34897878 PMCID: PMC9188629 DOI: 10.1111/jeu.12880] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The generation of efficient fluid flow is crucial for organismal development and homeostasis, sexual reproduction, and motility. Multi-ciliated cells possess fields of motile cilia that beat in synchrony to propel fluid. Ciliary arrays are remarkably conserved in their organization and function. Ciliates have polarized multi-ciliary arrays (MCAs) to promote fluid flow for cell motility. The ciliate cortex is decorated with hundreds of basal bodies (BB) forming linear rows along the cell's anterior-posterior axis. BBs scaffold and position cilia to form the organized ciliary array. Nascent BBs assemble at the base of BBs. As nascent BBs mature, they integrate into the cortical BB and cytoskeletal network and nucleate their own cilium. The organization of MCAs is balanced between cortical stability and cortical dynamism. The cortical cytoskeletal network both establishes and maintains a stable organization of the MCA in the face of mechanical forces exerted by ciliary beating. At the same time, MCA organization is plastic, such that it remodels for optimal ciliary mobility during development and in response to environmental conditions. Such plasticity promotes effective feeding and ecological behavior required for these organisms. Together, these properties allow an organism to effectively sense, adapt to, and move through its environment.
Collapse
Affiliation(s)
- Adam W. J. Soh
- Anschutz Medical Campus, Department of Cell and Developmental Biology, University of Colorado, Aurora, CO 80045
| | - Chad G. Pearson
- Anschutz Medical Campus, Department of Cell and Developmental Biology, University of Colorado, Aurora, CO 80045
| |
Collapse
|
20
|
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.
Collapse
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.
| |
Collapse
|
21
|
Mesdjian O, Wang C, Gsell S, D'Ortona U, Favier J, Viallat A, Loiseau E. Longitudinal to Transverse Metachronal Wave Transitions in an In Vitro Model of Ciliated Bronchial Epithelium. PHYSICAL REVIEW LETTERS 2022; 129:038101. [PMID: 35905353 DOI: 10.1103/physrevlett.129.038101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
Myriads of cilia beat on ciliated epithelia, which are ubiquitous in life. When ciliary beats are synchronized, metachronal waves emerge, whose direction of propagation depends on the living system in an unexplained way. We show on a reconstructed human bronchial epithelium in vitro that the direction of propagation is determined by the ability of mucus to be transported at the epithelial surface. Numerical simulations show that longitudinal waves maximize the transport of mucus while transverse waves, observed when the mucus is rigid and still, minimize the energy dissipated by the cilia.
Collapse
Affiliation(s)
- Olivier Mesdjian
- Aix Marseille University, CNRS, CINAM, Turing Centre for Living Systems, 13009 Marseille, France
| | - Chenglei Wang
- Aix Marseille University, CNRS, Centrale Marseille M2P2, France
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
| | - Simon Gsell
- Aix Marseille University, CNRS, Centrale Marseille M2P2, France
| | | | - Julien Favier
- Aix Marseille University, CNRS, Centrale Marseille M2P2, France
| | - Annie Viallat
- Aix Marseille University, CNRS, CINAM, Turing Centre for Living Systems, 13009 Marseille, France
| | - Etienne Loiseau
- Aix Marseille University, CNRS, CINAM, Turing Centre for Living Systems, 13009 Marseille, France
| |
Collapse
|
22
|
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.
Collapse
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
| |
Collapse
|
23
|
Tătulea-Codrean M, Lauga E. Elastohydrodynamic Synchronization of Rotating Bacterial Flagella. PHYSICAL REVIEW LETTERS 2022; 128:208101. [PMID: 35657856 DOI: 10.1103/physrevlett.128.208101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Revised: 02/03/2022] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
To rotate continuously without jamming, the flagellar filaments of bacteria need to be locked in phase. While several models have been proposed for eukaryotic flagella, the synchronization of bacterial flagella is less well understood. Starting from a reduced model of flexible and hydrodynamically coupled bacterial flagella, we rigorously coarse grain the equations of motion using the method of multiple scales, and hence show that bacterial flagella generically synchronize to zero phase difference via an elastohydrodynamic mechanism. Remarkably, the far-field rate of synchronization is maximized at an intermediate value of elastic compliance, with surprising implications for bacteria.
Collapse
Affiliation(s)
- Maria Tătulea-Codrean
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| |
Collapse
|
24
|
Zhou W, Peralta JD, Hao Z, Gravish N. Lateral contact yields longitudinal cohesion in active undulatory systems. Phys Rev E 2022; 105:054604. [PMID: 35706245 DOI: 10.1103/physreve.105.054604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
Many animals and robots move using undulatory motion of their bodies. When the bodies are in close proximity undulatory motion can lead to novel collective behavior such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multilink swimmers in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, ϕ. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and planar configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into planar equilibrium configurations that depend on the actuation phase difference. We propose a model for stable planar configurations of nearest-neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of planar and phase configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To study the contact forces and the time-averaged equilibrium between undulatory systems we perform simulations. To probe the interaction potential between undulatory swimmers we apply a small force to each swimmer longitudinally to separate them from the compatible configuration and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit attractive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.
Collapse
Affiliation(s)
- Wei Zhou
- Mechanical and Aerospace Engineering, University of California, San Diego, California 92093, USA
| | - Jaquelin Dezha Peralta
- Mechanical and Aerospace Engineering, University of California, San Diego, California 92093, USA
| | - Zhuonan Hao
- Mechanical and Aerospace Engineering, University of California, San Diego, California 92093, USA
| | - Nick Gravish
- Mechanical and Aerospace Engineering, University of California, San Diego, California 92093, USA
| |
Collapse
|
25
|
Day TC, Höhn SS, Zamani-Dahaj SA, Yanni D, Burnetti A, Pentz J, Honerkamp-Smith AR, Wioland H, Sleath HR, Ratcliff WC, Goldstein RE, Yunker PJ. Cellular organization in lab-evolved and extant multicellular species obeys a maximum entropy law. eLife 2022; 11:72707. [PMID: 35188101 PMCID: PMC8860445 DOI: 10.7554/elife.72707] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 01/04/2022] [Indexed: 12/29/2022] Open
Abstract
The prevalence of multicellular organisms is due in part to their ability to form complex structures. How cells pack in these structures is a fundamental biophysical issue, underlying their functional properties. However, much remains unknown about how cell packing geometries arise, and how they are affected by random noise during growth - especially absent developmental programs. Here, we quantify the statistics of cellular neighborhoods of two different multicellular eukaryotes: lab-evolved ‘snowflake’ yeast and the green alga Volvox carteri. We find that despite large differences in cellular organization, the free space associated with individual cells in both organisms closely fits a modified gamma distribution, consistent with maximum entropy predictions originally developed for granular materials. This ‘entropic’ cellular packing ensures a degree of predictability despite noise, facilitating parent-offspring fidelity even in the absence of developmental regulation. Together with simulations of diverse growth morphologies, these results suggest that gamma-distributed cell neighborhood sizes are a general feature of multicellularity, arising from conserved statistics of cellular packing.
Collapse
Affiliation(s)
- Thomas C Day
- School of Physics, Georgia Institute of Technology, Atlanta, United States
| | - Stephanie S Höhn
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Seyed A Zamani-Dahaj
- School of Physics, Georgia Institute of Technology, Atlanta, United States.,School of Biological Sciences, Georgia Institute of Technology, Atlanta, United States.,Quantitative Biosciences Graduate Program, Georgia Institute of Technology, Atlanta, United States
| | - David Yanni
- School of Physics, Georgia Institute of Technology, Atlanta, United States
| | - Anthony Burnetti
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, United States
| | - Jennifer Pentz
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, United States.,Department of Molecular Biology, Umeå University, Umeå, Sweden
| | - Aurelia R Honerkamp-Smith
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Hugo Wioland
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Hannah R Sleath
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
| | - William C Ratcliff
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, United States
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Peter J Yunker
- School of Physics, Georgia Institute of Technology, Atlanta, United States
| |
Collapse
|
26
|
Lesani A, Ramazani Sarbandi I, Mousavi H, Kazemnejad S, Moghimi Zand M. Lower reactive oxygen species production and faster swimming speed of human sperm cells on nanodiamond spin-coated glass substrates. J Biomed Mater Res B Appl Biomater 2022; 110:1391-1399. [PMID: 35080336 DOI: 10.1002/jbm.b.35007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 12/05/2021] [Accepted: 12/28/2021] [Indexed: 12/21/2022]
Abstract
The sperm selection stage is what assisted reproductive technologies have in common and is crucial as it affects the success of the treatment cycle. The employment of microfluidic platforms for sperm selection has emerged showing promising results. In microfluidic platforms, sperm cells encounter micro-confined environments meanwhile having contact with channel walls and surfaces. Modification of contact surfaces using nanoparticles leads to the alteration of surface characteristics which in turn affects sperm behavior especially motility which is an indicator for sperm health. In this article, we present the results of investigating the motility parameters of sperm cells in contact with surface-modified glass substrates using nanodiamond particles. The results show that the sperm swimming velocities are significantly improved within the range of 12%-52% compared to the control surface (untreated). Reactive oxygen species production is also decreased by 14% justifying the increase in swimming speed. Taken together, bonding these modified surfaces to sperm selection microfluidic devices could enhance their efficiency and further improve their outcomes offering new solutions to patients facing infertility.
Collapse
Affiliation(s)
- Ali Lesani
- Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Iman Ramazani Sarbandi
- Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Hengameh Mousavi
- Faculty of Physics, Nano Science and Technology, Damghan University, Damghan, Iran
| | - Somaieh Kazemnejad
- Nanobiotechnology Research Center, Avicenna Research Institute, ACECR, Tehran, Iran
| | - Mahdi Moghimi Zand
- Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| |
Collapse
|
27
|
Solovev A, Friedrich BM. Synchronization in cilia carpets and the Kuramoto model with local coupling: Breakup of global synchronization in the presence of noise. CHAOS (WOODBURY, N.Y.) 2022; 32:013124. [PMID: 35105113 DOI: 10.1063/5.0075095] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
Carpets of beating cilia represent a paradigmatic example of self-organized synchronization of noisy biological oscillators, characterized by traveling waves of cilia phase. We present a multi-scale model of a cilia carpet that comprises realistic hydrodynamic interactions between cilia computed for a chiral cilia beat pattern from unicellular Paramecium and active noise of the cilia beat. We demonstrate an abrupt loss of global synchronization beyond a characteristic noise strength. We characterize stochastic transitions between synchronized and disordered dynamics, which generalize the notion of phase slips in pairs of coupled noisy phase oscillators. Our theoretical work establishes a link between the two-dimensional Kuramoto model of phase oscillators with mirror-symmetric oscillator coupling and detailed models of biological oscillators with asymmetric, chiral interactions.
Collapse
|
28
|
A quantitative interspecies comparison of the respiratory mucociliary clearance mechanism. EUROPEAN BIOPHYSICS JOURNAL 2022; 51:51-65. [PMID: 35072746 PMCID: PMC8827335 DOI: 10.1007/s00249-021-01584-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Revised: 12/06/2021] [Accepted: 12/08/2021] [Indexed: 11/04/2022]
Abstract
Collectively coordinated ciliary activity propels the airway mucus, which lines the luminal surface of the vertebrate respiratory system, in cranial direction. Our contemporary understanding on how the quantitative characteristics of the metachronal wave field determines the resulting mucociliary transport is still limited, partly due to the sparse availability of quantitative observational data. We employed high-speed video reflection microscopy to image and quantitatively characterize the metachronal wave field as well as the mucociliary transport in excised bovine, porcine, ovine, lapine, turkey and ostrich samples. Image processing techniques were used to determine the ciliary beating frequency (CBF), the velocity and wavelength of the metachronal wave and the mucociliary transport velocity. The transport direction was found to strongly correlate with the mean wave propagation direction in all six species. The CBF yielded similar values (10–15 Hz) for all six species. Birds were found to exhibit higher transport speeds (130–260 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\upmu$$\end{document}μm/s) than mammals (20–80 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\upmu$$\end{document}μm/s). While the average transport direction significantly deviates from the tracheal long axis in mammals, no significant deviation was found in birds. The metachronal waves were found to propagate at about 4–8 times the speed of mucociliary transport in mammals, whereas in birds they propagate at about the transport speed. The mucociliary transport in birds is fast and roughly follows the TLA, whereas the transport is slower and proceeds along a left-handed spiral in mammals. The longer wavelengths and the lower ratio between the metachronal wave speed and the mucociliary transport speed provide evidence that the mucociliary clearance mechanism operates differently in birds than in mammals.
Collapse
|
29
|
Boselli F, Jullien J, Lauga E, Goldstein RE. Fluid Mechanics of Mosaic Ciliated Tissues. PHYSICAL REVIEW LETTERS 2021; 127:198102. [PMID: 34797132 PMCID: PMC7616087 DOI: 10.1103/physrevlett.127.198102] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 10/07/2021] [Indexed: 06/13/2023]
Abstract
In tissues as diverse as amphibian skin and the human airway, the cilia that propel fluid are grouped in sparsely distributed multiciliated cells (MCCs). We investigate fluid transport in this "mosaic" architecture, with emphasis on the trade-offs that may have been responsible for its evolutionary selection. Live imaging of MCCs in embryos of the frog Xenopus laevis shows that cilia bundles behave as active vortices that produce a flow field accurately represented by a local force applied to the fluid. A coarse-grained model that self-consistently couples bundles to the ambient flow reveals that hydrodynamic interactions between MCCs limit their rate of work so that they best shear the tissue at a finite but low area coverage, a result that mirrors findings for other sparse distributions such as cell receptors and leaf stomata.
Collapse
Affiliation(s)
- Francesco Boselli
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Jerome Jullien
- Wellcome Trust/Cancer Research UK Gurdon Institute, Tennis Court Road, Cambridge CB2 1QN, United Kingdom
- Department of Zoology, University of Cambridge, Cambridge CB2 1QN, United Kingdom
- Inserm, Nantes Université, CHU Nantes, CRTI-UMR 1064, F-44000 Nantes, France
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Raymond E. Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| |
Collapse
|
30
|
Abstract
Motile cilia can coordinate with each other to beat in the form of a metachronal wave, which can facilitate the self-propulsion of microorganisms such as Paramecium and can also be used for fluid transport such as mucus removal in trachea. How can we predict the collective behavior of arrays of many cilia coordinated by hydrodynamic interactions, and in particular, the properties of the emerging metachronal waves, from the single-cilium characteristics? We address this question using a bottom-up coarse-graining approach and present results that contribute to understanding how the dynamical self-organization of ciliary arrays can be controlled, which can have significant biological, medical, and engineering implications. On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.
Collapse
|
31
|
Lee SG, Lee SN, Baek J, Yoon JH, Lee H. Mechanical compression enhances ciliary beating through cytoskeleton remodeling in human nasal epithelial cells. Acta Biomater 2021; 128:346-356. [PMID: 33882353 DOI: 10.1016/j.actbio.2021.04.030] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 03/27/2021] [Accepted: 04/14/2021] [Indexed: 01/25/2023]
Abstract
Nasal inflammatory diseases, including nasal polyps and acute/chronic sinusitis, are characterized by impaired mucociliary clearance and eventually inflammation and infection. Contact of nasal polyps with adjacent nasal mucosa or stagnated mucus within the maxillary sinus produces compressive mechanical stresses on the apical surface of epithelium which can induce cytoskeleton remodeling in epithelial cells. In this study, we hypothesized that compressive stress modulates ciliary beating by altering the mechanical properties of the cytoskeleton of ciliated cell basal bodies. For the primary human nasal epithelial cells, we found that the applied compressive stress higher than the critical value of 1.0 kPa increased the stroke speed of cilia leading to the enhancement of ciliary beating frequency and mucociliary transportability. Immunostained images of the cytoskeleton showed reorganization and compactness of the actin filaments in the presence of compressive stress. Analysis of beating trajectory with the computational modeling for ciliary beating revealed that the stroke speed of cilium increased as the relative elasticity to viscosity of the surrounding cytoskeleton increases. These results suggest that the compressive stress on epithelial cells increases the ciliary beating speed through cytoskeleton remodeling to prevent mucus stagnation at the early stage of airway obstruction. Our study provides an insight into the defensive mechanism of airway epithelium against pathological conditions. STATEMENT OF SIGNIFICANCE: Cilia dynamics of the nasal epithelium is critical for not only maintaining normal breathing but preventing inflammatory diseases. It has been shown that mechanical compressive stresses can alter the shape and phenotype of epithelial cells. However, the effect of compressive stress on cilia dynamics is unclear. In this study, we demonstrated that the oscillation speed of cilia in human nasal epithelial cells was increased by the applied compressive stress experimentally. The computational simulation revealed that the change of ciliary beating dynamics was attributed to the viscoelastic properties of the reorganized cytoskeleton in response to compressive stress. Our results will be beneficial in understanding the defensive mechanism of airway epithelium against pathological conditions.
Collapse
|
32
|
Rode S, Elgeti J, Gompper G. Multi-ciliated microswimmers-metachronal coordination and helical swimming. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:76. [PMID: 34101070 PMCID: PMC8187229 DOI: 10.1140/epje/s10189-021-00078-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Accepted: 05/07/2021] [Indexed: 05/05/2023]
Abstract
The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with [Formula: see text]) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.
Collapse
Affiliation(s)
- Sebastian Rode
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Jens Elgeti
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| |
Collapse
|
33
|
Balasubramanian RN, McCourt RM. Volvox barberi (Chlorophyceae) actively forms two-dimensional flocks in culture. JOURNAL OF PHYCOLOGY 2021; 57:967-974. [PMID: 33523505 DOI: 10.1111/jpy.13139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 01/09/2021] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
Volvox barberi is a multicellular green alga forming spherical colonies of 10,000-50,000 differentiated somatic and germ cells. We observed that in culture, these colonies actively self-organized in just a few minutes into "flocks" that contained as many as 100 colonies moving and rotating collectively for hours. The colonies in flocks formed two-dimensional, irregular, active crystals, that is, geometric lattices within which individual colonies rotated separately. These groupings sometimes disassembled back into individual colonies just as quickly, but in some cases, flocks persisted over several hours. Close inspection of flock formation in the presence of a tracer dye suggested that colony and flock rotations were producing vortices in the fluid medium over a range spanning multiple flock diameters, perhaps providing a physical mechanism for aggregation.
Collapse
Affiliation(s)
| | - Richard M McCourt
- Academy of Natural Sciences of Drexel University, 1900 Benjamin Franklin Parkway, Philadelphia, Pennsylvania, 19103, USA
| |
Collapse
|
34
|
Byron ML, Murphy DW, Katija K, Hoover AP, Daniels J, Garayev K, Takagi D, Kanso E, Gemmell BJ, Ruszczyk M, Santhanakrishnan A. Metachronal motion across scales: current challenges and future directions. Integr Comp Biol 2021; 61:1674-1688. [PMID: 34048537 DOI: 10.1093/icb/icab105] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.
Collapse
Affiliation(s)
| | - David W Murphy
- University of South Florida, 4202 E. Fowler Ave, Tampa, FL, 33620, USA
| | - Kakani Katija
- Monterey Bay Aquarium Research Institute, 7700 Sandholdt Rd, Moss Landing, CA, 95039, USA
| | | | - Joost Daniels
- Monterey Bay Aquarium Research Institute, 7700 Sandholdt Rd, Moss Landing, CA, 95039, USA
| | - Kuvvat Garayev
- University of South Florida, 4202 E. Fowler Ave, Tampa, FL, 33620, USA
| | - Daisuke Takagi
- University of Hawaii at Manoa, 2500 Campus Rd, Honolulu, HI, 96822
| | - Eva Kanso
- University of Southern California, University Park, Los Angeles, CA, 90007
| | | | - Melissa Ruszczyk
- Georgia Institute of Technology, 310 Ferst Dr, Atlanta, GA, 30332, USA
| | | |
Collapse
|
35
|
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.
Collapse
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
| |
Collapse
|
36
|
Bauer D, Ishikawa H, Wemmer KA, Hendel NL, Kondev J, Marshall WF. Analysis of biological noise in the flagellar length control system. iScience 2021; 24:102354. [PMID: 33898946 PMCID: PMC8059064 DOI: 10.1016/j.isci.2021.102354] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Revised: 03/16/2021] [Accepted: 03/19/2021] [Indexed: 02/06/2023] Open
Abstract
Any proposed mechanism for organelle size control should be able to account not only for average size but also for the variation in size. We analyzed cell-to-cell variation and within-cell variation of length for the two flagella in Chlamydomonas, finding that cell-to-cell variation is dominated by cell size, whereas within-cell variation results from dynamic fluctuations. Fluctuation analysis suggests tubulin assembly is not directly coupled with intraflagellar transport (IFT) and that the observed length fluctuations reflect tubulin assembly and disassembly events involving large numbers of tubulin dimers. Length variation is increased in long-flagella mutants, an effect consistent with theoretical models for flagellar length regulation. Cells with unequal flagellar lengths show impaired swimming but improved gliding, raising the possibility that cells have evolved mechanisms to tune biological noise in flagellar length. Analysis of noise at the level of organelle size provides a way to probe the mechanisms determining cell geometry.
Collapse
Affiliation(s)
- David Bauer
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Hiroaki Ishikawa
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Kimberly A. Wemmer
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Nathan L. Hendel
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| | - Jane Kondev
- Department of Physics, Brandeis University, Abelson-Bass-Yalem Building, 97-301, Waltham, MA, USA
| | - Wallace F. Marshall
- Department of Biochemistry & Biophysics, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
- Center for Cellular Construction, University of California, San Francisco, 600 16th St., San Francisco, CA, USA
| |
Collapse
|
37
|
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] [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.
Collapse
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
| |
Collapse
|
38
|
Jones C, Gomez M, Muoio RM, Vidal A, Mcknight RA, Brubaker ND, Ahmed WW. Stochastic force dynamics of the model microswimmer Chlamydomonas reinhardtii: Active forces and energetics. Phys Rev E 2021; 103:032403. [PMID: 33862745 DOI: 10.1103/physreve.103.032403] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 02/03/2021] [Indexed: 01/26/2023]
Abstract
We study the stochastic force dynamics of a model microswimmer (Chlamydomonas reinhardtii), using a combined experimental, theoretical, and numerical approach. While swimming dynamics have been extensively studied using hydrodynamic approaches, which infer forces from the viscous flow field, we directly measure the stochastic forces generated by the microswimmer using an optical trap via the photon momentum method. We analyze the force dynamics by modeling the microswimmer as a self-propelled particle, à la active matter, and analyze its energetics using methods from stochastic thermodynamics. We find complex oscillatory force dynamics and power dissipation on the order of 10^{6}k_{B}T/s(∼fW).
Collapse
Affiliation(s)
- Corbyn Jones
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Mauricio Gomez
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Ryan M Muoio
- Department of Physics, California State University Fullerton, California 92831, USA
| | - Alex Vidal
- Department of Computer Science, California State University Fullerton, California 92831, USA
| | - R Anthony Mcknight
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Nicholas D Brubaker
- Department of Mathematics, California State University Fullerton, California 92831, USA
| | - Wylie W Ahmed
- Department of Physics, California State University Fullerton, California 92831, USA
| |
Collapse
|
39
|
Solovev A, Friedrich BM. Lagrangian mechanics of active systems. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:49. [PMID: 33834308 PMCID: PMC8032648 DOI: 10.1140/epje/s10189-021-00016-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 01/12/2021] [Indexed: 05/26/2023]
Abstract
We present a multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics of shape-changing immersed objects, e.g., biological microswimmers and active surfaces. The key idea is to consider principal shape changes as generalized coordinates and define conjugate generalized hydrodynamic friction forces. Conveniently, the corresponding generalized friction coefficients can be pre-computed and subsequently reused to solve dynamic equations of motion fast. This framework extends Lagrangian mechanics of dissipative systems to active surfaces and active microswimmers, whose shape dynamics is driven by internal forces. As an application case, we predict in-phase and anti-phase synchronization in pairs of cilia for an experimentally measured cilia beat pattern.
Collapse
|
40
|
Abstract
![]()
Manipulation and navigation of micro
and nanoswimmers in different
fluid environments can be achieved by chemicals, external fields,
or even motile cells. Many researchers have selected magnetic fields
as the active external actuation source based on the advantageous
features of this actuation strategy such as remote and spatiotemporal
control, fuel-free, high degree of reconfigurability, programmability,
recyclability, and versatility. This review introduces fundamental
concepts and advantages of magnetic micro/nanorobots (termed here
as “MagRobots”) as well as basic knowledge of magnetic
fields and magnetic materials, setups for magnetic manipulation, magnetic
field configurations, and symmetry-breaking strategies for effective
movement. These concepts are discussed to describe the interactions
between micro/nanorobots and magnetic fields. Actuation mechanisms
of flagella-inspired MagRobots (i.e., corkscrew-like motion and traveling-wave
locomotion/ciliary stroke motion) and surface walkers (i.e., surface-assisted
motion), applications of magnetic fields in other propulsion approaches,
and magnetic stimulation of micro/nanorobots beyond motion are provided
followed by fabrication techniques for (quasi-)spherical, helical,
flexible, wire-like, and biohybrid MagRobots. Applications of MagRobots
in targeted drug/gene delivery, cell manipulation, minimally invasive
surgery, biopsy, biofilm disruption/eradication, imaging-guided delivery/therapy/surgery,
pollution removal for environmental remediation, and (bio)sensing
are also reviewed. Finally, current challenges and future perspectives
for the development of magnetically powered miniaturized motors are
discussed.
Collapse
Affiliation(s)
- Huaijuan Zhou
- Center for Advanced Functional Nanorobots, Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Technicka 5, 166 28 Prague 6, Czech Republic
| | - Carmen C Mayorga-Martinez
- Center for Advanced Functional Nanorobots, Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Technicka 5, 166 28 Prague 6, Czech Republic
| | - Salvador Pané
- Multi-Scale Robotics Lab (MSRL), Institute of Robotics and Intelligent Systems (IRIS), ETH Zurich, Tannenstrasse 3, 8092 Zurich, Switzerland
| | - Li Zhang
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong 999077, China
| | - Martin Pumera
- Center for Advanced Functional Nanorobots, Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Technicka 5, 166 28 Prague 6, Czech Republic.,Department of Medical Research, China Medical University Hospital, China Medical University, No. 91 Hsueh-Shih Road, Taichung 40402, Taiwan.,Department of Chemistry and Biochemistry, Mendel University in Brno, Zemedelska 1, CZ-613 00 Brno, Czech Republic.,Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea.,Future Energy and Innovation Laboratory, Central European Institute of Technology, Brno University of Technology, Purkyňova 656/123, Brno CZ-612 00, Czech Republic
| |
Collapse
|
41
|
Mohammadinejad S, Faivre D, Klumpp S. Stokesian dynamics simulations of a magnetotactic bacterium. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:40. [PMID: 33759003 PMCID: PMC7987682 DOI: 10.1140/epje/s10189-021-00038-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 02/15/2021] [Indexed: 05/13/2023]
Abstract
The swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles ([Formula: see text]) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.
Collapse
Affiliation(s)
- Sarah Mohammadinejad
- Institute for the Dynamics of Complex Systems, University of Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany.
- Department Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424, Potsdam, Germany.
- Department of Biological Sciences, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran.
| | - Damien Faivre
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14424, Potsdam, Germany
- Aix-Marseille Université, CEA, CNRS, BIAM, 13108, Saint-Paul-lez-Durance, France
| | - Stefan Klumpp
- Institute for the Dynamics of Complex Systems, University of Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
- Department Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424, Potsdam, Germany
| |
Collapse
|
42
|
Clopés J, Winkler RG. Flagellar arrangements in elongated peritrichous bacteria: bundle formation and swimming properties. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:17. [PMID: 33683543 PMCID: PMC7940165 DOI: 10.1140/epje/s10189-021-00027-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Accepted: 01/25/2021] [Indexed: 05/26/2023]
Abstract
The surface distribution of flagella in peritrichous bacterial cells has been traditionally assumed to be random. Recently, the presence of a regular grid-like pattern of basal bodies has been suggested. Experimentally, the manipulation of the anchoring points of flagella in the cell membrane is difficult, and thus, elucidation of the consequences of a particular pattern on bacterial locomotion is challenging. We analyze the bundle formation process and swimming properties of Bacillus subtilis-like cells considering random, helical, and ring-like arrangements of flagella by means of mesoscale hydrodynamics simulations. Helical and ring patterns preferentially yield configurations with a single bundle, whereas configurations with no clear bundles are most likely for random anchoring. For any type of pattern, there is an almost equally low probability to form V-shaped bundle configurations with at least two bundles. Variation of the flagellum length yields a clear preference for a single major bundle in helical and ring patterns as soon as the flagellum length exceeds the body length. The average swimming speed of cells with a single or two bundles is rather similar, and approximately [Formula: see text] larger than that of cells of other types of flagellar organization. Considering the various anchoring patterns, rings yield the smallest average swimming speed independent of the type of bundle, followed by helical arrangements, and largest speeds are observed for random anchoring. Hence, a regular pattern provides no advantage in terms of swimming speed compared to random anchoring of flagella, but yields more likely single-bundle configurations.
Collapse
Affiliation(s)
- Judit Clopés
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany
- Institute for Theoretical Physics, RWTH Aachen University, 52074, Aachen, Germany
| | - Roland G Winkler
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany.
- Institute for Theoretical Physics, RWTH Aachen University, 52074, Aachen, Germany.
| |
Collapse
|
43
|
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.
Collapse
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.
| |
Collapse
|
44
|
Tanasijević I, Lauga E. Hydrodynamic synchronization in strong confinement. Phys Rev E 2021; 103:022403. [PMID: 33736031 DOI: 10.1103/physreve.103.022403] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 01/04/2021] [Indexed: 11/07/2022]
Abstract
Cellular appendages conferring motility, such as flagella and cilia, are known to synchronise their periodic beats. The origin of synchronization is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing, both of which can lead generically to stable phase locking. In order to help uncover the physical mechanism for hydrodynamic synchronization most essential overall in biology, we theoretically investigate in this paper the effect of strong confinement on the effectiveness of hydrodynamic synchronization. Following past work, we use minimal models of cilia where appendages are modeled as rigid spheres forced to move along circular trajectories near a rigid surface. Strong confinement is modeled by adding a second nearby surface, parallel to the first one, where the distance between the surfaces is much smaller than the typical distance between the cilia, which results in a qualitative change in the nature of hydrodynamic interactions. We calculate separately the impact of hydrodynamic confinement on the synchronization dynamics of the elastic compliance and the force modulation mechanisms and compare our results to the usual case with a single surface. Applying our results to the biologically relevant situation of nodal cilia, we show that force modulation is a mechanism that leads to phase-locked states under strong confinement that are very similar to those without confinement as a difference with the elastic compliance mechanism. Our results point therefore to the robustness of force modulation for synchronization, an important feature for biological dynamics that therefore suggests it could be the most essential physical mechanism overall in arrays of nodal cilia. We further examine the distinct biologically relevant situation of primary cilia and show in that case that the difference in robustness of the mechanisms is not as pronounced but still favors the force modulation.
Collapse
Affiliation(s)
- Ivan Tanasijević
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| |
Collapse
|
45
|
Chelakkot R, Hagan MF, Gopinath A. Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays. SOFT MATTER 2021; 17:1091-1104. [PMID: 33289748 DOI: 10.1039/d0sm01162b] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient - even in the absence of inter-filament hydrodynamic interactions - to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics - specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.
Collapse
Affiliation(s)
- Raghunath Chelakkot
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, India.
| | | | | |
Collapse
|
46
|
Stein DB, De Canio G, Lauga E, Shelley MJ, Goldstein RE. Swirling Instability of the Microtubule Cytoskeleton. PHYSICAL REVIEW LETTERS 2021; 126:028103. [PMID: 33512217 PMCID: PMC7616086 DOI: 10.1103/physrevlett.126.028103] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 11/29/2020] [Indexed: 05/12/2023]
Abstract
In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly Drosophila melanogaster have shown a transition from a spatially disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions, we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.
Collapse
Affiliation(s)
- David B. Stein
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Gabriele De Canio
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Michael J. Shelley
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA
| | - Raymond E. Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| |
Collapse
|
47
|
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.
Collapse
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
| |
Collapse
|
48
|
Schneiter M, Halm S, Odriozola A, Mogel H, Rička J, Stoffel MH, Zuber B, Frenz M, Tschanz SA. Multi-scale alignment of respiratory cilia and its relation to mucociliary function. J Struct Biol 2020; 213:107680. [PMID: 33359072 DOI: 10.1016/j.jsb.2020.107680] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Revised: 11/13/2020] [Accepted: 12/05/2020] [Indexed: 11/27/2022]
Abstract
The tracheobronchial tree is lined by a mucociliary epithelium containing millions of multiciliated cells. Their integrated oscillatory activity continuously propels an overlying pollution-protecting mucus layer in cranial direction, leading to mucociliary clearance - the primary defence mechanism of the airways. Mucociliary transport is commonly thought to co-emerge with the collective ciliary motion pattern under appropriate geometrical and rheological conditions. Proper ciliary alignment is therefore considered essential to establish mucociliary clearance in the respiratory system. Here, we used volume electron microscopy in combination with high-speed reflection contrast microscopy in order to examine ciliary orientation and its spatial organization, as well as to measure the propagation direction of metachronal waves and the direction of mucociliary transport on bovine tracheal epithelia with reference to the tracheal long axis (TLA). Ciliary orientation is measured in terms of the basal body orientation (BBO) and the axonemal orientation (AO), which are commonly considered to coincide, both equivalently indicating the effective stroke as well as the mucociliary transport direction. Our results, however, reveal that only the AO is in line with the mucociliary transport, which was found to run along a left-handed helical trajectory, whereas the BBO was found to be aligned with the TLA. Furthermore, we show that even if ciliary orientation remains consistent between adjacent cells, ciliary orientation exhibits a gradual shift within individual cells. Together with the symplectic beating geometry, this intracellular orientational pattern could provide for the propulsion of highly viscous mucus and likely constitutes a compromise between efficiency and robustness.
Collapse
Affiliation(s)
- Martin Schneiter
- Institute of Applied Physics, University of Bern, Sidlerstrasse 5, Switzerland; Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland
| | - Sebastian Halm
- Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland
| | - Adolfo Odriozola
- Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland
| | - Helga Mogel
- Division of Veterinary Anatomy, University of Bern, Länggassstrasse 120, Switzerland
| | - Jaroslav Rička
- Institute of Applied Physics, University of Bern, Sidlerstrasse 5, Switzerland
| | - Michael H Stoffel
- Division of Veterinary Anatomy, University of Bern, Länggassstrasse 120, Switzerland
| | - Benoît Zuber
- Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland.
| | - Martin Frenz
- Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland.
| | - Stefan A Tschanz
- Institute of Anatomy, University of Bern, Baltzerstrasse 2, Switzerland
| |
Collapse
|
49
|
Tiwari I, Parmananda P, Chelakkot R. Periodic oscillations in a string of camphor infused disks. SOFT MATTER 2020; 16:10334-10344. [PMID: 33237113 DOI: 10.1039/d0sm01393e] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The rhythmic beating motion of autonomously motile filaments has many practical applications. Here, we present an experimental study on a filament made of camphor infused paper disks, stitched together adjacent to each other using nylon thread. The filament displays spontaneous translatory motion when it is placed on the surface of water due to the surface tension gradients created by camphor molecules on the water surface. When this filament is clamped on one end, we obtain regular oscillatory motion instead of translation. The filament shows qualitatively different dynamics at different activity levels, which is controlled by the amount of camphor infused into the paper disks. For a better physical understanding of the filament dynamics, we develop a minimal numerical model involving a semi-flexible filament made of active polar disks, where the polarity is coupled to the instantaneous velocity of the particle. This model qualitatively reproduces different oscillatory modes of the filament. Moreover, our model reveals a rich dynamical state diagram of the system, as a function of filament activity and the coupling strength.
Collapse
Affiliation(s)
- Ishant Tiwari
- Department of Physics, Indian Institute of Technology - Bombay, Mumbai, Maharashtra 400076, India.
| | | | | |
Collapse
|
50
|
Asadzadeh SS, Kiørboe T, Larsen PS, Leys SP, Yahel G, Walther JH. Hydrodynamics of sponge pumps and evolution of the sponge body plan. eLife 2020; 9:e61012. [PMID: 33252039 PMCID: PMC7755389 DOI: 10.7554/elife.61012] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Accepted: 11/27/2020] [Indexed: 12/24/2022] Open
Abstract
Sponges are suspension feeders that filter vast amounts of water. Pumping is carried out by flagellated chambers that are connected to an inhalant and exhalant canal system. In 'leucon' sponges with relatively high-pressure resistance due to a complex and narrow canal system, pumping and filtering are only possible owing to the presence of a gasket-like structure (forming a canopy above the collar filters). Here, we combine numerical and experimental work and demonstrate how sponges that lack such sealing elements are able to efficiently pump and force the flagella-driven flow through their collar filter, thanks to the formation of a 'hydrodynamic gasket' above the collar. Our findings link the architecture of flagellated chambers to that of the canal system, and lend support to the current view that the sponge aquiferous system evolved from an open-type filtration system, and that the first metazoans were filter feeders.
Collapse
Affiliation(s)
- Seyed Saeed Asadzadeh
- National Institute of Aquatic Resources and Centre for Ocean Life, Technical University of DenmarkLyngbyDenmark
| | - Thomas Kiørboe
- National Institute of Aquatic Resources and Centre for Ocean Life, Technical University of DenmarkLyngbyDenmark
| | - Poul Scheel Larsen
- Department of Mechanical Engineering, Technical University of DenmarkLyngbyDenmark
| | - Sally P Leys
- Department of Biological Sciences, University of Alberta, CW 405 Biological Sciences BuildingEdmontonCanada
| | - Gitai Yahel
- The Faculty of Marine Science, Ruppin Academic CenterMichmoretIsrael
| | - Jens H Walther
- Department of Mechanical Engineering, Technical University of DenmarkLyngbyDenmark
- Computational Science and Engineering Laboratory, Swiss Federal Institute of Technology ZürichZürichSwitzerland
| |
Collapse
|