1
|
Ren X, Hernández-Herrera P, Montoya F, Darszon A, Corkidi G, Bloomfield-Gadêlha H. Fluid flow reconstruction around a free-swimming sperm in 3D. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.05.29.596379. [PMID: 38853842 PMCID: PMC11160703 DOI: 10.1101/2024.05.29.596379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2024]
Abstract
We investigate the dynamics and hydrodynamics of a human spermatozoa swimming freely in 3D. We simultaneously track the sperm flagellum and the sperm head orientation in the laboratory frame of reference via high-speed high-resolution 4D (3D+t) microscopy, and extract the flagellar waveform relative to the body frame of reference, as seen from a frame of reference that translates and rotates with the sperm in 3D. Numerical fluid flow reconstructions of sperm motility are performed utilizing the experimental 3D waveforms, with excellent accordance between predicted and observed 3D sperm kinematics. The reconstruction accuracy is validated by directly comparing the three linear and three angular sperm velocities with experimental measurements. Our microhydrodynamic analysis reveals a novel fluid flow pattern, characterized by a pair of vortices that circulate in opposition to each other along the sperm cell. Finally, we show that the observed sperm counter-vortices are not unique to the experimental beat, and can be reproduced by idealised waveform models, thus suggesting a fundamental flow structure for free-swimming sperm propelled by a 3D beating flagellum.
Collapse
Affiliation(s)
- Xiaomeng Ren
- School of Engineering Mathematics & Bristol Robotics Laboratory, University of Bristol, BS8 1UB Bristol, UK
| | | | - Fernando Montoya
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Alberto Darszon
- Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Gabriel Corkidi
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Hermes Bloomfield-Gadêlha
- School of Engineering Mathematics & Bristol Robotics Laboratory, University of Bristol, BS8 1UB Bristol, UK
| |
Collapse
|
2
|
Dhar T, Saintillan D. Active transport of a passive colloid in a bath of run-and-tumble particles. Sci Rep 2024; 14:11844. [PMID: 38783044 PMCID: PMC11116446 DOI: 10.1038/s41598-024-62396-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2024] [Accepted: 05/16/2024] [Indexed: 05/25/2024] Open
Abstract
The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity D of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratio, and high activity.
Collapse
Affiliation(s)
- Tanumoy Dhar
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA
| | - David Saintillan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA.
| |
Collapse
|
3
|
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
|
4
|
Boymelgreen A, Schiffbauer J, Khusid B, Yossifon G. Synthetic electrically driven colloids: a platform for understanding collective behavior in soft matter. Curr Opin Colloid Interface Sci 2022. [DOI: 10.1016/j.cocis.2022.101603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
5
|
Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Potential flow formed by doublet flow has been well applied in environmental applications and geothermal designs such as reservoir and fuel injectors. Most of the doublet flow is assumed based on the sink and source with equivalent strength and distance from the origin, forming the well-known Rankine oval structure when a far-field flow is superposed. A semi-analytical method is formulated to systematically investigate the unsymmetrical doublet flow with different strengths of sink and source. The general mathematical expression for unsymmetrical doublet flow is derived analytically before the streamline and the potential line can be visualised via a numerical approach. The results revealed that the doublet flows altered the Rankine oval structure to form aerofoil-like geometry. When the far-field flow interferes with the general Doublet configuration, unique flow structures such as convex, concave, and various wing shapes could be generated. The current study provides new insight on producing aerodynamic curves for the design of bio-inspired structures.
Collapse
|
6
|
Mondal D, Prabhune AG, Ramaswamy S, Sharma P. Strong confinement of active microalgae leads to inversion of vortex flow and enhanced mixing. eLife 2021; 10:e67663. [PMID: 34806977 PMCID: PMC8758135 DOI: 10.7554/elife.67663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 11/16/2021] [Indexed: 11/13/2022] Open
Abstract
Microorganisms swimming through viscous fluids imprint their propulsion mechanisms in the flow fields they generate. Extreme confinement of these swimmers between rigid boundaries often arises in natural and technological contexts, yet measurements of their mechanics in this regime are absent. Here, we show that strongly confining the microalga Chlamydomonas between two parallel plates not only inhibits its motility through contact friction with the walls but also leads, for purely mechanical reasons, to inversion of the surrounding vortex flows. Insights from the experiment lead to a simplified theoretical description of flow fields based on a quasi-2D Brinkman approximation to the Stokes equation rather than the usual method of images. We argue that this vortex flow inversion provides the advantage of enhanced fluid mixing despite higher friction. Overall, our results offer a comprehensive framework for analyzing the collective flows of strongly confined swimmers.
Collapse
Affiliation(s)
- Debasmita Mondal
- Department of Physics, Indian Institute of ScienceBangaloreIndia
| | - Ameya G Prabhune
- Department of Physics, Indian Institute of ScienceBangaloreIndia
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of ScienceBangaloreIndia
| | - Prerna Sharma
- Department of Physics, Indian Institute of ScienceBangaloreIndia
| |
Collapse
|
7
|
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
|
8
|
Giuliani N, Rossi M, Noselli G, DeSimone A. How Euglena gracilis swims: Flow field reconstruction and analysis. Phys Rev E 2021; 103:023102. [PMID: 33736112 DOI: 10.1103/physreve.103.023102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 01/19/2021] [Indexed: 12/21/2022]
Abstract
Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.
Collapse
Affiliation(s)
- Nicola Giuliani
- SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
| | - Massimiliano Rossi
- DTU-Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark
| | - Giovanni Noselli
- SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
| | - Antonio DeSimone
- SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy.,The BioRobotics Institute and Dept. of Excellence in Robotics and AI, Scuola Universitaria Superiore Pisa, Piazza Martiri della Libertà, 56127 Pisa, Italy
| |
Collapse
|
9
|
Bárdfalvy D, Anjum S, Nardini C, Morozov A, Stenhammar J. Symmetric Mixtures of Pusher and Puller Microswimmers Behave as Noninteracting Suspensions. PHYSICAL REVIEW LETTERS 2020; 125:018003. [PMID: 32678625 DOI: 10.1103/physrevlett.125.018003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as "pushers" and "pullers," display qualitatively different collective behaviors: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher-puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction χ of pullers is increased and disappears for χ≥0.5. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1∶1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer-swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1∶1 pusher-puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.
Collapse
Affiliation(s)
- Dóra Bárdfalvy
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Shan Anjum
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Cesare Nardini
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Joakim Stenhammar
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| |
Collapse
|
10
|
Gadêlha H, Hernández-Herrera P, Montoya F, Darszon A, Corkidi G. Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering. SCIENCE ADVANCES 2020; 6:eaba5168. [PMID: 32789171 PMCID: PMC7399739 DOI: 10.1126/sciadv.aba5168] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 06/18/2020] [Indexed: 05/21/2023]
Abstract
Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.
Collapse
Affiliation(s)
- Hermes Gadêlha
- Department of Engineering Mathematics, University of Bristol, BS8 1UB Bristol, UK
| | - Paul Hernández-Herrera
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Fernando Montoya
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Alberto Darszon
- Departamento de Genética del Desarrollo y Fisiología Molecular, Instituto de Biotecnología, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| | - Gabriel Corkidi
- Laboratorio de Imágenes y Visión por Computadora, Departamento de Ingeniería Celular y Biocatálisis, Universidad Nacional Autónoma de México, Cuernavaca, Mexico
| |
Collapse
|
11
|
Jeanneret R, Pushkin DO, Polin M. Confinement Enhances the Diversity of Microbial Flow Fields. PHYSICAL REVIEW LETTERS 2019; 123:248102. [PMID: 31922880 DOI: 10.1103/physrevlett.123.248102] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Revised: 07/22/2019] [Indexed: 06/10/2023]
Abstract
Despite their importance in many biological, ecological, and physical processes, microorganismal fluid flows under tight confinement have not been investigated experimentally. Strong screening of Stokelets in this geometry suggests that the flow fields of different microorganisms should be universally dominated by the 2D source dipole from the swimmer's finite-size body. Confinement therefore is poised to collapse differences across microorganisms, which are instead well established in bulk. We combine experiments and theoretical modeling to show that, in general, this is not correct. Our results demonstrate that potentially minute details like microswimmer spinning and the physical arrangement of the propulsion appendages have in fact a leading role in setting qualitative topological properties of the hydrodynamic flow fields of microswimmers under confinement. This is well captured by an effective 2D model, even under relatively weak confinement. These results imply that active confined hydrodynamics is much richer than in bulk and depends in a subtle manner on the size, shape, and propulsion mechanisms of the active components.
Collapse
Affiliation(s)
- Raphaël Jeanneret
- IMEDEA, University of the Balearic Islands, Carrer de Miquel Marquès, 21, 07190 Esporles, Spain
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Dmitri O Pushkin
- Mathematics Department, University of York, Heslington, York, YO10 5DD, United Kingdom
| | - Marco Polin
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
- Centre For Mechanochemical Cell Biology, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
12
|
Schoeller SF, Keaveny EE. From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions. J R Soc Interface 2019; 15:rsif.2017.0834. [PMID: 29563245 PMCID: PMC5908526 DOI: 10.1098/rsif.2017.0834] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Accepted: 02/26/2018] [Indexed: 11/12/2022] Open
Abstract
Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and propulsion mechanisms. Even for sperm cells, which have a stereotyped shape consisting of a cell body connected to a flexible flagellum, a wide range of collective dynamics is observed spanning from the formation of tightly packed groups to the display of larger-scale, turbulence-like motion. Using a detailed mathematical model that resolves flagellum dynamics, we perform simulations of sperm suspensions containing up to 1000 cells and explore the connection between individual and collective dynamics. We find that depending on the level of variation in individual dynamics from one swimmer to another, the sperm exhibit either a strong tendency to aggregate, or the suspension exhibits large-scale swirling. Hydrodynamic interactions govern the formation and evolution of both states. In addition, a quantitative analysis of the states reveals that the flows generated at the time scale of flagellum undulations contribute significantly to the overall energy in the surrounding fluid, highlighting the importance of resolving these flows.
Collapse
Affiliation(s)
- Simon F Schoeller
- Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| | - Eric E Keaveny
- Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| |
Collapse
|
13
|
Wei D, Dehnavi PG, Aubin-Tam ME, Tam D. Is the Zero Reynolds Number Approximation Valid for Ciliary Flows? PHYSICAL REVIEW LETTERS 2019; 122:124502. [PMID: 30978086 DOI: 10.1103/physrevlett.122.124502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Revised: 01/08/2019] [Indexed: 06/09/2023]
Abstract
Stokes equations are commonly used to model the hydrodynamic flow around cilia on the micron scale. The validity of the zero Reynolds number approximation is investigated experimentally with a flow velocimetry approach based on optical tweezers, which allows the measurement of periodic flows with high spatial and temporal resolution. We find that beating cilia generate a flow, which fundamentally differs from the stokeslet field predicted by Stokes equations. In particular, the flow velocity spatially decays at a faster rate and is gradually phase delayed at increasing distances from the cilia. This indicates that the quasisteady approximation and use of Stokes equations for unsteady ciliary flow are not always justified and the finite timescale for vorticity diffusion cannot be neglected. Our results have significant implications in studies of synchronization and collective dynamics of microswimmers.
Collapse
Affiliation(s)
- Da Wei
- Department of Bionanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Parviz Ghoddoosi Dehnavi
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Daniel Tam
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
| |
Collapse
|
14
|
Friedrich BM. Load response of shape-changing microswimmers scales with their swimming efficiency. Phys Rev E 2018; 97:042416. [PMID: 29758744 DOI: 10.1103/physreve.97.042416] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2017] [Indexed: 12/15/2022]
Abstract
External forces acting on a microswimmer can feed back on its self-propulsion mechanism. We discuss this load response for a generic microswimmer that swims by cyclic shape changes. We show that the change in cycle frequency is proportional to the Lighthill efficiency of self-propulsion. As a specific example, we consider Najafi's three-sphere swimmer. The force-velocity relation of a microswimmer implies a correction for a formal superposition principle for active and passive motion.
Collapse
|
15
|
Ranganathan M, Farutin A, Misbah C. Effect of Cytoskeleton Elasticity on Amoeboid Swimming. Biophys J 2018; 115:1316-1329. [PMID: 30177444 PMCID: PMC6170896 DOI: 10.1016/j.bpj.2018.08.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 07/28/2018] [Accepted: 08/02/2018] [Indexed: 01/09/2023] Open
Abstract
Recently, it has been reported that the cells of the immune system, as well as Dictyostelium amoebae, can swim in a bulk fluid by changing their shape repeatedly. We refer to this motion as amoeboid swimming. Here, we explore how the propulsion and the deformation of the cell emerge as an interplay between the active forces that the cell employs to activate the shape changes and the passive, viscoelastic response of the cell membrane, the cytoskeleton, and the surrounding environment. We introduce a model in which the cell is represented by an elastic capsule enclosing a viscous liquid. The motion of the cell is activated by time-dependent forces distributed along its surface. The model is solved numerically using the boundary integral formulation. The cell can swim in a fluid medium using cyclic deformations or strokes. We measure the swimming velocity of the cell as a function of the force amplitude, the stroke frequency, and the viscoelastic properties of the cell and the medium. We show that an increase in the shear modulus leads both to a regular slowdown of the swimming, which is more pronounced for more deflated swimmers, and to a tendency toward cell buckling. For a given stroke frequency, the swimming velocity shows a quadratic dependence on force amplitude for small forces, as expected, but saturates for large forces. We propose a scaling relationship for the dependence of swimming velocity on the relevant parameters that qualitatively reproduces the numerical results and allows us to define regimes in which the cell motility is dominated by elastic response or by the effective cortex viscosity. This leads to an estimate of the effective cortex viscosity of 103 Pa ⋅ s for which the two effects are comparable, which is close to that provided by several experiments.
Collapse
Affiliation(s)
- Madhav Ranganathan
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur, India
| | - Alexander Farutin
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, LIPhy, Grenoble, France
| | - Chaouqi Misbah
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, LIPhy, Grenoble, France.
| |
Collapse
|
16
|
Meng F, Matsunaga D, Golestanian R. Clustering of Magnetic Swimmers in a Poiseuille Flow. PHYSICAL REVIEW LETTERS 2018; 120:188101. [PMID: 29775341 DOI: 10.1103/physrevlett.120.188101] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Revised: 01/31/2018] [Indexed: 06/08/2023]
Abstract
We investigate the collective behavior of magnetic swimmers, which are suspended in a Poiseuille flow and placed under an external magnetic field, using analytical techniques and Brownian dynamics simulations. We find that the interplay between intrinsic activity, external alignment, and magnetic dipole-dipole interactions leads to longitudinal structure formation. Our work sheds light on a recent experimental observation of a clustering instability in this system.
Collapse
Affiliation(s)
- Fanlong Meng
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Daiki Matsunaga
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| |
Collapse
|
17
|
Abstract
We unveil orbital topologies of two nearby swimming microorganisms using an artificial microswimmer, called Quadroar. Depending on the initial conditions of the microswimmers, we find diverse families of attractors including dynamical equilibria, bound orbits, braids, and pursuit–evasion games. We also observe a hydrodynamic slingshot effect: a system of two hydrodynamically interacting swimmers moving along braids can advance in space faster than non-interacting swimmers that have the same actuation parameters and initial conditions as the interacting ones. Our findings suggest the existence of complex collective behaviors of microswimmers, from equilibrium to rapidly streaming states.
Collapse
|
18
|
Ishimoto K. Guidance of microswimmers by wall and flow: Thigmotaxis and rheotaxis of unsteady squirmers in two and three dimensions. Phys Rev E 2017; 96:043103. [PMID: 29347500 DOI: 10.1103/physreve.96.043103] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Indexed: 06/07/2023]
Abstract
The motions of an unsteady circular-disk squirmer and a spherical squirmer have been investigated in the presence of a no-slip infinite wall and a background shear flow in order to clarify the similarities and differences between two- and three-dimensional motions. Despite the similar bifurcation structure of the dynamical system, the stability of the fixed points differs due to the Hamiltonian structure of the disk squirmer. Once the unsteady oscillating surface velocity profile is considered, the disk squirmer can behave in a chaotic manner and cease to be confined in a near-wall region. In contrast, in an unsteady spherical squirmer, the dynamics is well attracted by a stable fixed point. Additional wall contact interactions lead to stable fixed points for the disk squirmer, and, in turn, the surface entrapment of the disk squirmer can be stabilized, regardless of the existence of the background flow. Finally, we consider spherical motion under a background flow. The separated time scales of the surface entrapment (thigmotaxis) and the turning toward the flow direction (rheotaxis) enable us to reduce the dynamics to two-dimensional phase space, and simple weather-vane mechanics can predict squirmer rheotaxis. The analogous structure of the phase plane with the wall contact in two and three dimensions implies that the two-dimensional disk swimmer successfully captures the nonlinear interactions, and thus two-dimensional approximation could be useful in designing microfluidic devices for the guidance of microswimmers and for clarifying the locomotions in a complex geometry.
Collapse
Affiliation(s)
- Kenta Ishimoto
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom; The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8501, Japan; and Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| |
Collapse
|
19
|
Ishimoto K, Gadêlha H, Gaffney EA, Smith DJ, Kirkman-Brown J. Coarse-Graining the Fluid Flow around a Human Sperm. PHYSICAL REVIEW LETTERS 2017; 118:124501. [PMID: 28388208 DOI: 10.1103/physrevlett.118.124501] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Indexed: 06/07/2023]
Abstract
The flagellar beat is extracted from human sperm digital imaging microscopy and used to determine the flow around the cell and its trajectory, via boundary element simulation. Comparison of the predicted cell trajectory with observation demonstrates that simulation can predict fine-scale sperm dynamics at the qualitative level. The flow field is also observed to reduce to a time-dependent summation of regularized Stokes flow singularities, approximated at leading order by a blinking force triplet. Such regularized singularity decompositions may be used to upscale cell level detail into population models of human sperm motility.
Collapse
Affiliation(s)
- Kenta Ishimoto
- The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8501, Japan
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Hermes Gadêlha
- Department of Mathematics, University of York, York YO10 5DD, United Kingdom
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - David J Smith
- School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
| | - Jackson Kirkman-Brown
- Institute for Metabolism and Systems Research, College of Medical and Dental Sciences, University of Birmingham, Birmingham B15 2TT, United Kingdom
- Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust, Birmingham B15 2TG, United Kingdom
| |
Collapse
|
20
|
Dölger J, Nielsen LT, Kiørboe T, Andersen A. Swimming and feeding of mixotrophic biflagellates. Sci Rep 2017; 7:39892. [PMID: 28054596 PMCID: PMC5215566 DOI: 10.1038/srep39892] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Accepted: 11/29/2016] [Indexed: 11/25/2022] Open
Abstract
Many unicellular flagellates are mixotrophic and access resources through both photosynthesis and prey capture. Their fitness depends on those processes as well as on swimming and predator avoidance. How does the flagellar arrangement and beat pattern of the flagellate affect swimming speed, predation risk due to flow-sensing predators, and prey capture? Here, we describe measured flows around two species of mixotrophic, biflagellated haptophytes with qualitatively different flagellar arrangements and beat patterns. We model the near cell flows using two symmetrically arranged point forces with variable position next to a no-slip sphere. Utilizing the observations and the model we find that puller force arrangements favour feeding, whereas equatorial force arrangements favour fast and quiet swimming. We determine the capture rates of both passive and motile prey, and we show that the flow facilitates transport of captured prey along the haptonema structure. We argue that prey capture alone cannot fulfil the energy needs of the observed species, and that the mixotrophic life strategy is essential for survival.
Collapse
Affiliation(s)
- Julia Dölger
- Technical University of Denmark, Department of Physics and Centre for Ocean Life, DK-2800 Kgs. Lyngby, Denmark
| | - Lasse Tor Nielsen
- Technical University of Denmark, National Institute of Aquatic Resources and Centre for Ocean Life, DK-2920 Charlottenlund, Denmark
| | - Thomas Kiørboe
- Technical University of Denmark, National Institute of Aquatic Resources and Centre for Ocean Life, DK-2920 Charlottenlund, Denmark
| | - Anders Andersen
- Technical University of Denmark, Department of Physics and Centre for Ocean Life, DK-2800 Kgs. Lyngby, Denmark
| |
Collapse
|
21
|
Eisenstecken T, Gompper G, Winkler RG. Conformational Properties of Active Semiflexible Polymers. Polymers (Basel) 2016; 8:E304. [PMID: 30974577 PMCID: PMC6431937 DOI: 10.3390/polym8080304] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Revised: 08/03/2016] [Accepted: 08/04/2016] [Indexed: 01/21/2023] Open
Abstract
The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surrounding active (Brownian) particles or from the inherent motion of the polymer itself, which may be composed of active Brownian particles. In the latter case, the respective monomers are independently propelled in directions changing diffusively. For the description of the polymer, we adopt the continuous Gaussian semiflexible polymer model. Specifically, the finite polymer extensibility is taken into account, which turns out to be essential for the polymer conformations. Our analytical calculations predict a strong dependence of the relaxation times on the activity. In particular, semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics to the flexible polymer dynamics with increasing activity. This leads to a significant activity-induced polymer shrinkage over a large range of self-propulsion velocities. For large activities, the polymers swell and their extension becomes comparable to the contour length. The scaling properties of the mean square end-to-end distance with respect to the polymer length and monomer activity are discussed.
Collapse
Affiliation(s)
- Thomas Eisenstecken
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| | - Roland G Winkler
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| |
Collapse
|
22
|
Winkler RG. Dynamics of flexible active Brownian dumbbells in the absence and the presence of shear flow. SOFT MATTER 2016; 12:3737-3749. [PMID: 26980630 DOI: 10.1039/c5sm02965a] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The dynamical properties of a flexible dumbbell composed of active Brownian particles are analytically analyzed. The dumbbell is considered as a simplified description of a linear active polymer. The two beads are independently propelled in directions which change in a diffusive manner. The relaxation behavior of the internal degree of freedom is tightly coupled to the dumbbell activity. The latter dominates the dynamics for strong propulsion. As is shown, limitations in bond stretching strongly influence the relaxation behavior. Similarly, under shear flow, activity determines the relaxation and tumbling behavior at strong propulsion. Moreover, shear leads to a preferred alignment and consequently to shear thinning. Thereby, a different power-law dependence on the shear rate compared to passive dumbbells under flow is found.
Collapse
Affiliation(s)
- Roland G Winkler
- Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany.
| |
Collapse
|