101
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Pessot G, Löwen H, Menzel AM. Binary pusher–puller mixtures of active microswimmers and their collective behaviour. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1496291] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Giorgio Pessot
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
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102
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Ng WM, Che HX, Guo C, Liu C, Low SC, Chieh Chan DJ, Mohamud R, Lim J. Artificial Magnetotaxis of Microbot: Magnetophoresis versus Self-Swimming. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:7971-7980. [PMID: 29882671 DOI: 10.1021/acs.langmuir.8b01210] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
An artificial magnetotactic microbot was created by integrating the microalgal cell with magnetic microbead for its potential application as biomotor in microscale environment. Here, we demonstrate the remote magnetotactic control of the microbot under a low gradient magnetic field (<100 T/m). We characterize the kinematic behavior of the microbots carrying magnetic microbeads of two different sizes, with diameter of 2 and 4.5 μm, in the absence and presence of magnetic field. In the absence of magnetic field, we observed the microbot showed a helical motion as a result of the misalignment between the thrust force and the symmetry axis after the attachment. The microbot bound with a larger magnetic microbead moved with higher translational velocity but rotated slower about its axis of rotation. The viscous force was balanced by the thrust force of the microbot, resulting in a randomized swimming behavior of the microbot at its terminal velocity. Meanwhile, under the influence of a low gradient magnetic field, we demonstrated that the directional control of the microbot was based on following principles: (1) magnetophoretic force was insignificant on influencing its perpendicular motion and (2) its parallel motion was dependent on both self-swimming and magnetophoresis, in which this cooperative effect was a function of separation distance from the magnet. As the microbot approached the magnet, the magnetophoretic force suppressed its self-swimming behavior, leading to a positive magnetotaxis of the microbot toward the source of magnetic field. Our experimental results and kinematic analysis revealed the contribution of mass density variation of particle-and-cell system on influencing its dynamical behavior.
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Affiliation(s)
- Wei Ming Ng
- School of Chemical Engineering , Universiti Sains Malaysia , 14300 Nibong Tebal , Penang , Malaysia
| | - Hui Xin Che
- School of Chemical Engineering , Universiti Sains Malaysia , 14300 Nibong Tebal , Penang , Malaysia
| | - Chen Guo
- State Key Laboratory of Biochemical Engineering and Key Laboratory of Green Process and Engineering, Institute of Process Engineering , Chinese Academy of Sciences , Beijing 100190 , People's Republic of China
| | - Chunzhao Liu
- State Key Laboratory of Biochemical Engineering and Key Laboratory of Green Process and Engineering, Institute of Process Engineering , Chinese Academy of Sciences , Beijing 100190 , People's Republic of China
| | - Siew Chun Low
- School of Chemical Engineering , Universiti Sains Malaysia , 14300 Nibong Tebal , Penang , Malaysia
| | - Derek Juinn Chieh Chan
- School of Chemical Engineering , Universiti Sains Malaysia , 14300 Nibong Tebal , Penang , Malaysia
| | - Rohimah Mohamud
- Department of Immunology, School of Medical Sciences , Universiti Sains Malaysia , 16150 Kubang Kerian , Kelantan , Malaysia
| | - JitKang Lim
- School of Chemical Engineering , Universiti Sains Malaysia , 14300 Nibong Tebal , Penang , Malaysia
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
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103
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Bertrand T, Zhao Y, Bénichou O, Tailleur J, Voituriez R. Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments. PHYSICAL REVIEW LETTERS 2018; 120:198103. [PMID: 29799236 DOI: 10.1103/physrevlett.120.198103] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Revised: 02/18/2018] [Indexed: 06/08/2023]
Abstract
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.
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Affiliation(s)
- Thibault Bertrand
- Laboratoire Jean Perrin, UMR 8237 CNRS, Sorbonne Université, 75005 Paris, France
| | - Yongfeng Zhao
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, 75205 Paris, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS, Sorbonne Université, 75005 Paris, France
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, 75205 Paris, France
| | - Raphaël Voituriez
- Laboratoire Jean Perrin, UMR 8237 CNRS, Sorbonne Université, 75005 Paris, France
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS, Sorbonne Université, 75005 Paris, France
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104
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Oliver N, Alpmann C, Barroso Á, Dewenter L, Woerdemann M, Denz C. Synchronization in pairs of rotating active biomotors. SOFT MATTER 2018; 14:3073-3077. [PMID: 29663004 DOI: 10.1039/c8sm00022k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Although synchronization is a well-known physical phenomenon, experimental studies of its emergence in living bacterial cells are still scarce. The difficulty in generating a controlled scenario to detect synchronization has limited the experimental outcomes so far. We present a realization based on holographic optical tweezers in which adhered pairs of self-propelled bacteria rotate in a plane. The separation distance between the bacteria determines the strength of the hydrodynamic coupling. Despite the noisy environment and autonomous dynamics of the living bacteria, we find evidence of phase locking and frequency entrainment in their rotation. The observation of higher order frequency synchronization is also discussed.
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Affiliation(s)
- Neus Oliver
- University of Muenster, Institute of Applied Physics, Corrensstr. 2/4, Muenster 48149, Germany.
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105
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Martínez-Pedrero F, Tierno P. Advances in colloidal manipulation and transport via hydrodynamic interactions. J Colloid Interface Sci 2018; 519:296-311. [PMID: 29505991 DOI: 10.1016/j.jcis.2018.02.062] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Revised: 02/19/2018] [Accepted: 02/19/2018] [Indexed: 01/31/2023]
Abstract
In this review article, we highlight many recent advances in the field of micromanipulation of colloidal particles using hydrodynamic interactions (HIs), namely solvent mediated long-range interactions. At the micrsocale, the hydrodynamic laws are time reversible and the flow becomes laminar, features that allow precise manipulation and control of colloidal matter. We focus on different strategies where externally operated microstructures generate local flow fields that induce the advection and motion of the surrounding components. In addition, we review cases where the induced flow gives rise to hydrodynamic bound states that may synchronize during the process, a phenomenon essential in different systems such as those that exhibit self-assembly and swarming.
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Affiliation(s)
- F Martínez-Pedrero
- Departamento de Química-Física I, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040, Spain.
| | - P Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, E-08028 Barcelona, Spain; Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, E-08028 Barcelona, Spain; Institut de Nanociència i Nanotecnologia, IN(2)UB, Universitat de Barcelona, E-08028 Barcelona, Spain
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106
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Ostapenko T, Schwarzendahl FJ, Böddeker TJ, Kreis CT, Cammann J, Mazza MG, Bäumchen O. Curvature-Guided Motility of Microalgae in Geometric Confinement. PHYSICAL REVIEW LETTERS 2018; 120:068002. [PMID: 29481277 DOI: 10.1103/physrevlett.120.068002] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Indexed: 06/08/2023]
Abstract
Microorganisms, such as bacteria and microalgae, often live in habitats consisting of a liquid phase and a plethora of interfaces. The precise ways in which these motile microbes behave in their confined environment remain unclear. Using experiments and Brownian dynamics simulations, we study the motility of a single Chlamydomonas microalga in an isolated microhabitat with controlled geometric properties. We demonstrate how the geometry of the habitat controls the cell's navigation in confinement. The probability of finding the cell swimming near the boundary increases with the wall curvature, as seen for both circular and elliptical chambers. The theory, utilizing an asymmetric dumbbell model of the cell and steric wall interactions, captures this curvature-guided navigation quantitatively with no free parameters.
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Affiliation(s)
- Tanya Ostapenko
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
| | - Fabian Jan Schwarzendahl
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
- Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| | - Thomas J Böddeker
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
| | - Christian Titus Kreis
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
- Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| | - Jan Cammann
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
| | - Marco G Mazza
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
| | - Oliver Bäumchen
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, D-37077 Göttingen, Germany
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107
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Tanneru HK, Suresh R, Rengaswamy R. On modeling and optimization of micro-photosynthetic power cells. Comput Chem Eng 2017. [DOI: 10.1016/j.compchemeng.2017.02.015] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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108
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Saggiorato G, Alvarez L, Jikeli JF, Kaupp UB, Gompper G, Elgeti J. Human sperm steer with second harmonics of the flagellar beat. Nat Commun 2017; 8:1415. [PMID: 29123094 PMCID: PMC5680276 DOI: 10.1038/s41467-017-01462-y] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 09/20/2017] [Indexed: 12/21/2022] Open
Abstract
Sperm are propelled by bending waves traveling along their flagellum. For steering in gradients of sensory cues, sperm adjust the flagellar waveform. Symmetric and asymmetric waveforms result in straight and curved swimming paths, respectively. Two mechanisms causing spatially asymmetric waveforms have been proposed: an average flagellar curvature and buckling. We image flagella of human sperm tethered with the head to a surface. The waveform is characterized by a fundamental beat frequency and its second harmonic. The superposition of harmonics breaks the beat symmetry temporally rather than spatially. As a result, sperm rotate around the tethering point. The rotation velocity is determined by the second-harmonic amplitude and phase. Stimulation with the female sex hormone progesterone enhances the second-harmonic contribution and, thereby, modulates sperm rotation. Higher beat frequency components exist in other flagellated cells; therefore, this steering mechanism might be widespread and could inspire the design of synthetic microswimmers.
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Affiliation(s)
- Guglielmo Saggiorato
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany
| | - Luis Alvarez
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany.
| | - Jan F Jikeli
- Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Biophysical Imaging, Institute of Innate Immunity, University Hospital Bonn, 53127, Bonn, Germany
| | - U Benjamin Kaupp
- Department of Molecular Sensory Systems, Center of Advanced European Studies and Research (CAESAR), 53175, Bonn, Germany
| | - Gerhard Gompper
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany
| | - Jens Elgeti
- Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany.
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109
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Belovs M, Livanovičs R, Cēbers A. Synchronized rotation in swarms of magnetotactic bacteria. Phys Rev E 2017; 96:042408. [PMID: 29347499 DOI: 10.1103/physreve.96.042408] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 11/07/2022]
Abstract
Self-organizing behavior has been widely reported in both natural and artificial systems, typically distinguishing between temporal organization (synchronization) and spatial organization (swarming). Swarming has been experimentally observed in systems of magnetotactic bacteria under the action of external magnetic fields. Here we present a model of ensembles of magnetotactic bacteria in which hydrodynamic interactions lead to temporal synchronization in addition to the swarming. After a period of stabilization during which the bacteria form a quasiregular hexagonal lattice structure, the entire swarm begins to rotate in a direction opposite to the direction of the rotation of the magnetic field. We thus illustrate an emergent mechanism of macroscopic motion arising from the synchronized microscopic rotations of hydrodynamically interacting bacteria, reminiscent of the recently proposed concept of swarmalators.
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Affiliation(s)
- M Belovs
- MMML Laboratory, Department of Physics, University of Latvia, Zeļļu-23, Rīga, LV-1002, Latvia
| | - R Livanovičs
- MMML Laboratory, Department of Physics, University of Latvia, Zeļļu-23, Rīga, LV-1002, Latvia
| | - A Cēbers
- MMML Laboratory, Department of Physics, University of Latvia, Zeļļu-23, Rīga, LV-1002, Latvia
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110
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111
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Lushi E, Kantsler V, Goldstein RE. Scattering of biflagellate microswimmers from surfaces. Phys Rev E 2017; 96:023102. [PMID: 28950627 DOI: 10.1103/physreve.96.023102] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 11/07/2022]
Abstract
We use a three-bead-spring model to investigate the dynamics of biflagellate microswimmers near a surface. While the primary dynamics and scattering are governed by geometric-dependent direct contact, the fluid flows generated by the swimmer locomotion are important in orienting it toward or away from the surface. Flagellar noise and in particular cell spinning about the main axis help a surface-trapped swimmer escape, whereas the time a swimmer spends at the surface depends on the incident angle. The dynamics results from a nuanced interplay of direct collisions, hydrodynamics, noise, and the swimmer geometry. We show that to correctly capture the dynamics of a biflagellate swimmer, minimal models need to resolve the shape asymmetry.
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Affiliation(s)
- Enkeleida Lushi
- Courant Institute of Mathematical Sciences, New York University, New York 10003, USA
| | - Vasily Kantsler
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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112
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Abstract
Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.
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Affiliation(s)
- François Detcheverry
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
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113
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Nili H, Kheyri M, Abazari J, Fahimniya A, Naji A. Population splitting of rodlike swimmers in Couette flow. SOFT MATTER 2017; 13:4494-4506. [PMID: 28584884 DOI: 10.1039/c7sm00293a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of the shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of the swimming direction for a finite fraction of swimmers from down- to upstream or vice versa, depending on the swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsion-dominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Péclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.
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Affiliation(s)
- Hossein Nili
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran.
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114
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Phototaxis beyond turning: persistent accumulation and response acclimation of the microalga Chlamydomonas reinhardtii. Sci Rep 2017; 7:3447. [PMID: 28615673 PMCID: PMC5471259 DOI: 10.1038/s41598-017-03618-8] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2016] [Accepted: 05/02/2017] [Indexed: 11/08/2022] Open
Abstract
Phototaxis is an important reaction to light displayed by a wide range of motile microorganisms. Flagellated eukaryotic microalgae in particular, like the model organism Chlamydomonas reinhardtii, steer either towards or away from light by a rapid and precisely timed modulation of their flagellar activity. Cell steering, however, is only the beginning of a much longer process which ultimately allows cells to determine their light exposure history. This process is not well understood. Here we present a first quantitative study of the long timescale phototactic motility of Chlamydomonas at both single cell and population levels. Our results reveal that the phototactic strategy adopted by these microorganisms leads to an efficient exposure to light, and that the phototactic response is modulated over typical timescales of tens of seconds. The adaptation dynamics for phototaxis and chlorophyll fluorescence show a striking quantitative agreement, suggesting that photosynthesis controls quantitatively how cells navigate a light field.
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115
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Optimal run-and-tumble-based transportation of a Janus particle with active steering. Proc Natl Acad Sci U S A 2017; 114:E2580-E2589. [PMID: 28292904 DOI: 10.1073/pnas.1616013114] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Although making artificial micrometric swimmers has been made possible by using various propulsion mechanisms, guiding their motion in the presence of thermal fluctuations still remains a great challenge. Such a task is essential in biological systems, which present a number of intriguing solutions that are robust against noisy environmental conditions as well as variability in individual genetic makeup. Using synthetic Janus particles driven by an electric field, we present a feedback-based particle-guiding method quite analogous to the "run-and-tumbling" behavior of Escherichia coli but with a deterministic steering in the tumbling phase: the particle is set to the run state when its orientation vector aligns with the target, whereas the transition to the "steering" state is triggered when it exceeds a tolerance angle [Formula: see text] The active and deterministic reorientation of the particle is achieved by a characteristic rotational motion that can be switched on and off by modulating the ac frequency of the electric field, which is reported in this work. Relying on numerical simulations and analytical results, we show that this feedback algorithm can be optimized by tuning the tolerance angle [Formula: see text] The optimal resetting angle depends on signal to noise ratio in the steering state, and it is shown in the experiment. The proposed method is simple and robust for targeting, despite variability in self-propelling speeds and angular velocities of individual particles.
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116
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Nava-Sedeño JM, Hatzikirou H, Peruani F, Deutsch A. Extracting cellular automaton rules from physical Langevin equation models for single and collective cell migration. J Math Biol 2017; 75:1075-1100. [PMID: 28243720 DOI: 10.1007/s00285-017-1106-9] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2016] [Revised: 01/29/2017] [Indexed: 11/29/2022]
Abstract
Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically. In this paper, we introduce a method to obtain lattice-gas cellular automaton interaction rules from physically-motivated "off-lattice" Langevin equation models for migrating cells. In particular, we consider Langevin equations related to single cell movement (movement of cells independent of each other) and collective cell migration (movement influenced by cell-cell interactions). As examples of collective cell migration, two different alignment mechanisms are studied: polar and nematic alignment. Both kinds of alignment have been observed in biological systems such as swarms of amoebae and myxobacteria. Polar alignment causes cells to align their velocities parallel to each other, whereas nematic alignment drives cells to align either parallel or antiparallel to each other. Under appropriate assumptions, we have derived the LGCA transition probability rule from the steady-state distribution of the off-lattice Fokker-Planck equation. Comparing alignment order parameters between the original Langevin model and the derived LGCA for both mechanisms, we found different areas of agreement in the parameter space. Finally, we discuss potential reasons for model disagreement and propose extensions to the CA rule derivation methodology.
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Affiliation(s)
- J M Nava-Sedeño
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062, Dresden, Germany.
| | - H Hatzikirou
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062, Dresden, Germany.,Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Center for Infection Research, Inhoffenstraße 7, 38124, Braunschweig, Germany
| | - F Peruani
- Laboratoire J. A. Dieudonné, UMR 7351 CNRS, Parc Valrose, Université Côte d'Azur, 06108, Nice Cedex 02, France
| | - A Deutsch
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062, Dresden, Germany
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117
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Zeitz M, Wolff K, Stark H. Active Brownian particles moving in a random Lorentz gas. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:23. [PMID: 28236113 DOI: 10.1140/epje/i2017-11510-0] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Accepted: 02/02/2017] [Indexed: 06/06/2023]
Abstract
Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density [Formula: see text] the ABPs are trapped, their long-time diffusion below [Formula: see text] is strongly influenced by the propulsion speed v0. With increasing v0, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.
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Affiliation(s)
- Maria Zeitz
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany.
| | - Katrin Wolff
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
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118
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Wheeler RJ. Use of chiral cell shape to ensure highly directional swimming in trypanosomes. PLoS Comput Biol 2017; 13:e1005353. [PMID: 28141804 PMCID: PMC5308837 DOI: 10.1371/journal.pcbi.1005353] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Revised: 02/14/2017] [Accepted: 01/10/2017] [Indexed: 11/23/2022] Open
Abstract
Swimming cells typically move along a helical path or undergo longitudinal rotation as they swim, arising from chiral asymmetry in hydrodynamic drag or propulsion bending the swimming path into a helix. Helical paths are beneficial for some forms of chemotaxis, but why asymmetric shape is so prevalent when a symmetric shape would also allow highly directional swimming is unclear. Here, I analyse the swimming of the insect life cycle stages of two human parasites; Trypanosoma brucei and Leishmania mexicana. This showed quantitatively how chirality in T. brucei cell shape confers highly directional swimming. High speed videomicrographs showed that T. brucei, L. mexicana and a T. brucei RNAi morphology mutant have a range of shape asymmetries, from wild-type T. brucei (highly chiral) to L. mexicana (near-axial symmetry). The chiral cells underwent longitudinal rotation while swimming, with more rapid longitudinal rotation correlating with swimming path directionality. Simulation indicated hydrodynamic drag on the chiral cell shape caused rotation, and the predicted geometry of the resulting swimming path matched the directionality of the observed swimming paths. This simulation of swimming path geometry showed that highly chiral cell shape is a robust mechanism through which microscale swimmers can achieve highly directional swimming at low Reynolds number. It is insensitive to random variation in shape or propulsion (biological noise). Highly symmetric cell shape can give highly directional swimming but is at risk of giving futile circular swimming paths in the presence of biological noise. This suggests the chiral T. brucei cell shape (associated with the lateral attachment of the flagellum) may be an adaptation associated with the bloodstream-inhabiting lifestyle of this parasite for robust highly directional swimming. It also provides a plausible general explanation for why swimming cells tend to have strong asymmetries in cell shape or propulsion. Swimming cells often follow a helical swimming path, however the advantage of helical paths over a simple straight line path is not clear. To analyse this phenomenon, I analysed the swimming of the human parasites Trypanosoma brucei (which causes sleeping sickness/trypanosomiasis) and Leishmania mexicana (which causes leishmaniasis). Using new computational methods to determine the three dimensional shape of swimming cells I showed that T. brucei have a helical shape which causes rotation as the cell swims, and the geometry of the resulting swimming path makes the cell movement highly directional. In contrast, L. mexicana are symmetrical, do not rotate, and their swimming paths are curved and have low directionality. Using a T. brucei mutant I showed that the cell structure responsible for the helical shape while swimming is the flagellum attachment zone. This explains a key function of this structure. Finally, simulations showed the phenomenon of rotation while swimming is a way cells can ensure highly directional swimming along a controlled helical path, overcoming random variation in cell shape or propulsion. This provides a general explanation for why swimming cells are often asymmetric and tend to follow helical paths.
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Affiliation(s)
- Richard John Wheeler
- Sir William Dunn School of Pathology, University of Oxford, Oxford, United Kingdom
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- * E-mail:
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119
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Khatami M, Wolff K, Pohl O, Ejtehadi MR, Stark H. Active Brownian particles and run-and-tumble particles separate inside a maze. Sci Rep 2016; 6:37670. [PMID: 27876867 PMCID: PMC5120314 DOI: 10.1038/srep37670] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Accepted: 11/01/2016] [Indexed: 11/09/2022] Open
Abstract
A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.
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Affiliation(s)
- Maryam Khatami
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Katrin Wolff
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Oliver Pohl
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Mohammad Reza Ejtehadi
- Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
- School of Nano-Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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120
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Yang O, Peng Y, Liu Z, Tang C, Xu X, Cheng X. Dynamics of ellipsoidal tracers in swimming algal suspensions. Phys Rev E 2016; 94:042601. [PMID: 27841492 DOI: 10.1103/physreve.94.042601] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2016] [Indexed: 11/07/2022]
Abstract
Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers-the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging the dynamics of passive tracers? Here, we investigated the diffusion of isolated ellipsoids in algal C. reinhardtii suspensions-a model for puller-type active fluids. In combination with our previous results on pusher-type E. coli suspensions [Peng et al., Phys. Rev. Lett. 116, 068303 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.068303], we showed that the dynamics of asymmetric tracers show a profound difference in pushers and pullers due to their rotational degree of freedom. Although the laboratory-frame translation and rotation of ellipsoids are enhanced in both pushers and pullers, similar to spherical tracers, the anisotropic diffusion in the body frame of ellipsoids shows opposite trends in the two classes of active fluids. An ellipsoid diffuses fastest along its major axis when immersed in pullers, whereas it diffuses slowest along the major axis in pushers. This striking difference can be qualitatively explained using a simple hydrodynamic model. In addition, our study on algal suspensions reveals that the influence of the near-field advection of algal swimming flows on the translation and rotation of ellipsoids shows different ranges and strengths. Our work provides not only new insights into universal organizing principles of active fluids, but also a convenient tool for detecting the class of active particles.
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Affiliation(s)
- Ou Yang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Yi Peng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Zhengyang Liu
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Chao Tang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Xinliang Xu
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Xiang Cheng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
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121
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Ilse SE, Holm C, de Graaf J. Surface roughness stabilizes the clustering of self-propelled triangles. J Chem Phys 2016; 145:134904. [PMID: 27782450 DOI: 10.1063/1.4963804] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sven Erik Ilse
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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122
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Barry MT, Rusconi R, Guasto JS, Stocker R. Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton. J R Soc Interface 2016; 12:rsif.2015.0791. [PMID: 26538558 DOI: 10.1098/rsif.2015.0791] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Fluid flow, ubiquitous in natural and man-made environments, has the potential to profoundly impact the transport of microorganisms, including phytoplankton in aquatic habitats and bioreactors. Yet, the effect of ambient flow on the swimming behaviour of phytoplankton has remained poorly understood, largely owing to the difficulty of observing cell-flow interactions at the microscale. Here, we present microfluidic experiments where we tracked individual cells for four species of motile phytoplankton exposed to a spatially non-uniform fluid shear rate, characteristic of many flows in natural and artificial environments. We observed that medium-to-high mean shear rates (1-25 s(-1)) produce heterogeneous cell concentrations in the form of regions of accumulation and regions of depletion. The location of these regions relative to the flow depends on the cells' propulsion mechanism, body shape and flagellar arrangement, as captured by an effective aspect ratio. Species having a large effective aspect ratio accumulated in the high-shear regions, owing to shear-induced alignment of the swimming orientation with the fluid streamlines. Species having an effective aspect ratio close to unity exhibited little preferential accumulation at low-to-moderate flow rates, but strongly accumulated in the low-shear regions under high flow conditions, potentially owing to an active, behavioural response of cells to shear. These observations demonstrate that ambient fluid flow can strongly affect the motility and spatial distribution of phytoplankton and highlight the rich dynamics emerging from the interaction between motility, morphology and flow.
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Affiliation(s)
- Michael T Barry
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Roberto Rusconi
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Jeffrey S Guasto
- Department of Mechanical Engineering, Tufts University, 200 College Avenue, Medford, MA 02155, USA
| | - Roman Stocker
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, Stefano Franscini Platz 5, 8093 Zurich, Switzerland
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123
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Diz-Muñoz A, Romanczuk P, Yu W, Bergert M, Ivanovitch K, Salbreux G, Heisenberg CP, Paluch EK. Steering cell migration by alternating blebs and actin-rich protrusions. BMC Biol 2016; 14:74. [PMID: 27589901 PMCID: PMC5010735 DOI: 10.1186/s12915-016-0294-x] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Accepted: 08/08/2016] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND High directional persistence is often assumed to enhance the efficiency of chemotactic migration. Yet, cells in vivo usually display meandering trajectories with relatively low directional persistence, and the control and function of directional persistence during cell migration in three-dimensional environments are poorly understood. RESULTS Here, we use mesendoderm progenitors migrating during zebrafish gastrulation as a model system to investigate the control of directional persistence during migration in vivo. We show that progenitor cells alternate persistent run phases with tumble phases that result in cell reorientation. Runs are characterized by the formation of directed actin-rich protrusions and tumbles by enhanced blebbing. Increasing the proportion of actin-rich protrusions or blebs leads to longer or shorter run phases, respectively. Importantly, both reducing and increasing run phases result in larger spatial dispersion of the cells, indicative of reduced migration precision. A physical model quantitatively recapitulating the migratory behavior of mesendoderm progenitors indicates that the ratio of tumbling to run times, and thus the specific degree of directional persistence of migration, are critical for optimizing migration precision. CONCLUSIONS Together, our experiments and model provide mechanistic insight into the control of migration directionality for cells moving in three-dimensional environments that combine different protrusion types, whereby the proportion of blebs to actin-rich protrusions determines the directional persistence and precision of movement by regulating the ratio of tumbling to run times.
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Affiliation(s)
- Alba Diz-Muñoz
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, 01307, Germany.
- International Institute of Molecular and Cell Biology, Warsaw, 02-109, Poland.
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Heidelberg, 69117, Germany.
| | - Pawel Romanczuk
- Max Planck Institute for the Physics of Complex Systems, Dresden, 01187, Germany.
- Department of Biology, Institute of Theoretical Biology, Humboldt University, Berlin, 10115, Germany.
| | - Weimiao Yu
- Institute of Molecular and Cell Biology, A-STAR, Singapore, 138673, Singapore
| | - Martin Bergert
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, 01307, Germany
- International Institute of Molecular and Cell Biology, Warsaw, 02-109, Poland
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Heidelberg, 69117, Germany
- Medical Research Council Laboratory for Molecular Cell Biology, University College London, WC1E 6BT, London, UK
| | - Kenzo Ivanovitch
- Medical Research Council Laboratory for Molecular Cell Biology, University College London, WC1E 6BT, London, UK
- Present address: Department of Cardiovascular Development and Repair, Centro Nacional de Investigaciones Cardiovasculares (CNIC), 28029, Madrid, Spain
| | - Guillaume Salbreux
- Max Planck Institute for the Physics of Complex Systems, Dresden, 01187, Germany
- The Francis Crick Institute, Lincoln's Inn Fields Laboratories, 44 Lincolns Inn Fields, London, WC2A 3LY, UK
| | | | - Ewa K Paluch
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, 01307, Germany
- International Institute of Molecular and Cell Biology, Warsaw, 02-109, Poland
- Medical Research Council Laboratory for Molecular Cell Biology, University College London, WC1E 6BT, London, UK
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124
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Lushi E. Stability and dynamics of anisotropically tumbling chemotactic swimmers. Phys Rev E 2016; 94:022414. [PMID: 27627341 DOI: 10.1103/physreve.94.022414] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Indexed: 06/06/2023]
Abstract
Microswimmers such as bacteria perform random walks known as run-and-tumbles to move up chemoattractant gradients and as a result aggregate with others. It is also known that such micro-swimmers can self-organize into macroscopic patterns due to interactions with neighboring cells through the fluidic environment they live in. While the pattern formation resulting from chemotactic and hydrodynamic interactions separately and together have been previously investigated, the effect of the anisotropy in the tumbles of microswimmers has been unexplored. Here we show through linear analysis and full nonlinear simulations that the slight anisotropy in the individual swimmer tumbles can alter the collective pattern formation in nontrivial ways. We show that tumbling anisotropy diminishes the magnitude of the chemotactic aggregates but may result in more such aggregation peaks.
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Affiliation(s)
- Enkeleida Lushi
- School of Engineering, Brown University, Providence, Rhode Island 02912, USA and Courant Institute of Mathematical Sciences, New York, New York, 10012, USA
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125
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Martin M, Barzyk A, Bertin E, Peyla P, Rafai S. Photofocusing: Light and flow of phototactic microswimmer suspension. Phys Rev E 2016; 93:051101. [PMID: 27300822 DOI: 10.1103/physreve.93.051101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Indexed: 05/12/2023]
Abstract
We explore in this paper the phenomenon of photofocusing: a coupling between flow vorticity and biased swimming of microalgae toward a light source that produces a focusing of the microswimmer suspension. We combine experiments that investigate the stationary state of this phenomenon as well as the transition regime with analytical and numerical modeling. We show that the experimentally observed scalings on the width of the focalized region and the establishment length as a function of the flow velocity are well described by a simple theoretical model.
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Affiliation(s)
- Matthieu Martin
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, F-38000 Grenoble, France
| | - Alexandre Barzyk
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, F-38000 Grenoble, France
| | - Eric Bertin
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, F-38000 Grenoble, France
| | - Philippe Peyla
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, F-38000 Grenoble, France
| | - Salima Rafai
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes, CNRS, F-38000 Grenoble, France
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126
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Witkowski O, Ikegami T. Emergence of Swarming Behavior: Foraging Agents Evolve Collective Motion Based on Signaling. PLoS One 2016; 11:e0152756. [PMID: 27119340 PMCID: PMC4847771 DOI: 10.1371/journal.pone.0152756] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Accepted: 03/18/2016] [Indexed: 11/18/2022] Open
Abstract
Swarming behavior is common in biology, from cell colonies to insect swarms and bird flocks. However, the conditions leading to the emergence of such behavior are still subject to research. Since Reynolds' boids, many artificial models have reproduced swarming behavior, focusing on details ranging from obstacle avoidance to the introduction of fixed leaders. This paper presents a model of evolved artificial agents, able to develop swarming using only their ability to listen to each other's signals. The model simulates a population of agents looking for a vital resource they cannot directly detect, in a 3D environment. Instead of a centralized algorithm, each agent is controlled by an artificial neural network, whose weights are encoded in a genotype and adapted by an original asynchronous genetic algorithm. The results demonstrate that agents progressively evolve the ability to use the information exchanged between each other via signaling to establish temporary leader-follower relations. These relations allow agents to form swarming patterns, emerging as a transient behavior that improves the agents' ability to forage for the resource. Once they have acquired the ability to swarm, the individuals are able to outperform the non-swarmers at finding the resource. The population hence reaches a neutral evolutionary space which leads to a genetic drift of the genotypes. This reductionist approach to signal-based swarming not only contributes to shed light on the minimal conditions for the evolution of a swarming behavior, but also more generally it exemplifies the effect communication can have on optimal search patterns in collective groups of individuals.
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Affiliation(s)
- Olaf Witkowski
- Department of Interdisciplinary Studies, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku 153-8902 Tokyo, Japan
- ELSI Origins Network, Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-1 Ookayama, Meguro-ku 152-8550 Tokyo, Japan
- * E-mail:
| | - Takashi Ikegami
- Department of Interdisciplinary Studies, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku 153-8902 Tokyo, Japan
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127
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de Graaf J, Menke H, Mathijssen AJTM, Fabritius M, Holm C, Shendruk TN. Lattice-Boltzmann hydrodynamics of anisotropic active matter. J Chem Phys 2016; 144:134106. [DOI: 10.1063/1.4944962] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Henri Menke
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | | | - Marc Fabritius
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Tyler N. Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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128
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Barsanti L, Coltelli P, Evangelista V, Frassanito AM, Gualtieri P. Swimming patterns of the quadriflagellate Tetraflagellochloris mauritanica (Chlamydomonadales, Chlorophyceae). JOURNAL OF PHYCOLOGY 2016; 52:209-218. [PMID: 27037586 DOI: 10.1111/jpy.12384] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Accepted: 12/04/2015] [Indexed: 06/05/2023]
Abstract
Chlamydomonadales are elective subjects for the investigation of the problems related to locomotion and transport in biological fluid dynamics, whose resolution could enhance searching efficiency and assist in the avoidance of dangerous environments. In this paper, we elucidate the swimming behavior of Tetraflagellochloris mauritanica, a unicellular-multicellular alga belonging to the order Chlamydomonadales. This quadriflagellate alga has a complex swimming motion consisting of alternating swimming phases connected by in-place random reorientations and resting phases. It is capable of both forward and backward swimming, both being normal modes of swimming. The complex swimming behavior resembles the run-and-tumble motion of peritrichous bacteria, with in-place reorientation taking the place of tumbles. In the forward swimming, T. mauritanica shows a very efficient flagellar beat, with undulatory retrograde waves that run along the flagella to their tip. In the backward swimming, the flagella show a nonstereotypical synchronization mode, with a pattern that does not fit any of the modes present in the other Chlamydomonadales so far investigated.
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Affiliation(s)
- Laura Barsanti
- Istituto di Biofisica, CNR, Via Moruzzi 1, Pisa, 56124, Italy
| | - Primo Coltelli
- Istituto di Scienza e Tecnologia Informazione, CNR, Via Moruzzi 1, Pisa, 56124, Italy
| | | | | | - Paolo Gualtieri
- Istituto di Biofisica, CNR, Via Moruzzi 1, Pisa, 56124, Italy
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129
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Brumley DR, Polin M, Pedley TJ, Goldstein RE. Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin. J R Soc Interface 2016; 12:20141358. [PMID: 26040592 PMCID: PMC4528573 DOI: 10.1098/rsif.2014.1358] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour—possibly influenced by both mechanical interactions and direct biological regulation—is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.
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Affiliation(s)
- Douglas R Brumley
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Marco Polin
- Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Timothy J Pedley
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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130
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Nasouri B, Elfring GJ. Hydrodynamic interactions of cilia on a spherical body. Phys Rev E 2016; 93:033111. [PMID: 27078451 DOI: 10.1103/physreve.93.033111] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 12/15/2022]
Abstract
Microorganisms develop coordinated beating patterns on surfaces lined with cilia known as metachronal waves. For a chain of cilia attached to a flat ciliate, it has been shown that hydrodynamic interactions alone can lead the system to synchronize. However, several microorganisms possess a curve-shaped ciliate body and so to understand the effect of this geometry on the formation of metachronal waves, we evaluate the hydrodynamic interactions of cilia near a large spherical body. Using a minimal model, we show that for a chain of cilia around the sphere, the natural periodicity in the geometry leads the system to synchronize. We also report an emergent wavelike behavior when an asymmetry is introduced to the system.
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Affiliation(s)
- Babak Nasouri
- Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada
| | - Gwynn J Elfring
- Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada
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131
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Rein M, Heinß N, Schmid F, Speck T. Collective Behavior of Quorum-Sensing Run-and-Tumble Particles under Confinement. PHYSICAL REVIEW LETTERS 2016; 116:058102. [PMID: 26894736 DOI: 10.1103/physrevlett.116.058102] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Indexed: 06/05/2023]
Abstract
We study a generic model for quorum-sensing bacteria in circular confinement. Every bacterium produces signaling molecules, the local concentration of which triggers a response when a certain threshold is reached. If this response lowers the motility, then an aggregation of bacteria occurs which differs fundamentally from standard motility-induced phase separation due to the long-ranged nature of the concentration of signal molecules. We analyze this phenomenon analytically and by numerical simulations employing two different protocols leading to stationary cluster and ring morphologies, respectively.
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Affiliation(s)
- Markus Rein
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Nike Heinß
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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132
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Küchler N, Löwen H, Menzel AM. Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields. Phys Rev E 2016; 93:022610. [PMID: 26986380 DOI: 10.1103/physreve.93.022610] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Indexed: 06/05/2023]
Abstract
Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an "egglike" shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.
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Affiliation(s)
- Niklas Küchler
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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133
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Kirkegaard JB, Marron AO, Goldstein RE. Motility of Colonial Choanoflagellates and the Statistics of Aggregate Random Walkers. PHYSICAL REVIEW LETTERS 2016; 116:038102. [PMID: 26849616 PMCID: PMC7616083 DOI: 10.1103/physrevlett.116.038102] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2015] [Indexed: 06/05/2023]
Abstract
We illuminate the nature of the three-dimensional random walks of microorganisms composed of individual organisms adhered together. Such aggregate random walkers are typified by choanoflagellates, eukaryotes that are the closest living relatives of animals. In the colony-forming species Salpingoeca rosetta we show that the beating of each flagellum is stochastic and uncorrelated with others, and the vectorial sum of the flagellar propulsion manifests as stochastic helical swimming. A quantitative theory for these results is presented and species variability discussed.
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Affiliation(s)
- Julius B Kirkegaard
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Alan O Marron
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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134
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Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells. Proc Natl Acad Sci U S A 2015; 112:15904-9. [PMID: 26655343 DOI: 10.1073/pnas.1515159112] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Rheotaxis, the directed response to fluid velocity gradients, has been shown to facilitate stable upstream swimming of mammalian sperm cells along solid surfaces, suggesting a robust physical mechanism for long-distance navigation during fertilization. However, the dynamics by which a human sperm orients itself relative to an ambient flow is poorly understood. Here, we combine microfluidic experiments with mathematical modeling and 3D flagellar beat reconstruction to quantify the response of individual sperm cells in time-varying flow fields. Single-cell tracking reveals two kinematically distinct swimming states that entail opposite turning behaviors under flow reversal. We constrain an effective 2D model for the turning dynamics through systematic large-scale parameter scans, and find good quantitative agreement with experiments at different shear rates and viscosities. Using a 3D reconstruction algorithm to identify the flagellar beat patterns causing left or right turning, we present comprehensive 3D data demonstrating the rolling dynamics of freely swimming sperm cells around their longitudinal axis. Contrary to current beliefs, this 3D analysis uncovers ambidextrous flagellar waveforms and shows that the cell's turning direction is not defined by the rolling direction. Instead, the different rheotactic turning behaviors are linked to a broken mirror symmetry in the midpiece section, likely arising from a buckling instability. These results challenge current theoretical models of sperm locomotion.
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135
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Quaranta G, Aubin-Tam ME, Tam D. Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella. PHYSICAL REVIEW LETTERS 2015; 115:238101. [PMID: 26684142 DOI: 10.1103/physrevlett.115.238101] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 05/27/2023]
Abstract
The influence of hydrodynamic forces on eukaryotic flagella synchronization is investigated by triggering phase locking between a controlled external flow and the flagella of C. reinhardtii. Hydrodynamic forces required for synchronization are over an order of magnitude larger than hydrodynamic forces experienced in physiological conditions. Our results suggest that synchronization is due instead to coupling through cell internal fibers connecting the flagella. This conclusion is confirmed by observations of the vfl3 mutant, with impaired mechanical connection between the flagella.
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Affiliation(s)
- Greta Quaranta
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
| | - Marie-Eve Aubin-Tam
- Department of Bionanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Daniel Tam
- Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CD Delft, Netherlands
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136
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Patteson AE, Gopinath A, Goulian M, Arratia PE. Running and tumbling with E. coli in polymeric solutions. Sci Rep 2015; 5:15761. [PMID: 26507950 PMCID: PMC4938119 DOI: 10.1038/srep15761] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2015] [Accepted: 09/29/2015] [Indexed: 12/24/2022] Open
Abstract
Run-and-tumble motility is widely used by swimming microorganisms including numerous prokaryotic and eukaryotic organisms. Here, we experimentally investigate the run-and-tumble dynamics of the bacterium E. coli in polymeric solutions. We find that even small amounts of polymer in solution can drastically change E. coli dynamics: cells tumble less and their velocity increases, leading to an enhancement in cell translational diffusion and a sharp decline in rotational diffusion. We show that suppression of tumbling is due to fluid viscosity while the enhancement in swimming speed is mainly due to fluid elasticity. Visualization of single fluorescently labeled DNA polymers reveals that the flow generated by individual E. coli is sufficiently strong to stretch polymer molecules and induce elastic stresses in the fluid, which in turn can act on the cell in such a way to enhance its transport. Our results show that the transport and spread of chemotactic cells can be independently modified and controlled by the fluid material properties.
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Affiliation(s)
- A E Patteson
- Department of Mechanical Engineering &Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
| | - A Gopinath
- Department of Mechanical Engineering &Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104.,School of Engineering, University of California Merced, Merced, CA 95343
| | - M Goulian
- Department of Biology, University of Pennsylvania, Philadelphia, PA 19104
| | - P E Arratia
- Department of Mechanical Engineering &Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
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137
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Sandoval M, Jimenez A. Two-dimensional motion of Brownian swimmers in linear flows. J Biol Phys 2015; 42:199-212. [PMID: 26428909 DOI: 10.1007/s10867-015-9401-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2015] [Accepted: 09/07/2015] [Indexed: 11/28/2022] Open
Abstract
The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.
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Affiliation(s)
- Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico, Distrito Federal, 09340, Mexico.
| | - Alonso Jimenez
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico, Distrito Federal, 09340, Mexico
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138
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Funfak A, Fisch C, Abdel Motaal HT, Diener J, Combettes L, Baroud CN, Dupuis-Williams P. Paramecium swimming and ciliary beating patterns: a study on four RNA interference mutations. Integr Biol (Camb) 2015; 7:90-100. [PMID: 25383612 DOI: 10.1039/c4ib00181h] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Paramecium cells swim and feed by beating their thousands of cilia in coordinated patterns. The organization of these patterns and its relationship with cell motility has been the subject of a large body of work, particularly as a model for ciliary beating in human organs where similar organization is seen. However the rapid motion of the cells makes quantitative measurements very challenging. Here we provide detailed measurements of the swimming of Paramecium cells from high-speed video at high magnification, as they move in microfluidic channels. An image analysis protocol allows us to decouple the cell movement from the motion of the cilia, thus allowing us to measure the ciliary beat frequency (CBF) and the spatio-temporal organization into metachronal waves along the cell periphery. Two distinct values of the CBF appear at different regions of the cell: most of the cilia beat in the range of 15 to 45 Hz, while the cilia in the peristomal region beat at almost double the frequency. The body and peristomal CBF display a nearly linear relation with the swimming velocity. Moreover the measurements do not display a measurable correlation between the swimming velocity and the metachronal wave velocity on the cell periphery. These measurements are repeated for four RNAi silenced mutants, where proteins specific to the cilia or to their connection to the cell base are depleted. We find that the mutants whose ciliary structure is affected display similar swimming to the control cells albeit with a reduced efficiency, while the mutations that affect the cilia's anchoring to the cell lead to strongly reduced ability to swim. This reduction in motility can be related to a loss of coordination between the ciliary beating in different parts of the cell.
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Affiliation(s)
- Anette Funfak
- Department of Mechanics, LadHyX, Ecole Polytechnique-CNRS, F-91128 Palaiseau, France.
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139
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Hadjivasiliou Z, Iwasa Y, Pomiankowski A. Cell-cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes. J R Soc Interface 2015; 12:20150342. [PMID: 26156301 PMCID: PMC4535405 DOI: 10.1098/rsif.2015.0342] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Accepted: 06/16/2015] [Indexed: 11/29/2022] Open
Abstract
While sex requires two parents, there is no obvious need for them to be differentiated into distinct mating types or sexes. Yet this is the predominate state of nature. Here, we argue that mating types could play a decisive role because they prevent the apparent inevitability of self-stimulation during sexual signalling. We rigorously assess this hypothesis by developing a model for signaller-detector dynamics based on chemical diffusion, chemotaxis and cell movement. Our model examines the conditions under which chemotaxis improves partner finding. Varying parameter values within ranges typical of protists and their environments, we show that simultaneous secretion and detection of a single chemoattractant can cause a multifold movement impediment and severely hinder mate finding. Mutually exclusive roles result in faster pair formation, even when cells conferring the same roles cannot pair up. This arrangement also allows the separate mating types to optimize their signalling or detecting roles, which is effectively impossible for cells that are both secretors and detectors. Our findings suggest that asymmetric roles in sexual chemotaxis (and possibly other forms of sexual signalling) are crucial, even without morphological differences, and may underlie the evolution of gametic differentiation among both mating types and sexes.
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Affiliation(s)
- Zena Hadjivasiliou
- Centre for Mathematics, Physics and Engineering in the Life Sciences and Experimental Biology (CoMPLEX), University College London, Gower Street, London WC1E 6BT, UK Department of Genetics, Evolution and Environment, University College London, Gower Street, London WC1E 6BT, UK
| | - Yoh Iwasa
- Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan
| | - Andrew Pomiankowski
- Centre for Mathematics, Physics and Engineering in the Life Sciences and Experimental Biology (CoMPLEX), University College London, Gower Street, London WC1E 6BT, UK Department of Genetics, Evolution and Environment, University College London, Gower Street, London WC1E 6BT, UK
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140
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ten Hagen B, Wittkowski R, Takagi D, Kümmel F, Bechinger C, Löwen H. Can the self-propulsion of anisotropic microswimmers be described by using forces and torques? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194110. [PMID: 25923010 DOI: 10.1088/0953-8984/27/19/194110] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The self-propulsion of artificial and biological microswimmers (or active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e. that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand resistance matrix and formally external effective forces and torques. This is consistent with experimental findings on the circular motion of artificial asymmetric microswimmers driven by self-diffusiophoresis. The concept of effective self-propulsion forces and torques significantly facilitates the understanding of the swimming paths, e.g. for a microswimmer under gravity. However, this concept has its limitations when the self-propulsion mechanism of a swimmer is disturbed either by another particle in its close vicinity or by interactions with obstacles, such as a wall.
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Affiliation(s)
- Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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141
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Elgeti J, Winkler RG, Gompper G. Physics of microswimmers--single particle motion and collective behavior: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:056601. [PMID: 25919479 DOI: 10.1088/0034-4885/78/5/056601] [Citation(s) in RCA: 647] [Impact Index Per Article: 71.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.
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Affiliation(s)
- J Elgeti
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
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142
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Soto R, Golestanian R. Self-assembly of active colloidal molecules with dynamic function. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052304. [PMID: 26066174 DOI: 10.1103/physreve.91.052304] [Citation(s) in RCA: 48] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2015] [Indexed: 05/27/2023]
Abstract
Catalytically active colloids maintain nonequilibrium conditions in which they produce and deplete chemicals and hence effectively act as sources and sinks of molecules. While individual colloids that are symmetrically coated do not exhibit any form of dynamical activity, the concentration fields resulting from their chemical activity decay as 1/r and produce gradients that attract or repel other colloids depending on their surface chemistry and ambient variables. This results in a nonequilibrium analog of ionic systems, but with the remarkable novel feature of action-reaction symmetry breaking. We study solutions of such chemically active colloids in dilute conditions when they join up to form molecules via generalized ionic bonds and discuss how we can achieve structures with time-dependent functionality. In particular, we study a molecule that adopts a spontaneous oscillatory pattern of conformations and another that exhibits a run-and-tumble dynamics similar to bacteria. Our study shows that catalytically active colloids could be used for designing self-assembled structures that possess dynamical functionalities that are determined by their prescribed three-dimensional structures, a strategy that follows the design principle of proteins.
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Affiliation(s)
- Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas Universidad de Chile, Av. Blanco Encalada 2008, Santiago, Chile
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
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143
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Tung CK, Hu L, Fiore AG, Ardon F, Hickman DG, Gilbert RO, Suarez SS, Wu M. Microgrooves and fluid flows provide preferential passageways for sperm over pathogen Tritrichomonas foetus. Proc Natl Acad Sci U S A 2015; 112:5431-6. [PMID: 25870286 PMCID: PMC4418881 DOI: 10.1073/pnas.1500541112] [Citation(s) in RCA: 64] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Successful mammalian reproduction requires that sperm migrate through a long and convoluted female reproductive tract before reaching oocytes. For many years, fertility studies have focused on biochemical and physiological requirements of sperm. Here we show that the biophysical environment of the female reproductive tract critically guides sperm migration, while at the same time preventing the invasion of sexually transmitted pathogens. Using a microfluidic model, we demonstrate that a gentle fluid flow and microgrooves, typically found in the female reproductive tract, synergistically facilitate bull sperm migration toward the site of fertilization. In contrast, a flagellated sexually transmitted bovine pathogen, Tritrichomonas foetus, is swept downstream under the same conditions. We attribute the differential ability of sperm and T. foetus to swim against flow to the distinct motility types of sperm and T. foetus; specifically, sperm swim using a posterior flagellum and are near-surface swimmers, whereas T. foetus swims primarily via three anterior flagella and demonstrates much lower attraction to surfaces. This work highlights the importance of biophysical cues within the female reproductive tract in the reproductive process and provides insight into coevolution of males and females to promote fertilization while suppressing infection. Furthermore, the results provide previously unidentified directions for the development of in vitro fertilization devices and contraceptives.
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Affiliation(s)
| | - Lian Hu
- Biomedical Sciences, and Family Planning Research Institute, Center of Reproductive Medicine, Tongji Medical College, Huazhong University of Science and Technology, 430030 Wuhan, China
| | | | | | | | | | | | - Mingming Wu
- Departments of Biological and Environmental Engineering,
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144
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Kaiser A, Sokolov A, Aranson IS, Lowen H. Mechanisms of Carrier Transport Induced by a Microswimmer Bath. IEEE Trans Nanobioscience 2015; 14:260-6. [DOI: 10.1109/tnb.2014.2361652] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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145
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de Graaf J, Rempfer G, Holm C. Diffusiophoretic Self-Propulsion for Partially Catalytic Spherical Colloids. IEEE Trans Nanobioscience 2015; 14:272-88. [DOI: 10.1109/tnb.2015.2403255] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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146
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Romanczuk P, Salbreux G. Optimal chemotaxis in intermittent migration of animal cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042720. [PMID: 25974540 DOI: 10.1103/physreve.91.042720] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2014] [Indexed: 06/04/2023]
Abstract
Animal cells can sense chemical gradients without moving and are faced with the challenge of migrating towards a target despite noisy information on the target position. Here we discuss optimal search strategies for a chaser that moves by switching between two phases of motion ("run" and "tumble"), reorienting itself towards the target during tumble phases, and performing persistent migration during run phases. We show that the chaser average run time can be adjusted to minimize the target catching time or the spatial dispersion of the chasers. We obtain analytical results for the catching time and for the spatial dispersion in the limits of small and large ratios of run time to tumble time and scaling laws for the optimal run times. Our findings have implications for optimal chemotactic strategies in animal cell migration.
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Affiliation(s)
- P Romanczuk
- Department of Ecology and Evolutionary Biology, Princeton University, New Jersey 80544, USA
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany
| | - G Salbreux
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187 Dresden, Germany
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147
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Andersen A, Wadhwa N, Kiørboe T. Quiet swimming at low Reynolds number. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042712. [PMID: 25974532 DOI: 10.1103/physreve.91.042712] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
The stresslet provides a simple model of the flow created by a small, freely swimming and neutrally buoyant aquatic organism and shows that the far field fluid disturbance created by such an organism in general decays as one over distance squared. Here we discuss a quieter swimming mode that eliminates the stresslet component of the flow and leads to a faster spatial decay of the fluid disturbance described by a force quadrupole that decays as one over distance cubed. Motivated by recent experimental results on fluid disturbances due to small aquatic organisms, we demonstrate that a three-Stokeslet model of a swimming organism which uses breast stroke type kinematics is an example of such a quiet swimmer. We show that the fluid disturbance in both the near field and the far field is significantly reduced by appropriately arranging the propulsion apparatus, and we find that the far field power laws are valid surprisingly close to the organism. Finally, we discuss point force models as a general framework for hypothesis generation and experimental exploration of fluid mediated predator-prey interactions in the planktonic world.
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Affiliation(s)
- Anders Andersen
- Department of Physics and Centre for Ocean Life, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Navish Wadhwa
- Department of Physics and Centre for Ocean Life, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Thomas Kiørboe
- National Institute for Aquatic Resources and Centre for Ocean Life, Technical University of Denmark, DK-2920 Charlottenlund, Denmark
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148
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Bennett RR, Golestanian R. A steering mechanism for phototaxis in Chlamydomonas. J R Soc Interface 2015; 12:20141164. [PMID: 25589576 PMCID: PMC4345482 DOI: 10.1098/rsif.2014.1164] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Accepted: 12/16/2014] [Indexed: 11/12/2022] Open
Abstract
Chlamydomonas shows both positive and negative phototaxis. It has a single eyespot near its equator, and as the cell rotates during the forward motion, the light signal received by the eyespot varies. We use a simple mechanical model of Chlamydomonas that couples the flagellar beat pattern to the light intensity at the eyespot to demonstrate a mechanism for phototactic steering that is consistent with observations. The direction of phototaxis is controlled by a parameter in our model, and the steering mechanism is robust to noise. Our model shows switching between directed phototaxis when the light is on and run-and-tumble behaviour in the dark.
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Affiliation(s)
- Rachel R Bennett
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
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149
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Kavre I, Vilfan A, Babič D. Hydrodynamic synchronization of autonomously oscillating optically trapped particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:031002. [PMID: 25871041 DOI: 10.1103/physreve.91.031002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Indexed: 06/04/2023]
Abstract
Ellipsoidal micron-sized colloidal particles can oscillate spontaneously when trapped in a focused laser beam. If two oscillating particles are held in proximity their oscillations synchronize through hydrodynamic interactions. The degree of synchronization depends on the distance between the oscillators and on their orientation. Due to the anisotropic nature of hydrodynamic coupling the synchronization is strongest when particles are arranged along the direction of oscillations. Similar behavior is observed for many oscillating particles arranged in a row. Experimental observations are well reproduced with a model that uses a phenomenological description of the optical force and hydrodynamic interactions. Our results show that oscillating ellipsoidal particles can serve as a model system for studying hydrodynamic synchronization between biological cilia.
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Affiliation(s)
- Ivna Kavre
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Andrej Vilfan
- J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| | - Dušan Babič
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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150
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Colin R, Zhang R, Wilson LG. Fast, high-throughput measurement of collective behaviour in a bacterial population. J R Soc Interface 2015; 11:20140486. [PMID: 25030384 DOI: 10.1098/rsif.2014.0486] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards 'a better life'. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s(-1) can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.
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Affiliation(s)
- R Colin
- The Rowland Institute at Harvard, 100 Edwin H. Land Boulevard, Cambridge, MA 02142, USA
| | - R Zhang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - L G Wilson
- The Rowland Institute at Harvard, 100 Edwin H. Land Boulevard, Cambridge, MA 02142, USA
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