1
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Klimek A, Mondal D, Block S, Sharma P, Netz RR. Data-driven classification of individual cells by their non-Markovian motion. Biophys J 2024; 123:1173-1183. [PMID: 38515300 PMCID: PMC11140416 DOI: 10.1016/j.bpj.2024.03.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 03/11/2024] [Accepted: 03/18/2024] [Indexed: 03/23/2024] Open
Abstract
We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.
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Affiliation(s)
- Anton Klimek
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Debasmita Mondal
- Department of Physics, Indian Institute of Science, Bangalore, India; James Franck Institute, University of Chicago, Chicago, Illinois
| | - Stephan Block
- Institut für Chemie und Biochemie, Freie Universität Berlin, Berlin, Germany
| | - Prerna Sharma
- Department of Physics, Indian Institute of Science, Bangalore, India; Department of Bioengineering, Indian Institute of Science, Bangalore, India
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany.
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2
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Kurzthaler C, Zhao Y, Zhou N, Schwarz-Linek J, Devailly C, Arlt J, Huang JD, Poon WCK, Franosch T, Tailleur J, Martinez VA. Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli. PHYSICAL REVIEW LETTERS 2024; 132:038302. [PMID: 38307047 DOI: 10.1103/physrevlett.132.038302] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 11/29/2023] [Accepted: 12/01/2023] [Indexed: 02/04/2024]
Abstract
We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.
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Affiliation(s)
- Christina Kurzthaler
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Yongfeng Zhao
- Center for Soft Condensed Matter Physics and Interdisciplinary Research and School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- School of Biomedical Sciences, Li Ka Shing Faculty of Medicine, University of Hong Kong, Pok Fu Lam, Hong Kong, China
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Nan Zhou
- ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311200, China
| | - Jana Schwarz-Linek
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Clemence Devailly
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Jochen Arlt
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Jian-Dong Huang
- School of Biomedical Sciences, Li Ka Shing Faculty of Medicine, University of Hong Kong, Pok Fu Lam, Hong Kong, China
- CAS Key Laboratory of Quantitative Engineering Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Wilson C K Poon
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Julien Tailleur
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
| | - Vincent A Martinez
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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3
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Villa-Torrealba A, Navia S, Soto R. Kinetic modeling of the chemotactic process in run-and-tumble bacteria. Phys Rev E 2023; 107:034605. [PMID: 37072994 DOI: 10.1103/physreve.107.034605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 03/14/2023] [Indexed: 04/20/2023]
Abstract
The chemotactic process of run-and-tumble bacteria results from modulating the tumbling rate in response to changes in chemoattractant gradients felt by the bacteria. The response has a characteristic memory time and is subject to important fluctuations. These ingredients are considered in a kinetic description of chemotaxis, allowing the computation of the stationary mobility and the relaxation times needed to reach the steady state. For large memory times, these relaxation times become large, implying that finite-time measurements give rise to nonmonotonic currents as a function of the imposed chemoattractant gradient, contrary to the stationary regime where the response is monotonic. The case of an inhomogeneous signal is analyzed. Contrary to the usual Keller-Segel model, the response is nonlocal, and the bacterial profile is smoothed with a characteristic length that grows with the memory time. Finally, the case of traveling signals is considered, where appreciable differences appear compared to memoryless chemotactic descriptions.
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Affiliation(s)
- Andrea Villa-Torrealba
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Simón Navia
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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4
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Dubay MM, Acres J, Riekeles M, Nadeau JL. Recent advances in experimental design and data analysis to characterize prokaryotic motility. J Microbiol Methods 2023; 204:106658. [PMID: 36529156 DOI: 10.1016/j.mimet.2022.106658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/13/2022] [Accepted: 12/13/2022] [Indexed: 12/23/2022]
Abstract
Bacterial motility plays a key role in important cell processes such as chemotaxis and biofilm formation, but is challenging to quantify due to the small size of the individual microorganisms and the complex interplay of biological and physical factors that influence motility phenotypes. Swimming, the first type of motility described in bacteria, still remains largely unquantified. Light microscopy has enabled qualitative characterization of swimming patterns seen in different strains, such as run and tumble, run-reverse-flick, run and slow, stop and coil, and push and pull, which has allowed for elucidation of the underlying physics. However, quantifying these behaviors (e.g., identifying run distances and speeds, turn angles and behavior by surfaces or cell-cell interactions) remains a challenging task. A qualitative and quantitative understanding of bacterial motility is needed to bridge the gap between experimentation, omics analysis, and bacterial motility theory. In this review, we discuss the strengths and limitations of how phase contrast microscopy, fluorescence microscopy, and digital holographic microscopy have been used to quantify bacterial motility. Approaches to automated software analysis, including cell recognition, tracking, and track analysis, are also discussed with a view to providing a guide for experimenters to setting up the appropriate imaging and analysis system for their needs.
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Affiliation(s)
- Megan Marie Dubay
- Department of Physics, Portland State University, 1719 SW 10(th) Ave., Portland, OR 97201, United States of America
| | - Jacqueline Acres
- Department of Physics, Portland State University, 1719 SW 10(th) Ave., Portland, OR 97201, United States of America
| | - Max Riekeles
- Astrobiology Group, Center of Astronomy and Astrophysics, Technical University Berlin, Hardenbergstraße 36A, 10623 Berlin, Germany
| | - Jay L Nadeau
- Department of Physics, Portland State University, 1719 SW 10(th) Ave., Portland, OR 97201, United States of America.
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5
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Abstract
A huge number of bacterial species are motile by flagella, which allow them to actively move toward favorable environments and away from hazardous areas and to conquer new habitats. The general perception of flagellum-mediated movement and chemotaxis is dominated by the Escherichia coli paradigm, with its peritrichous flagellation and its famous run-and-tumble navigation pattern, which has shaped the view on how bacteria swim and navigate in chemical gradients. However, a significant amount-more likely the majority-of bacterial species exhibit a (bi)polar flagellar localization pattern instead of lateral flagella. Accordingly, these species have evolved very different mechanisms for navigation and chemotaxis. Here, we review the earlier and recent findings on the various modes of motility mediated by polar flagella. Expected final online publication date for the Annual Review of Microbiology, Volume 76 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Kai M Thormann
- Institute of Microbiology and Molecular Biology, Justus Liebig University Gießen, Gießen, Germany;
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany;
| | - Marco J Kühn
- Institute of Bioengineering and Global Health Institute, School of Life Sciences, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;
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6
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Nakamura K, Kobayashi TJ. Connection between the Bacterial Chemotactic Network and Optimal Filtering. PHYSICAL REVIEW LETTERS 2021; 126:128102. [PMID: 33834835 DOI: 10.1103/physrevlett.126.128102] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.
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Affiliation(s)
- Kento Nakamura
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan
| | - Tetsuya J Kobayashi
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan
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7
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Mitterwallner BG, Schreiber C, Daldrop JO, Rädler JO, Netz RR. Non-Markovian data-driven modeling of single-cell motility. Phys Rev E 2021; 101:032408. [PMID: 32289977 DOI: 10.1103/physreve.101.032408] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 01/07/2020] [Indexed: 01/23/2023]
Abstract
Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extracted memory function we formulate a generalized exactly solvable cell migration model which indicates that negative friction generates cell persistence over long timescales. The nonequilibrium character of cell motion is investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model that involves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process.
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Affiliation(s)
- Bernhard G Mitterwallner
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Christoph Schreiber
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Jan O Daldrop
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Joachim O Rädler
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany and Physik Fakultät, Ludwig Maximilians Universität, 80539 München, Germany
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8
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Valderrama-Gómez MÁ, Schomer RA, Savageau MA, Parales RE. TaxisPy: A Python-based software for the quantitative analysis of bacterial chemotaxis. J Microbiol Methods 2020; 175:105918. [PMID: 32512119 DOI: 10.1016/j.mimet.2020.105918] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 04/09/2020] [Accepted: 04/10/2020] [Indexed: 10/24/2022]
Abstract
Several species of bacteria are able to modify their swimming behavior in response to chemical attractants or repellents. Methods for the quantitative analysis of bacterial chemotaxis such as quantitative capillary assays are tedious and time-consuming. Computer-based video analysis of swimming bacteria represents a valuable method to directly assess their chemotactic response. Even though multiple studies have used this approach to elucidate various aspects of bacterial chemotaxis, to date, no computer software for such analyses is freely available. Here, we introduce TaxisPy, a Python-based software for the quantitative analysis of bacterial chemotaxis. The software comes with an intuitive graphical user interface and can be accessed easily through Docker on any operating system. Using a video of freely swimming cells as input, TaxisPy estimates the culture's average tumbling frequency over time. We demonstrate the utility of the software by assessing the effect of different concentrations of the attractant shikimate on the swimming behavior of Pseudomonas putida F1 and by capturing the adaptation process that Escherichia coli undergoes after being exposed to l-aspartate.
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Affiliation(s)
- Miguel Á Valderrama-Gómez
- Department of Microbiology & Molecular Genetics, College of Biological Sciences, University of California, Davis, USA.
| | - Rebecca A Schomer
- Department of Microbiology & Molecular Genetics, College of Biological Sciences, University of California, Davis, USA
| | - Michael A Savageau
- Department of Microbiology & Molecular Genetics, College of Biological Sciences, University of California, Davis, USA; Department of Biomedical Engineering, University of California, Davis, USA
| | - Rebecca E Parales
- Department of Microbiology & Molecular Genetics, College of Biological Sciences, University of California, Davis, USA
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9
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Villa-Torrealba A, Chávez-Raby C, de Castro P, Soto R. Run-and-tumble bacteria slowly approaching the diffusive regime. Phys Rev E 2020; 101:062607. [PMID: 32688514 DOI: 10.1103/physreve.101.062607] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacements. Moreover, the excess kurtosis can assume large positive values. In model (ii) it is possible for some distributions of tumbling angles that the MSD reaches a linear time dependence but, still, the dynamics remains non-Gaussian for long times. This is also the case in model (iii) for small rotational diffusivity. For all models, the long-time diffusion coefficients are also obtained. The theoretical approach, which relies on eigenvalue and angular Fourier expansions of the van Hove function, is in excellent agreement with the simulations.
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Affiliation(s)
- Andrea Villa-Torrealba
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Cristóbal Chávez-Raby
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Pablo de Castro
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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10
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Alirezaeizanjani Z, Großmann R, Pfeifer V, Hintsche M, Beta C. Chemotaxis strategies of bacteria with multiple run modes. SCIENCE ADVANCES 2020; 6:eaaz6153. [PMID: 32766440 PMCID: PMC7385427 DOI: 10.1126/sciadv.aaz6153] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Accepted: 03/20/2020] [Indexed: 06/11/2023]
Abstract
Bacterial chemotaxis-a fundamental example of directional navigation in the living world-is key to many biological processes, including the spreading of bacterial infections. Many bacterial species were recently reported to exhibit several distinct swimming modes-the flagella may, for example, push the cell body or wrap around it. How do the different run modes shape the chemotaxis strategy of a multimode swimmer? Here, we investigate chemotactic motion of the soil bacterium Pseudomonas putida as a model organism. By simultaneously tracking the position of the cell body and the configuration of its flagella, we demonstrate that individual run modes show different chemotactic responses in nutrition gradients and, thus, constitute distinct behavioral states. On the basis of an active particle model, we demonstrate that switching between multiple run states that differ in their speed and responsiveness provides the basis for robust and efficient chemotaxis in complex natural habitats.
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Affiliation(s)
| | - Robert Großmann
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Veronika Pfeifer
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Marius Hintsche
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
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11
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Ilan Y. Overcoming randomness does not rule out the importance of inherent randomness for functionality. J Biosci 2019; 44:132. [PMID: 31894113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Randomness is intrinsic to many natural processes. It is also clear that, under certain conditions, disorders are not associated with functionality. Several examples in which overcoming, suppressing, or combining both randomness and non-randomness is required are drawn from various fields. However, the need to suppress or overcome randomness does not negate its importance under certain conditions and its significance in valid processes and organ functions. Randomness should be acknowledged rather than ignored or suppressed; it can be viewed, at worst, as a disturbing disorder that may be treated to produce order, or, at best, as a 'beneficial disorder' that can be considered as a higher level of functionality.
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Affiliation(s)
- Yaron Ilan
- Department of Medicine, Hadassah-Hebrew University Medical Center, Jerusalem, Israel,
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12
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Ilan Y. Overcoming randomness does not rule out the importance of inherent randomness for functionality. J Biosci 2019. [DOI: 10.1007/s12038-019-9958-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Stürmer J, Seyrich M, Stark H. Chemotaxis in a binary mixture of active and passive particles. J Chem Phys 2019; 150:214901. [DOI: 10.1063/1.5080543] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Julian Stürmer
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Maximilian Seyrich
- 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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14
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Chaki S, Chakrabarti R. Enhanced diffusion, swelling, and slow reconfiguration of a single chain in non-Gaussian active bath. J Chem Phys 2019; 150:094902. [DOI: 10.1063/1.5086152] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Subhasish Chaki
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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15
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Abstract
Microorganisms use chemotaxis, regulated by internal complex chemical pathways, to swim along chemical gradients to find better living conditions. Artificial microswimmers can mimic such a strategy by a pure physical process called diffusiophoresis, where they drift and orient along the gradient in a chemical density field. Similarly, for other forms of taxis in nature such as photo- or thermotaxis the phoretic counterpart exists. In this Account, we concentrate on the chemotaxis of self-phoretic active colloids. They are driven by self-electro- and diffusiophoresis at the particle surface and thereby acquire a swimming speed. During this process, they also produce nonuniform chemical fields in their surroundings through which they interact with other colloids by translational and rotational diffusiophoresis. In combination with active motion, this gives rise to effective phoretic attraction and repulsion and thereby to diverse emergent collective behavior. A particular appealing example is dynamic clustering in dilute suspensions first reported by a group from Lyon. A subtle balance of attraction and repulsion causes very dynamic clusters, which form and resolve again. This is in stark contrast to the relatively static clusters of motility-induced phase separation at larger densities. To treat chemotaxis in active colloids confined to a plane, we formulate two Langevin equations for position and orientation, which include translational and rotational diffusiophoretic drift velocities. The colloids are chemical sinks and develop their long-range chemical profiles instantaneously. For dense packings, we include screening of the chemical fields. We present a state diagram in the two diffusiophoretic parameters governing translational, as well as rotational, drift and, thereby, explore the full range of phoretic attraction and repulsion. The identified states range from a gaslike phase over dynamic clustering states 1 and 2, which we distinguish through their cluster size distributions, to different types of collapsed states. The latter include a full chemotactic collapse for translational phoretic attraction. Turning it into an effective repulsion, with increasing strength first the collapsed cluster starts to fluctuate at the rim, then oscillates, and ultimately becomes a static collapsed cloud. We also present a state diagram without screening. Finally, we summarize how the famous Keller-Segel model derives from our Langevin equations through a multipole expansion of the full one-particle distribution function in position and orientation. The Keller-Segel model gives a continuum equation for treating chemotaxis of microorganisms on the level of their spatial density. Our theory is extensible to mixtures of active and passive particles and allows to include a dipolar correction to the chemical field resulting from the dipolar symmetry of Janus colloids.
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Affiliation(s)
- Holger Stark
- Technische Universität Berlin, Institute of Theoretical Physics, Hardenbergstrasse 36, D-10623 Berlin, Germany
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16
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Adhyapak TC, Jabbari-Farouji S. Flow properties and hydrodynamic interactions of rigid spherical microswimmers. Phys Rev E 2017; 96:052608. [PMID: 29347781 DOI: 10.1103/physreve.96.052608] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2017] [Indexed: 06/07/2023]
Abstract
We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals that hydrodynamic interactions among rigid-bodied microswimmers differ considerably from those among the corresponding point-force dipoles. Our results are relevant for the study of collective behavior of hydrodynamically interacting microswimmers by means of Stokesian dynamics simulations at moderate concentrations.
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Affiliation(s)
- Tapan Chandra Adhyapak
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Sara Jabbari-Farouji
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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