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Alexandre A, Anderson L, Collin-Dufresne T, Guérin T, Dean DS. Self-phoretic oscillatory motion in a harmonic trap. Phys Rev E 2024; 109:064147. [PMID: 39020931 DOI: 10.1103/physreve.109.064147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2024] [Accepted: 05/15/2024] [Indexed: 07/20/2024]
Abstract
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations that take place along a circle or a straight line. Our results are confirmed by numerical simulations.
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Affiliation(s)
- Arthur Alexandre
- Laboratory of Computational Biology and Theoretical Biophysics, Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | | | | | | | - David S Dean
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Université Bordeaux, F-33400 Talence, France
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2
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Albers T, Delnoij S, Schramma N, Jalaal M. Billiards with Spatial Memory. PHYSICAL REVIEW LETTERS 2024; 132:157101. [PMID: 38682997 DOI: 10.1103/physrevlett.132.157101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2024] [Accepted: 03/20/2024] [Indexed: 05/01/2024]
Abstract
Many classes of active matter develop spatial memory by encoding information in space. We present a framework based on mathematical billiards, wherein particles remember their past trajectories. Despite its deterministic rules, such a system is strongly nonergodic and exhibits intermittent statistics and complex pattern formation. We show how these features emerge from the dynamic change of topology. Our work illustrates how the dynamics of a single-body system can dramatically change with spatial memory, laying the groundwork to further explore systems with complex memory kernels.
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Affiliation(s)
- Thijs Albers
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Stijn Delnoij
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Nico Schramma
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Maziyar Jalaal
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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3
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Tang ZS, Li JJ, Zhu WJ, Ai BQ. Collective self-optimization of binary mixed heterogeneous populations. Phys Rev E 2024; 109:024405. [PMID: 38491669 DOI: 10.1103/physreve.109.024405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 01/16/2024] [Indexed: 03/18/2024]
Abstract
To maximize the survival chances of society members, collective self-organization must balance individual interests with promoting the collective welfare. Although situations where group members have equal optimal values are clear, how varying optimal values impacts group dynamics remains unclear. To address this gap, we conducted a self-optimization study of a binary system incorporating communication-enabled active particles with distinct optimal values. We demonstrate that similar particles will spontaneously aggregate and separate from each other to maximize their individual benefits during the process of self-optimization. Our research shows that both types of particles can produce the optimal field values at low density. However, only one type of particle can achieve the optimal field values at medium density. At high densities, neither type of particle is effective in reaching the optimal field values. Interestingly, we observed that during the self-optimization process, the mixture demixed spontaneously under certain circumstances of mixed particles. Particles with higher optimal values developed into larger clusters, while particles with lower optimal values migrated outside of these clusters, resulting in the separation of the mixture. To achieve this separation, suitable noise intensity, particle density, and the significant difference in optimal values were necessary. Our results provide a more profound comprehension of the self-optimization of synthetic or biological agents' communication and provide valuable insight into separating binary species and mixtures.
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Affiliation(s)
- Zhao-Sha Tang
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
| | - Jia-Jian Li
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
| | - Wei-Jing Zhu
- School of Photoelectric Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China
| | - Bao-Quan Ai
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
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4
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Varga L, Libál A, Reichhardt C, Reichhardt CJO. Pattern formation and flocking for particles near the jamming transition on resource gradient substrates. Phys Rev E 2022; 106:064602. [PMID: 36671186 DOI: 10.1103/physreve.106.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.
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Affiliation(s)
- L Varga
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - A Libál
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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5
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Daftari K, Newhall KA. Self-avoidant memory effects on enhanced diffusion in a stochastic model of environmentally responsive swimming droplets. Phys Rev E 2022; 105:024609. [PMID: 35291191 DOI: 10.1103/physreve.105.024609] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Enhanced diffusion is an emergent property of many experimental microswimmer systems that usually arises from a combination of ballistic motion with random reorientations. A subset of these systems, autophoretic droplet swimmers that move as a result of Marangoni stresses, have additionally been shown to respond to local, self-produced chemical gradients that can mediate self-avoidance or self-attraction. Via this mechanism, we present a mathematical model constructed to encode experimentally observed self-avoidant memory and numerically study the effect of this particular memory on the enhanced diffusion of such swimming droplets. To disentangle the enhanced diffusion due to the random reorientations from the enhanced diffusion due to the self-avoidant memory, we compare to the widely used active Brownian model. Paradoxically, we find that the enhanced diffusion is substantially suppressed by the self-avoidant memory relative to that predicted by only an equivalent reorientation persistence timescale in the active Brownian model. We attribute this to transient self-caging that we propose is novel for self-avoidant systems. Additionally, we further explore the model parameter space by computing emergent parameters that capture the velocity and reorientation persistence, thus finding a finite parameter domain in which enhanced diffusion is observable.
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Affiliation(s)
- Katherine Daftari
- Mathematics Department, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Katherine A Newhall
- Mathematics Department, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
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6
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Liebchen B, Mukhopadhyay AK. Interactions in active colloids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:083002. [PMID: 34788232 DOI: 10.1088/1361-648x/ac3a86] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 11/16/2021] [Indexed: 06/13/2023]
Abstract
The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.
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Affiliation(s)
- Benno Liebchen
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | - Aritra K Mukhopadhyay
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
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7
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Zampetaki AV, Liebchen B, Ivlev AV, Löwen H. Collective self-optimization of communicating active particles. Proc Natl Acad Sci U S A 2021; 118:e2111142118. [PMID: 34853169 PMCID: PMC8670500 DOI: 10.1073/pnas.2111142118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/25/2021] [Indexed: 01/05/2023] Open
Abstract
The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource-such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins-while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared "resource field," the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.
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Affiliation(s)
- Alexandra V Zampetaki
- Center for Astrochemical Studies, Max-Planck-Institut für Extraterrestrische Physik, 85741 Garching, Germany
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
| | - Benno Liebchen
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | - Alexei V Ivlev
- Center for Astrochemical Studies, Max-Planck-Institut für Extraterrestrische Physik, 85741 Garching, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
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8
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Ouazan-Reboul V, Agudo-Canalejo J, Golestanian R. Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:113. [PMID: 34478002 PMCID: PMC8416889 DOI: 10.1140/epje/s10189-021-00118-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 08/24/2021] [Indexed: 05/27/2023]
Abstract
Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis-Menten-like dependence of the particles' activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.
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Affiliation(s)
- Vincent Ouazan-Reboul
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077, Göttingen, Germany
| | - Jaime Agudo-Canalejo
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077, Göttingen, Germany
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077, Göttingen, Germany.
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, UK.
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9
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Meyer H, Rieger H. Optimal Non-Markovian Search Strategies with n-Step Memory. PHYSICAL REVIEW LETTERS 2021; 127:070601. [PMID: 34459631 DOI: 10.1103/physrevlett.127.070601] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 07/19/2021] [Accepted: 07/22/2021] [Indexed: 06/13/2023]
Abstract
Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a migrating cell that is repelled from the diffusive chemotactic signal that it secretes on its way, denoted as an autochemotactic searcher. To analyze the efficiency of this class of non-Markovian search processes, we present a general formalism that allows one to compute the mean first-passage time (MFPT) for a given set of conditional transition probabilities for non-Markovian random walks on a lattice. We show that the optimal choice of the n-step transition probabilities decreases the MFPT systematically and substantially with an increasing number of steps. It turns out that the optimal search strategies can be reduced to simple cycles defined by a small parameter set and that mirror-asymmetric walks are more efficient. For the autochemotactic searcher, we show that an optimal coupling between the searcher and the chemical reduces the MFPT to 1/3 of the one for a Markovian random walk.
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Affiliation(s)
- Hugues Meyer
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
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10
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Tarama S, Egelhaaf SU, Löwen H. Traveling band formation in feedback-driven colloids. Phys Rev E 2019; 100:022609. [PMID: 31574772 DOI: 10.1103/physreve.100.022609] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Indexed: 06/10/2023]
Abstract
Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.
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Affiliation(s)
- Sonja Tarama
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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11
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Abstract
A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence the dynamics. It has been discussed recently [Kranz et al., Phys. Rev. Lett. 117, 038101 (2016)] that the self-interaction may localize the organism above a critical coupling χc to the trail. Here, we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings χ < χc. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.
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Affiliation(s)
- W Till Kranz
- Institute for Theoretical Physics, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
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12
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Abstract
The ability to navigate in chemical gradients, called chemotaxis, is crucial for the survival of microorganisms. It allows them to find food and to escape from toxins. Many microorganisms can produce the chemicals to which they respond themselves and use chemotaxis for signaling, which can be seen as a basic form of communication, allowing ensembles of microorganisms to coordinate their behavior, for example, during embryogenesis, biofilm formation, or cellular aggregation. For example, Dictyostelium cells use signaling as a survival strategy: when starving, they produce certain chemicals toward which other cells show taxis. This leads to aggregation of the cells resulting in a multicellular aggregate that can sustain long starvation periods. Remarkably, the past decade has led to the development of synthetic microswimmers, which can self-propel through a solvent, analogously to bacteria and other microorganisms. The mechanism underlying the self-propulsion of synthetic microswimmers like camphor boats, droplet swimmers, and in particular autophoretic Janus colloids involves the production of certain chemicals. As we will discuss in this Account, the same chemicals (phoretic fields) involved in the self-propulsion of a (Janus) microswimmer also act on other ones and bias their swimming direction toward (or away from) the producing microswimmer. Synthetic microswimmers therefore provide a synthetic analogue to motile microorganisms interacting by taxis toward (or away from) self-produced chemical fields. In this Account, we review recent progress in the theoretical description of synthetic chemotaxis mainly based on simulations and field theoretical descriptions. We will begin with single motile particles leaving chemical trails behind with which they interact themselves, leading to effects like self-trapping or self-avoidance. Besides these self-interactions, in ensembles of synthetic motile particles each particle also responds to the chemicals produced by other particles, inducing chemical (or phoretic) cross-interactions. When these interactions are attractive, they commonly lead to clusters, even at low particle density. These clusters may either proceed toward macrophase separation, resembling Dictyostelium aggregation, or, as shown very recently, lead to dynamic clusters of self-limited size (dynamic clustering) as seen in experiments in autophoretic Janus colloids. Besides the classical case where chemical interactions are attractive, this Account discusses, as its main focus, repulsive chemical interactions, which can create a new and less known avenue to pattern formation in active systems leading to a variety of pattern, including clusters which are surrounded by shells of chemicals, traveling waves and more complex continuously reshaping patterns. In all these cases "synthetic signalling" can crucially determine the collective behavior of synthetic microswimmer ensembles and can be used as a design principle to create patterns in motile active particles.
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Affiliation(s)
- Benno Liebchen
- 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
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13
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Vuijk HD, Sharma A, Mondal D, Sommer JU, Merlitz H. Pseudochemotaxis in inhomogeneous active Brownian systems. Phys Rev E 2018; 97:042612. [PMID: 29758623 DOI: 10.1103/physreve.97.042612] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Indexed: 06/08/2023]
Abstract
We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.
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Affiliation(s)
- Hidde D Vuijk
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
| | - Abhinav Sharma
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
| | - Debasish Mondal
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
- Indian Institute of Technology, Department of Chemistry, 517506 Tirupati, India
| | - Jens-Uwe Sommer
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
- Technische Universität Dresden, Institute of Theoretical Physics, 01069 Dresden, Germany
| | - Holger Merlitz
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
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14
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Koorehdavoudi H, Bogdan P, Wei G, Marculescu R, Zhuang J, Carlsen RW, Sitti M. Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens. Proc Math Phys Eng Sci 2017; 473:20170154. [PMID: 28804259 PMCID: PMC5549567 DOI: 10.1098/rspa.2017.0154] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Accepted: 06/15/2017] [Indexed: 12/19/2022] Open
Abstract
To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration.
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Affiliation(s)
- Hana Koorehdavoudi
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
| | - Paul Bogdan
- Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2560, USA
| | - Guopeng Wei
- Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Radu Marculescu
- Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Jiang Zhuang
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Rika Wright Carlsen
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.,Department of Engineering, Robert Morris University, Pittsburgh, PA 15108, USA
| | - Metin Sitti
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.,Physical Intelligence Department, Max-Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
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15
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Abstract
Chemotaxis and autochemotaxis play an important role in many essential biological processes. We present a self-propelling artificial swimmer system that exhibits chemotaxis as well as negative autochemotaxis. Oil droplets in an aqueous surfactant solution are driven by interfacial Marangoni flows induced by micellar solubilization of the oil phase. We demonstrate that chemotaxis along micellar surfactant gradients can guide these swimmers through a microfluidic maze. Similarly, a depletion of empty micelles in the wake of a droplet swimmer causes negative autochemotaxis and thereby trail avoidance. We studied autochemotaxis quantitatively in a microfluidic device of bifurcating channels: Branch choices of consecutive swimmers are anticorrelated, an effect decaying over time due to trail dispersion. We modeled this process by a simple one-dimensional diffusion process and stochastic Langevin dynamics. Our results are consistent with a linear surfactant gradient force and diffusion constants appropriate for micellar diffusion and provide a measure of autochemotactic feedback strength vs. stochastic forces. This assay is readily adaptable for quantitative studies of both artificial and biological autochemotactic systems.
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16
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Vasiev B. Modelling Chemotactic Motion of Cells in Biological Tissues. PLoS One 2016; 11:e0165570. [PMID: 27798687 PMCID: PMC5087904 DOI: 10.1371/journal.pone.0165570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2016] [Accepted: 10/13/2016] [Indexed: 11/19/2022] Open
Abstract
Developmental processes in biology are underlined by proliferation, differentiation and migration of cells. The latter two are interlinked since cellular differentiation is governed by the dynamics of morphogens which, in turn, is affected by the movement of cells. Mutual effects of morphogenetic and cell movement patterns are enhanced when the movement is due to chemotactic response of cells to the morphogens. In this study we introduce a mathematical model to analyse how this interplay can result in a steady movement of cells in a tissue and associated formation of travelling waves in a concentration field of morphogen. Using the model we have identified four chemotactic scenarios for migration of single cell or homogeneous group of cells in a tissue. Such a migration can take place if moving cells are (1) repelled by a chemical produced by themselves or (2) attracted by a chemical produced by the surrounding cells in a tissue. Furthermore, the group of cells can also move if cells in surrounding tissue are (3) repelled by a chemical produced by moving cells or (4) attracted by a chemical produced by surrounding cells themselves. The proposed mechanisms can underlie migration of cells during embryonic development as well as spread of metastatic cells.
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Affiliation(s)
- Bakhtier Vasiev
- Department of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom
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17
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Kranz WT, Gelimson A, Zhao K, Wong GCL, Golestanian R. Effective Dynamics of Microorganisms That Interact with Their Own Trail. PHYSICAL REVIEW LETTERS 2016; 117:038101. [PMID: 27472143 DOI: 10.1103/physrevlett.117.038101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2015] [Indexed: 06/06/2023]
Abstract
Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For a moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.
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Affiliation(s)
- W Till Kranz
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Anatolij Gelimson
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Kun Zhao
- Key Laboratory of Systems Bioengineering, Ministry of Education, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People's Republic of China
- Bioengineering Department, Chemistry and Biochemistry Department, California Nano Systems Institute, UCLA, Los Angeles, California 90095-1600, USA
| | - Gerard C L Wong
- Bioengineering Department, Chemistry and Biochemistry Department, California Nano Systems Institute, UCLA, Los Angeles, California 90095-1600, USA
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
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18
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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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19
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Gelimson A, Golestanian R. Collective dynamics of dividing chemotactic cells. PHYSICAL REVIEW LETTERS 2015; 114:028101. [PMID: 25635562 DOI: 10.1103/physrevlett.114.028101] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Indexed: 06/04/2023]
Abstract
The large scale behavior of a population of cells that grow and interact through the concentration field of the chemicals they secrete is studied using dynamical renormalization group methods. The combination of the effective long-range chemotactic interaction and lack of number conservation leads to a rich variety of phase behavior in the system, which includes a sharp transition from a phase that has moderate (or controlled) growth and regulated chemical interactions to a phase with strong (or uncontrolled) growth and no chemical interactions. The transition point has nontrivial critical exponents. Our results might help shed light on the interplay between chemical signaling and growth in tissues and colonies, and in particular on the challenging problem of cancer metastasis.
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Affiliation(s)
- Anatolij Gelimson
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
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20
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Meyer M, Schimansky-Geier L, Romanczuk P. Active Brownian agents with concentration-dependent chemotactic sensitivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022711. [PMID: 25353513 DOI: 10.1103/physreve.89.022711] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Indexed: 06/04/2023]
Abstract
We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.
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Affiliation(s)
- Marcel Meyer
- Department of Physics, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Lutz Schimansky-Geier
- Department of Physics, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Pawel Romanczuk
- Physikalisch-Technische Bundesanstalt, Abbestraße 2-12, 10587 Berlin, Germany
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21
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Marsden EJ, Valeriani C, Sullivan I, Cates ME, Marenduzzo D. Chemotactic clusters in confined run-and-tumble bacteria: a numerical investigation. SOFT MATTER 2014; 10:157-165. [PMID: 24652099 DOI: 10.1039/c3sm52358f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a simulation study of pattern formation in an ensemble of chemotactic run-and-tumble bacteria, focussing on the effect of spatial confinement, either within traps or inside a maze. These geometries are inspired by previous experiments probing pattern formation in chemotactic strains of E. coli under these conditions. Our main result is that a microscopic model of chemotactic run-and-tumble particles which themselves secrete a chemoattractant is able to reproduce the main experimental observations, namely the formation of bacterial aggregates within traps and in dead ends of a maze. Our simulations also demonstrate that stochasticity plays a key role and leads to a hysteretic response when the chemotactic sensitivity is varied. We compare the results of run-and-tumble particles with simulations performed with a simplified version of the model where the active particles are smooth swimmers which respond to chemotactic gradients by rotating towards the source of chemoattractant. This class of models leads again to aggregation, but with quantitative and qualitative differences in, for instance, the size and shape of clusters.
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Affiliation(s)
- E J Marsden
- SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK.
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22
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Taktikos J, Zaburdaev V, Stark H. Modeling a self-propelled autochemotactic walker. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041924. [PMID: 22181192 DOI: 10.1103/physreve.84.041924] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2011] [Indexed: 05/31/2023]
Abstract
We develop a minimal model for the stochastic dynamics of microorganisms where individuals communicate via autochemotaxis. This means that microorganisms, such as bacteria, amoebae, or cells, follow the gradient of a chemical that they produce themselves to attract or repel each other. A microorganism is represented as a self-propelled particle or walker with constant speed while its velocity direction diffuses on the unit circle. We study the autochemotactic response of a single self-propelled walker whose dynamics is non-Markovian. We show that its long-time dynamics is always diffusive by deriving analytic expressions for its diffusion coefficient in the weak- and strong-coupling case. We confirm our findings by numerical simulations.
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Affiliation(s)
- Johannes Taktikos
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
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23
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Hoell C, Löwen H. Theory of microbe motion in a poisoned environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:042903. [PMID: 22181211 DOI: 10.1103/physreve.84.042903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2011] [Revised: 09/01/2011] [Indexed: 05/31/2023]
Abstract
The motility of a microorganism which tries to avoid a poisoned environment by chemotaxis is studied within a simple model which couples its velocity to the concentration field of the poison. The latter is time independent but inhomogeneous in space. The presence of the poison is assumed to irreversibly reduce the propulsion speed. The model is solved analytically for different couplings of the total poison dose experienced by the microbe to the propulsion mechanism. In a stationary poison field resulting from a constant emission of a fixed point source, we find a power law for the distance traveled by the microbe as a function of time with a nonuniversal exponent which depends on the coupling in the model. With an inverted sign in the couplings, the acceleration of microbe motion induced by a food field can also be described.
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Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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24
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Sengupta A, Kruppa T, Löwen H. Chemotactic predator-prey dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031914. [PMID: 21517532 DOI: 10.1103/physreve.83.031914] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2010] [Revised: 01/17/2011] [Indexed: 05/30/2023]
Abstract
A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law t¹/³ with time t and ultimately crosses over to diffusion again. This allows us to classify the motility and dynamics of various predatory microbes and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.
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Affiliation(s)
- Ankush Sengupta
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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25
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Valeriani C, Allen RJ, Marenduzzo D. Non-equilibrium dynamics of an active colloidal “chucker”. J Chem Phys 2010; 132:204904. [DOI: 10.1063/1.3428663] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
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