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Chan CW, Yang Z, Gan Z, Zhang R. Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets. J Chem Phys 2024; 161:014904. [PMID: 38953449 DOI: 10.1063/5.0207355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 05/31/2024] [Indexed: 07/04/2024] Open
Abstract
In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.
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Affiliation(s)
- Chung Wing Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
| | - Zheng Yang
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
- Interdisciplinary Programs Office, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Zecheng Gan
- Thrust of Advanced Materials, and Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou), Guangdong, China
- Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Rui Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
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2
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Meyer H, Rieger H. Alignment interaction and band formation in assemblies of autochemorepulsive walkers. Phys Rev E 2023; 108:034604. [PMID: 37849087 DOI: 10.1103/physreve.108.034604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 08/18/2023] [Indexed: 10/19/2023]
Abstract
Chemotaxis refers to the motion of an organism induced by chemical stimuli and is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, autochemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of autochemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segel model in the continuous limit, for which we describe the rich phase behavior. We first rationalize the chemically mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.
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Affiliation(s)
- Hugues Meyer
- Department of Theoretical Physics & Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics & Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
- INM-Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany
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3
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Ma Z, Ni R. Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles. J Chem Phys 2022; 156:021102. [PMID: 35032980 DOI: 10.1063/5.0077389] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
One of the most intriguing phenomena in active matter has been the gas-liquid-like motility-induced phase separation (MIPS) observed in repulsive active particles. However, experimentally, no particle can be a perfect sphere, and the asymmetric shape, mass distribution, or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The nonvanishing current in non-equilibrium steady states microscopically originates from the motility "relieved" by automatic rotation, which breaks the detailed balance at the continuum level. This suggests that no equilibrium-like phase separation theory can be constructed for chiral active colloids even with tiny active torque, in which no visible collective motion exists. This mechanism also sheds light on the understanding of dynamic clusters observed in a variety of active matter systems.
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Affiliation(s)
- Zhan Ma
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459, Singapore
| | - Ran Ni
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459, Singapore
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4
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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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5
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Perez LJ, Bhattacharjee T, Datta SS, Parashar R, Sund NL. Impact of confined geometries on hopping and trapping of motile bacteria in porous media. Phys Rev E 2021; 103:012611. [PMID: 33601519 DOI: 10.1103/physreve.103.012611] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 01/04/2021] [Indexed: 11/07/2022]
Abstract
We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.
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Affiliation(s)
- Lazaro J Perez
- Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada 89512, USA
| | - Tapomoy Bhattacharjee
- The Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, USA
| | - Sujit S Datta
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Rishi Parashar
- Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada 89512, USA
| | - Nicole L Sund
- Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada 89512, USA
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6
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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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7
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Jin C, Vachier J, Bandyopadhyay S, Macharashvili T, Maass CC. Fine balance of chemotactic and hydrodynamic torques: When microswimmers orbit a pillar just once. Phys Rev E 2019; 100:040601. [PMID: 31770913 DOI: 10.1103/physreve.100.040601] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Indexed: 11/07/2022]
Abstract
We study the detention statistics of self-propelling droplet microswimmers attaching to microfluidic pillars. These droplets show negative autochemotaxis: they shed a persistent repulsive trail of spent fuel that biases them to detach from pillars in a specific size range after orbiting them just once. We have designed a microfluidic assay recording microswimmers in pillar arrays of varying diameter, derived detention statistics via digital image analysis, and interpreted these statistics via the Langevin dynamics of an active Brownian particle model. By comparing data from orbits with and without residual chemical field, we can independently estimate quantities such as hydrodynamic and chemorepulsive torques, chemical coupling constants and diffusion coefficients, as well as their dependence on environmental factors such as wall curvature. This type of analysis is generalizable to many kinds of microswimmers.
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Affiliation(s)
- Chenyu Jin
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
| | - Jérémy Vachier
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
| | - Soumya Bandyopadhyay
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | | | - Corinna C Maass
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
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8
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Sevilla FJ, Rodríguez RF, Gomez-Solano JR. Generalized Ornstein-Uhlenbeck model for active motion. Phys Rev E 2019; 100:032123. [PMID: 31640041 DOI: 10.1103/physreve.100.032123] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Indexed: 06/10/2023]
Abstract
We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)10.1103/PhysRevE.90.012111]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.
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Affiliation(s)
- Francisco J Sevilla
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
| | - Rosalío F Rodríguez
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
- FENOMEC, Universidad Nacional Autónoma de México, Apdo. Postal 20-726, 01000, Ciudad de México, México
| | - Juan Ruben Gomez-Solano
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
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9
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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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10
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Huang Z, Chen P, Zhu G, Yang Y, Xu Z, Yan LT. Bacteria-Activated Janus Particles Driven by Chemotaxis. ACS NANO 2018; 12:6725-6733. [PMID: 29791803 DOI: 10.1021/acsnano.8b01842] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In the development of biocompatible nano-/micromotors for drug and cargo delivery, motile bacteria represent an excellent energy source for biomedical applications. Despite intense research of the fabrication of bacteria-based motors, how to effectively utilize the instinctive responses of bacteria to environmental stimuli in the fabrication process, particularly, chemotaxis, remains an urgent and critical issue. Here, by developing a molecular-dynamics model of bacterial chemotaxis, we present an investigation of the transport of a bacteria-activated Janus particle driven by chemotaxis. Upon increasing the stimuli intensity, we find that the transport of the Janus particle undergoes an intriguing second-order state transition: from a composite random walk, combining power-law-distributed truncated Lévy flights with Brownian jiggling, to an enhanced directional transport with size-dependent reversal of locomotion. A state diagram of Janus-particle transport depending on the stimuli intensity and particle size is presented, which allows approaches to realize controllable and predictable propulsion directions. The physical mechanism of these transport behaviors is revealed by performing a theoretical modeling based on the bacterial noise and Janus geometries. Our findings could provide a fundamental insight into the physics underlying the transport of anisotropic particles driven by microorganisms and highlight stimulus-response techniques and asymmetrical design as a versatile strategy to possess a wide array of potential applications for future biocompatible nano-/microdevices.
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Affiliation(s)
- Zihan Huang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
| | - Pengyu Chen
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
| | - Guolong Zhu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
| | - Ye Yang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
| | - Ziyang Xu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering , Tsinghua University , Beijing 100084 , China
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11
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Jin C, Hokmabad BV, Baldwin KA, Maass CC. Chemotactic droplet swimmers in complex geometries. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:054003. [PMID: 29243668 DOI: 10.1088/1361-648x/aaa208] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Chemotaxis1 and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22; Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.
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Affiliation(s)
- Chenyu Jin
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
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12
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Pineda M, Eftimie R. Modelling the collective response of heterogeneous cell populations to stationary gradients and chemical signal relay. Phys Biol 2017; 14:066003. [PMID: 28862157 DOI: 10.1088/1478-3975/aa89b4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
The directed motion of cell aggregates toward a chemical source occurs in many relevant biological processes. Understanding the mechanisms that control this complex behavior is of great relevance for our understanding of developmental biological processes and many diseases. In this paper, we consider a self-propelled particle model for the movement of heterogeneous subpopulations of chemically interacting cells towards an imposed stable chemical gradient. Our simulations show explicitly how self-organisation of cell populations (which could lead to engulfment or complete cell segregation) can arise from the heterogeneity of chemotactic responses alone. This new result complements current theoretical and experimental studies that emphasise the role of differential cell-cell adhesion on self-organisation and spatial structure of cellular aggregates. We also investigate how the speed of individual cell aggregations increases with the chemotactic sensitivity of the cells, and decreases with the number of cells inside the aggregates.
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Affiliation(s)
- M Pineda
- Department of Chemical Engineering, University College London, Roberts Building, Torrington Place, London WC1E 7JE, United Kingdom
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13
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Kurzthaler C, Franosch T. Intermediate scattering function of an anisotropic Brownian circle swimmer. SOFT MATTER 2017; 13:6396-6406. [PMID: 28872170 DOI: 10.1039/c7sm00873b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.
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Affiliation(s)
- Christina Kurzthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
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14
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Jashnsaz H, Al Juboori M, Weistuch C, Miller N, Nguyen T, Meyerhoff V, McCoy B, Perkins S, Wallgren R, Ray BD, Tsekouras K, Anderson GG, Pressé S. Hydrodynamic Hunters. Biophys J 2017; 112:1282-1289. [PMID: 28355554 PMCID: PMC5376100 DOI: 10.1016/j.bpj.2017.02.011] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2016] [Revised: 02/06/2017] [Accepted: 02/07/2017] [Indexed: 11/30/2022] Open
Abstract
The Gram-negative Bdellovibrio bacteriovorus (BV) is a model bacterial predator that hunts other bacteria and may serve as a living antibiotic. Despite over 50 years since its discovery, it is suggested that BV probably collides into its prey at random. It remains unclear to what degree, if any, BV uses chemical cues to target its prey. The targeted search problem by the predator for its prey in three dimensions is a difficult problem: it requires the predator to sensitively detect prey and forecast its mobile prey’s future position on the basis of previously detected signal. Here instead we find that rather than chemically detecting prey, hydrodynamics forces BV into regions high in prey density, thereby improving its odds of a chance collision with prey and ultimately reducing BV’s search space for prey. We do so by showing that BV’s dynamics are strongly influenced by self-generated hydrodynamic flow fields forcing BV onto surfaces and, for large enough defects on surfaces, forcing BV in orbital motion around these defects. Key experimental controls and calculations recapitulate the hydrodynamic origin of these behaviors. While BV’s prey (Escherichia coli) are too small to trap BV in hydrodynamic orbit, the prey are also susceptible to their own hydrodynamic fields, substantially confining them to surfaces and defects where mobile predator and prey density is now dramatically enhanced. Colocalization, driven by hydrodynamics, ultimately reduces BV’s search space for prey from three to two dimensions (on surfaces) even down to a single dimension (around defects). We conclude that BV’s search for individual prey remains random, as suggested in the literature, but confined, however—by generic hydrodynamic forces—to reduced dimensionality.
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Affiliation(s)
- Hossein Jashnsaz
- Department of Physics, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Mohammed Al Juboori
- Biomedical Engineering, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Corey Weistuch
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York; Department of Biochemistry and Cell Biology, Stony Brook University, Stony Brook, New York
| | - Nicholas Miller
- Biomedical Engineering, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Tyler Nguyen
- Stark Neurosciences Research Institute, Indiana University School of Medicine (ISUM), Indianapolis, Indiana
| | - Viktoria Meyerhoff
- Mechanical Engineering, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Bryan McCoy
- Department of Chemistry and Chemical Biology, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Stephanie Perkins
- Department of Biology, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Ross Wallgren
- Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Bruce D Ray
- Department of Physics, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Konstantinos Tsekouras
- Department of Physics, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana
| | - Gregory G Anderson
- Department of Biology, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana.
| | - Steve Pressé
- Department of Physics, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana; Department of Chemistry and Chemical Biology, Indiana University - Purdue University Indianapolis (IUPUI), Indianapolis, Indiana; Cellular and Integrative Physiology Department, Indiana University School of Medicine (IUSM), Indianapolis, Indiana.
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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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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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17
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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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18
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Pohl O, Stark H. Dynamic clustering and chemotactic collapse of self-phoretic active particles. PHYSICAL REVIEW LETTERS 2014; 112:238303. [PMID: 24972234 DOI: 10.1103/physrevlett.112.238303] [Citation(s) in RCA: 119] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2014] [Indexed: 06/03/2023]
Abstract
Recent experiments with self-phoretic particles at low concentrations show a pronounced dynamic clustering [I. Theurkauff et al., Phys. Rev. Lett. 108, 268303 (2012)]. We model this situation by taking into account the translational and rotational diffusiophoretic motion, which the active particles perform in their self-generated chemical field. Our Brownian dynamics simulations show pronounced dynamic clustering only when these two phoretic contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them by power-law-exponential distributions. In case of mere attraction a chemotactic collapse occurs directly from the gaslike into the collapsed state, which we also predict by mapping our Langevin dynamics on the Keller-Segel model for bacterial chemotaxis.
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Affiliation(s)
- Oliver Pohl
- 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 and Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, California 93106, USA
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19
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Taktikos J, Stark H, Zaburdaev V. How the motility pattern of bacteria affects their dispersal and chemotaxis. PLoS One 2013; 8:e81936. [PMID: 24391710 PMCID: PMC3876982 DOI: 10.1371/journal.pone.0081936] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2013] [Accepted: 10/25/2013] [Indexed: 11/18/2022] Open
Abstract
Most bacteria at certain stages of their life cycle are able to move actively; they can swim in a liquid or crawl on various surfaces. A typical path of the moving cell often resembles the trajectory of a random walk. However, bacteria are capable of modifying their apparently random motion in response to changing environmental conditions. As a result, bacteria can migrate towards the source of nutrients or away from harmful chemicals. Surprisingly, many bacterial species that were studied have several distinct motility patterns, which can be theoretically modeled by a unifying random walk approach. We use this approach to quantify the process of cell dispersal in a homogeneous environment and show how the bacterial drift velocity towards the source of attracting chemicals is affected by the motility pattern of the bacteria. Our results open up the possibility of accessing additional information about the intrinsic response of the cells using macroscopic observations of bacteria moving in inhomogeneous environments.
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Affiliation(s)
- Johannes Taktikos
- Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany
- Technische Universität Berlin, Institut für Theoretische Physik, Berlin, Germany
- Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts, United States
- * E-mail:
| | - Holger Stark
- Technische Universität Berlin, Institut für Theoretische Physik, Berlin, Germany
| | - Vasily Zaburdaev
- Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany
- Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts, United States
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20
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Abstract
Using computational modeling, we show that self-oscillating Belousov-Zhabotinsky (BZ) gels can both emit and sense a chemical signal and thus drive neighboring gel pieces to spontaneously self-aggregate, so that the system exhibits autochemotaxis. To the best of our knowledge, this is the closest system to the ultimate self-recombining material, which can be divided into separated parts and the parts move autonomously to assemble into a structure resembling the original, uncut sample. We also show that the gels' coordinated motion can be controlled by light, allowing us to achieve selective self-aggregation and control over the shape of the gel aggregates. By exposing the BZ gels to specific patterns of light and dark, we design a BZ gel "train" that leads the movement of its "cargo." Our findings pave the way for creating reconfigurable materials from self-propelled elements, which autonomously communicate with neighboring units and thereby actively participate in constructing the final structure.
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21
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Taktikos J, Zaburdaev V, Stark H. Collective dynamics of model microorganisms with chemotactic signaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051901. [PMID: 23004782 DOI: 10.1103/physreve.85.051901] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2012] [Indexed: 06/01/2023]
Abstract
Various microorganisms use chemotaxis for signaling among individuals-a common strategy for communication that is responsible for the formation of microcolonies. We model the microorganisms as autochemotactic active random walkers and describe them by an appropriate Langevin dynamics. It consists of rotational diffusion of the walker's velocity direction and a deterministic torque that aligns the velocity direction along the gradient of a self-generated chemical field. To account for finite size, each microorganism is treated as a soft disk. Its velocity is modified when it overlaps with other walkers according to a linear force-velocity relation and a harmonic repulsion force. We analyze two-walker collisions by presenting typical trajectories and by determining a state diagram that distinguishes between free walker, metastable, and bounded cluster states. We mention an analogy to Kramer's escape problem. Finally, we investigate relevant properties of many-walker systems and describe characteristics of cluster formation in unbounded geometry and in confinement.
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Affiliation(s)
- Johannes Taktikos
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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