1
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Li Y, Zarei Z, Tran PN, Wang Y, Baskaran A, Fraden S, Hagan MF, Hong P. A machine learning approach to robustly determine director fields and analyze defects in active nematics. SOFT MATTER 2024; 20:1869-1883. [PMID: 38318759 DOI: 10.1039/d3sm01253k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.
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Affiliation(s)
- Yunrui Li
- Computer Science Department, Brandeis University, USA.
| | - Zahra Zarei
- Physics Department, Brandeis University, USA
| | - Phu N Tran
- Physics Department, Brandeis University, USA
| | - Yifei Wang
- Computer Science Department, Brandeis University, USA.
| | | | - Seth Fraden
- Physics Department, Brandeis University, USA
| | | | - Pengyu Hong
- Computer Science Department, Brandeis University, USA.
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2
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Venkatareddy N, Lin ST, Maiti PK. Phase behavior of active and passive dumbbells. Phys Rev E 2023; 107:034607. [PMID: 37073042 DOI: 10.1103/physreve.107.034607] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 03/08/2023] [Indexed: 04/20/2023]
Abstract
We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.
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Affiliation(s)
- Nayana Venkatareddy
- Department of Physics, Indian Institute of Science, C. V. Raman Ave,Bengaluru 560012, India
| | - Shiang-Tai Lin
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617
| | - Prabal K Maiti
- Department of Physics, Indian Institute of Science, C. V. Raman Ave,Bengaluru 560012, India
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3
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Tejedor AR, Carracedo R, Ramírez J. Molecular dynamics simulations of active entangled polymers reptating through a passive mesh. POLYMER 2023. [DOI: 10.1016/j.polymer.2023.125677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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4
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Whitelam S, Schmit JD. Low-dissipation self-assembly protocols of active sticky particles. JOURNAL OF CRYSTAL GROWTH 2022; 600:126912. [PMID: 36968622 PMCID: PMC10035568 DOI: 10.1016/j.jcrysgro.2022.126912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We use neuroevolutionary learning to identify time-dependent protocols for low-dissipation self-assembly in a model of generic active particles with interactions. When the time allotted for assembly is sufficiently long, low-dissipation protocols use only interparticle attractions, producing an amount of entropy that scales as the number of particles. When time is too short to allow assembly to proceed via diffusive motion, low-dissipation assembly protocols instead require particle self-propulsion, producing an amount of entropy that scales with the number of particles and the swim length required to cause assembly. Self-propulsion therefore provides an expensive but necessary mechanism for inducing assembly when time is of the essence.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Jeremy D. Schmit
- Department of Physics, Kansas State University, Manhattan, KS, 66506, USA
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5
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Geiß D, Kroy K, Holubec V. Signal propagation and linear response in the delay Vicsek model. Phys Rev E 2022; 106:054612. [PMID: 36559364 DOI: 10.1103/physreve.106.054612] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that (1) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (2) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (3) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; and (4) the linear response breaks down when orientation conservation is broken.
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Affiliation(s)
- Daniel Geiß
- Institute for Theoretical Physics, University of Leipzig, 04103 Leipzig, Germany
- Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
| | - Klaus Kroy
- Institute for Theoretical Physics, University of Leipzig, 04103 Leipzig, Germany
| | - Viktor Holubec
- Faculty of Mathematics and Physics, Charles University, CZ-180 00 Prague, Czech Republic
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6
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Newman SA. Inherency and agency in the origin and evolution of biological functions. Biol J Linn Soc Lond 2022. [DOI: 10.1093/biolinnean/blac109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
Abstract
Although discussed by 20th century philosophers in terms drawn from the sciences of non-living systems, in recent decades biological function has been considered in relationship to organismal capability and purpose. Bringing two phenomena generally neglected in evolutionary theory (i.e. inherency and agency) to bear on questions of function leads to a rejection of the adaptationist ‘selected effects’ notion of biological function. I review work showing that organisms such as the placozoans can thrive with almost no functional embellishments beyond those of their constituent cells and physical properties of their simple tissues. I also discuss work showing that individual tissue cells and their artificial aggregates exhibit agential behaviours that are unprecedented in the histories of their respective lineages. I review findings on the unique metazoan mechanism of developmental gene expression that has recruited, during evolution, inherent ancestral cellular functionalities into specialized cell types and organs of the different animal groups. I conclude that most essential functions in animal species are inherent to the cells from which they evolved, not selected effects, and that many of the others are optional ‘add-ons’, a status inimical to fitness-based models of evolution positing that traits emerge from stringent cycles of selection to meet external challenges.
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Affiliation(s)
- Stuart A Newman
- Department of Cell Biology & Anatomy, New York Medical College , Valhalla, NY 10595 , USA
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7
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Geiß D, Kroy K, Holubec V. Information conduction and convection in noiseless Vicsek flocks. Phys Rev E 2022; 106:014609. [PMID: 35974505 DOI: 10.1103/physreve.106.014609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse-grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.
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Affiliation(s)
- Daniel Geiß
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
- Max Planck Institute for Mathematics in the Sciences, D-04103 Leipzig, Germany
| | - Klaus Kroy
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Viktor Holubec
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
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8
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Sesé-Sansa E, Levis D, Pagonabarraga I. Phase separation of self-propelled disks with ferromagnetic and nematic alignment. Phys Rev E 2021; 104:054611. [PMID: 34942723 DOI: 10.1103/physreve.104.054611] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 10/25/2021] [Indexed: 11/06/2022]
Abstract
We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.
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Affiliation(s)
- Elena Sesé-Sansa
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, Ecole Polytechnique Fédérale de Lausanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - Demian Levis
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, Ecole Polytechnique Fédérale de Lausanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland.,Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,UBICS University of Barcelona Institute of Complex Systems, Martí i Franquès 1, E08028 Barcelona, Spain
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9
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Torrik A, Naji A, Zarif M. Dimeric colloidal inclusion in a chiral active bath: Effective interactions and chirality-induced torque. Phys Rev E 2021; 104:064610. [PMID: 35030934 DOI: 10.1103/physreve.104.064610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
Colloidal inclusions suspended in a bath of smaller particles experience an effective bath-mediated attraction at small intersurface separations, which is known as the depletion interaction. In an active bath of nonchiral self-propelled particles, the effective force changes from attraction to repulsion, an effect that is suppressed when the active bath particles are chiral. Using Brownian dynamics simulations, we study the effects of channel confinement and bath chirality on the effective forces and torques that are mediated between two inclusions that may be fixed within the channel or may be allowed to rotate freely as a rigid dimer around its center of mass. We show that the confinement has a strong effect on the effective interactions, depending on the orientation of the dimer relative to the channel walls. The active particle chirality leads to a force imbalance and, hence, a net torque on the inclusion dimer, which we investigate as a function of the bath chirality strength and the channel height.
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Affiliation(s)
- Abdolhalim Torrik
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
| | - Ali Naji
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Mahdi Zarif
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
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10
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Zhou Z, Joshi C, Liu R, Norton MM, Lemma L, Dogic Z, Hagan MF, Fraden S, Hong P. Machine learning forecasting of active nematics. SOFT MATTER 2021; 17:738-747. [PMID: 33220675 DOI: 10.1039/d0sm01316a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.
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11
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Mauleon-Amieva A, Mosayebi M, Hallett JE, Turci F, Liverpool TB, van Duijneveldt JS, Royall CP. Competing active and passive interactions drive amoebalike crystallites and ordered bands in active colloids. Phys Rev E 2020; 102:032609. [PMID: 33075940 DOI: 10.1103/physreve.102.032609] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 08/21/2020] [Indexed: 06/11/2023]
Abstract
Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.
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Affiliation(s)
- Abraham Mauleon-Amieva
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
- Bristol Centre for Functional Nanomaterials, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - Majid Mosayebi
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- BrisSynBio, Life Sciences Building, Tyndall Avenue, Bristol BS8 1TQ, United Kingdom
| | - James E Hallett
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - Francesco Turci
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Tanniemola B Liverpool
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- BrisSynBio, Life Sciences Building, Tyndall Avenue, Bristol BS8 1TQ, United Kingdom
| | | | - C Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
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12
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Herrera P, Apaza L, Sandoval M. One-dimensional displacement of active matter on curved substrates. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1711974] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Pedro Herrera
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
| | - Leonardo Apaza
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
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13
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Gutierrez-Martinez LL, Sandoval M. Inertial effects on trapped active matter. J Chem Phys 2020; 153:044906. [DOI: 10.1063/5.0011270] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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14
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Maloney RC, Hall CK. Clustering and Phase Separation in Mixtures of Dipolar and Active Particles in an External Field. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:6378-6387. [PMID: 32418424 DOI: 10.1021/acs.langmuir.0c00516] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Directing the assembly of colloidal particles through the use of external electric or magnetic fields shows promise for the creation of reconfigurable materials. Self-propelled particles can also be used to dynamically drive colloidal systems to nonequilibrium steady states. We investigate colloidal systems that combine both of these methods of directed assembly, simulating mixtures of passive dipolar colloids and active soft spheres in an external magnetic field using Brownian dynamics in two dimensions. In these systems, the dipolar particles align in the direction of the external field, but the active particles are unaffected by the field. The phase behaviors exhibited included a percolated dipolar network, dipolar string-fluid, isotropic fluid, and phase-separated state. We find that the external field allows the dipolar particles to form a percolated network more easily compared to when no external field is present. Additionally, the mixture phase separates at lower active particle velocity in an external field than when no field is present. Our results suggest that combining multiple methods of directing colloidal assembly could lead to new pathways to fabricate reconfigurable materials.
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Affiliation(s)
- Ryan C Maloney
- Department of Chemical Engineering, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27606, United States
| | - Carol K Hall
- Department of Chemical Engineering, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27606, United States
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15
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Agrawal M, Glotzer SC. Scale-free, programmable design of morphable chain loops of kilobots and colloidal motors. Proc Natl Acad Sci U S A 2020; 117:8700-8710. [PMID: 32265280 PMCID: PMC7183195 DOI: 10.1073/pnas.1922635117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Micron-scale robots require systems that can morph into arbitrary target configurations controlled by external agents such as heat, light, electricity, and chemical environment. Achieving this behavior using conventional approaches is challenging because the available materials at these scales are not programmable like their macroscopic counterparts. To overcome this challenge, we propose a design strategy to make a robotic machine that is both programmable and compatible with colloidal-scale physics. Our strategy uses motors in the form of active colloidal particles that constantly propel forward. We sequence these motors end-to-end in a closed chain forming a two-dimensional loop that folds under its mechanical constraints. We encode the target loop shape and its motion by regulating six design parameters, each scale-invariant and achievable at the colloidal scale. We demonstrate the plausibility of our design strategy using centimeter-scale robots called kilobots We use Brownian dynamics simulation to explore the large design space beyond that possible with kilobots, and present an analytical theory to aid the design process. Multiple loops can also be fused together to achieve several complex shapes and robotic behaviors, demonstrated by folding a letter shape "M," a dynamic gripper, and a dynamic pacman The material-agnostic, scale-free, and programmable nature of our design enables building a variety of reconfigurable and autonomous robots at both colloidal scales and macroscales.
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Affiliation(s)
- Mayank Agrawal
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136
| | - Sharon C Glotzer
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136;
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2136
- Biointerfaces Institute, University of Michigan, Ann Arbor, MI 48109-2136
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16
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Apaza L, Sandoval M. Homotopy analysis and Padé approximants applied to active Brownian motion. Phys Rev E 2020; 101:032103. [PMID: 32290001 DOI: 10.1103/physreve.101.032103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 02/15/2020] [Indexed: 06/11/2023]
Abstract
We apply the homotopy analysis method to the motion of noninteracting active Brownian particles (ABPs) under a general situation such as in the presence of external fields, external torques, or even moving on non-Euclidean geometries. Within this framework, a general expression as a series solution in time for the probability density function (PDF) satisfying the Fokker-Planck (FP) equation is elucidated. Using the latter PDF, their respective mean values (first and second moments) are also found in general. Applications of the present technique are offered by solving classic ABP situations, namely free noninteracting ABPs, ABPs under a Poiseuille flow, and even ABPs confined to move on any Riemannian manifold. To improve the convergence of the obtained series solution for each situation, Padé approximants are incorporated. It is worth mentioning that the offered methodology may exactly be applied to other fields such as chemistry, biology, or econophysics where a FP equation governs the system.
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Affiliation(s)
- Leonardo Apaza
- Department of Physics, Universidad Autonoma, Metropolitana-Iztapalapa, Mexico City 09340, Mexico
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma, Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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17
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Abstract
It has been discovered that active matter generates novel physical quantities such as the swim pressure. This quantity arises from the exchange of extra momentum between active particles and the boundaries of the system. Given its origin, this quantity can exist at different scales; hence microorganisms and larger organisms like fish or birds generate their own swim pressure. For larger organisms or for high swimming speeds, inertia cannot necessarily be neglected; hence in this paper, we start by calculating analytically the effect of finite translational and rotational particles' inertia on the diffusion of a system of noninteracting spherical active Brownian particles. From this analysis, an enhanced diffusion coefficient due to rotational inertia is obtained, and an alternative effective persistence length and an alternative reorientation time, both sensitive to rotational inertia, are also identified. Afterwards, and to see the implications of finite inertia on bulk properties, the pressure of this system is elucidated by calculating its respective swim and Reynolds pressures. It is found that their sum becomes asymptotically sensitive to the square root of its rotational inertia. To validate our analytical results, Langevin dynamics simulations are also performed showing an excellent agreement between our theoretical predictions and the numerical results.
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Affiliation(s)
- Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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18
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Hartmann R, Singh PK, Pearce P, Mok R, Song B, Díaz-Pascual F, Dunkel J, Drescher K. Emergence of three-dimensional order and structure in growing biofilms. NATURE PHYSICS 2019; 15:251-256. [PMID: 31156716 PMCID: PMC6544526 DOI: 10.1038/s41567-018-0356-9] [Citation(s) in RCA: 152] [Impact Index Per Article: 30.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Accepted: 10/19/2018] [Indexed: 05/22/2023]
Abstract
Surface-attached bacterial biofilms are self-replicating active liquid crystals and the dominant form of bacterial life on earth (1-4). In conventional liquid crystals and solid-state materials, the interaction potentials between the molecules that comprise the system determine the material properties. However, for growth-active biofilms it is unclear whether potential-based descriptions can account for the experimentally observed morphologies, and which potentials would be relevant. Here, we overcame previous limitations of single-cell imaging techniques (5,6) to reconstruct and track all individual cells inside growing three-dimensional (3D) biofilms with up to 10,000 individuals. Based on these data, we identify, constrain, and provide a microscopic basis for an effective cell-cell interaction potential, which captures and predicts the growth dynamics, emergent architecture, and local liquid crystalline order of Vibrio cholerae biofilms. Furthermore, we show how external fluid flows control the microscopic structure and 3D morphology of biofilms. Our analysis implies that local cellular order and global biofilm architecture in these active bacterial communities can arise from mechanical cell-cell interactions, which cells can modulate by regulating the production of particular matrix components. These results establish an experimentally validated foundation for improved continuum theories of active matter and thereby contribute to solving the important problem of controlling biofilm growth.
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Affiliation(s)
- Raimo Hartmann
- Max Planck Institute for Terrestrial Microbiology, 35043 Marburg,
DE
- Department of Physics, Philipps-Universität Marburg, 35032
Marburg, DE
| | - Praveen K. Singh
- Max Planck Institute for Terrestrial Microbiology, 35043 Marburg,
DE
| | - Philip Pearce
- Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
| | - Rachel Mok
- Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA
| | - Boya Song
- Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
| | | | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
- Correspondence to: ;
| | - Knut Drescher
- Max Planck Institute for Terrestrial Microbiology, 35043 Marburg,
DE
- Department of Physics, Philipps-Universität Marburg, 35032
Marburg, DE
- Correspondence to: ;
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19
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Lemma LM, DeCamp SJ, You Z, Giomi L, Dogic Z. Statistical properties of autonomous flows in 2D active nematics. SOFT MATTER 2019; 15:3264-3272. [PMID: 30920553 PMCID: PMC6924514 DOI: 10.1039/c8sm01877d] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs the motion of individual kinesin motors.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
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20
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Abstract
We formulate the dynamics of overdamped Brownian active particles (swimmers) moving on any Riemannian 2-manifold. To characterize such dynamics at short times, an analytical expression for the variance of swimmers diffusing on any Riemmanian 2-manifold is derived. To show the generality of the present work, we apply the latter dynamics to swimmers moving on the surface of a spheroid and a torus, and offer analytical expressions for both their long-time variances and steady angular marginal probability density functions. Finally, Brownian dynamics simulations are used to validate our theoretical findings.
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Affiliation(s)
- Leonardo Apaza
- Faculty of Pure and Natural Sciences, Universidad Mayor de San Andres, La Paz, Bolivia
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21
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Zumaya M, Larralde H, Aldana M. Delay in the dispersal of flocks moving in unbounded space using long-range interactions. Sci Rep 2018; 8:15872. [PMID: 30367121 PMCID: PMC6203710 DOI: 10.1038/s41598-018-34208-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Accepted: 10/03/2018] [Indexed: 01/18/2023] Open
Abstract
Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart. While the phase transition has been thoroughly studied, the conditions to keep the flock cohesive in open space are still poorly understood. Here we extend the Vicsek model of collective motion by introducing long-range alignment interactions between the particles. We show that just a small number of these interactions is enough for the system to build up long lasting ordered states of collective motion in open space and in the presence of noise. This finding was verified for other models in addition to the Vicsek one, suggesting its generality and revealing the importance that long-range interactions can have for the cohesion of the flock.
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Affiliation(s)
- Martín Zumaya
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Chamilpa, Código Postal, 62210, Cuernavaca, Morelos, Mexico
- Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de México, Mexico
| | - Hernán Larralde
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Chamilpa, Código Postal, 62210, Cuernavaca, Morelos, Mexico
| | - Maximino Aldana
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad s/n, Colonia Chamilpa, Código Postal, 62210, Cuernavaca, Morelos, Mexico.
- Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de México, Mexico.
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22
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Yang QS, Fan QW, Shen ZL, Xia YQ, Tian WD, Chen K. Beating of grafted chains induced by active Brownian particles. J Chem Phys 2018; 148:214904. [PMID: 29884058 DOI: 10.1063/1.5029967] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the interplay between active Brownian particles (ABPs) and a "hairy" surface in two-dimensional geometry. We find that the increase of propelling force leads to and enhances inhomogeneous accumulation of ABPs inside the brush region. Oscillation of chain bundles (beating like cilia) is found in company with the formation and disassembly of a dynamic cluster of ABPs at large propelling forces. Meanwhile chains are stretched and pushed down due to the effective shear force by ABPs. The decrease of the average brush thickness with propelling force reflects the growth of the beating amplitude of chain bundles. Furthermore, the beating phenomenon is investigated in a simple single-chain system. We find that the chain swings regularly with a major oscillatory period, which increases with chain length and decreases with the increase of propelling force. We build a theory to describe the phenomenon and the predictions on the relationship between the period and amplitude for various chain lengths, and propelling forces agree very well with simulation data.
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Affiliation(s)
- Qiu-Song Yang
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Qing-Wei Fan
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Zhuang-Lin Shen
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Yi-Qi Xia
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Wen-de Tian
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Kang Chen
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
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23
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Das SK. Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model. J Chem Phys 2018; 146:044902. [PMID: 28147512 DOI: 10.1063/1.4974256] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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24
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Ferreiro-Córdova C, Toner J, Löwen H, Wensink HH. Long-time anomalous swimmer diffusion in smectic liquid crystals. Phys Rev E 2018; 97:062606. [PMID: 30011607 DOI: 10.1103/physreve.97.062606] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Indexed: 06/08/2023]
Abstract
The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.
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Affiliation(s)
- Claudia Ferreiro-Córdova
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - John Toner
- Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Henricus H Wensink
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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25
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Sandoval M, Hidalgo-Gonzalez JC, Jimenez-Aquino JI. Self-driven particles in linear flows and trapped in a harmonic potential. Phys Rev E 2018; 97:032603. [PMID: 29776142 DOI: 10.1103/physreve.97.032603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 06/08/2023]
Abstract
We present analytical expressions for the mean-square displacement of self-driven particles in general linear flows and trapped in a harmonic potential. The general expressions are applied to three types of linear flows, namely, shear flow, solid-body rotation flow, and extensional flow. By using Brownian dynamics simulations, the effect of trapping and external linear flows on the particles' distribution is also elucidated. These simulations also enabled us to validate our theoretical results.
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Affiliation(s)
- Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
| | | | - Jose I Jimenez-Aquino
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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26
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Lee RM, Yue H, Rappel WJ, Losert W. Inferring single-cell behaviour from large-scale epithelial sheet migration patterns. J R Soc Interface 2018; 14:rsif.2017.0147. [PMID: 28490603 DOI: 10.1098/rsif.2017.0147] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Accepted: 04/13/2017] [Indexed: 12/22/2022] Open
Abstract
Cell migration plays an important role in a wide variety of biological processes and can incorporate both individual cell motion and collective behaviour. The emergent properties of collective migration are receiving increasing attention as collective motion's role in diseases such as metastatic cancer becomes clear. Yet, how individual cell behaviour influences large-scale, multi-cell collective motion remains unclear. In this study, we provide insight into the mechanisms behind collective migration by studying cell migration in a spreading monolayer of epithelial MCF10A cells. We quantify migration using particle image velocimetry and find that cell groups have features of motion that span multiple length scales. Comparing our experimental results to a model of collective cell migration, we find that cell migration within the monolayer can be affected in qualitatively different ways by cell motion at the boundary, yet it is not necessary to introduce leader cells at the boundary or specify other large-scale features to recapitulate this large-scale phenotype in simulations. Instead, in our model, collective motion can be enhanced by increasing the overall activity of the cells or by giving the cells a stronger coupling between their motion and polarity. This suggests that investigating the activity and polarity persistence of individual cells will add insight into the collective migration phenotypes observed during development and disease.
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Affiliation(s)
- Rachel M Lee
- Department of Physics, University of Maryland, College Park, MD, USA
| | - Haicen Yue
- Department of Physics, University of California, San Diego, CA, USA
| | | | - Wolfgang Losert
- Department of Physics, University of Maryland, College Park, MD, USA
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27
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Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics. ENTROPY 2017. [DOI: 10.3390/e19100562] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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28
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Apaza L, Sandoval M. Brownian self-driven particles on the surface of a sphere. Phys Rev E 2017; 96:022606. [PMID: 28950475 DOI: 10.1103/physreve.96.022606] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2017] [Indexed: 11/07/2022]
Abstract
We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.
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Affiliation(s)
- Leonardo Apaza
- Faculty of Pure and Natural Sciences, Universidad Mayor de San Andres, La Paz, Bolivia
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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29
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30
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Fan WTL, Pak OS, Sandoval M. Ellipsoidal Brownian self-driven particles in a magnetic field. Phys Rev E 2017; 95:032605. [PMID: 28415285 DOI: 10.1103/physreve.95.032605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2016] [Indexed: 06/07/2023]
Abstract
We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.
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Affiliation(s)
- Wai-Tong Louis Fan
- Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - On Shun Pak
- Department of Mechanical Engineering, Santa Clara University, Santa Clara, California 95053, USA
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Distrito Federal 09340, Mexico
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31
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Abstract
Biomolecular condensates are micron-scale compartments in eukaryotic cells that lack surrounding membranes but function to concentrate proteins and nucleic acids. These condensates are involved in diverse processes, including RNA metabolism, ribosome biogenesis, the DNA damage response and signal transduction. Recent studies have shown that liquid-liquid phase separation driven by multivalent macromolecular interactions is an important organizing principle for biomolecular condensates. With this physical framework, it is now possible to explain how the assembly, composition, physical properties and biochemical and cellular functions of these important structures are regulated.
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32
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Husain K, Rao M. Emergent Structures in an Active Polar Fluid: Dynamics of Shape, Scattering, and Merger. PHYSICAL REVIEW LETTERS 2017; 118:078104. [PMID: 28256860 DOI: 10.1103/physrevlett.118.078104] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2016] [Indexed: 06/06/2023]
Abstract
Spatially localized defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar "actin" filaments and "myosin" motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile-we derive effective equations of motion for these "extended particles" and analyze their shape, kinetics, interactions, and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger. Our results are relevant for the dynamics of actomyosin-dense structures at the cell cortex, reconstituted actomyosin complexes, and 2D active colloidal gels.
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Affiliation(s)
- Kabir Husain
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bellary Road, Bangalore 560 065, India
| | - Madan Rao
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bellary Road, Bangalore 560 065, India
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33
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Toner J, Löwen H, Wensink HH. Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media. Phys Rev E 2016; 93:062610. [PMID: 27415323 DOI: 10.1103/physreve.93.062610] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Indexed: 06/06/2023]
Abstract
Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to tlnt of the mean-square displacement with time t. This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.
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Affiliation(s)
- John Toner
- Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Henricus H Wensink
- Laboratoire de Physique des Solides, UMR 8502, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
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34
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Slowman AB, Evans MR, Blythe RA. Jamming and Attraction of Interacting Run-and-Tumble Random Walkers. PHYSICAL REVIEW LETTERS 2016; 116:218101. [PMID: 27284675 DOI: 10.1103/physrevlett.116.218101] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2015] [Indexed: 06/06/2023]
Abstract
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state. This stationary distribution has a rich structure comprising three components: a jammed component, where the particles are adjacent and block each other; an attractive component, where the probability distribution for the distance between particles decays exponentially; and an extended component in which the distance between particles is uniformly distributed. The attraction between the particles is sufficiently strong that even in the limit where continuous space is recovered for a finite system, the two walkers spend a finite fraction of time in a jammed configuration. Our results potentially provide a route to understanding the motility-induced phase separation characteristic of active matter from a microscopic perspective.
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Affiliation(s)
- A B Slowman
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M R Evans
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - R A Blythe
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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