1
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Dupont T, Giordano S, Cleri F, Blossey R. Short-time expansion of one-dimensional Fokker-Planck equations with heterogeneous diffusion. Phys Rev E 2024; 109:064106. [PMID: 39020937 DOI: 10.1103/physreve.109.064106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 05/07/2024] [Indexed: 07/20/2024]
Abstract
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter 0≤α≤1 of the stochastic integral. The kernel of the Fokker-Planck equation (the propagator) can be expressed as a product of a singular and a regular term. While the singular term can be given in closed form, the regular term can be computed from a Taylor expansion whose coefficients obey simple ordinary differential equations. We illustrate the application of our approach with examples taken from statistical physics and biophysics. Furthermore, we show how our formalism allows us to define a class of stochastic equations which can be treated exactly. The convergence of the expansion cannot be guaranteed independently from the discretization parameter α.
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Affiliation(s)
| | | | - Fabrizio Cleri
- University of Lille, Institut d'Électronique, de Microélectronique et de Nanotechnologie (IEMN CNRS UMR8520) and Departement de Physique, F-59652 Villeneuve d'Ascq, France
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2
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Tarama M, Mori K, Yamamoto R. Mechanochemical subcellular-element model of crawling cells. Front Cell Dev Biol 2022; 10:1046053. [PMID: 36544905 PMCID: PMC9760904 DOI: 10.3389/fcell.2022.1046053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 11/11/2022] [Indexed: 12/12/2022] Open
Abstract
Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.
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Affiliation(s)
- Mitsusuke Tarama
- Department of Physics, Kyushu University, Fukuoka, Japan,*Correspondence: Mitsusuke Tarama,
| | - Kenji Mori
- Department of Chemical Engineering, Kyoto University, Kyoto, Japan
| | - Ryoichi Yamamoto
- Department of Chemical Engineering, Kyoto University, Kyoto, Japan
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3
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Pagès DL, Dornier E, de Seze J, Gontran E, Maitra A, Maciejewski A, Wang L, Luan R, Cartry J, Canet-Jourdan C, Raingeaud J, Lemahieu G, Lebel M, Ducreux M, Gelli M, Scoazec JY, Coppey M, Voituriez R, Piel M, Jaulin F. Cell clusters adopt a collective amoeboid mode of migration in confined nonadhesive environments. SCIENCE ADVANCES 2022; 8:eabp8416. [PMID: 36179021 PMCID: PMC9524834 DOI: 10.1126/sciadv.abp8416] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Accepted: 08/03/2022] [Indexed: 05/28/2023]
Abstract
Cell migration is essential to living organisms and deregulated in cancer. Single cell's migration ranges from traction-dependent mesenchymal motility to contractility-driven propulsive amoeboid locomotion, but collective cell migration has only been described as a focal adhesion-dependent and traction-dependent process. Here, we show that cancer cell clusters, from patients and cell lines, migrate without focal adhesions when confined into nonadhesive microfabricated channels. Clusters coordinate and behave like giant super cells, mobilizing their actomyosin contractility at the rear to power their migration. This polarized cortex does not sustain persistent retrograde flows, of cells or actin, like in the other modes of migration but rather harnesses fluctuating cell deformations, or jiggling. Theoretical physical modeling shows this is sufficient to create a gradient of friction forces and trigger directed cluster motion. This collective amoeboid mode of migration could foster metastatic spread by enabling cells to cross a wide spectrum of environments.
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Affiliation(s)
- Diane-Laure Pagès
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
- Université Paris-Saclay, Inserm, Institut Gustave Roussy, Dynamique des Cellules Tumorales, Villejuif 94800, France
| | | | - Jean de Seze
- Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, Sorbonne Université, CNRS, Paris 75005, France
| | - Emilie Gontran
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
| | - Ananyo Maitra
- Laboratoire Jean Perrin, UMR 8237 CNRS/Sorbonne Université, Paris 75255, France
| | - Aurore Maciejewski
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
- Université Paris-Saclay, Inserm, Institut Gustave Roussy, Dynamique des Cellules Tumorales, Villejuif 94800, France
| | - Li Wang
- Institut Curie and Institut Pierre Gilles de Gennes, PSL Research University, CNRS, UMR 144, Paris 75005, France
| | - Rui Luan
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
| | - Jérôme Cartry
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
| | - Charlotte Canet-Jourdan
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
- Université Paris-Saclay, Inserm, Institut Gustave Roussy, Dynamique des Cellules Tumorales, Villejuif 94800, France
| | - Joël Raingeaud
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
| | | | | | - Michel Ducreux
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
- Département de Médecine Oncologique, Gustave Roussy, Université Paris-Saclay, Villejuif F-94805, France
| | - Maximiliano Gelli
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
- Département de Chirurgie Viscérale, Gustave Roussy, Villejuif F-94805, France
| | - Jean-Yves Scoazec
- Service de Pathologie, Département de Biologie et Pathologie Médicale, Gustave Roussy, Villejuif F-94805, France
- Faculté de Médecine, Université Paris Saclay, Le Kremlin-Bicêtre F-94270, France
| | - Mathieu Coppey
- Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, Sorbonne Université, CNRS, Paris 75005, France
| | - Raphaël Voituriez
- Laboratoire Jean Perrin, UMR 8237 CNRS/Sorbonne Université, Paris 75255, France
- Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/Sorbonne Université, Paris 75255, France
| | - Matthieu Piel
- Institut Curie and Institut Pierre Gilles de Gennes, PSL Research University, CNRS, UMR 144, Paris 75005, France
| | - Fanny Jaulin
- Inserm U-1279, Gustave Roussy, Villejuif F-94805, France
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4
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Plati A, Puglisi A. Collective Drifts in Vibrated Granular Packings: The Interplay of Friction and Structure. PHYSICAL REVIEW LETTERS 2022; 128:208001. [PMID: 35657874 DOI: 10.1103/physrevlett.128.208001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Revised: 02/18/2022] [Accepted: 04/04/2022] [Indexed: 06/15/2023]
Abstract
We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stick slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.
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Affiliation(s)
- A Plati
- Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - A Puglisi
- Department of Physics, University of Rome Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems-CNR, Piazzale Aldo Moro 2, 00185 Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
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5
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Vladimirova N, Shavit M, Belan S, Falkovich G. Second-harmonic generation as a minimal model of turbulence. Phys Rev E 2021; 104:014129. [PMID: 34412364 DOI: 10.1103/physreve.104.014129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 05/27/2021] [Indexed: 11/07/2022]
Abstract
When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering a noise-driven system, we show that when one mode is pumped and another dissipates, the statistics of such cascades is never close to Gaussian, no matter what is the relation between interaction and noise. One finds substantial phase correlation in the limit of strong interaction or weak noise. Surprisingly, the mutual information between modes increases and entropy decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information, or entropy deficit, is encoded, and how singular measures form. For an instability-driven system, such as laser, even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from the equilibrium the conversion into the second harmonic is weakly affected by noise.
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Affiliation(s)
- N Vladimirova
- Brown University, Providence, Rhode Island 02912, USA.,Weizmann Institute of Science, Rehovot 76100, Israel
| | - M Shavit
- Weizmann Institute of Science, Rehovot 76100, Israel
| | - S Belan
- Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia.,National Research University Higher School of Economics, 101000 Moscow, Russia
| | - G Falkovich
- Weizmann Institute of Science, Rehovot 76100, Israel
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6
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Breoni D, Löwen H, Blossey R. Active noise-driven particles under space-dependent friction in one dimension. Phys Rev E 2021; 103:052602. [PMID: 34134234 DOI: 10.1103/physreve.103.052602] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 04/14/2021] [Indexed: 12/24/2022]
Abstract
We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate x, which is simultaneously exposed to a space-dependent friction coefficient γ(x), a confining potential U(x) and nonequilibrium (i.e., active) noise. Specifically, we consider frictions γ(x)=γ_{0}+γ_{1}|x|^{p} and potentials U(x)∝|x|^{n} with exponents p=1,2 and n=0,1,2. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behavior displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values (p,n). The PDFs interpolate between Laplacian, Gaussian, and bimodal distributions, whereby a change between these different behaviors can be achieved by a tuning of the friction strengths ratio γ_{0}/γ_{1}. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.
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Affiliation(s)
- D Breoni
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitässtraße 1, 40225 Düsseldorf, Germany
| | - H Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitässtraße 1, 40225 Düsseldorf, Germany
| | - R Blossey
- University of Lille, UGSF CNRS UMR8576, 59000 Lille, France
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7
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Belan S, Kardar M. Active motion of passive asymmetric dumbbells in a non-equilibrium bath. J Chem Phys 2021; 154:024109. [PMID: 33445886 DOI: 10.1063/5.0030623] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein-Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v∥l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.
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Affiliation(s)
- Sergey Belan
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, 1-A Akademika Semenova av., 142432 Chernogolovka, Russia
| | - Mehran Kardar
- Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA
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8
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Vishen AS, Prost J, Rao M. Breakdown of effective temperature, power law interactions, and self-propulsion in a momentum-conserving active fluid. Phys Rev E 2020; 100:062602. [PMID: 31962504 DOI: 10.1103/physreve.100.062602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Indexed: 11/07/2022]
Abstract
The simplest extensions of single-particle dynamics in a momentum-conserving active fluid-an active suspension of two colloidal particles or a single particle confined by a wall-exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero-entropy production rate. This is a consequence of hydrodynamic interactions that introduce multiplicative noise in the stochastic description of particle positions. This results in fluctuation-induced interactions that depend on distance as a power law. We find that the dynamics of activated colloids in a passive fluid, with stochastic forcing localized on the particle, is different from that of passive colloids in an active fluctuating fluid.
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Affiliation(s)
- Amit Singh Vishen
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore 560065, India
| | - Jacques Prost
- Mechanobiology Institute and Department of Biological Sciences, National University of Singapore, Singapore 117411.,Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, 75005 Paris, France
| | - Madan Rao
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore 560065, India
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9
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Mayett D, Bitten N, Das M, Schwarz JM. Chase-and-run dynamics in cell motility and the molecular rupture of interacting active elastic dimers. Phys Rev E 2017; 96:032407. [PMID: 29346935 DOI: 10.1103/physreve.96.032407] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2016] [Indexed: 06/07/2023]
Abstract
Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model composed of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading from the interacting motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the threshold force and, therefore, posit that active rupture, or rupture via active forces, is a mechanosensitive means to regulate dynamics between cells. Since the parameters in the model differentiate between N- and E-cadherins, we make predictions for the interactions between a placodelike cell and a neural crestlike cell in a microchannel as well as discuss how our results inform chase-and-run dynamics found in a group of placode cells interacting with a group of neural crest cells. In particular, an argument was made in the latter case that the feedback between cadherins and cell-substrate interaction via integrins was necessary to obtain the chase-and-run behavior. Based on our two-cell results, we argue that this feedback accentuates, but is not necessary for, the chase-and-run behavior.
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Affiliation(s)
- David Mayett
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| | - Nicholas Bitten
- School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Moumita Das
- School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - J M Schwarz
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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10
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Kumar N, Soni H, Ramaswamy S, Sood AK. Flocking at a distance in active granular matter. Nat Commun 2014; 5:4688. [PMID: 25181961 DOI: 10.1038/ncomms5688] [Citation(s) in RCA: 135] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 07/14/2014] [Indexed: 11/09/2022] Open
Abstract
The self-organized motion of vast numbers of creatures in a single direction is a spectacular example of emergent order. Here, we recreate this phenomenon using actuated nonliving components. We report here that millimetre-sized tapered rods, rendered motile by contact with an underlying vibrated surface and interacting through a medium of spherical beads, undergo a phase transition to a state of spontaneous alignment of velocities and orientations above a threshold bead area fraction. Guided by a detailed simulation model, we construct an analytical theory of this flocking transition, with two ingredients: a moving rod drags beads; neighbouring rods reorient in the resulting flow like a weathercock in the wind. Theory and experiment agree on the structure of our phase diagram in the plane of rod and bead concentrations and power-law spatial correlations near the phase boundary. Our discovery suggests possible new mechanisms for the collective transport of particulate or cellular matter.
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Affiliation(s)
- Nitin Kumar
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
| | - Harsh Soni
- 1] Department of Physics, Indian Institute of Science, Bangalore 560 012, India [2] TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Osman Sagar Road, Narsingi, Hyderabad 500 075, India
| | - Sriram Ramaswamy
- 1] Department of Physics, Indian Institute of Science, Bangalore 560 012, India [2] TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Osman Sagar Road, Narsingi, Hyderabad 500 075, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India
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11
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Lopez JH, Das M, Schwarz JM. Active elastic dimers: cells moving on rigid tracks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032707. [PMID: 25314473 DOI: 10.1103/physreve.90.032707] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2014] [Indexed: 06/04/2023]
Abstract
Experiments suggest that the migration of some cells in the three-dimensional extracellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and α-actinin-driven extendability, while the friction coefficients of the two beads describe the catch and slip-bond behaviors of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch-bond behavior of integrins at the front of the cell and slip-bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch-bond behavior and the dynamics of cross linking, and the addition of active noise on the motion of the cell. Our model highlights the role of α-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.
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Affiliation(s)
- J H Lopez
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| | - Moumita Das
- School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - J M Schwarz
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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12
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Makhnovskii YA, Rozenbaum VM, Sheu SY, Yang DY, Trakhtenberg LI, Lin SH. Fluctuation-induced transport of two coupled particles: Effect of the interparticle interaction. J Chem Phys 2014; 140:214108. [DOI: 10.1063/1.4880416] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Speer D, Eichhorn R, Evstigneev M, Reimann P. Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061132. [PMID: 23005076 DOI: 10.1103/physreve.85.061132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2012] [Indexed: 06/01/2023]
Abstract
We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.
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Affiliation(s)
- David Speer
- Universität Bielefeld, Fakultät für Physik, 33615 Bielefeld, Germany
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14
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Romanczuk P, Ebeling W, Erdmann U, Schimansky-Geier L. Active particles with broken symmetry. CHAOS (WOODBURY, N.Y.) 2011; 21:047517. [PMID: 22225391 DOI: 10.1063/1.3669493] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We discuss and analyze the driving a polar active particle with a head-tail asymmetry based on the dynamics of an internal motor variable driven by an energy depot and a broken symmetry of friction with respect to the internal degree of freedom. We show that such a driving may be advantageous for driving large masses with small energy uptake from the environment and exhibits interesting properties such as resonance-driven optimal propulsion.
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Affiliation(s)
- Pawel Romanczuk
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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15
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Romanczuk P, Schimansky-Geier L. Brownian motion with active fluctuations. PHYSICAL REVIEW LETTERS 2011; 106:230601. [PMID: 21770491 DOI: 10.1103/physrevlett.106.230601] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2010] [Indexed: 05/31/2023]
Abstract
We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.
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Affiliation(s)
- Pawel Romanczuk
- Institute of Physics, Humboldt University at Berlin, Berlin, Germany.
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16
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von Gehlen S, Evstigneev M, Reimann P. Ratchet effect of a dimer with broken friction symmetry in a symmetric potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031114. [PMID: 19391909 DOI: 10.1103/physreve.79.031114] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2009] [Indexed: 05/27/2023]
Abstract
The one-dimensional overdamped Brownian motion of a dimer consisting of two harmonically interacting components is considered. Both components are coupled to the same heat bath and feel the same spatially periodic symmetric potential, whose amplitude is modulated periodically in time. The friction coefficients may differ between dimer components, thus breaking the dynamical symmetry of the system. In the absence of any external bias, a ratchet effect (directed transport) arises generically. Two accurate approximations for the dimer's velocity and diffusion coefficient are obtained for weak and strong couplings. The velocity of the system can be maximized for each direction by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exist two optimal coupling strengths at which the velocity is the largest.
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