1
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Ignés-Mullol J, Sagués F. Experiments with active and driven synthetic colloids in complex fluids. Curr Opin Colloid Interface Sci 2022. [DOI: 10.1016/j.cocis.2022.101636] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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2
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Maggs JE, Morales GJ. Time-integral iteration method for two-dimensional anomalous transport. Phys Rev E 2022; 106:045201. [PMID: 36397469 DOI: 10.1103/physreve.106.045201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
A methodology is developed to describe time-dependent phenomena associated with nonlocal transport in complex, two-dimensional geometries. It is an extension of the ''iterative method" introduced previously to solve steady-state transport problems [Maggs and Morales, Phys. Rev. E 99, 013307 (2019)10.1103/PhysRevE.99.013307], and it is based on the ''jumping particle" concepts associated with the continuous-time random walk (CTRW) model. The method presented explicitly evaluates the time integral contained in the CTRW master equation. A modified version of the Mittag-Leffler function is used for the waiting-time probability distributions to incorporate memory effects. Calculations of the propagation of ''anomalous transport waves" in various systems, with and without memory, illustrate the technique.
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Affiliation(s)
- J E Maggs
- Department of Physics and Astronomy, University of California, Los Angeles, California 90025, USA
| | - G J Morales
- Department of Physics and Astronomy, University of California, Los Angeles, California 90025, USA
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3
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Fernández Casafuz AB, De Rossi MC, Bruno L. Intracellular motor-driven transport of rodlike smooth organelles along microtubules. Phys Rev E 2021; 101:062416. [PMID: 32688554 DOI: 10.1103/physreve.101.062416] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 06/01/2020] [Indexed: 12/21/2022]
Abstract
Molecular motors are fascinating proteins that use the energy of ATP hydrolysis to drive vesicles and organelles along cytoskeleton filaments toward their final destination within the cell. Several copies of these proteins bind to the cargo and take turns transporting the cargo attaching to and detaching from the track stochastically. Despite the relevance of molecular motors to cell physiology, key aspects of their collective functioning are still unknown. In this work we propose a one-dimensional model for the transport of extensive and smooth organelles driven by molecular motors. We ran numerical simulations to study the behavior of the cargo for different motor configurations, focusing on the transport properties observable in the experiments, e.g., average speed of the organelle and variations in length. We found that active motors drive the cargo using two different mechanisms: Either they locate in front of the cargo and pull the organelle or they situate at the cargo lagging edge and push. Variations in the organelle length is in close relation with the fraction of motors in each configuration, which depends on the resisting load. The results of this model were contrasted with experimental data obtained from the tracking of rodlike mitochondria during active transport in Xenopus laevis melanophores.
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Affiliation(s)
- A B Fernández Casafuz
- Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
| | - M C De Rossi
- Departamento de Química Biológica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
| | - L Bruno
- Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina.,Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
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4
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Guisoni N, Mazzitello KI, Diambra L. Alternating regimes of motion in a model with cell-cell interactions. Phys Rev E 2020; 101:062408. [PMID: 32688606 DOI: 10.1103/physreve.101.062408] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2019] [Accepted: 05/26/2020] [Indexed: 11/07/2022]
Abstract
Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra- and extracellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases, cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we have considered a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolve according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In one case, the next orientation of the driving field depends on the previous direction of the field. In the other case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Different cell densities are considered to reveal the effect of cell-cell interactions. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction-coefficient and cell-density-dependent manner. Furthermore, we observe alternating regimes in the mean-square displacement, with normal and anomalous diffusion. The crossovers between diffusive and directed motion regimes are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement, the duration of the diffusive regime decreases, particularly in high-density cultures.
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Affiliation(s)
- Nara Guisoni
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CONICET, 1900 La Plata, Buenos Aires, Argentina
| | - Karina I Mazzitello
- Instituto de Investigaciones Científicas y Tecnológicas en Electrónica, Universidad Nacional de Mar del Plata, CONICET, B7608 Mar del Plata, Buenos Aires, Argentina
| | - Luis Diambra
- Centro Regional de Estudios Genómicos, Universidad Nacional de La Plata, CONICET, 1900 La Plata, Buenos Aires, Argentina
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5
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Apparent stiffness of vimentin intermediate filaments in living cells and its relation with other cytoskeletal polymers. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2020; 1867:118726. [PMID: 32320724 DOI: 10.1016/j.bbamcr.2020.118726] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Revised: 04/11/2020] [Accepted: 04/15/2020] [Indexed: 12/12/2022]
Abstract
The cytoskeleton is a complex network of interconnected biopolymers intimately involved in the generation and transmission of forces. Several mechanical properties of microtubules and actin filaments have been extensively explored in cells. In contrast, intermediate filaments (IFs) received comparatively less attention despite their central role in defining cell shape, motility and adhesion during physiological processes as well as in tumor progression. Here, we explored relevant biophysical properties of vimentin IFs in living cells combining confocal microscopy and a filament tracking routine that allows localizing filaments with ~20 nm precision. A Fourier-based analysis showed that IFs curvatures followed a thermal-like behavior characterized by an apparent persistence length (lp*) similar to that measured in aqueous solution. Additionally, we determined that certain perturbations of the cytoskeleton affect lp* and the lateral mobility of IFs as assessed in cells in which either the microtubule dynamic instability was reduced or actin filaments were partially depolymerized. Our results provide relevant clues on how vimentin IFs mechanically couple with microtubules and actin filaments in cells and support a role of this network in the response to mechanical stress.
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6
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Pagès JM, Ignés-Mullol J, Sagués F. Anomalous Diffusion of Motile Colloids Dispersed in Liquid Crystals. PHYSICAL REVIEW LETTERS 2019; 122:198001. [PMID: 31144957 DOI: 10.1103/physrevlett.122.198001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 06/09/2023]
Abstract
We study the superdiffusion of driven colloidal particles dispersed in a nematic liquid crystal. While motion is ballistic in the driving direction, our experiments show that transversal fluctuations become superdiffusive depending on the topological defect pattern around the inclusions. The phenomenon can be reproduced with different driving methods and propulsion speeds, while it is strongly dependent on particle size and temperature. We propose a mechanism based on the geometry of the liquid crystal backflow around the inclusions to justify the persistence of thermal fluctuations and to explain the observed temperature and particle size dependence of the superdiffusive behavior based on material and geometrical parameters.
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Affiliation(s)
- Josep M Pagès
- Departament de Ciència de Materials i Química Física, and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
| | - Jordi Ignés-Mullol
- Departament de Ciència de Materials i Química Física, and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
| | - Francesc Sagués
- Departament de Ciència de Materials i Química Física, and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
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7
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Kuśmierz Ł, Gudowska-Nowak E. Subdiffusive continuous-time random walks with stochastic resetting. Phys Rev E 2019; 99:052116. [PMID: 31212503 DOI: 10.1103/physreve.99.052116] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2018] [Indexed: 06/09/2023]
Abstract
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk scheme and independent resetting events generated uniformly in time according to the Poisson point process. In the first model the whole process is reset to the initial state, whereas in the second model only the position is subject to resets. The distinction between these two models arises from the non-Markovian character of the subdiffusive process. We derive exact expressions for the two lowest moments of the full propagator, stationary distributions, and first hitting time statistics. We also show, with an example of a constant drift, how these models can be generalized to include external forces. Possible applications to data analysis and modeling of biological systems are also discussed.
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Affiliation(s)
- Łukasz Kuśmierz
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Ewa Gudowska-Nowak
- Marian Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
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8
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Korabel N, Waigh TA, Fedotov S, Allan VJ. Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate. PLoS One 2018; 13:e0207436. [PMID: 30475848 PMCID: PMC6261056 DOI: 10.1371/journal.pone.0207436] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2018] [Accepted: 10/31/2018] [Indexed: 11/19/2022] Open
Abstract
Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental trajectories of organelles inside a living cell and propose a mathematical model that describes the previously reported transition from sub-diffusive to super-diffusive motion. In order to explain super-diffusive behaviour at long times, we introduce non-Markovian detachment kinetics of the cargo: the rate of detachment is inversely proportional to the time since the last attachment. Recently, we observed the non-Markovian detachment rate experimentally in eukaryotic cells. Here we further discuss different scenarios of how this effective non-Markovian detachment rate could arise. The non-Markovian model is successful in simultaneously describing the time averaged variance (the time averaged mean squared displacement corrected for directed motion), the mean first passage time of trajectories and the multiple peaks observed in the distributions of cargo velocities. We argue that non-Markovian kinetics could be biologically beneficial compared to the Markovian kinetics commonly used for modelling, by increasing the average distance the cargoes travel when a microtubule is blocked by other filaments. In turn, sub-diffusion allows cargoes to reach neighbouring filaments with higher probability, which promotes active motion along the microtubules.
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Affiliation(s)
- Nickolay Korabel
- School of Mathematics, University of Manchester, Manchester, United Kingdom
- * E-mail:
| | - Thomas A. Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
- The Photon Science Institute, University of Manchester, Manchester, United Kingdom
| | - Sergei Fedotov
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Viki J. Allan
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, Manchester, United Kingdom
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9
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Goychuk I. Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol. Biosystems 2018; 177:56-65. [PMID: 30419266 DOI: 10.1016/j.biosystems.2018.11.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Revised: 11/06/2018] [Accepted: 11/07/2018] [Indexed: 11/17/2022]
Abstract
Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
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10
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Mogre SS, Koslover EF. Multimodal transport and dispersion of organelles in narrow tubular cells. Phys Rev E 2018; 97:042402. [PMID: 29758750 DOI: 10.1103/physreve.97.042402] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2017] [Indexed: 11/07/2022]
Abstract
Intracellular components explore the cytoplasm via active motor-driven transport in conjunction with passive diffusion. We model the motion of organelles in narrow tubular cells using analytical techniques and numerical simulations to study the efficiency of different transport modes in achieving various cellular objectives. Our model describes length and time scales over which each transport mode dominates organelle motion, along with various metrics to quantify exploration of intracellular space. For organelles that search for a specific target, we obtain the average capture time for given transport parameters and show that diffusion and active motion contribute to target capture in the biologically relevant regime. Because many organelles have been found to tether to microtubules when not engaged in active motion, we study the interplay between immobilization due to tethering and increased probability of active transport. We derive parameter-dependent conditions under which tethering enhances long-range transport and improves the target capture time. These results shed light on the optimization of intracellular transport machinery and provide experimentally testable predictions for the effects of transport regulation mechanisms such as tethering.
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Affiliation(s)
- Saurabh S Mogre
- Department of Physics, University of California San Diego, La Jolla, California 92093, USA
| | - Elena F Koslover
- Department of Physics, University of California San Diego, La Jolla, California 92093, USA
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11
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Goychuk I. Viscoelastic subdiffusion in a random Gaussian environment. Phys Chem Chem Phys 2018; 20:24140-24155. [PMID: 30206605 DOI: 10.1039/c8cp05238g] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several kBT, in the units of thermal energy), and strong (5-10kBT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compared with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
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12
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Mankin R, Laas K, Laas T, Paekivi S. Memory effects for a stochastic fractional oscillator in a magnetic field. Phys Rev E 2018; 97:012145. [PMID: 29448378 DOI: 10.1103/physreve.97.012145] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2017] [Indexed: 06/08/2023]
Abstract
The problem of random motion of harmonically trapped charged particles in a constant external magnetic field is studied. A generalized three-dimensional Langevin equation with a power-law memory kernel is used to model the interaction of Brownian particles with the complex structure of viscoelastic media (e.g., dusty plasmas). The influence of a fluctuating environment is modeled by an additive fractional Gaussian noise. In the long-time limit the exact expressions of the first-order and second-order moments of the fluctuating position for the Brownian particle subjected to an external periodic force in the plane perpendicular to the magnetic field have been calculated. Also, the particle's angular momentum is found. It is shown that an interplay of external periodic forcing, memory, and colored noise can generate a variety of cooperation effects, such as memory-induced sign reversals of the angular momentum, multiresonance versus Larmor frequency, and memory-induced particle confinement in the absence of an external trapping field. Particularly in the case without external trapping, if the memory exponent is lower than a critical value, we find a resonancelike behavior of the anisotropy in the particle position distribution versus the driving frequency, implying that it can be efficiently excited by an oscillating electric field. Similarities and differences between the behaviors of the models with internal and external noises are also discussed.
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Affiliation(s)
- Romi Mankin
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Katrin Laas
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Tõnu Laas
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Sander Paekivi
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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13
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Pegoraro AF, Janmey P, Weitz DA. Mechanical Properties of the Cytoskeleton and Cells. Cold Spring Harb Perspect Biol 2017; 9:9/11/a022038. [PMID: 29092896 DOI: 10.1101/cshperspect.a022038] [Citation(s) in RCA: 151] [Impact Index Per Article: 21.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
SUMMARYThe cytoskeleton is the major mechanical structure of the cell; it is a complex, dynamic biopolymer network comprising microtubules, actin, and intermediate filaments. Both the individual filaments and the entire network are not simple elastic solids but are instead highly nonlinear structures. Appreciating the mechanics of biopolymer networks is key to understanding the mechanics of cells. Here, we review the mechanical properties of cytoskeletal polymers and discuss the implications for the behavior of cells.
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Affiliation(s)
- Adrian F Pegoraro
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
| | - Paul Janmey
- Institute for Medicine and Engineering and Department of Physiology, Perelman School of Medicine, and Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - David A Weitz
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
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14
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Tavakoli M, Taylor JN, Li CB, Komatsuzaki T, Pressé S. Single Molecule Data Analysis: An Introduction. ADVANCES IN CHEMICAL PHYSICS 2017. [DOI: 10.1002/9781119324560.ch4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Meysam Tavakoli
- Physics Department; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
| | - J. Nicholas Taylor
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
| | - Chun-Biu Li
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
- Department of Mathematics; Stockholm University; 106 91 Stockholm Sweden
| | - Tamiki Komatsuzaki
- Research Institute for Electronic Science; Hokkaido University; Kita 20 Nishi 10 Kita-Ku Sapporo 001-0020 Japan
| | - Steve Pressé
- Physics Department; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
- Department of Chemistry and Chemical Biology; Indiana University-Purdue University Indianapolis; Indianapolis IN 46202 USA
- Department of Cell and Integrative Physiology; Indiana University School of Medicine; Indianapolis IN 46202 USA
- Department of Physics and School of Molecular Sciences; Arizona State University; Tempe AZ 85287 USA
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15
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Lee A, Tsekouras K, Calderon C, Bustamante C, Pressé S. Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis. Chem Rev 2017; 117:7276-7330. [PMID: 28414216 PMCID: PMC5487374 DOI: 10.1021/acs.chemrev.6b00729] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.
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Affiliation(s)
- Antony Lee
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Jason L. Choy Laboratory of Single-Molecule Biophysics, University of California at Berkeley, Berkeley, California 94720, United States
| | - Konstantinos Tsekouras
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
| | | | - Carlos Bustamante
- Jason L. Choy Laboratory of Single-Molecule Biophysics, University of California at Berkeley, Berkeley, California 94720, United States
- Biophysics Graduate Group, University of California at Berkeley, Berkeley, California 94720, United States
- Institute for Quantitative Biosciences-QB3, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Howard Hughes Medical Institute, University of California at Berkeley, Berkeley, California 94720, United States
- Kavli Energy Nanosciences Institute, University of California at Berkeley, Berkeley, California 94720, United States
| | - Steve Pressé
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, United States
- Department of Chemistry and Chemical Biology, Indiana University–Purdue University Indianapolis, Indianapolis, Indiana 46202, United States
- Department of Cell and Integrative Physiology, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287, United States
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
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16
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Hafner AE, Santen L, Rieger H, Shaebani MR. Run-and-pause dynamics of cytoskeletal motor proteins. Sci Rep 2016; 6:37162. [PMID: 27849013 PMCID: PMC5111058 DOI: 10.1038/srep37162] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Accepted: 10/25/2016] [Indexed: 11/23/2022] Open
Abstract
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. When attached to cytoskeletal filaments, the motor exhibits distinct states of motility: active motion along the filaments, and pause phase in which it remains stationary for a finite time interval. The transition probabilities between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of individual non-interacting molecular motors on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition probabilities between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition probabilities, and address the role of initial conditions of motion on the resulting dynamics.
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Affiliation(s)
- Anne E. Hafner
- Department of Theoretical Physics, Saarland University, 66041 Saarbrücken, Germany
| | - Ludger Santen
- Department of Theoretical Physics, Saarland University, 66041 Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics, Saarland University, 66041 Saarbrücken, Germany
| | - M. Reza Shaebani
- Department of Theoretical Physics, Saarland University, 66041 Saarbrücken, Germany
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17
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An Intermittent Model for Intracellular Motions of Gold Nanostars by k-Space Scattering Image Correlation. Biophys J 2016; 109:2246-58. [PMID: 26636936 DOI: 10.1016/j.bpj.2015.10.025] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2015] [Revised: 10/09/2015] [Accepted: 10/21/2015] [Indexed: 11/20/2022] Open
Abstract
Anisotropic metallic nanoparticles have been devised as powerful potential tools for in vivo imaging, photothermal therapy, and drug delivery thanks to plasmon-enhanced absorption and scattering cross sections, ease in synthesis and functionalization, and controlled cytotoxicity. The rational design of all these applications requires the characterization of the nanoparticles intracellular trafficking pathways. In this work, we exploit live-cell time-lapse confocal reflectance microscopy and image correlation in both direct and reciprocal space to investigate the intracellular transport of branched gold nanostars (GNSs). Different transport mechanisms, spanning from pure Brownian diffusion to (sub-)ballistic superdiffusion, are revealed by temporal and spatio-temporal image correlation spectroscopy on the tens-of-seconds timescale. According to these findings, combined with numerical simulations and with a Bayesian (hidden Markov model-based) analysis of single particle tracking data, we ascribe the superdiffusive, subballistic behavior characterizing the GNSs dynamics to a two-state switching between Brownian diffusion in the cytoplasm and molecular motor-mediated active transport. For the investigation of intermittent-type transport phenomena, we derive an analytical theoretical framework for Fourier-space image correlation spectroscopy (kICS). At first, we evaluate the influence of all the dynamic and kinetic parameters (the diffusion coefficient, the drift velocity, and the transition rates between the diffusive and the active transport regimes) on simulated kICS correlation functions. Then we outline a protocol for data analysis and employ it to derive whole-cell maps for each parameter underlying the GNSs intracellular dynamics. Capable of identifying even simpler transport phenomena, whether purely diffusive or ballistic, our intermittent kICS approach allows an exhaustive investigation of the dynamics of GNSs and biological macromolecules.
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Goychuk I. Molecular machines operating on the nanoscale: from classical to quantum. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2016; 7:328-50. [PMID: 27335728 PMCID: PMC4901870 DOI: 10.3762/bjnano.7.31] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2015] [Accepted: 01/29/2016] [Indexed: 05/18/2023]
Abstract
The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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19
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Campagnola G, Nepal K, Schroder BW, Peersen OB, Krapf D. Superdiffusive motion of membrane-targeting C2 domains. Sci Rep 2015; 5:17721. [PMID: 26639944 PMCID: PMC4671060 DOI: 10.1038/srep17721] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2015] [Accepted: 11/04/2015] [Indexed: 11/09/2022] Open
Abstract
Membrane-targeting domains play crucial roles in the recruitment of signalling molecules to the plasma membrane. For most peripheral proteins, the protein-to-membrane interaction is transient. After proteins dissociate from the membrane they have been observed to rebind following brief excursions in the bulk solution. Such membrane hops can have broad implications for the efficiency of reactions on membranes. We study the diffusion of membrane-targeting C2 domains using single-molecule tracking in supported lipid bilayers. The ensemble-averaged mean square displacement (MSD) exhibits superdiffusive behaviour. However, traditional time-averaged MSD analysis of individual trajectories remains linear and does not reveal superdiffusion. Our observations are explained in terms of bulk excursions that introduce jumps with a heavy-tail distribution. These hopping events allow proteins to explore large areas in a short time. The experimental results are shown to be consistent with analytical models of bulk-mediated diffusion and numerical simulations.
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Affiliation(s)
- Grace Campagnola
- Department of Biochemistry and Molecular Biology, Colorado State University, Fort Collins, CO 80523, USA
| | - Kanti Nepal
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA
| | - Bryce W Schroder
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA
| | - Olve B Peersen
- Department of Biochemistry and Molecular Biology, Colorado State University, Fort Collins, CO 80523, USA.,School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA
| | - Diego Krapf
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA.,Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA
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Cairoli A, Baule A. Anomalous processes with general waiting times: functionals and multipoint structure. PHYSICAL REVIEW LETTERS 2015; 115:110601. [PMID: 26406815 DOI: 10.1103/physrevlett.115.110601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2014] [Indexed: 06/05/2023]
Abstract
Many transport processes in nature exhibit anomalous diffusive properties with nontrivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multipoint structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.
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Affiliation(s)
- Andrea Cairoli
- School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, United Kingdom
| | - Adrian Baule
- School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, United Kingdom
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21
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Reverey JF, Jeon JH, Bao H, Leippe M, Metzler R, Selhuber-Unkel C. Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii. Sci Rep 2015; 5:11690. [PMID: 26123798 PMCID: PMC5155589 DOI: 10.1038/srep11690] [Citation(s) in RCA: 126] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Accepted: 06/01/2015] [Indexed: 12/21/2022] Open
Abstract
Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.
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Affiliation(s)
- Julia F Reverey
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
| | - Jae-Hyung Jeon
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea
| | - Han Bao
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
| | - Matthias Leippe
- Zoological Institute, Comparative Immunobiology, Christian-Albrechts-Universität zu Kiel, Olshausenstr.40, D-24098 Kiel, Germany
| | - Ralf Metzler
- 1] Institute of Physics &Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany [2] Department of Physics, Tampere University of Technology, FI-30101 Tampere, Finland
| | - Christine Selhuber-Unkel
- Institute for Materials Science, Biocompatible Nanomaterials, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
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Goychuk I, Kharchenko VO, Metzler R. Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion. Phys Chem Chem Phys 2015; 16:16524-35. [PMID: 24985765 DOI: 10.1039/c4cp01234h] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
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23
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Lateral motion and bending of microtubules studied with a new single-filament tracking routine in living cells. Biophys J 2015; 106:2625-35. [PMID: 24940780 DOI: 10.1016/j.bpj.2014.04.046] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2013] [Revised: 04/07/2014] [Accepted: 04/18/2014] [Indexed: 12/24/2022] Open
Abstract
The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.
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24
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Goychuk I. Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechano-chemical coupling and anharmonicity of tether. Phys Biol 2015; 12:016013. [PMID: 25635368 DOI: 10.1088/1478-3975/12/1/016013] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in viscoelastic cytosol by (i) including mechano-chemical coupling between cyclic conformational fluctuations of the motor protein driven by the reaction of ATP hydrolysis and its translational motion within the simplest two-state model of hand-over-hand motion of kinesin, and also (ii) by taking into account the anharmonicity of the tether between the motor and the cargo (its maximally possible extension length). It is shown that the major earlier results such as occurrence of normal versus anomalous transport depending on the amplitude of binding potential, cargo size and the motor turnover frequency not only survive in this more realistic model, but the results also look very similar for the correspondingly adjusted parameters. However, this more realistic model displays a substantially larger thermodynamic efficiency due to a bidirectional mechano-chemical coupling. For realistic parameters, the maximal thermodynamic efficiency can transiently be about 50% as observed for kinesins, and even larger, surprisingly also in a novel strongly anomalous (sub)transport regime, where the motor enzymatic turnovers become also anomalously slow and cannot be characterized by a turnover rate. Here anomalously slow dynamics of the cargo enforces anomalously slow cyclic kinetics of the motor protein.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
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25
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Mankin R, Laas K, Lumi N, Rekker A. Cage effect for the velocity correlation functions of a Brownian particle in viscoelastic shear flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042127. [PMID: 25375458 DOI: 10.1103/physreve.90.042127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2014] [Indexed: 06/04/2023]
Abstract
The long-time limit behavior of velocity correlation functions (VCFs) for an underdamped Brownian particle in an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law memory kernel. The influence of a fluctuating environment is modeled by an additive external fractional Gaussian noise. The exact expressions of the correlation functions of the fluctuating components of velocity for the Brownian particle in the shear plane have been calculated. Also, the particle's angular momentum is found. It is shown that in a certain region of the system parameters an interplay of the shear flow, memory effects, and external noise can induce a bounded long-time behavior of the VCFs, even in the shear flow direction, where in the case of internal noise the velocity process is subdiffusive, i.e., unbounded in time. Moreover, we find resonant behavior of the VCFs and the angular momentum versus the shear oscillation frequency, implying that they can be efficiently excited by oscillatory shear. The role of the initial positional distribution of particles is also discussed.
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Affiliation(s)
- Romi Mankin
- Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Katrin Laas
- Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Neeme Lumi
- Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Astrid Rekker
- Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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26
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Bouzat S. Influence of molecular motors on the motion of particles in viscoelastic media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062707. [PMID: 25019814 DOI: 10.1103/physreve.89.062707] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2013] [Indexed: 06/03/2023]
Abstract
We study theoretically and by numerical simulations the motion of particles driven by molecular motors in a viscoelastic medium representing the cell cytoplasm. For this, we consider a generalized Langevin equation coupled to a stochastic stepping dynamics for the motors that takes into account the action of each motor separately. In the absence of motors, the model produces subdiffusive motion of particles characterized by a power-law scaling of the mean square displacement versus the lag time as t^{α}, with 0<α<1, similar to that observed in cells. Our results show how the action of the motors can induce a transition to a superdiffusive regime at large lag times with the characteristics of those found in experiments reported in the literature. We also show that at small lag times, the motors can act as static crosslinkers that slow down the natural subdiffusive transport. An analysis of previously reported experimental data in the relevant time scales provides evidence of this phenomenon. Finally, we study the effect of a harmonic potential representing an optical trap, and we show a way to approach to a macroscopic description of the active transport in cells. This last point stresses the relevance of the molecular motors for generating not only directed motion to specific targets, but also fast diffusivelike random motion.
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Affiliation(s)
- Sebastián Bouzat
- Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche (CNEA), (8400) Bariloche, Río Negro, Argentina
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27
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Head DA, Briels WJ, Gompper G. Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032705. [PMID: 24730872 DOI: 10.1103/physreve.89.032705] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2013] [Indexed: 06/03/2023]
Abstract
In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.
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Affiliation(s)
- D A Head
- School of Computing, Leeds University, Leeds LS2 9JT, United Kingdom
| | - W J Briels
- Computational Biophysics, University of Twente, 7500 AE Enschede, The Netherlands
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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28
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Otero MG, Alloatti M, Cromberg LE, Almenar-Queralt A, Encalada SE, Pozo Devoto VM, Bruno L, Goldstein LSB, Falzone TL. Fast axonal transport of the proteasome complex depends on membrane interaction and molecular motor function. J Cell Sci 2014; 127:1537-49. [PMID: 24522182 DOI: 10.1242/jcs.140780] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Protein degradation by the ubiquitin-proteasome system in neurons depends on the correct delivery of the proteasome complex. In neurodegenerative diseases, aggregation and accumulation of proteins in axons link transport defects with degradation impairments; however, the transport properties of proteasomes remain unknown. Here, using in vivo experiments, we reveal the fast anterograde transport of assembled and functional 26S proteasome complexes. A high-resolution tracking system to follow fluorescent proteasomes revealed three types of motion: actively driven proteasome axonal transport, diffusive behavior in a viscoelastic axonema and proteasome-confined motion. We show that active proteasome transport depends on motor function because knockdown of the KIF5B motor subunit resulted in impairment of the anterograde proteasome flux and the density of segmental velocities. Finally, we reveal that neuronal proteasomes interact with intracellular membranes and identify the coordinated transport of fluorescent proteasomes with synaptic precursor vesicles, Golgi-derived vesicles, lysosomes and mitochondria. Taken together, our results reveal fast axonal transport as a new mechanism of proteasome delivery that depends on membrane cargo 'hitch-hiking' and the function of molecular motors. We further hypothesize that defects in proteasome transport could promote abnormal protein clearance in neurodegenerative diseases.
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Affiliation(s)
- Maria G Otero
- Instituto de Biología Celular y Neurociencias (UBA-CONICET), Facultad de Medicina, Universidad de Buenos Aires, Buenos Aires CP 1121, Argentina
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29
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Aubertin K, Bonneau S, Silva AKA, Bacri JC, Gallet F, Wilhelm C. Impact of photosensitizers activation on intracellular trafficking and viscosity. PLoS One 2013; 8:e84850. [PMID: 24386423 PMCID: PMC3874004 DOI: 10.1371/journal.pone.0084850] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Accepted: 11/19/2013] [Indexed: 11/19/2022] Open
Abstract
The intracellular microenvironment is essential for the efficiency of photo-induced therapies, as short-lived reactive oxygen species generated must diffuse through their intracellular surrounding medium to reach their cellular target. Here, by combining measurements of local cytoplasmic dissipation and active trafficking, we found that photosensitizers activation induced small changes in surrounding viscosity but a massive decrease in diffusion. These effects are the signature of a return to thermodynamic equilibrium of the system after photo-activation and correlated with depolymerization of the microtubule network, as shown in a reconstituted system. These mechanical measurements were performed with two intracellular photosensitizing chlorins having similar quantum yield of singlet oxygen production but different intracellular localizations (cytoplasmic for mTHPC, endosomal for TPCS2a). These two agents demonstrated different intracellular impact.
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Affiliation(s)
- Kelly Aubertin
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Stéphanie Bonneau
- Laboratoire Jean Perrin-CNRS, Université Pierre et Marie Curie, Paris 6, Paris, France
| | - Amanda K. A. Silva
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Jean-Claude Bacri
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - François Gallet
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
| | - Claire Wilhelm
- Laboratoire Matière et Systèmes Complexes (MSC), CNRS and Université Paris Diderot, Paris, France
- * E-mail:
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30
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When size does matter: organelle size influences the properties of transport mediated by molecular motors. Biochim Biophys Acta Gen Subj 2013; 1830:5095-103. [DOI: 10.1016/j.bbagen.2013.06.043] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2013] [Revised: 05/07/2013] [Accepted: 06/29/2013] [Indexed: 12/18/2022]
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31
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Mankin R, Laas K, Lumi N. Memory effects for a trapped Brownian particle in viscoelastic shear flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042142. [PMID: 24229150 DOI: 10.1103/physreve.88.042142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2013] [Indexed: 06/02/2023]
Abstract
The long-time limit behavior of the positional distribution for an underdamped Brownian particle in a fluctuating harmonic potential well, which is simultaneously exposed to an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law-type memory kernel. The influence of a fluctuating environment is modeled by a multiplicative white noise (fluctuations of the stiffness of the trapping potential) and by an additive internal fractional Gaussian noise. The exact expressions of the second-order moments of the fluctuating position for the Brownian particle in the shear plane have been calculated. Also, shear-induced cross correlation between particle fluctuations along orthogonal directions as well as the angular momentum are found. It is shown that interplay of shear flow, memory, and multiplicative noise can generate a variety of cooperation effects, such as energetic instability, multiresonance versus the shear frequency, and memory-induced anomalous diffusion in the direction of the shear flow. Particularly, two different critical memory exponents have been found, which mark dynamical transitions from a stationary regime to a subdiffusive (or superdiffusive) regime of the system. Similarities and differences between the behaviors of the models with oscillatory and nonoscillatory shear flow are also discussed.
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Affiliation(s)
- Romi Mankin
- Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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32
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Harrison AW, Kenwright DA, Waigh TA, Woodman PG, Allan VJ. Modes of correlated angular motion in live cells across three distinct time scales. Phys Biol 2013; 10:036002. [DOI: 10.1088/1478-3975/10/3/036002] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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33
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Cherstvy AG, Metzler R. Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes. Phys Chem Chem Phys 2013; 15:20220-35. [DOI: 10.1039/c3cp53056f] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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34
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Kenwright DA, Harrison AW, Waigh TA, Woodman PG, Allan VJ. First-passage-probability analysis of active transport in live cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031910. [PMID: 23030947 DOI: 10.1103/physreve.86.031910] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2011] [Indexed: 06/01/2023]
Abstract
The first-passage-probability can be used as an unbiased method for determining the phases of motion of individual organelles within live cells. Using high speed microscopy, we observe individual lipid droplet tracks and analyze the motor protein driven motion. At short passage lengths (<10(-2)μm), a log-normal distribution in the first-passage-probability as a function of time is observed, which switches to a Gaussian distribution at longer passages due to the running motion of the motor proteins. The mean first-passage times (<t(FPT)>) as a function of the passage length (L), averaged over a number of runs for a single lipid droplet, follow a power law distribution <t(FPT)>~L(α), α>2, at short times due to a passive subdiffusive process. This changes to another power law at long times where 1<α<2, corresponding to sub-ballistic superdiffusive motion, an active process. Subdiffusive passive mean square displacements are observed as a function of time, <r(2)>~t(β), where 0<β<1 at short times again crossing over to an active sub-ballistic superdiffusive result 1<β<2 at longer times. Consecutive runs of the lipid droplets add additional independent Gaussian peaks to a cumulative first-passage-probability distribution indicating that the speeds of sequential phases of motion are independent and biochemically well regulated. As a result we propose a model for motor driven lipid droplets that exhibits a sequential run behavior with occasional pauses.
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Affiliation(s)
- David A Kenwright
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
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Bertseva E, Grebenkov D, Schmidhauser P, Gribkova S, Jeney S, Forró L. Optical trapping microrheology in cultured human cells. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:63. [PMID: 22821510 DOI: 10.1140/epje/i2012-12063-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2011] [Revised: 11/08/2011] [Accepted: 06/20/2012] [Indexed: 05/26/2023]
Abstract
We present the microrheological study of the two close human epithelial cell lines: non-cancerous HCV29 and cancerous T24. The optical tweezers tracking was applied to extract the several seconds long trajectories of endogenous lipid granules at time step of 1μs. They were analyzed using a recently proposed equation for mean square displacement (MSD) in the case of subdiffusion influenced by an optical trap. This equation leads to an explicit form for viscoelastic moduli. The moduli of the two cell lines were found to be the same within the experimental accuracy for frequencies 10(2) - 10(5) Hz. For both cell lines subdiffusion was observed with the exponent close to 3/4, the value predicted by the theory of semiflexible polymers. For times longer than 0.1s the MSD of cancerous cells exceeds the MSD of non-cancerous cells for all values of the trapping force. Such behavior can be interpreted as a signature of the active processes and prevents the extraction of the low-frequency viscoelastic moduli for the living cells by passive microrheology.
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Affiliation(s)
- E Bertseva
- Laboratory of Physics of Complex Matter, Ecole polytechnique federale de Lausanne (EPFL), Lausanne VD, Switzerland.
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36
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Akimoto T. Distributional response to biases in deterministic superdiffusion. PHYSICAL REVIEW LETTERS 2012; 108:164101. [PMID: 22680721 DOI: 10.1103/physrevlett.108.164101] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2011] [Indexed: 06/01/2023]
Abstract
We report on a novel response to biases in deterministic superdiffusion. For its reduced map, we show using infinite ergodic theory that the time-averaged velocity (TAV) is intrinsically random and its distribution obeys the generalized arcsine distribution. A distributional limit theorem indicates that the TAV response to a bias appears in the distribution, which is an example of what we term a distributional response induced by a bias. Although this response in single trajectories is intrinsically random, the ensemble-averaged TAV response is linear.
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Affiliation(s)
- Takuma Akimoto
- Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan.
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37
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Robert D, Aubertin K, Bacri JC, Wilhelm C. Magnetic nanomanipulations inside living cells compared with passive tracking of nanoprobes to get consensus for intracellular mechanics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011905. [PMID: 22400589 DOI: 10.1103/physreve.85.011905] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Indexed: 05/31/2023]
Abstract
During the last decade, the development of nanomaterials to penetrate inside living cells has been the focus of a large number of studies, with applications for the biomedical field. However, the further dynamics of these nanomaterials inside the cells is dictated by the intracellular environment and in particular its mechanical properties. The mechanical characteristics of the cell interior can be probed with either active or passive microrheological approaches. However, active intracellular microrheology is still in its infancy, owing to the difficulty of inserting probes that can be manipulated by external forces. Here we review recent active microrheology studies using magnetic nanoprobes inserted into endosomes or phagosomes as useful approaches for measuring frequency-dependent viscoelasticity, for mapping the viscoelastic landscape, as well as for identifying the contribution of individual cytoskeleton components and the influence of cell motility. The results of such direct measurements challenge the validity of more typical passive approaches in which the spontaneous displacement of embedded nanoprobes is measured. Here we discuss that one must distinguish probes suitable for use in conditions of thermal equilibrium, whose movements reflect the mechanical environment from probes that interact actively with the cytoplasm and cytoskeleton, in a state of nonequilibrium for which fluctuation-dissipation theorem no longer holds. However, when data on these probes' viscoelastic microenvironment is available, such passive probe movements can yield useful information on the forces responsible for intracellular activity.
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Affiliation(s)
- Damien Robert
- Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université Paris 7, 75013 Paris, France
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Despósito MA. Superdiffusion induced by a long-correlated external random force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061114. [PMID: 22304047 DOI: 10.1103/physreve.84.061114] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2011] [Indexed: 05/31/2023]
Abstract
We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes.
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Affiliation(s)
- M A Despósito
- Departamento de Física e Instituto de Física de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, ES-1428 Buenos Aires, Argentina.
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da Silva AJ, Lima RF, Moret MA. Nonextensivity and self-affinity in the mammalian neuromuscular junction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041925. [PMID: 22181193 DOI: 10.1103/physreve.84.041925] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2011] [Revised: 07/05/2011] [Indexed: 05/31/2023]
Abstract
We study time series and the spontaneous miniature end-plate potentials (MEPPs) of mammals recorded at neuromuscular junctions using two different approaches: generalized thermostatistics and detrended fluctuation analysis (DFA). Classical concepts establish that the magnitude of these potentials is characterized by Gaussian statistics and that their intervals are randomly displayed. First we show that MEPP distributions adequately satisfy the q-Gaussian distributions that maximize the Tsallis entropy, indicating their nonextensive and nonequilibrium behavior. We then examine the intervals between the miniature potentials via DFA, where the profile of the intervals between events configures a deviation from the expected random behavior. Some possible physiological substrates for these findings are discussed.
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Affiliation(s)
- A J da Silva
- Departamento de Fisiologia e Biofísica, Instituto de Ciências Biológicas, Universidade Federal de Minas Gerais, CEP 31270-910 Belo Horizonte, Minas Gerais, Brazil.
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40
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Mankin R, Laas K, Sauga A. Generalized Langevin equation with multiplicative noise: temporal behavior of the autocorrelation functions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061131. [PMID: 21797326 DOI: 10.1103/physreve.83.061131] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2011] [Revised: 05/20/2011] [Indexed: 05/31/2023]
Abstract
The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.
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Affiliation(s)
- R Mankin
- Institute of Mathematics and Natural Sciences, Tallinn University, Tallinn, Estonia
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Bruno L, Salierno M, Wetzler DE, Despósito MA, Levi V. Mechanical properties of organelles driven by microtubule-dependent molecular motors in living cells. PLoS One 2011; 6:e18332. [PMID: 21483765 PMCID: PMC3069964 DOI: 10.1371/journal.pone.0018332] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2010] [Accepted: 02/25/2011] [Indexed: 11/18/2022] Open
Abstract
The organization of the cytoplasm is regulated by molecular motors which transport organelles and other cargoes along cytoskeleton tracks. Melanophores have pigment organelles or melanosomes that move along microtubules toward their minus and plus end by the action of cytoplasmic dynein and kinesin-2, respectively. In this work, we used single particle tracking to characterize the mechanical properties of motor-driven organelles during transport along microtubules. We tracked organelles with high temporal and spatial resolutions and characterized their dynamics perpendicular to the cytoskeleton track. The quantitative analysis of these data showed that the dynamics is due to a spring-like interaction between melanosomes and microtubules in a viscoelastic microenvironment. A model based on a generalized Langevin equation explained these observations and predicted that the stiffness measured for the motor complex acting as a linker between organelles and microtubules is ∼ one order smaller than that determined for motor proteins in vitro. This result suggests that other biomolecules involved in the interaction between motors and organelles contribute to the mechanical properties of the motor complex. We hypothesise that the high flexibility observed for the motor linker may be required to improve the efficiency of the transport driven by multiple copies of motor molecules.
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Affiliation(s)
- Luciana Bruno
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Ciudad de Buenos Aires, Argentina
| | - Marcelo Salierno
- Departamento de Química Biológica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires, Argentina
| | - Diana E. Wetzler
- Departamento de Química Biológica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires, Argentina
| | - Marcelo A. Despósito
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Ciudad de Buenos Aires, Argentina
| | - Valeria Levi
- Departamento de Química Biológica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires, Argentina
- * E-mail:
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