1
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Pannone M. The Pathologically Evolving Aggregation-State of Cells in Cancerous Tissues as Interpreted by Fractal and Multi-Fractal Dispersion Theory in Saturated Porous Formations. Bioengineering (Basel) 2024; 11:469. [PMID: 38790336 PMCID: PMC11117603 DOI: 10.3390/bioengineering11050469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2024] [Revised: 04/24/2024] [Accepted: 05/03/2024] [Indexed: 05/26/2024] Open
Abstract
A recent author's fractal fluid-dynamic dispersion theory in porous media has focused on the derivation of the associated nonergodic (or effective) macrodispersion coefficients by a 3-D stochastic Lagrangian approach. As shown by the present study, the Fickian (i.e., the asymptotic constant) component of a properly normalized version of these coefficients exhibits a clearly detectable minimum in correspondence with the same fractal dimension (d ≅ 1.7) that seems to characterize the diffusion-limited aggregation state of cells in advanced stages of cancerous lesion progression. That circumstance suggests that such a critical fractal dimension, which is also reminiscent of the colloidal state of solutions (and may therefore identify the microscale architecture of both living and non-living two-phase systems in state transition conditions) may actually represent a sort of universal nature imprint. Additionally, it suggests that the closed-form analytical solution that was provided for the effective macrodispersion coefficients in fractal porous media may be a reliable candidate as a physically-based descriptor of blood perfusion dynamics in healthy as well as cancerous tissues. In order to evaluate the biological meaningfulness of this specific fluid-dynamic parameter, a preliminary validation is performed by comparison with the results of imaging-based clinical surveys. Moreover, a multifractal extension of the theory is proposed and discussed in view of a perspective interpretative diagnostic utilization.
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Affiliation(s)
- Marilena Pannone
- School of Engineering, University of Basilicata, 85100 Potenza, Italy
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2
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Chen Y, Wang X, Ge M. Lévy-walk-like Langevin dynamics with random parameters. CHAOS (WOODBURY, N.Y.) 2024; 34:013109. [PMID: 38198676 DOI: 10.1063/5.0174613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 12/05/2023] [Indexed: 01/12/2024]
Abstract
Anomalous diffusion phenomena have been widely found in systems within an inhomogeneous complex environment. For Lévy walk in an inhomogeneous complex environment, we characterize the particle's trajectory through an underdamped Langevin system coupled with a subordinator. The influence of the inhomogeneous environment on the particle's motion is parameterized by the random system parameters, relaxation timescale τ, and velocity diffusivity σ. We find that the two random parameters make different effects on the original superdiffusion behavior of the Lévy walk. The random σ contributes to a trivial result after an ensemble average, which is independent of the specific distribution of σ. By contrast, we find that a specific distribution of τ, a modified Lévy distribution with a finite mean, slows down the decaying rate of the velocity correlation function with respect to the lag time. However, the random τ does not promote the diffusion behavior in a direct way, but plays a competition role to the superdiffusion of the original Lévy walk. In addition, the effect of the random τ is also related to the specific subordinator in the coupled Langevin model, which corresponds to the distribution of the flight time of the Lévy walk. The random system parameters are capable of leading to novel dynamics, which needs detailed analyses, rather than an intuitive judgment, especially in complex systems.
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Affiliation(s)
- Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Mengyan Ge
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
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3
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Liang Y, Wang W, Metzler R, Cherstvy AG. Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks. Phys Rev E 2023; 108:034113. [PMID: 37849140 DOI: 10.1103/physreve.108.034113] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 08/07/2023] [Indexed: 10/19/2023]
Abstract
How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to such conditions? We address these questions in the current study. To describe different types of non-Brownian motion of particles-including power-law anomalous, ultraslow or logarithmic, as well as superfast or exponential diffusion-we here develop and analyze a generalized stochastic process of scaled-fractional Brownian motion (SFBM). The time- and space-SFBM processes are, respectively, constructed based on FBM running with nonlinear time and space clocks. The fundamental statistical characteristics such as non-Gaussianity of particle displacements, nonergodicity, as well as aging are quantified for time- and space-SFBM by selecting different clocks. The latter parametrize power-law anomalous, ultraslow, and superfast diffusion. The results of our computer simulations are fully consistent with the analytical predictions for several functional forms of clocks. We thoroughly examine the behaviors of the probability-density function, the mean-squared displacement, the time-averaged mean-squared displacement, as well as the aging factor. Our results are applicable for rationalizing the impact of nonlinear time and space properties superimposed onto the FBM-type dynamics. SFBM offers a general framework for a universal and more precise model-based description of anomalous, nonergodic, non-Gaussian, and aging diffusion in single-molecule-tracking observations.
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Affiliation(s)
- Yingjie Liang
- College of Mechanics and Materials, Hohai University, 211100 Nanjing, China
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Wei Wang
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Andrey G Cherstvy
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
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4
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Shi H, Du L, Huang F, Guo W. Weak ergodicity breaking and anomalous diffusion in collective motion of active particles under spatiotemporal disorder. Phys Rev E 2023; 107:024114. [PMID: 36932613 DOI: 10.1103/physreve.107.024114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
The effects of spatiotemporal disorder, i.e., both the noise and quenched disorder, on the dynamics of active particles in two dimensions are investigated. We demonstrate that within the tailored parameter regime, nonergodic superdiffusion and nonergodic subdiffusion occur in the system, identified by the observable quantities (the mean squared displacement and ergodicity-breaking parameter) averaged over both the noise and realizations of quenched disorder. Their origins are attributed to the competition effects between the neighbor alignment and spatiotemporal disorder on the collective motion of active particles. These results may be helpful for further understanding the nonequilibrium transport process of active particles, as well as for detection of the transport of self-propelled particles in complex and crowded environments.
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Affiliation(s)
- Hongda Shi
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Luchun Du
- Department of Physics, Yunnan University, Kunming 650091, China
| | - Feijie Huang
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Wei Guo
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
- Yunnan Key Laboratory of Metal-Organic Molecular Materials and Devices, Kunming University, Kunming 650214, China
- National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China
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5
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Singh P. Extreme value statistics and arcsine laws for heterogeneous diffusion processes. Phys Rev E 2022; 105:024113. [PMID: 35291128 DOI: 10.1103/physreve.105.024113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Heterogeneous diffusion with a spatially changing diffusion coefficient arises in many experimental systems such as protein dynamics in the cell cytoplasm, mobility of cajal bodies, and confined hard-sphere fluids. Here, we showcase a simple model of heterogeneous diffusion where the diffusion coefficient D(x) varies in a power-law way, i.e., D(x)∼|x|^{-α} with the exponent α>-1. This model is known to exhibit anomalous scaling of the mean-squared displacement (MSD) of the form ∼t^{2/2+α} and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all α, the exact probability distributions of the maximum spatial displacement M(t) and arg-maximum t_{m}(t) (i.e., the time at which this maximum is reached) till duration t. In the second part of our paper, we analyze the statistical properties of the residence time t_{r}(t) and the last-passage time t_{ℓ}(t) and compute their distributions exactly for all values of α. Our study unravels that the heterogeneous version (α≠0) displays many rich and contrasting features compared to that of the standard Brownian motion (BM). For example, while for BM (α=0), the distributions of t_{m}(t),t_{r}(t), and t_{ℓ}(t) are all identical (á la "arcsine laws" due to Lévy), they turn out to be significantly different for nonzero α. Another interesting property of t_{r}(t) is the existence of a critical α (which we denote by α_{c}=-0.3182) such that the distribution exhibits a local maximum at t_{r}=t/2 for α<α_{c} whereas it has minima at t_{r}=t/2 for α≥α_{c}. The underlying reasoning for this difference hints at the very contrasting natures of the process for α≥α_{c} and α<α_{c} which we thoroughly examine in our paper. All our analytical results are backed by extensive numerical simulations.
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Affiliation(s)
- Prashant Singh
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
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6
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Wang W, Cherstvy AG, Kantz H, Metzler R, Sokolov IM. Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes. Phys Rev E 2021; 104:024105. [PMID: 34525678 DOI: 10.1103/physreve.104.024105] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Accepted: 07/14/2021] [Indexed: 12/12/2022]
Abstract
How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼(1/r)-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.
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Affiliation(s)
- Wei Wang
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.,IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany
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7
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Higham JE, Shahnam M, Vaidheeswaran A. Anomalous diffusion in a bench-scale pulsed fluidized bed. Phys Rev E 2021; 103:043103. [PMID: 34005865 DOI: 10.1103/physreve.103.043103] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 03/23/2021] [Indexed: 11/07/2022]
Abstract
We present our analysis on microrheology of a bench-scale pulsed fluidized bed, which represents a weakly confined system. Nonlinear gas-particle and particle-particle interactions resulting from pulsed flow are associated with harmonic and subharmonic modes. While periodic structured bubble patterns are observed at the mesoscale, particle-scale measurements reveal anomalous diffusion in the driven granular medium. We use single-particle tracks to analyze ergodicity and ageing properties at two pulsing frequencies having remarkably different mesoscale features. The scaling of ensemble-averaged mean-squared displacement is not unique. The distribution of time-averaged mean-squared displacements is non-Gaussian, asymmetric, and has a finite trivial contribution from particles in crowded quasistatic surroundings. Results indicate weak ergodicity breaking, which along with ageing characterizes the nonstationary and out-of-equilibrium dynamics.
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Affiliation(s)
- Jonathan E Higham
- University of Liverpool, School of Environmental Sciences, Department of Geography and Planning, Roxby Building, Liverpool, L69 7ZT, United Kingdom
| | - Mehrdad Shahnam
- National Energy Technology Laboratory 3610 Collins Ferry Road, Morgantown, West Virginia 26505, USA
| | - Avinash Vaidheeswaran
- National Energy Technology Laboratory 3610 Collins Ferry Road, Morgantown, West Virginia 26505, USA
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8
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Xu Y, Liu X, Li Y, Metzler R. Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes. Phys Rev E 2021; 102:062106. [PMID: 33466052 DOI: 10.1103/physreve.102.062106] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 10/22/2020] [Indexed: 01/03/2023]
Abstract
Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.
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Affiliation(s)
- Yong Xu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China
| | - Xuemei Liu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Yongge Li
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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9
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Sun ZY, Yu X. Anomalous diffusion of discrete solitons driven by evolving disorder. Phys Rev E 2020; 101:062211. [PMID: 32688546 DOI: 10.1103/physreve.101.062211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
- International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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10
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Cao X, Zhang B, Zhao N. Effective temperature scaled dynamics of a flexible polymer in an active bath. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1730992] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Xiuli Cao
- College of Chemistry, Sichuan University, Chengdu, China
| | - Bingjie Zhang
- College of Chemistry, Sichuan University, Chengdu, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu, China
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11
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Guerrero BV, Chakraborty B, Zuriguel I, Garcimartín A. Nonergodicity in silo unclogging: Broken and unbroken arches. Phys Rev E 2019; 100:032901. [PMID: 31639941 DOI: 10.1103/physreve.100.032901] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Indexed: 11/07/2022]
Abstract
We report an experiment on the unclogging dynamics in a two-dimensional silo submitted to a sustained gentle vibration. We find that arches present a jerking motion where rearrangements in the positions of their beads are interspersed with quiescent periods. This behavior occurs for both arches that break down and those that withstand the external perturbation: Arches evolve until they either collapse or get trapped in a stable configuration. This evolution is described in terms of a scalar variable characterizing the arch shape that can be modeled as a continuous-time random walk. By studying the diffusivity of this variable, we show that the unclogging is a weakly nonergodic process. Remarkably, arches that do not collapse explore different configurations before settling in one of them and break ergodicity much in the same way than arches that break down.
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Affiliation(s)
- B V Guerrero
- Dep. Física y Mat. Apl., Fac. Ciencias, Universidad de Navarra, 31080 Pamplona, Spain
| | - B Chakraborty
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - I Zuriguel
- Dep. Física y Mat. Apl., Fac. Ciencias, Universidad de Navarra, 31080 Pamplona, Spain
| | - A Garcimartín
- Dep. Física y Mat. Apl., Fac. Ciencias, Universidad de Navarra, 31080 Pamplona, Spain
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12
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Witzel P, Götz M, Lanoiselée Y, Franosch T, Grebenkov DS, Heinrich D. Heterogeneities Shape Passive Intracellular Transport. Biophys J 2019; 117:203-213. [PMID: 31278001 DOI: 10.1016/j.bpj.2019.06.009] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Revised: 05/22/2019] [Accepted: 06/11/2019] [Indexed: 01/06/2023] Open
Abstract
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion that controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, non-biomotor-shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150-nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: 1) sample-based variability, 2) rarely occurring strong motion events, 3) ergodicity breaking/aging, and 4) spatiotemporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A, to our knowledge, novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, whereas cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.
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Affiliation(s)
- Patrick Witzel
- Faculty for Chemistry and Pharmacy, Julius-Maximilians-Universität Würzburg, Würzburg, Germany; Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany
| | - Maria Götz
- Faculty for Chemistry and Pharmacy, Julius-Maximilians-Universität Würzburg, Würzburg, Germany; Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany
| | - Yann Lanoiselée
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Palaiseau, France
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
| | - Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS-Ecole Polytechnique, Palaiseau, France
| | - Doris Heinrich
- Fraunhofer Institute for Silicate Research ISC, Würzburg, Germany; Leiden Institute of Physics, Huygens-Kamerlingh Onnes Laboratory, Leiden University, Leiden, the Netherlands.
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13
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Guzman-Sepulveda JR, Argueta-Morales R, DeCampli WM, Dogariu A. Real-time intraoperative monitoring of blood coagulability via coherence-gated light scattering. Nat Biomed Eng 2017. [DOI: 10.1038/s41551-017-0028] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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14
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Budini AA. Inhomogeneous diffusion and ergodicity breaking induced by global memory effects. Phys Rev E 2016; 94:052142. [PMID: 27967169 DOI: 10.1103/physreve.94.052142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Indexed: 06/06/2023]
Abstract
We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.
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Affiliation(s)
- Adrián A Budini
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, (8400) Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, (8400) Bariloche, Argentina
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15
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Loch-Olszewska H, Sikora G, Janczura J, Weron A. Identifying ergodicity breaking for fractional anomalous diffusion: Criteria for minimal trajectory length. Phys Rev E 2016; 94:052136. [PMID: 27967179 DOI: 10.1103/physreve.94.052136] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2016] [Indexed: 06/06/2023]
Abstract
In this paper, we study ergodic properties of α-stable autoregressive fractionally integrated moving average (ARFIMA) processes which form a large class of anomalous diffusions. A crucial practical question is how long trajectories one needs to observe in an experiment in order to claim that the analyzed data are ergodic or not. This will be solved by checking the asymptotic convergence to 0 of the empirical estimator F(n) for the dynamical functional D(n) defined as a Fourier transform of the n-lag increments of the ARFIMA process. Moreover, we introduce more flexible concept of the ε-ergodicity.
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Affiliation(s)
- Hanna Loch-Olszewska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Grzegorz Sikora
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Joanna Janczura
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Aleksander Weron
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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16
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17
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Cherstvy AG, Metzler R. Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes. Phys Chem Chem Phys 2016; 18:23840-52. [DOI: 10.1039/c6cp03101c] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
We investigate the diffusive and ergodic properties of massive and confined particles in a model disordered medium, in which the local diffusivity fluctuates in time while its mean has a power law dependence on the diffusion time.
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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18
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Oliveira SMD, Neeli-Venkata R, Goncalves NSM, Santinha JA, Martins L, Tran H, Mäkelä J, Gupta A, Barandas M, Häkkinen A, Lloyd-Price J, Fonseca JM, Ribeiro AS. Increased cytoplasm viscosity hampers aggregate polar segregation inEscherichia coli. Mol Microbiol 2015; 99:686-99. [DOI: 10.1111/mmi.13257] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/25/2015] [Indexed: 12/11/2022]
Affiliation(s)
- Samuel M. D. Oliveira
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Ramakanth Neeli-Venkata
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Nadia S. M. Goncalves
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - João A. Santinha
- UNINOVA; Instituto de Desenvolvimento de Novas Tecnologias; Campus FCT-UNL; 2829-516 Caparica Portugal
| | - Leonardo Martins
- UNINOVA; Instituto de Desenvolvimento de Novas Tecnologias; Campus FCT-UNL; 2829-516 Caparica Portugal
| | - Huy Tran
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Jarno Mäkelä
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Abhishekh Gupta
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Marilia Barandas
- UNINOVA; Instituto de Desenvolvimento de Novas Tecnologias; Campus FCT-UNL; 2829-516 Caparica Portugal
| | - Antti Häkkinen
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - Jason Lloyd-Price
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
| | - José M. Fonseca
- UNINOVA; Instituto de Desenvolvimento de Novas Tecnologias; Campus FCT-UNL; 2829-516 Caparica Portugal
| | - Andre S. Ribeiro
- Laboratory of Biosystem Dynamics; Department of Signal Processing; Tampere University of Technology; 33101 Tampere Finland
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