1
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Seckler H, Metzler R, Kelty-Stephen DG, Mangalam M. Multifractal spectral features enhance classification of anomalous diffusion. Phys Rev E 2024; 109:044133. [PMID: 38755826 DOI: 10.1103/physreve.109.044133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/19/2024] [Indexed: 05/18/2024]
Abstract
Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.
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Affiliation(s)
- Henrik Seckler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Damian G Kelty-Stephen
- Department of Psychology, State University of New York at New Paltz, New Paltz, New York 12561, USA
| | - Madhur Mangalam
- Department of Biomechanics and Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, Nebraska 68182, USA
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2
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Zhan Z, Wang X. Ergodic criterion of a random diffusivity model. Phys Rev E 2024; 109:044115. [PMID: 38755829 DOI: 10.1103/physreve.109.044115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 03/06/2024] [Indexed: 05/18/2024]
Abstract
The random diffusivity, initially proposed to explain Brownian yet non-Gaussian diffusion, has garnered significant attention due to its capacity not only for elucidating the internal physical mechanism of non-Gaussian diffusion, but also for establishing an analytical framework to characterize particle motion in complex environments. In this paper, based on the correlation function C(t_{1},t_{2})=〈D(t_{1})D(t_{2})〉 of random diffusivity D(t), we quantitatively propose a general criterion of determining the ergodic property of the Langevin equation with the arbitrary random diffusivity D(t). Due to the critical role of correlation function C(t_{1},t_{2}), we derive the criterion for the two cases with stationary diffusivity or nonstationary diffusivity, respectively. By utilizing the quantitative criterion, we can directly judge the ergodic properties of the random diffusivity model based on the correlation function C(t_{1},t_{2}) of random diffusivity D(t). Several typical diffusivities, including the common square of the Brownian motion and of the (fractional) Ornstein-Uhlenbeck process, are found to contribute to different ergodic properties, which validates our proposed criterion built on the correlation function C(t_{1},t_{2}).
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Affiliation(s)
- Zhongshuai Zhan
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, 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
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3
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Luo X, Bao JD, Fan WY. Multiple diffusive behaviors of the random walk in inhomogeneous environments. Phys Rev E 2024; 109:014130. [PMID: 38366502 DOI: 10.1103/physreve.109.014130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 12/20/2023] [Indexed: 02/18/2024]
Abstract
Anomalous diffusive behaviors are observed in highly inhomogeneous but relatively stable environments such as intracellular media and are increasingly attracting attention. In this paper we develop a coupled continuous-time random walk model in which the waiting time is power-law coupled with the local environmental diffusion coefficient. We provide two forms of the waiting time density, namely, a heavy-tailed density and an exponential density. For different waiting time densities, anomalous diffusions with the diffusion exponent between 0 and 2 and Brownian yet non-Gaussian diffusion can be realized within the present model. The diffusive behaviors are analyzed and discussed by deriving the mean-squared displacement and probability density function. In addition we derive the effective jump length density corresponding to the decoupled form to help distinguish the diffusion types. Our model unifies two kinds of anomalous diffusive behavior with different characteristics in the same inhomogeneous environment into a theoretical framework. The model interprets the random motion of particles in a complex inhomogeneous environment and reproduces the experimental results of different biological and physical systems.
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Affiliation(s)
- Xiao Luo
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Wen-Yue Fan
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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4
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Requena B, Masó-Orriols S, Bertran J, Lewenstein M, Manzo C, Muñoz-Gil G. Inferring pointwise diffusion properties of single trajectories with deep learning. Biophys J 2023; 122:4360-4369. [PMID: 37853693 PMCID: PMC10698275 DOI: 10.1016/j.bpj.2023.10.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 09/14/2023] [Accepted: 10/13/2023] [Indexed: 10/20/2023] Open
Abstract
To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5β1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.
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Affiliation(s)
- Borja Requena
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
| | - Sergi Masó-Orriols
- Facultat de Ciències, Tecnologia I Enginyeries, Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), Vic, Spain; Institut de Recerca i Innovació en Ciències de la Vida i de la Salut a la Catalunya Central (IRIS-CC), Vic, Barcelona, Spain
| | - Joan Bertran
- Facultat de Ciències, Tecnologia I Enginyeries, Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), Vic, Spain; Institut de Recerca i Innovació en Ciències de la Vida i de la Salut a la Catalunya Central (IRIS-CC), Vic, Barcelona, Spain
| | - Maciej Lewenstein
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain; ICREA, Pg. Lluís Companys 23, Barcelona, Spain
| | - Carlo Manzo
- Facultat de Ciències, Tecnologia I Enginyeries, Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), Vic, Spain; Institut de Recerca i Innovació en Ciències de la Vida i de la Salut a la Catalunya Central (IRIS-CC), Vic, Barcelona, Spain.
| | - Gorka Muñoz-Gil
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria.
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5
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Hu M, Chen H, Wang H, Burov S, Barkai E, Wang D. Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping. ACS NANO 2023; 17:21708-21718. [PMID: 37879044 DOI: 10.1021/acsnano.3c06897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2023]
Abstract
In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.
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Affiliation(s)
- Ming Hu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Hongbo Chen
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
| | - Hongru Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Stanislav Burov
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Dapeng Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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6
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Akimoto T. Statistics of the number of renewals, occupation times, and correlation in ordinary, equilibrium, and aging alternating renewal processes. Phys Rev E 2023; 108:054113. [PMID: 38115500 DOI: 10.1103/physreve.108.054113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 10/16/2023] [Indexed: 12/21/2023]
Abstract
The renewal process is a point process where an interevent time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the renewal process, where the interevent time distribution alternates between two distributions. We investigate statistical properties of the number of renewals and occupation times for one of the two states in alternating renewal processes. When both means of the interevent times are finite, the alternating renewal process can reach an equilibrium. On the other hand, an alternating renewal process shows aging when one of the means diverges. We provide analytical calculations for the moments of the number of renewals, occupation time statistics, and the correlation function for several case studies in the interevent-time distributions. We show anomalous fluctuations for the number of renewals and occupation times when the second moment of interevent time diverges. When the mean interevent time diverges, distributional limit theorems for the number of events and occupation times are shown analytically. These are known as the Mittag-Leffler distribution and the generalized arcsine law in probability theory.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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7
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Seckler H, Szwabiński J, Metzler R. Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories. J Phys Chem Lett 2023; 14:7910-7923. [PMID: 37646323 DOI: 10.1021/acs.jpclett.3c01351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
Single-particle traces of the diffusive motion of molecules, cells, or animals are by now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics is vital in understanding the observed systems. Typically, the task is to decipher the exact type of diffusion and/or to determine the system parameters. The tools used in this endeavor are currently being revolutionized by modern machine-learning techniques. In this Perspective we provide an overview of recently introduced methods in machine-learning for diffusive time series, most notably, those successfully competing in the anomalous diffusion challenge. As such methods are often criticized for their lack of interpretability, we focus on means to include uncertainty estimates and feature-based approaches, both improving interpretability and providing concrete insight into the learning process of the machine. We expand the discussion by examining predictions on different out-of-distribution data. We also comment on expected future developments.
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Affiliation(s)
- Henrik Seckler
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Janusz Szwabiński
- Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
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8
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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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9
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Sakamoto K, Akimoto T, Muramatsu M, Sansom MSP, Metzler R, Yamamoto E. Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity. PNAS NEXUS 2023; 2:pgad258. [PMID: 37593200 PMCID: PMC10427746 DOI: 10.1093/pnasnexus/pgad258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Revised: 06/22/2023] [Accepted: 07/27/2023] [Indexed: 08/19/2023]
Abstract
Cell membranes phase separate into ordered L o and disordered L d domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in L o and L d domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into L o and L d domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the L o domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.
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Affiliation(s)
- Ken Sakamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Mayu Muramatsu
- Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Mark S P Sansom
- Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, UK
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, Potsdam-Golm 14476, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Eiji Yamamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
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10
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Kosztołowicz T. Subdiffusion with particle immobilization process described by a differential equation with Riemann-Liouville-type fractional time derivative. Phys Rev E 2023; 108:014132. [PMID: 37583171 DOI: 10.1103/physreve.108.014132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 06/29/2023] [Indexed: 08/17/2023]
Abstract
An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann-Liouville type which is a differential-integral operator with the kernel defined by the Laplace transform; the kernel controls the immobilization process. We propose a method for calculating the inverse Laplace transform providing the kernel in the time domain. In the long time limit the subdiffusion-immobilization process reaches a stationary state in which the probability density of a particle distribution is an exponential function.
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Affiliation(s)
- Tadeusz Kosztołowicz
- Institute of Physics, Jan Kochanowski University, Uniwersytecka 7, 25-406 Kielce, Poland
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11
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Boscolo AL, Junior VBDS, Barreiro LA. Normal and anomalous diffusion in a bouncing ball over an irregular surface. Phys Rev E 2023; 107:045001. [PMID: 37198794 DOI: 10.1103/physreve.107.045001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 03/22/2023] [Indexed: 05/19/2023]
Abstract
The problem of a bouncing ball on a nonplanar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in the horizontal distribution of the particle. On the x axis, normal and superdiffusion are observed. For the probability density's functional form, a scaling hypothesis is presented.
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Affiliation(s)
- Ana Laura Boscolo
- Institute of Geosciences and Exact Sciences, Physics Department, São Paulo State University (Unesp), CEP 13506-900, Rio Claro, São Paulo, Brazil
| | - Valdir Barbosa da Silva Junior
- Institute of Geosciences and Exact Sciences, Physics Department, São Paulo State University (Unesp), CEP 13506-900, Rio Claro, São Paulo, Brazil
| | - Luiz Antonio Barreiro
- Institute of Geosciences and Exact Sciences, Physics Department, São Paulo State University (Unesp), CEP 13506-900, Rio Claro, São Paulo, Brazil
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12
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Garibo-I-Orts Ò, Firbas N, Sebastiá L, Conejero JA. Gramian angular fields for leveraging pretrained computer vision models with anomalous diffusion trajectories. Phys Rev E 2023; 107:034138. [PMID: 37072993 DOI: 10.1103/physreve.107.034138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 02/28/2023] [Indexed: 04/20/2023]
Abstract
Anomalous diffusion is present at all scales, from atomic to large ones. Some exemplary systems are ultracold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, arthropods' free movement, and birds' migration patterns. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent α with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge [Muñoz-Gil et al., Nat. Commun. 12, 6253 (2021)2041-172310.1038/s41467-021-26320-w]. Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian angular fields (GAF) to encode one-dimensional trajectories as images (Gramian matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pretrained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime and infer the anomalous diffusion exponent α. Short raw trajectories of lengths between 10 and 50 are commonly encountered in single-particle tracking experiments and are the most difficult ones to characterize. We show that GAF images can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting.
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Affiliation(s)
- Òscar Garibo-I-Orts
- GRID-Grupo de Investigacion en Ciencia de Datos Valencian International University-VIU, Carrer Pintor Sorolla 21, 46002 València, Spain
| | - Nicolas Firbas
- DBS-Department of Biological Sciences, National University of Singapore 16 Science Drive 4, Singapore 117558, Singapore
| | - Laura Sebastiá
- VRAIN-Valencian Research Institute for Artificial Intelligence Universitat Politècnica de València, Cami de Vera s/n, 46022 València, Spain
| | - J Alberto Conejero
- Instituto Universitario de Matemática Pura y Aplicada Universitat Politècnica de València, Cami de Vera s/n, 46022 València, Spain
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13
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Scott S, Weiss M, Selhuber-Unkel C, Barooji YF, Sabri A, Erler JT, Metzler R, Oddershede LB. Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking. Phys Chem Chem Phys 2023; 25:1513-1537. [PMID: 36546878 DOI: 10.1039/d2cp01384c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.
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Affiliation(s)
- Shane Scott
- Institute of Physiology, Kiel University, Hermann-Rodewald-Straße 5, 24118 Kiel, Germany
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
| | - Christine Selhuber-Unkel
- Institute for Molecular Systems Engineering, Heidelberg University, D-69120 Heidelberg, Germany.,Max Planck School Matter to Life, Jahnstraße 29, D-69120 Heidelberg, Germany
| | - Younes F Barooji
- Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
| | - Adal Sabri
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
| | - Janine T Erler
- BRIC, University of Copenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen, Denmark.
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.,Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
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14
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Seckler H, Metzler R. Bayesian deep learning for error estimation in the analysis of anomalous diffusion. Nat Commun 2022; 13:6717. [PMID: 36344559 PMCID: PMC9640593 DOI: 10.1038/s41467-022-34305-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 10/20/2022] [Indexed: 11/09/2022] Open
Abstract
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.
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Affiliation(s)
- Henrik Seckler
- Institute for Physics & Astronomy, University of Potsdam, 14476, Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476, Potsdam-Golm, Germany.
- Asia Pacific Centre for Theoretical Physics, Pohang, 37673, Republic of Korea.
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15
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Kumar U, Pushpavanam S. The effect of subdiffusion on the stability of autocatalytic systems. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.118230] [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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16
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Stochastic particle unbinding modulates growth dynamics and size of transcription factor condensates in living cells. Proc Natl Acad Sci U S A 2022; 119:e2200667119. [PMID: 35881789 PMCID: PMC9351496 DOI: 10.1073/pnas.2200667119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
Abstract
Living cells organize internal compartments by forming molecular condensates that operate as versatile biochemical “hubs.” Their occurrence is particularly relevant in the nucleus where they regulate, amongst others, gene transcription. However, the biophysics of transcription factor (TF) condensation remains highly unexplored. Through single-molecule experiments in living cells, theory, and simulations, we assessed the diffusion, growth dynamics, and sizes of TF condensates of the nuclear progesterone receptor (PR). Interestingly, PR condensates obey classical growth dynamics at shorter times but deviate at longer times, reaching finite sizes at steady-state. We demonstrate that condensate growth dynamics and nanoscale-size arrested growth is regulated by molecular escaping from condensates, providing an exquisite control of condensate size in nonequilibrium systems such as living cells. Liquid–liquid phase separation (LLPS) is emerging as a key physical principle for biological organization inside living cells, forming condensates that play important regulatory roles. Inside living nuclei, transcription factor (TF) condensates regulate transcriptional initiation and amplify the transcriptional output of expressed genes. However, the biophysical parameters controlling TF condensation are still poorly understood. Here we applied a battery of single-molecule imaging, theory, and simulations to investigate the physical properties of TF condensates of the progesterone receptor (PR) in living cells. Analysis of individual PR trajectories at different ligand concentrations showed marked signatures of a ligand-tunable LLPS process. Using a machine learning architecture, we found that receptor diffusion within condensates follows fractional Brownian motion resulting from viscoelastic interactions with chromatin. Interestingly, condensate growth dynamics at shorter times is dominated by Brownian motion coalescence (BMC), followed by a growth plateau at longer timescales that result in nanoscale condensate sizes. To rationalize these observations, we extended on the BMC model by including the stochastic unbinding of particles within condensates. Our model reproduced the BMC behavior together with finite condensate sizes at the steady state, fully recapitulating our experimental data. Overall, our results are consistent with condensate growth dynamics being regulated by the escaping probability of PR molecules from condensates. The interplay between condensation assembly and molecular escaping maintains an optimum physical condensate size. Such phenomena must have implications for the biophysical regulation of other nuclear condensates and could also operate in multiple biological scenarios.
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17
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Wang W, Metzler R, Cherstvy AG. Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models. Phys Chem Chem Phys 2022; 24:18482-18504. [DOI: 10.1039/d2cp01741e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...
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18
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Wang X, Chen Y. Ergodic property of random diffusivity system with trapping events. Phys Rev E 2022; 105:014106. [PMID: 35193240 DOI: 10.1103/physreve.105.014106] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 12/10/2021] [Indexed: 12/25/2022]
Abstract
A Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an α-stable subordinator with α<1. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble- and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model with any kind of diffusivity, including the critical case where the model presents normal diffusion.
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Affiliation(s)
- Xudong Wang
- School of Science, Nanjing University of Science and Technology, Nanjing, 210094, P.R. China
| | - Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing, 210094, P.R. China
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19
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Muñoz-Gil G, Volpe G, Garcia-March MA, Aghion E, Argun A, Hong CB, Bland T, Bo S, Conejero JA, Firbas N, Garibo I Orts Ò, Gentili A, Huang Z, Jeon JH, Kabbech H, Kim Y, Kowalek P, Krapf D, Loch-Olszewska H, Lomholt MA, Masson JB, Meyer PG, Park S, Requena B, Smal I, Song T, Szwabiński J, Thapa S, Verdier H, Volpe G, Widera A, Lewenstein M, Metzler R, Manzo C. Objective comparison of methods to decode anomalous diffusion. Nat Commun 2021; 12:6253. [PMID: 34716305 PMCID: PMC8556353 DOI: 10.1038/s41467-021-26320-w] [Citation(s) in RCA: 57] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 09/30/2021] [Indexed: 11/17/2022] Open
Abstract
Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.
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Affiliation(s)
- Gorka Muñoz-Gil
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Origovägen 6B, SE-41296, Gothenburg, Sweden.
| | - Miguel Angel Garcia-March
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain
| | - Erez Aghion
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, DE-01187, Dresden, Germany
| | - Aykut Argun
- Department of Physics, University of Gothenburg, Origovägen 6B, SE-41296, Gothenburg, Sweden
| | - Chang Beom Hong
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Tom Bland
- The Francis Crick Institute, 1 Midland Road, London, NW1 1AT, UK
| | - Stefano Bo
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, DE-01187, Dresden, Germany
| | - J Alberto Conejero
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain
| | - Nicolás Firbas
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain
| | - Òscar Garibo I Orts
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain
| | - Alessia Gentili
- Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK
| | - Zihan Huang
- School of Physics and Electronics, Hunan University, Changsha, 410082, China
| | - Jae-Hyung Jeon
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Hélène Kabbech
- Department of Cell Biology, Erasmus University Medical Center, Dr. Molewaterplein 40, 3015, GD, Rotterdam, the Netherlands
| | - Yeongjin Kim
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Patrycja Kowalek
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wrocław, Poland
| | - Diego Krapf
- Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado, 80523, USA
| | - Hanna Loch-Olszewska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wrocław, Poland
| | - Michael A Lomholt
- PhyLife, Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230, Odense M, Denmark
| | - Jean-Baptiste Masson
- Institut Pasteur, Université de Paris, USR 3756 (C3BI/DBC) & Neuroscience department CNRS UMR 3751, Decision and Bayesian Computation lab, F-75015, Paris, France
| | - Philipp G Meyer
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, DE-01187, Dresden, Germany
| | - Seongyu Park
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Borja Requena
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain
| | - Ihor Smal
- Department of Cell Biology, Erasmus University Medical Center, Dr. Molewaterplein 40, 3015, GD, Rotterdam, the Netherlands
| | - Taegeun Song
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
- Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul, Korea
- Department of Data Information and Physics, Kongju National University, Kongju, 32588, Korea
| | - Janusz Szwabiński
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wrocław, Poland
| | - Samudrajit Thapa
- Institute of Physics & Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, D-14476, Potsdam-Golm, Germany
- Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 69978, Israel
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Hippolyte Verdier
- Institut Pasteur, Université de Paris, USR 3756 (C3BI/DBC) & Neuroscience department CNRS UMR 3751, Decision and Bayesian Computation lab, F-75015, Paris, France
| | - Giorgio Volpe
- Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK
| | - Artur Widera
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663, Kaiserslautern, Germany
| | - Maciej Lewenstein
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluís Companys 23, 08010, Barcelona, Spain
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, D-14476, Potsdam-Golm, Germany
| | - Carlo Manzo
- ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain.
- Facultat de Ciències i Tecnologia, Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), C. de la Laura,13, 08500, Vic, Spain.
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20
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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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21
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Yamamoto E, Akimoto T, Mitsutake A, Metzler R. Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution. PHYSICAL REVIEW LETTERS 2021; 126:128101. [PMID: 33834804 DOI: 10.1103/physrevlett.126.128101] [Citation(s) in RCA: 45] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3 nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.
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Affiliation(s)
- Eiji Yamamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Ayori Mitsutake
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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22
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Zhou F, Wang H, Zhang Z. Diffusion of Anisotropic Colloids in Periodic Arrays of Obstacles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:11866-11872. [PMID: 32927949 DOI: 10.1021/acs.langmuir.0c01884] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Colloidal suspensions in confined geometries exhibit rich diffusion dynamics governed by particle shapes and particle-confinement interactions. Here, we propose a colloidal system, consisting of ellipsoids in periodic array of obstacles, to investigate the confined diffusion of anisotropic colloids. From the obstacle density-dependent diffusion, we discover a decoupling of translational and rotational diffusion in which only rotational motion is localized while translational motion remains diffusive. Moreover, by evaluating the probability distributions of displacements, we found Brownian but non-Gaussian diffusion behaviors with increasing the obstacle densities, which originates from the shape anisotropy of the colloid and the multiplicity of the local configurations of the ellipsoids with respect to the obstacle. Our results suggest that the shape anisotropy and spatial confinements play a vital role in the diffusion dynamics. It is important for understanding the transportations of anisotropic objects in complex environments.
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Affiliation(s)
- Fang Zhou
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China
| | - Huaguang Wang
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China
| | - Zexin Zhang
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
- Institute for Advanced Study, Soochow University, Suzhou 215006, China
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23
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Akimoto T, Sera T, Yamato K, Yano K. Aging arcsine law in Brownian motion and its generalization. Phys Rev E 2020; 102:032103. [PMID: 33075938 DOI: 10.1103/physreve.102.032103] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 08/12/2020] [Indexed: 06/11/2023]
Abstract
Classical arcsine law states that the fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive an aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as an aging distributional limit theorem in renewal processes.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Toru Sera
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kosuke Yamato
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kouji Yano
- Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
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24
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Kwon S, Sung BJ. Heterogeneous kinetics of the loop formation of a single polymer chain in crowded and disordered media. Phys Rev E 2019; 100:042501. [PMID: 31770886 DOI: 10.1103/physreve.100.042501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Indexed: 11/06/2022]
Abstract
The cytoplasmic volume of cells is occupied and crowded by a variety of macromolecules, such as proteins and cytoskeleton structures. Such diverse macromolecules make the cell cytoplasm not only structurally heterogeneous but also dynamically heterogeneous: Some macromolecules may diffuse freely inside cell cytoplasm at certain timescales while others hardly diffuse. Studies on the effects of the dynamic heterogeneity on reaction kinetics have been limited even though the effects of the crowdedness and structural heterogeneity were investigated extensively. In this study, we employ a simple model of mixtures of mobile and immobile matrix particles, tune the degree of dynamic heterogeneity by changing the fraction of immobile matrix particles, and investigate reaction kinetics in such heterogeneous media. We employ the loop formation of a single polymer chain as a model reaction and perform Langevin dynamics simulations. We find that the free-energy barrier of the loop formation is decreased as the systems become more crowded with matrix particles. But the free-energy barrier is not sensitive to the dynamic heterogeneity. As dynamic heterogeneity increases with an increase in the fraction of immobile matrix particles, however, the diffusivity of the system decreases significantly. The decrease in the diffusion (due to the dynamic heterogeneity) and the decrease in the free-energy barrier (due to the crowdedness) lead together to a complicated trend of the loop formation kinetics. As the volume fraction of immobile matrix particles reaches a critical value at the percolation transition, the reaction kinetics becomes significantly heterogeneous and the survival probability distribution of the chain loop formation becomes stretched-exponential. We also illustrate that the heterogeneous reaction rate near the percolation transition relates closely to the structures of local pores in which the polymer is located.
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Affiliation(s)
- Seulki Kwon
- Department of Chemistry, Sogang University, Seoul 04107, Republic of Korea
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, Republic of Korea
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25
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Aquino T, Lapeyre GJ, Dentz M. Survival and confinement under quenched disorder. Phys Chem Chem Phys 2019; 21:23598-23610. [PMID: 31621720 DOI: 10.1039/c9cp03792f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We study the survival and confinement of random walkers under quenched disorder characterized by spatially-varying waiting times and decay rates. Spatial heterogeneity and segregation lead to a dynamic coupling between transport and reaction, resulting in history-dependent dynamics exhibiting long survivals and confinement. The survival probability decays as a power law, in contrast to the classical exponential law for decay at a homogeneous rate. The mean squared displacement shows dimension-dependent subdiffusive growth followed by localization, with stronger confinement in higher dimensions.
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Affiliation(s)
- Tomás Aquino
- Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.
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26
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Hachiya Y, Uneyama T, Kaneko T, Akimoto T. Unveiling diffusive states from center-of-mass trajectories in glassy dynamics. J Chem Phys 2019; 151:034502. [DOI: 10.1063/1.5100640] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuto Hachiya
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Takashi Uneyama
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Toshihiro Kaneko
- Department of Mechanical Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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27
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Donth C, Weiss M. Quantitative assessment of the spatial crowding heterogeneity in cellular fluids. Phys Rev E 2019; 99:052415. [PMID: 31212416 DOI: 10.1103/physreve.99.052415] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Indexed: 11/07/2022]
Abstract
Mammalian cells are crowded with macromolecules, supramolecular complexes, and organelles, all of which equip intracellular fluids, e.g., the cytoplasm, with a dynamic and spatially heterogeneous occupied volume fraction. Diffusion in such fluids has been reported to be heterogeneous, i.e., even individual single-particle trajectories feature spatiotemporally varying transport characteristics. Complementing diffusion-based experiments, we have used here an imaging approach to assess the spatial heterogeneity of the nucleoplasm and the cytoplasm in living interphase cells. As a result, we find that the cytoplasm is more crowded and more heterogeneous than the nucleoplasm on several length scales. This phenomenon even persists in dividing cells, where the mitotic spindle region and its periphery form a contiguous fluid but remain nucleoplasmlike and cytoplasmlike, respectively.
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Affiliation(s)
- Claudia Donth
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany
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28
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Uneyama T, Miyaguchi T, Akimoto T. Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity. Phys Rev E 2019; 99:032127. [PMID: 30999488 DOI: 10.1103/physreve.99.032127] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Indexed: 06/09/2023]
Abstract
We study the relaxation behavior of the Ornstein-Uhlenbeck (OU) process with time-dependent and fluctuating diffusivity. In this process, the dynamics of the position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions of the transfer matrix for general FD processes. We apply our general theory to two simple FD processes where the FD is described by the Markovian two-state model or an OU-type process. We show analytic expressions of the relaxation functions in these models and their asymptotic forms. We also show that the relaxation behavior of the OU process with an FD is qualitatively different from those obtained from conventional models such as the generalized Langevin equation.
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Affiliation(s)
- Takashi Uneyama
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Tomoshige Miyaguchi
- Department of Mathematics, Naruto University of Education, Naruto, Tokushima 772-8502, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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29
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Bressloff PC, Lawley SD, Murphy P. Protein concentration gradients and switching diffusions. Phys Rev E 2019; 99:032409. [PMID: 30999457 DOI: 10.1103/physreve.99.032409] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2019] [Indexed: 06/09/2023]
Abstract
Morphogen gradients play a vital role in developmental biology by enabling embryonic cells to infer their spatial location and determine their developmental fate accordingly. The standard mechanism for generating a morphogen gradient involves a morphogen being produced from a localized source and subsequently degrading. While this mechanism is effective over the length and time scales of tissue development, it fails over typical subcellular length scales due to the rapid dissipation of spatial asymmetries. In a recent theoretical work, we found an alternative mechanism for generating concentration gradients of diffusing molecules, in which the molecules switch between spatially constant diffusivities at switching rates that depend on the spatial location of a molecule. Independently, an experimental and computational study later found that Caenorhabditis elegans zygotes rely on this mechanism for cell polarization. In this paper, we extend our analysis of switching diffusivities to determine its role in protein concentration gradient formation. In particular, we determine how switching diffusivities modifies the standard theory and show how space-dependent switching diffusivities can yield a gradient in the absence of a localized source. Our mathematical analysis yields explicit formulas for the intracellular concentration gradient which closely match the results of previous experiments and numerical simulations.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
| | - Sean D Lawley
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
| | - Patrick Murphy
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
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30
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Furukawa K, Kuronuma S, Judai K. Water fluctuation in methanol, ethanol, and 1-propanol aqueous-mixture probed by Brownian motion. J Chem Phys 2018; 149:244505. [PMID: 30599750 DOI: 10.1063/1.5064750] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
The origin of the driving force in Brownian motion is the collision between the colloidal particle and the molecules of the surrounding fluid. Therefore, Brownian motion contains information on the local solvent structures of the surrounding colloid. The mean square displacement in a water-ethanol mixture is greater than that anticipated from the macroscopic shear viscosity, indicating that the microscopic movement of Brownian motion involves the local information on the water-ethanol mixture on a molecular level, i.e., an inhomogeneity in the Brownian particle size (∼1 μm). Here, the Brownian motion of mixtures of water and methanol, ethanol, and 1-propanol are systematically investigated. Similar discrepancies between the microscopic and macroscopic viscosities are observed at low alcohol molar concentrations, for all the alcohol mixtures. This means that inhomogeneity with water fluctuation is important in explanation of the unusual Brownian diffusions of alcohol aqueous solutions. The Brownian motion also reveals a thermal energy conversion mechanism between translation and rotation.
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Affiliation(s)
- Kazuki Furukawa
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan
| | - Sumito Kuronuma
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan
| | - Ken Judai
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan
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31
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Sikora G, Wyłomańska A, Krapf D. Recurrence statistics for anomalous diffusion regime change detection. Comput Stat Data Anal 2018. [DOI: 10.1016/j.csda.2018.07.014] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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32
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Mardoukhi Y, Jeon JH, Chechkin AV, Metzler R. Fluctuations of random walks in critical random environments. Phys Chem Chem Phys 2018; 20:20427-20438. [PMID: 30043029 DOI: 10.1039/c8cp03212b] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.
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Affiliation(s)
- Yousof Mardoukhi
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
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33
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Vitali S, Sposini V, Sliusarenko O, Paradisi P, Castellani G, Pagnini G. Langevin equation in complex media and anomalous diffusion. J R Soc Interface 2018; 15:20180282. [PMID: 30158182 PMCID: PMC6127165 DOI: 10.1098/rsif.2018.0282] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 07/30/2018] [Indexed: 11/30/2022] Open
Abstract
The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.
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Affiliation(s)
- Silvia Vitali
- Department of Physics and Astronomy, Bologna University, Viale Berti Pichat 6/2, 40126 Bologna, Italy
| | - Vittoria Sposini
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany
- BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
| | - Oleksii Sliusarenko
- BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
| | - Paolo Paradisi
- BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
- ISTI-CNR, Institute of Information Science and Technologies 'A. Faedo' (Consiglio Nazionale delle Ricerche), Via Moruzzi 1, 56124 Pisa, Italy
| | - Gastone Castellani
- Department of Physics and Astronomy, Bologna University, Viale Berti Pichat 6/2, 40126 Bologna, Italy
| | - Gianni Pagnini
- BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
- Ikerbasque-Basque Foundation for Science, Calle de María Díaz de Haro 3, 48013 Bilbao, Basque Country, Spain
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34
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Stylianidou S, Lampo TJ, Spakowitz AJ, Wiggins PA. Strong disorder leads to scale invariance in complex biological systems. Phys Rev E 2018; 97:062410. [PMID: 30011517 DOI: 10.1103/physreve.97.062410] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Indexed: 11/07/2022]
Abstract
Despite the innate complexity of the cell, emergent scale-invariant behavior is observed in many biological systems. We investigate one example of this phenomenon: the dynamics of large complexes in the bacterial cytoplasm. The observed dynamics of these complexes is scale invariant in three measures of dynamics: mean-squared displacement (MSD), velocity autocorrelation function, and the step-size distribution. To investigate the physical mechanism for this emergent scale invariance, we explore minimal models in which mobility is modeled as diffusion on a rough free-energy landscape in one dimension. We discover that all three scale-invariant characteristics emerge generically in the strong disorder limit. (Strong disorder is defined by the divergence of the ensemble-averaged hop time between lattice sites.) In particular, we demonstrate how the scale invariance of the relative step-size distribution can be understood from the perspective of extreme-value theory in statistics (EVT). We show that the Gumbel scale parameter is simply related to the MSD scaling parameter. The EVT mechanism of scale invariance is expected to be generic to strongly disordered systems and therefore a powerful tool for the analysis of other systems in biology and beyond.
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Affiliation(s)
- Stella Stylianidou
- Departments Physics, Bioengineering and Microbiology, University of Washington, Seattle, Washington 98195, USA
| | - Thomas J Lampo
- Department of Chemical Engineering, Applied Physics, Materials Science and Biophysics Program, Stanford University, Stanford, California 94305, USA
| | - Andrew J Spakowitz
- Department of Chemical Engineering, Applied Physics, Materials Science and Biophysics Program, Stanford University, Stanford, California 94305, USA
| | - Paul A Wiggins
- Departments Physics, Bioengineering and Microbiology, University of Washington, Seattle, Washington 98195, USA
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35
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Karch S, Broichhagen J, Schneider J, Böning D, Hartmann S, Schmid B, Tripal P, Palmisano R, Alzheimer C, Johnsson K, Huth T. A New Fluorogenic Small-Molecule Labeling Tool for Surface Diffusion Analysis and Advanced Fluorescence Imaging of β-Site Amyloid Precursor Protein-Cleaving Enzyme 1 Based on Silicone Rhodamine: SiR-BACE1. J Med Chem 2018; 61:6121-6139. [PMID: 29939737 DOI: 10.1021/acs.jmedchem.8b00387] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
β-site APP-cleaving enzyme 1 (BACE1) is a major player in the pathogenesis of Alzheimer's disease. Structural and functional fluorescence microscopy offers a powerful approach to learn about the physiology and pathophysiology of this protease. Up to now, however, common labeling techniques require genetic manipulation, use large antibodies, or are not compatible with live cell imaging. Fluorescent small molecules that specifically bind to the protein of interest can overcome these limitations. Herein, we introduce SiR-BACE1, a conjugate of the BACE1 inhibitor S-39 and SiR647, as a novel fluorogenic, tag-free, and antibody-free label for BACE1. We present its chemical development, characterize its photophysical and pharmacologic properties, and evaluate its behavior in solution, in overexpression systems, and in native brain tissue. We demonstrate its applicability in confocal, stimulated emission depletion and dynamic single-molecule microscopy. The first functional studies with SiR-BACE1 on the surface mobility of BACE1 revealed a markedly confined diffusion pattern.
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Affiliation(s)
- Sandra Karch
- Institute of Physiology and Pathophysiology , Friedrich-Alexander-Universität Erlangen-Nürnberg , Universitaetsstrasse 17 , 91054 Erlangen , Germany
| | - Johannes Broichhagen
- Department of Chemical Biology , Max Planck Institute for Medical Research , Jahnstrasse 29 , 69120 Heidelberg , Germany.,Laboratory of Protein Engineering, Institut des Sciences et Ingénierie Chimiques, Sciences de Base , École Polytechnique Fédérale Lausanne , 1015 Lausanne , Switzerland
| | - Julia Schneider
- Institute of Physiology and Pathophysiology , Friedrich-Alexander-Universität Erlangen-Nürnberg , Universitaetsstrasse 17 , 91054 Erlangen , Germany
| | - Daniel Böning
- Max Planck Institute for the Science of Light , Staudtstrasse 2 , 91058 Erlangen , Germany
| | - Stephanie Hartmann
- Institute of Physiology and Pathophysiology , Friedrich-Alexander-Universität Erlangen-Nürnberg , Universitaetsstrasse 17 , 91054 Erlangen , Germany
| | - Benjamin Schmid
- Optical Imaging Centre , Friedrich-Alexander-Universität Erlangen-Nürnberg , Hartmannstrasse 14 , 91052 Erlangen , Germany
| | - Philipp Tripal
- Optical Imaging Centre , Friedrich-Alexander-Universität Erlangen-Nürnberg , Hartmannstrasse 14 , 91052 Erlangen , Germany
| | - Ralf Palmisano
- Optical Imaging Centre , Friedrich-Alexander-Universität Erlangen-Nürnberg , Hartmannstrasse 14 , 91052 Erlangen , Germany
| | - Christian Alzheimer
- Institute of Physiology and Pathophysiology , Friedrich-Alexander-Universität Erlangen-Nürnberg , Universitaetsstrasse 17 , 91054 Erlangen , Germany
| | - Kai Johnsson
- Department of Chemical Biology , Max Planck Institute for Medical Research , Jahnstrasse 29 , 69120 Heidelberg , Germany.,Laboratory of Protein Engineering, Institut des Sciences et Ingénierie Chimiques, Sciences de Base , École Polytechnique Fédérale Lausanne , 1015 Lausanne , Switzerland
| | - Tobias Huth
- Institute of Physiology and Pathophysiology , Friedrich-Alexander-Universität Erlangen-Nürnberg , Universitaetsstrasse 17 , 91054 Erlangen , Germany
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36
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Akimoto T, Barkai E, Saito K. Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes. Phys Rev E 2018; 97:052143. [PMID: 29906876 DOI: 10.1103/physreve.97.052143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2018] [Indexed: 06/08/2023]
Abstract
Tracking tracer particles in heterogeneous environments plays an important role in unraveling material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of such disorder realizations sometimes become considerably large. When we investigate the sample-to-sample fluctuations, fundamental averaging procedures are a thermal average for a single disorder realization and the disorder average for different disorder realizations. Here we report on non-self-averaging phenomena in quenched trap models with finite system sizes, where we consider the periodic and the reflecting boundary conditions. Sample-to-sample fluctuations of diffusivity greatly exceed trajectory-to-trajectory fluctuations of diffusivity in the corresponding annealed model. For a single disorder realization, the time-averaged mean square displacement and position-dependent observables converge to constants because of the existence of the equilibrium distribution. This is a manifestation of ergodicity. As a result, the time-averaged quantities depend neither on the initial condition nor on the thermal histories but depend crucially on the disorder realization.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Eli Barkai
- Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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37
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Muñoz-Gil G, Charalambous C, García-March MA, Garcia-Parajo MF, Manzo C, Lewenstein M, Celi A. Transient subdiffusion from an Ising environment. Phys Rev E 2018; 96:052140. [PMID: 29347809 DOI: 10.1103/physreve.96.052140] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Indexed: 11/07/2022]
Abstract
We introduce a model in which a particle performs a continuous-time random walk (CTRW) coupled to an environment with Ising dynamics. The particle shows locally varying diffusivity determined by the geometrical properties of the underlying Ising environment, that is, the diffusivity depends on the size of the connected area of spins pointing in the same direction. The model shows anomalous diffusion when the Ising environment is at critical temperature. We show that any finite scale introduced by a temperature different from the critical one, or a finite size of the environment, cause subdiffusion only during a transient time. The characteristic time, at which the system returns to normal diffusion after the subdiffusive plateau depends on the limiting scale and on how close the temperature is to criticality. The system also displays apparent ergodicity breaking at intermediate time, while ergodicity breaking at longer time occurs only under the idealized infinite environment at the critical temperature.
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Affiliation(s)
- G Muñoz-Gil
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C Charalambous
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M A García-March
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M F Garcia-Parajo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - C Manzo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,Universitat de Vic-Universitat Central de Catalunya (UVic-UCC), C. de la Laura, 13, 08500 Vic, Spain
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - A Celi
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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38
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Cherstvy AG, Nagel O, Beta C, Metzler R. Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells. Phys Chem Chem Phys 2018; 20:23034-23054. [DOI: 10.1039/c8cp04254c] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Oliver Nagel
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Carsten Beta
- 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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39
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Furukawa K, Judai K. Brownian motion probe for water-ethanol inhomogeneous mixtures. J Chem Phys 2017; 147:244502. [DOI: 10.1063/1.5007813] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kazuki Furukawa
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan
| | - Ken Judai
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan
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40
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Michieletto D, Nahali N, Rosa A. Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers. PHYSICAL REVIEW LETTERS 2017; 119:197801. [PMID: 29219489 DOI: 10.1103/physrevlett.119.197801] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Indexed: 06/07/2023]
Abstract
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and, yet, they display a large number of topological constraints. To understand their role, here we systematically probe the response of solutions of rings at various densities to "random pinning" perturbations. We show that these perturbations trigger non-Gaussian and heterogeneous dynamics, eventually leading to nonergodic and glassy behavior. We then derive universal scaling relations for the values of solution density and polymer length marking the onset of vitrification in unperturbed solutions. Finally, we directly connect the heterogeneous dynamics of the rings with their spatial organization and mutual interpenetration. Our results suggest that deviations from the typical behavior observed in systems of linear polymers may originate from architecture-specific (threading) topological constraints.
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Affiliation(s)
- Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, United Kingdom
| | - Negar Nahali
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
| | - Angelo Rosa
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
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41
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Akimoto T, Yamamoto E. Detection of transition times from single-particle-tracking trajectories. Phys Rev E 2017; 96:052138. [PMID: 29347678 DOI: 10.1103/physreve.96.052138] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Indexed: 06/07/2023]
Abstract
In heterogeneous environments, the diffusivity is not constant but changes with time. It is important to detect changes in the diffusivity from single-particle-tracking trajectories in experiments. Here, we devise a novel method for detecting the transition times of the diffusivity from trajectory data. A key idea of this method is the introduction of a characteristic time scale of the diffusive states, which is obtained by a fluctuation analysis of the time-averaged mean square displacements. We test our method in silico by using the Langevin equation with a fluctuating diffusivity. We show that our method can successfully detect the transition times of diffusive states and obtain the diffusion coefficient as a function of time. This method will provide a quantitative description of the fluctuating diffusivity in heterogeneous environments and can be applied to time series with transitions of states.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Eiji Yamamoto
- Graduate School of Science and Technology, Keio University, Yokohama, Kanagawa 223-8522, Japan
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42
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Miyaguchi T. Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor. Phys Rev E 2017; 96:042501. [PMID: 29347492 DOI: 10.1103/physreve.96.042501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 06/07/2023]
Abstract
There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.
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Affiliation(s)
- Tomoshige Miyaguchi
- Department of Mathematics, Naruto University of Education, Tokushima 772-8502, Japan
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43
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Russian A, Dentz M, Gouze P. Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media. Phys Rev E 2017; 96:022156. [PMID: 28950545 DOI: 10.1103/physreve.96.022156] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Indexed: 06/07/2023]
Abstract
Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency R_{n}, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.
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Affiliation(s)
- Anna Russian
- Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milano, Italy
| | - Marco Dentz
- Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain
| | - Philippe Gouze
- Géosciences, Université de Montpellier, CNRS, Montpellier, France
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44
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Ergodicity breaking on the neuronal surface emerges from random switching between diffusive states. Sci Rep 2017; 7:5404. [PMID: 28710444 PMCID: PMC5511290 DOI: 10.1038/s41598-017-05911-y] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Accepted: 06/05/2017] [Indexed: 12/27/2022] Open
Abstract
Stochastic motion on the surface of living cells is critical to promote molecular encounters that are necessary for multiple cellular processes. Often the complexity of the cell membranes leads to anomalous diffusion, which under certain conditions it is accompanied by non-ergodic dynamics. Here, we unravel two manifestations of ergodicity breaking in the dynamics of membrane proteins in the somatic surface of hippocampal neurons. Three different tagged molecules are studied on the surface of the soma: the voltage-gated potassium and sodium channels Kv1.4 and Nav1.6 and the glycoprotein CD4. In these three molecules ergodicity breaking is unveiled by the confidence interval of the mean square displacement and by the dynamical functional estimator. Ergodicity breaking is found to take place due to transient confinement effects since the molecules alternate between free diffusion and confined motion.
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45
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Bressloff PC, Lawley SD. Hybrid colored noise process with space-dependent switching rates. Phys Rev E 2017; 96:012129. [PMID: 29347173 DOI: 10.1103/physreve.96.012129] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Indexed: 11/07/2022]
Abstract
A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ→0) and fast switching limit (ε→0) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ε,κ→0 with ε/κ^{2} fixed.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
| | - Sean D Lawley
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
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Bressloff PC, Lawley SD. Temporal disorder as a mechanism for spatially heterogeneous diffusion. Phys Rev E 2017; 95:060101. [PMID: 28709308 DOI: 10.1103/physreve.95.060101] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 01/15/2023]
Abstract
A fundamental issue in analyzing diffusion in heterogeneous media is interpreting the space dependence of the associated diffusion coefficient. This reflects the well-known Ito-Stratonovich dilemma for continuous stochastic processes with multiplicative noise. In order to resolve this dilemma it is necessary to introduce additional constraints regarding the underlying physical system. Here we introduce a mechanism for generating nonlinear Brownian motion based on a form of temporal disorder. Motivated by switching processes in molecular biology, we consider a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast-switching limit one obtains Brownian motion with a space-dependent diffusivity. We show that the resulting multiplicative noise process is of the Ito form. In particular, we solve a first-passage time problem for finite switching rates and show that the mean first-passage time reduces to the Ito version in the fast-switching limit.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
| | - Sean D Lawley
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
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Budini AA. Memory-induced diffusive-superdiffusive transition: Ensemble and time-averaged observables. Phys Rev E 2017; 95:052110. [PMID: 28618554 DOI: 10.1103/physreve.95.052110] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Indexed: 06/07/2023]
Abstract
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination of the number of both right and left previous transitions. The diffusion process is nonstationary, and its probability develops the phenomenon of aging. Depending on the characteristic memory parameters, the ensemble behavior may be normal, superdiffusive, or ballistic. In contrast, the time-averaged mean squared displacement is equal to that of a normal undriven random walk, which renders the process nonergodic. In addition, and similarly to Lévy walks [Godec and Metzler, Phys. Rev. Lett. 110, 020603 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.020603], for trajectories of finite duration the time-averaged displacement apparently become random with properties that depend on the measurement time and also on the memory properties. These features are related to the nonstationary power-law decay of the transition probabilities to their stationary values. Time-averaged response to a bias is also calculated. In contrast with Lévy walks [Froemberg and Barkai, Phys. Rev. E 87, 030104(R) (2013)PLEEE81539-375510.1103/PhysRevE.87.030104], the response always vanishes asymptotically.
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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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Jain R, Sebastian KL. Lévy flight with absorption: A model for diffusing diffusivity with long tails. Phys Rev E 2017; 95:032135. [PMID: 28415215 DOI: 10.1103/physreve.95.032135] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 06/07/2023]
Abstract
We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016)JPCBFK1520-610610.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., 〈x^{2}(T)〉∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., π_{e}(D)∼e^{-D/D_{0}}. In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., π_{e}(D)∼D^{-1-α} with 0<α<1. We find that in the short time limit, the width of displacement distribution is proportional to sqrt[T], implying that the diffusion is Fickian. But for long times, the width is proportional to T^{1/2α} which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2α which preserves its shape at all times.
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Affiliation(s)
- Rohit Jain
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
| | - K L Sebastian
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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Charalambous C, Muñoz-Gil G, Celi A, Garcia-Parajo MF, Lewenstein M, Manzo C, García-March MA. Nonergodic subdiffusion from transient interactions with heterogeneous partners. Phys Rev E 2017; 95:032403. [PMID: 28415278 DOI: 10.1103/physreve.95.032403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 06/07/2023]
Abstract
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which a particle performs continuous Brownian motion with changes of diffusion coefficients induced by transient molecular interactions with diffusive binding partners. In spite of the exponential distribution of waiting times, the model shows subdiffusion and nonergodicity similar to the heavy-tailed continuous time random walk. The dependence of these properties on the density of binding partners is analyzed and discussed. Our work provides an experimentally testable microscopic model to investigate the nature of nonergodicity in disordered media.
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Affiliation(s)
- C Charalambous
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - G Muñoz-Gil
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - A Celi
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M F Garcia-Parajo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA - Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA - Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - C Manzo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), C. de la Laura, 13, 08500 Vic, Spain
| | - M A García-March
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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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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