1
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Yi H, Gong D, Daddysman MK, Renn M, Scherer NF. Distinct Sub- to Superdiffuse Insulin Granule Transport Behaviors in β-Cells Are Strongly Affected by Granule Age. J Phys Chem B 2024; 128:6246-6256. [PMID: 38861346 DOI: 10.1021/acs.jpcb.4c01403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2024]
Abstract
Intracellular transport is a complex process that is difficult to describe by a single general model for motion. Here, we study the transport of insulin containing vesicles, termed granules, in live MIN6 cells. We characterize how the observed heterogeneity is affected by different intracellular factors by constructing a MIN6 cell line by CRISPR-CAS9 that constitutively expresses mCherry fused to insulin and is thus packaged in granules. Confocal microscopy imaging and single particle tracking of the granule transport provide long trajectories of thousands of single granule trajectories for statistical analysis. Mean squared displacement (MSD), angle correlation distribution, and step size distribution analysis allowed identifying five distinct granule transport subpopulations, from nearly immobile and subdiffusive to run-pause and superdiffusive. The subdiffusive subpopulation recapitulates the subordinated random walk we reported earlier (Tabei, 2013; ref 18). We show that the transport characteristics of the five subpopulations have a strong dependence on the age of insulin granules. The five subpopulations also reflect the effect of local microtubule and actin networks on transport in different cellular regions. Our results provide robust metrics to clarify the heterogeneity of granule transport and demonstrate the roles of microtubule versus actin networks with granule age since initial packaging in the Golgi.
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Affiliation(s)
- Hannah Yi
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, United States
| | - Daozheng Gong
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, United States
- Graduate Program in Biophysical Science, University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew K Daddysman
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, United States
| | - Martha Renn
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, United States
| | - Norbert F Scherer
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, United States
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2
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Rajyaguru A, Metzler R, Dror I, Grolimund D, Berkowitz B. Diffusion in Porous Rock Is Anomalous. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2024; 58:8946-8954. [PMID: 38736287 PMCID: PMC11112742 DOI: 10.1021/acs.est.4c01386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Revised: 04/30/2024] [Accepted: 05/01/2024] [Indexed: 05/14/2024]
Abstract
Molecular diffusion of chemical species in subsurface environments─rock formations, soil sediments, marine, river, and lake sediments─plays a critical role in a variety of dynamic processes, many of which affect water chemistry. We investigate and demonstrate the occurrence of anomalous (non-Fickian) diffusion behavior, distinct from classically assumed Fickian diffusion. We measured molecular diffusion through a series of five chalk and dolomite rock samples over a period of about two months. We demonstrate that in all cases, diffusion behavior is significantly different than Fickian. We then analyze the results using a continuous time random walk framework that can describe anomalous diffusion in heterogeneous porous materials such as rock. This methodology shows extreme long-time tailing of tracer advance as compared to conventional Fickian diffusion processes. The finding that distinct anomalous diffusion occurs ubiquitously implies that diffusion-driven processes in subsurface zones should be analyzed using tools that account for non-Fickian diffusion.
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Affiliation(s)
- Ashish Rajyaguru
- Department
of Earth and Planetary Sciences, Weizmann
Institute of Science, Rehovot 7610001, Israel
| | - Ralf Metzler
- Institute
for Physics and Astronomy, University of
Potsdam, 14476 Potsdam, Germany
- Asia
Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Ishai Dror
- Department
of Earth and Planetary Sciences, Weizmann
Institute of Science, Rehovot 7610001, Israel
| | | | - Brian Berkowitz
- Department
of Earth and Planetary Sciences, Weizmann
Institute of Science, Rehovot 7610001, Israel
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3
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Gu Q, Shanahan L, Hart JW, Belser S, Shofer N, Atatüre M, Knowles HS. Simultaneous Nanorheometry and Nanothermometry Using Intracellular Diamond Quantum Sensors. ACS NANO 2023; 17:20034-20042. [PMID: 37791968 PMCID: PMC10604098 DOI: 10.1021/acsnano.3c05285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/15/2023] [Indexed: 10/05/2023]
Abstract
The viscoelasticity of the cytoplasm plays a critical role in cell morphology, cell division, and intracellular transport. Viscoelasticity is also interconnected with other biophysical properties, such as temperature, which is known to influence cellular bioenergetics. Probing the connections between intracellular temperature and cytoplasmic viscoelasticity provides an exciting opportunity for the study of biological phenomena, such as metabolism and disease progression. The small length scales and transient nature of changes in these parameters combined with their complex interdependencies pose a challenge for biosensing tools, which are often limited to a single readout modality. Here, we present a dual-mode quantum sensor capable of performing simultaneous nanoscale thermometry and rheometry in dynamic cellular environments. We use nitrogen-vacancy centers in diamond nanocrystals as biocompatible sensors for in vitro measurements. We combine subdiffraction resolution single-particle tracking in a fluidic environment with optically detected magnetic resonance spectroscopy to perform simultaneous sensing of viscoelasticity and temperature. We use our sensor to demonstrate probing of the temperature-dependent viscoelasticity in complex media at the nanoscale. We then investigate the interplay between intracellular forces and the cytoplasmic rheology in live cells. Finally, we identify different rheological regimes and reveal evidence of active trafficking and details of the nanoscale viscoelasticity of the cytoplasm.
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Affiliation(s)
| | | | | | - Sophia Belser
- Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge CB3 0HE, United
Kingdom
| | - Noah Shofer
- Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge CB3 0HE, United
Kingdom
| | - Mete Atatüre
- Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge CB3 0HE, United
Kingdom
| | - Helena S. Knowles
- Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge CB3 0HE, United
Kingdom
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4
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Janczura J, Magdziarz M, Metzler R. Parameter estimation of the fractional Ornstein-Uhlenbeck process based on quadratic variation. CHAOS (WOODBURY, N.Y.) 2023; 33:103125. [PMID: 37832518 DOI: 10.1063/5.0158843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/26/2023] [Indexed: 10/15/2023]
Abstract
Modern experiments routinely produce extensive data of the diffusive dynamics of tracer particles in a large range of systems. Often, the measured diffusion turns out to deviate from the laws of Brownian motion, i.e., it is anomalous. Considerable effort has been put in conceiving methods to extract the exact parameters underlying the diffusive dynamics. Mostly, this has been done for unconfined motion of the tracer particle. Here, we consider the case when the particle is confined by an external harmonic potential, e.g., in an optical trap. The anomalous particle dynamics is described by the fractional Ornstein-Uhlenbeck process, for which we establish new estimators for the parameters. Specifically, by calculating the empirical quadratic variation of a single trajectory, we are able to recover the subordination process governing the particle motion and use it as a basis for the parameter estimation. The statistical properties of the estimators are evaluated from simulations.
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Affiliation(s)
- Joanna Janczura
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Marcin Magdziarz
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
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5
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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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6
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Höll M, Nissan A, Berkowitz B, Barkai E. Controls that expedite first-passage times in disordered systems. Phys Rev E 2023; 108:034124. [PMID: 37849182 DOI: 10.1103/physreve.108.034124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 08/28/2023] [Indexed: 10/19/2023]
Abstract
First-passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We study the statistical properties of the first-passage time of biased processes in different models, and we employ the big-jump principle that shows the dominance of the maximum trapping time on the first-passage time. We demonstrate that the removal of this maximum significantly expedites transport. As the disorder increases, the system enters a phase where the removal shows a dramatic effect. Our results show how we may speed up transport in strongly disordered systems exploiting scale invariance. In contrast to the disordered systems studied here, the removal principle has essentially no effect in homogeneous systems; this indicates that improving the conductance of a poorly conducting system is, theoretically, relatively easy as compared to a homogeneous system.
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Affiliation(s)
- Marc Höll
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel
| | - Alon Nissan
- Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland
| | - Brian Berkowitz
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel
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7
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Wei Q, Wang W, Zhou H, Metzler R, Chechkin A. Time-fractional Caputo derivative versus other integrodifferential operators in generalized Fokker-Planck and generalized Langevin equations. Phys Rev E 2023; 108:024125. [PMID: 37723675 DOI: 10.1103/physreve.108.024125] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Accepted: 07/21/2023] [Indexed: 09/20/2023]
Abstract
Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous diffusion in a large variety of complex systems. The equivalent formulations in terms of Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits of continuous-time random walks and are associated with the Mittag-Leffler relaxation of Fourier modes, interpolating between a short-time stretched exponential and a long-time inverse power-law scaling. More recently, a number of other integrodifferential operators have been proposed, including the Caputo-Fabrizio and Atangana-Baleanu forms. Moreover, the conformable derivative has been introduced. We study here the dynamics of the associated generalized Fokker-Planck equations from the perspective of the moments, the time-averaged mean-squared displacements, and the autocovariance functions. We also study generalized Langevin equations based on these generalized operators. The differences between the Fokker-Planck and Langevin equations with different integrodifferential operators are discussed and compared with the dynamic behavior of established models of scaled Brownian motion and fractional Brownian motion. We demonstrate that the integrodifferential operators with exponential and Mittag-Leffler kernels are not suitable to be introduced to Fokker-Planck and Langevin equations for the physically relevant diffusion scenarios discussed in our paper. The conformable and Caputo Langevin equations are unveiled to share similar properties with scaled and fractional Brownian motion, respectively.
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Affiliation(s)
- Qing Wei
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
| | - Wei Wang
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
| | - Hongwei Zhou
- School of Energy and Mining Engineering, China University of Mining and Technology, Beijing 100083, People's Republic of China
| | - Ralf Metzler
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Aleksei Chechkin
- University of Potsdam, Institute of Physics & Astronomy, 14476 Potsdam-Golm, Germany
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
- Akhiezer Institute for Theoretical Physics National Science Center, Kharkiv Institute of Physics and Technology, Akademichna 1, Kharkiv 61108, Ukraine
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8
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Kumar P, Chakrabarti R. Dynamics of self-propelled tracer particles inside a polymer network. Phys Chem Chem Phys 2023; 25:1937-1946. [PMID: 36541408 DOI: 10.1039/d2cp04253c] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ3, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.
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Affiliation(s)
- Praveen Kumar
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
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9
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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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10
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Kim Y, Joo S, Kim WK, Jeon JH. Active Diffusion of Self-Propelled Particles in Flexible Polymer Networks. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Yeongjin Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang37673, Republic of Korea
| | - Sungmin Joo
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang37673, Republic of Korea
| | - Won Kyu Kim
- School of Computational Sciences, Korea Institute for Advanced Study (KIAS), Seoul02455, Republic of Korea
| | - Jae-Hyung Jeon
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang37673, Republic of Korea
- Asia Pacific Center for Theoretical Physics (APCTP), Pohang37673, Republic of Korea
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11
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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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12
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Li J, Xie J, Godec A, Weninger KR, Liu C, Smith JC, Hong L. Non-ergodicity of a globular protein extending beyond its functional timescale. Chem Sci 2022; 13:9668-9677. [PMID: 36091909 PMCID: PMC9400594 DOI: 10.1039/d2sc03069a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 07/18/2022] [Indexed: 11/21/2022] Open
Abstract
Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble. Here, by performing single-molecule fluorescence resonance energy transfer (smFRET) experiments and molecular dynamics (MD) simulations of a multi-domain globular protein, cytoplasmic protein-tyrosine phosphatase (SHP2), we demonstrate that the functional inter-domain motion is observationally non-ergodic over the time spans 10−12 to 10−7 s and 10−1 to 102 s. The difference between observational non-ergodicity and simple non-convergence is discussed. In comparison, a single-strand DNA of similar size behaves ergodically with an energy landscape resembling a one-dimensional linear chain. The observed non-ergodicity results from the hierarchical connectivity of the high-dimensional energy landscape of the protein molecule. As the characteristic time for the protein to conduct its dephosphorylation function is ∼10 s, our findings suggest that, due to the non-ergodicity, individual, seemingly identical protein molecules can be dynamically and functionally different. Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble.![]()
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Affiliation(s)
- Jun Li
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - JingFei Xie
- Interdisciplinary Research Center on Biology and Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 201203, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - Aljaž Godec
- Mathematical BioPhysics Group, Max Planck Institute for Biophysical Chemistry, Göttingen 37077, Germany
| | - Keith R. Weninger
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Cong Liu
- Interdisciplinary Research Center on Biology and Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 201203, China
| | - Jeremy C. Smith
- UT/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Liang Hong
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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13
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Fox ZR, Barkai E, Krapf D. Aging power spectrum of membrane protein transport and other subordinated random walks. Nat Commun 2021; 12:6162. [PMID: 34697310 PMCID: PMC8546023 DOI: 10.1038/s41467-021-26465-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 10/04/2021] [Indexed: 11/09/2022] Open
Abstract
Single-particle tracking offers detailed information about the motion of molecules in complex environments such as those encountered in live cells, but the interpretation of experimental data is challenging. One of the most powerful tools in the characterization of random processes is the power spectral density. However, because anomalous diffusion processes in complex systems are usually not stationary, the traditional Wiener-Khinchin theorem for the analysis of power spectral densities is invalid. Here, we employ a recently developed tool named aging Wiener-Khinchin theorem to derive the power spectral density of fractional Brownian motion coexisting with a scale-free continuous time random walk, the two most typical anomalous diffusion processes. Using this analysis, we characterize the motion of voltage-gated sodium channels on the surface of hippocampal neurons. Our results show aging where the power spectral density can either increase or decrease with observation time depending on the specific parameters of both underlying processes.
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Affiliation(s)
- Zachary R Fox
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA
- The Center for Nonlinear Studies and Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, Israel
| | - Diego Krapf
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA.
- Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA.
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14
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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: 21] [Impact Index Per Article: 7.0] [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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