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Buenaventura A, Saito T, Kanao T, Matsunaga D, Matsui TS, Deguchi S. Intracellular Macromolecular Crowding within Individual Stress Fibers Analyzed by Fluorescence Correlation Spectroscopy. Cell Mol Bioeng 2024; 17:165-176. [PMID: 39050511 PMCID: PMC11263330 DOI: 10.1007/s12195-024-00803-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Accepted: 05/06/2024] [Indexed: 07/27/2024] Open
Abstract
Introduction The diffusion of cell components such as proteins is crucial to the function of all living cells. The abundance of macromolecules in cells is likely to cause a state of macromolecular crowding, but its effects on the extent of diffusion remain poorly understood. Methods Here we investigate the diffusion rate in three distinct locations in mesenchymal cell types, namely the open cytoplasm, the stress fibers in the open cytoplasm, and those below the nucleus using three kinds of biologically inert green fluorescent proteins (GFPs), namely a monomer, dimer, and trimer GFP. Fluorescence correlation spectroscopy (FCS) was used to determine the diffusion coefficients. Results We show that diffusion tends to be lowered on average in stress fibers and is significantly lower in those located below the nucleus. Our data suggest that the diffusive properties of GFPs, and potentially other molecules as well, are hindered by macromolecular crowding. However, although the size dependence on protein diffusion was also studied for monomer, dimer, and trimer GFPs, there was no significant difference in the diffusion rates among the GFPs of these sizes. These results could be attributed to the lack of significant change in protein size among the selected GFP multimers. Conclusion The data presented here would provide a basis for better understanding of the complex protein diffusion in the nonuniform cytoplasm, shedding light on cellular responses to mechanical stress, their local mechanical properties, and reduced turnover in senescent cells.
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Affiliation(s)
- Aria Buenaventura
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
| | - Takumi Saito
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
- Graduate School of Biomedical Engineering, Tohoku University, Sendai, 980-0812 Japan
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, USA
- Nanobiology Institute, Yale University, West Haven, USA
| | - Taiga Kanao
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
| | - Daiki Matsunaga
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
| | - Tsubasa S. Matsui
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
| | - Shinji Deguchi
- Division of Bioengineering, Osaka University, Toyonaka, 560-0043 Japan
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2
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Liang Y, Wang W, Metzler R. Aging and confinement in subordinated fractional Brownian motion. Phys Rev E 2024; 109:064144. [PMID: 39020934 DOI: 10.1103/physreve.109.064144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 05/29/2024] [Indexed: 07/20/2024]
Abstract
We study the effects of aging properties of subordinated fractional Brownian motion (FBM) with drift and in harmonic confinement, when the measurement of the stochastic process starts a time t_{a}>0 after its original initiation at t=0. Specifically, we consider the aged versions of the ensemble mean-squared displacement (MSD) and the time-averaged MSD (TAMSD), along with the aging factor. Our results are favorably compared with simulations results. The aging subordinated FBM exhibits a disparity between MSD and TAMSD and is thus weakly nonergodic, while strong aging is shown to effect a convergence of the MSD and TAMSD. The information on the aging factor with respect to the lag time exhibits an identical form to the aging behavior of subdiffusive continuous-time random walks (CTRW). The statistical properties of the MSD and TAMSD for the confined subordinated FBM are also derived. At long times, the MSD in the harmonic potential has a stationary value, that depends on the Hurst index of the parental (nonequilibrium) FBM. The TAMSD of confined subordinated FBM does not relax to a stationary value but increases sublinearly with lag time, analogously to confined CTRW. Specifically, short aging times t_{a} in confined subordinated FBM do not affect the aged MSD, while for long aging times the aged MSD has a power-law increase and is identical to the aged TAMSD.
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3
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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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4
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Kumar G, Ardekani AM. Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion. Mol Pharm 2024; 21:2212-2222. [PMID: 38572979 DOI: 10.1021/acs.molpharmaceut.3c00973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 μs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.
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Affiliation(s)
- Gaurav Kumar
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Arezoo M Ardekani
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, United States
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5
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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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6
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Alfano C, Fichou Y, Huber K, Weiss M, Spruijt E, Ebbinghaus S, De Luca G, Morando MA, Vetri V, Temussi PA, Pastore A. Molecular Crowding: The History and Development of a Scientific Paradigm. Chem Rev 2024; 124:3186-3219. [PMID: 38466779 PMCID: PMC10979406 DOI: 10.1021/acs.chemrev.3c00615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 02/13/2024] [Accepted: 02/26/2024] [Indexed: 03/13/2024]
Abstract
It is now generally accepted that macromolecules do not act in isolation but "live" in a crowded environment, that is, an environment populated by numerous different molecules. The field of molecular crowding has its origins in the far 80s but became accepted only by the end of the 90s. In the present issue, we discuss various aspects that are influenced by crowding and need to consider its effects. This Review is meant as an introduction to the theme and an analysis of the evolution of the crowding concept through time from colloidal and polymer physics to a more biological perspective. We introduce themes that will be more thoroughly treated in other Reviews of the present issue. In our intentions, each Review may stand by itself, but the complete collection has the aspiration to provide different but complementary perspectives to propose a more holistic view of molecular crowding.
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Affiliation(s)
- Caterina Alfano
- Structural
Biology and Biophysics Unit, Fondazione
Ri.MED, 90100 Palermo, Italy
| | - Yann Fichou
- CNRS,
Bordeaux INP, CBMN UMR 5248, IECB, University
of Bordeaux, F-33600 Pessac, France
| | - Klaus Huber
- Department
of Chemistry, University of Paderborn, 33098 Paderborn, Germany
| | - Matthias Weiss
- Experimental
Physics I, Physics of Living Matter, University
of Bayreuth, 95440 Bayreuth, Germany
| | - Evan Spruijt
- Institute
for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Simon Ebbinghaus
- Lehrstuhl
für Biophysikalische Chemie and Research Center Chemical Sciences
and Sustainability, Research Alliance Ruhr, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Giuseppe De Luca
- Dipartimento
di Scienze e Tecnologie Biologiche, Chimiche e Farmaceutiche, Università degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy
| | | | - Valeria Vetri
- Dipartimento
di Fisica e Chimica − Emilio Segrè, Università degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy
| | | | - Annalisa Pastore
- King’s
College London, Denmark
Hill Campus, SE5 9RT London, United Kingdom
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7
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Tirumala NA, Redpath GMI, Skerhut SV, Dolai P, Kapoor-Kaushik N, Ariotti N, Vijay Kumar K, Ananthanarayanan V. Single-molecule imaging of stochastic interactions that drive dynein activation and cargo movement in cells. J Cell Biol 2024; 223:e202210026. [PMID: 38240798 PMCID: PMC10798859 DOI: 10.1083/jcb.202210026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Revised: 07/10/2023] [Accepted: 12/13/2023] [Indexed: 01/22/2024] Open
Abstract
Cytoplasmic dynein 1 (dynein) is the primary minus end-directed motor protein in most eukaryotic cells. Dynein remains in an inactive conformation until the formation of a tripartite complex comprising dynein, its regulator dynactin, and a cargo adaptor. How this process of dynein activation occurs is unclear since it entails the formation of a three-protein complex inside the crowded environs of a cell. Here, we employed live-cell, single-molecule imaging to visualize and track fluorescently tagged dynein. First, we observed that only ∼30% of dynein molecules that bound to the microtubule (MT) engaged in minus end-directed movement, and that too for a short duration of ∼0.6 s. Next, using high-resolution imaging in live and fixed cells and using correlative light and electron microscopy, we discovered that dynactin and endosomal cargo remained in proximity to each other and to MTs. We then employed two-color imaging to visualize cargo movement effected by single motor binding. Finally, we performed long-term imaging to show that short movements are sufficient to drive cargo to the perinuclear region of the cell. Taken together, we discovered a search mechanism that is facilitated by dynein's frequent MT binding-unbinding kinetics: (i) in a futile event when dynein does not encounter cargo anchored in proximity to the MT, dynein dissociates and diffuses into the cytoplasm, (ii) when dynein encounters cargo and dynactin upon MT binding, it moves cargo in a short run. Several of these short runs are undertaken in succession for long-range directed movement. In conclusion, we demonstrate that dynein activation and cargo capture are coupled in a step that relies on the reduction of dimensionality to enable minus end-directed transport in cellulo and that complex cargo behavior emerges from stochastic motor-cargo interactions.
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Affiliation(s)
| | - Gregory Michael Ian Redpath
- EMBL Australia Node in Single Molecule Science, Department of Molecular MedicineSchool of Biomedical Sciences, University of New South Wales, Sydney, Australia
| | - Sarah Viktoria Skerhut
- EMBL Australia Node in Single Molecule Science, Department of Molecular MedicineSchool of Biomedical Sciences, University of New South Wales, Sydney, Australia
| | - Pritha Dolai
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, India
| | | | - Nicholas Ariotti
- Electron Microscopy Unit, University of New South Wales, Sydney, Australia
| | - K. Vijay Kumar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, India
| | - Vaishnavi Ananthanarayanan
- EMBL Australia Node in Single Molecule Science, Department of Molecular MedicineSchool of Biomedical Sciences, University of New South Wales, Sydney, Australia
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8
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Bhattacharyya S, Sayer T, Montoya-Castillo A. Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries. J Phys Chem Lett 2024; 15:1382-1389. [PMID: 38288689 DOI: 10.1021/acs.jpclett.3c03380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.
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Affiliation(s)
- Srijan Bhattacharyya
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
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9
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Lingam M. Information Transmission via Molecular Communication in Astrobiological Environments. ASTROBIOLOGY 2024; 24:84-99. [PMID: 38109216 DOI: 10.1089/ast.2023.0069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2023]
Abstract
The ubiquity of information transmission via molecular communication between cells is comprehensively documented on Earth; this phenomenon might even have played a vital role in the origin(s) and early evolution of life. Motivated by these considerations, a simple model for molecular communication entailing the diffusion of signaling molecules from transmitter to receiver is elucidated. The channel capacity C (maximal rate of information transmission) and an optimistic heuristic estimate of the actual information transmission rate ℐ are derived for this communication system; the two quantities, especially the latter, are demonstrated to be broadly consistent with laboratory experiments and more sophisticated theoretical models. The channel capacity exhibits a potentially weak dependence on environmental parameters, whereas the actual information transmission rate may scale with the intercellular distance d as ℐ ∝ d-4 and could vary substantially across settings. These two variables are roughly calculated for diverse astrobiological environments, ranging from Earth's upper oceans (C ∼ 3.1 × 103 bits/s; ℐ ∼ 4.7 × 10-2 bits/s) and deep sea hydrothermal vents (C ∼ 4.2 × 103 bits/s; ℐ ∼ 1.2 × 10-1 bits/s) to the hydrocarbon lakes and seas of Titan (C ∼ 3.8 × 103 bits/s; ℐ ∼ 2.6 × 10-1 bits/s).
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Affiliation(s)
- Manasvi Lingam
- Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne, Florida, USA
- Department of Physics, The University of Texas at Austin, Austin, Texas, USA
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10
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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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11
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Ye Z, Zhang C, Yuan J, Xiao L. Ligand-Receptor Interaction Triggers Hopping and Sliding Motions on Living Cell Membranes. J Am Chem Soc 2023; 145:25177-25185. [PMID: 37947087 DOI: 10.1021/jacs.3c06925] [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: 11/12/2023]
Abstract
Exploring the surface-capturing and releasing processes of nanocargo on the living cell membrane is critical for understanding the membrane translocation process. In this work, we achieve total internal reflection scattering (TIRS) illumination on a commercial dark-field optical microscope without the introduction of any additional optical components. By gradually reducing the diaphragm size in the excitation light path, the angle of the incident beam can be well manipulated. Under optimal conditions, the excitation light can be totally reflected at the glass/water interface, resulting in a thin layer of evanescent field for TIRS illumination. Due to the exponential decay feature of the evanescent field, the displacement of the nanocargo along the vertical direction can be directly resolved in the intensity track. With this method, we selectively monitor the dynamics of the transferrin-modified nanocargo on the living cell membrane. Transition between confined diffusion and long-range searching is involved in the binding site recognition process, which exhibits non-Gaussian and nonergodic-like behavior. More interestingly, 2D fast sliding and 3D hopping motions are also distinguished on the fluidic cell membrane, which is essentially modulated by the strength of ligand-receptor interactions, as revealed by the free-energy profiles. These heterogeneous and dynamic interactions together control the diffusion mode of the nanocargo on the lipid membrane and, thus, determine the cellular translocation efficiency.
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Affiliation(s)
- Zhongju Ye
- Department of Chemistry, Zhengzhou University, Zhengzhou 450001, China
| | - Chen Zhang
- Department of Chemistry, Zhengzhou University, Zhengzhou 450001, China
| | - Jie Yuan
- School of Chemistry and Chemical Engineering, Henan Normal University, Xinxiang 453007, China
| | - Lehui Xiao
- College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China
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12
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Valdés Gómez A, Sevilla FJ. Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies. Phys Rev E 2023; 108:054117. [PMID: 38115432 DOI: 10.1103/physreve.108.054117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 10/04/2023] [Indexed: 12/21/2023]
Abstract
We analyze fractional Brownian motion and scaled Brownian motion on the two-dimensional sphere S^{2}. We find that the intrinsic long-time correlations that characterize fractional Brownian motion collude with the specific dynamics (navigation strategies) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for S^{2} (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, nonequilibrium stationary distributions are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger et al. New J. Phys. 21, 022002 (2019)1367-263010.1088/1367-2630/ab075f; Vojta et al. Phys. Rev. E 102, 032108 (2020)2470-004510.1103/PhysRevE.102.032108]; however, in the case analyzed here, there are no boundaries that affect the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the equilibrium distribution on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times toward the stationary distribution depend on the particular value of the Hurst parameter. We also show that on S^{2}, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on S^{2}, and the numerical results obtained from our numerical method to generate ensemble of trajectories.
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Affiliation(s)
- Adriano Valdés Gómez
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Alcaldía Coyoacán, C.P. 04510 Ciudad Universitaria, Ciudad de México, México
- BBVA AI Factory México
| | - Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
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13
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Costa AC, Vergassola M. Fluctuating landscapes and heavy tails in animal behavior. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.03.522580. [PMID: 36747746 PMCID: PMC9900741 DOI: 10.1101/2023.01.03.522580] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales. This immense variability hampers quantitative reasoning and renders the identification of universal principles elusive. Through data analysis and theory, we here show that slow non-ergodic drives generally give rise to heavy-tailed statistics in behaving animals. We leverage high-resolution recordings of C. elegans locomotion to extract a self-consistent reduced order model for an inferred reaction coordinate, bridging from sub-second chaotic dynamics to long-lived stochastic transitions among metastable states. The slow mode dynamics exhibits heavy-tailed first passage time distributions and correlation functions, and we show that such heavy tails can be explained by dynamics on a time-dependent potential landscape. Inspired by these results, we introduce a generic model in which we separate faster mixing modes that evolve on a quasi-stationary potential, from slower non-ergodic modes that drive the potential landscape, and reflect slowly varying internal states. We show that, even for simple potential landscapes, heavy tails emerge when barrier heights fluctuate slowly and strongly enough. In particular, the distribution of first passage times and the correlation function can asymptote to a power law, with related exponents that depend on the strength and nature of the fluctuations. We support our theoretical findings through direct numerical simulations.
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Affiliation(s)
- Antonio Carlos Costa
- Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Massimo Vergassola
- Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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14
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Liang Y, Wang W, Metzler R. Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift. Phys Rev E 2023; 108:024143. [PMID: 37723819 DOI: 10.1103/physreve.108.024143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 08/11/2023] [Indexed: 09/20/2023]
Abstract
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the trapping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time." We derive the statistical properties of this process such as non-Gaussianity and nonergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean-squared displacements. We place a specific emphasis on the comparisons between the cases with and without drift.
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Affiliation(s)
- Yingjie Liang
- College of Mechanics and Materials, Hohai University, 211100 Nanjing, China
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Wei Wang
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
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15
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Valizadeh N, Hamzehpour H, Samadpour M, Najafi MN. Edwards-Wilkinson depinning transition in fractional Brownian motion background. Sci Rep 2023; 13:12300. [PMID: 37516759 PMCID: PMC10387108 DOI: 10.1038/s41598-023-39191-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 07/21/2023] [Indexed: 07/31/2023] Open
Abstract
There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards-Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time [Formula: see text] that separates the dynamics into two distinct regimes: for [Formula: see text], we observe the typical behavior of pinned surfaces, while for [Formula: see text], the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ([Formula: see text]) and correlated ([Formula: see text]) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent [Formula: see text] to increase monotonically with H.
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Affiliation(s)
- N Valizadeh
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - H Hamzehpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran.
| | - M Samadpour
- Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran
| | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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16
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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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17
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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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18
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Walhout PK, He Z, Dutagaci B, Nawrocki G, Feig M. Molecular Dynamics Simulations of Rhodamine B Zwitterion Diffusion in Polyelectrolyte Solutions. J Phys Chem B 2022; 126:10256-10272. [PMID: 36440862 PMCID: PMC9813770 DOI: 10.1021/acs.jpcb.2c06281] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Polyelectrolytes continue to find wide interest and application in science and engineering, including areas such as water purification, drug delivery, and multilayer thin films. We have been interested in the dynamics of small molecules in a variety of polyelectrolyte (PE) environments; in this paper, we report simulations and analysis of the small dye molecule rhodamine B (RB) in several very simple polyelectrolyte solutions. Translational diffusion of the RB zwitterion has been measured in fully atomistic, 2 μs long molecular dynamics simulations in four different polyelectrolyte solutions. Two solutions contain the common polyanion sodium poly(styrene sulfonate) (PSS), one with a 30-mer chain and the other with 10 trimers. The other two solutions contain the common polycation poly(allyldimethylammonium) chloride (PDDA), one with two 15-mers and the other with 10 trimers. RB diffusion was also simulated in several polymer-free solutions to verify its known experimental value for the translational diffusion coefficient, DRB, of 4.7 × 10-6 cm2/s at 300 K. RB diffusion was slowed in all four simulated PE solutions, but to varying degrees. DRB values of 3.07 × 10-6 and 3.22 × 10-6 cm2/s were found in PSS 30-mer and PSS trimer solutions, respectively, whereas PDDA 15-mer and trimer solutions yielded values of 2.19 × 10-6 and 3.34 × 10-6 cm2/s. Significant associations between RB and the PEs were analyzed and interpreted via a two-state diffusion model (bound and free diffusion) that describes the data well. Crowder size effects and anomalous diffusion were also analyzed. Finally, RB translation along the polyelectrolytes during association was characterized.
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Affiliation(s)
| | - Zhe He
- Wheaton College, Chemistry Department, 501 College Ave, Wheaton, IL 60187
| | - Bercem Dutagaci
- Michigan State University, Biochemistry and Molecular Biology, 603 Wilson Road, Room 218, East Lansing, MI 48824
| | - Grzegorz Nawrocki
- Michigan State University, Biochemistry and Molecular Biology, 603 Wilson Road, Room 218, East Lansing, MI 48824
| | - Michael Feig
- Michigan State University, Biochemistry and Molecular Biology, 603 Wilson Road, Room 218, East Lansing, MI 48824
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19
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Kimura M, Akimoto T. Occupation time statistics of the fractional Brownian motion in a finite domain. Phys Rev E 2022; 106:064132. [PMID: 36671174 DOI: 10.1103/physreve.106.064132] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 12/09/2022] [Indexed: 06/17/2023]
Abstract
We study statistics of occupation times for a fractional Brownian motion (fBm), which is a typical model of a non-Markov process. Due to the non-Markovian nature, recurrence times to the origin depend on the history. Numerical simulations indicate that dependence on the sum of successive recurrence times becomes weak. As a result, the distribution of the occupation time in a finite domain follows the Mittag-Leffler distribution when the Hurst exponent of the fBm is close to 1/2. We show this distributional behavior of a time-averaged observable by renewal theory. This result is an extension of the distributional limit theorem known as the Darling-Kac theorem in general Markov processes to non-Markov processes.
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Affiliation(s)
- Mutsumi Kimura
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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20
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Runfola C, Vitali S, Pagnini G. The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm. ROYAL SOCIETY OPEN SCIENCE 2022; 9:221141. [PMID: 36340511 PMCID: PMC9627453 DOI: 10.1098/rsos.221141] [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: 09/21/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules' displacement and we derive the corresponding Fokker-Planck equation. Molecules' distribution emerges to be related to the Krätzel function and its Fokker-Planck equation to be a fractional diffusion equation in the Erdélyi-Kober sense. The irreducibility of the derived Fokker-Planck equation to those of other literature models is also discussed.
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Affiliation(s)
- C. Runfola
- Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
| | - S. Vitali
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
- Eurecat, Centre Tecnológic de Catalunya, Unit of Digital Health, Data Analytics in Medicine, E-08005 Barcelona, Catalunya, Spain
| | - G. Pagnini
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
- Ikerbasque – Basque Foundation for Science, Plaza Euskadi 5, E-48009 Bilbao, Basque Country, Spain
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21
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Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets. iScience 2022; 25:105122. [PMID: 36185357 PMCID: PMC9523355 DOI: 10.1016/j.isci.2022.105122] [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: 08/04/2022] [Revised: 08/27/2022] [Accepted: 09/08/2022] [Indexed: 11/20/2022] Open
Abstract
Dynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients Deff decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems. DNA diffusion measured in cell-sized droplets with differential dynamic microscopy Combination of crowding and confinement leads to subdiffusion and slowing Diffusion coefficients of DNA decrease strongly with decreasing droplet size Polymer scaling theories and depletion effects predict observed dynamics
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22
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Ling Y, Lysy M, Seim I, Newby J, Hill DB, Cribb J, Forest MG. Measurement error correction in particle tracking microrheology. Ann Appl Stat 2022. [DOI: 10.1214/21-aoas1565] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Yun Ling
- Department of Statistics and Actuarial Science, University of Waterloo
| | - Martin Lysy
- Department of Statistics and Actuarial Science, University of Waterloo
| | - Ian Seim
- Department of Applied Physical Sciences, University of North Carolina at Chapel Hill
| | - Jay Newby
- Department of Mathematical and Statistical Sciences, University of Alberta
| | - David B. Hill
- Marsico Lung Institute, University of North Carolina at Chapel Hill
| | - Jeremy Cribb
- Department of Physics and Astronomy, University of North Carolina at Chapel Hill
| | - M. Gregory Forest
- Department of Biomedical Engineering, University of North Carolina at Chapel Hill
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23
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Landfield H, Wang M. Determination of Hydrophobic Polymer Clustering in Concentrated Aqueous Solutions through Single-Particle Tracking Diffusion Studies. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Harrison Landfield
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Muzhou Wang
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States
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24
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Schmitt S, Renzer G, Benrath J, Best A, Jiang S, Landfester K, Butt HJ, Simonutti R, Crespy D, Koynov K. Monitoring the Formation of Polymer Nanoparticles with Fluorescent Molecular Rotors. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Sascha Schmitt
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Galit Renzer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Jennifer Benrath
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Andreas Best
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Shuai Jiang
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Katharina Landfester
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Hans-Jürgen Butt
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Roberto Simonutti
- Department of Material Science, University Milano Bicocca, Via R Cozzi 55, I-20125 Milan, Italy
| | | | - Kaloian Koynov
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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25
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Słyk E, Skóra T, Kondrat S. How macromolecules softness affects diffusion under crowding. SOFT MATTER 2022; 18:5366-5370. [PMID: 35833511 DOI: 10.1039/d2sm00357k] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Diffusion in a macromolecularly crowded environment is essential for many intracellular processes, from metabolism and catalysis to gene transcription and translation. So far, theoretical and experimental work has focused on anomalous subdiffusion, and the effects of interactions, shapes, and composition, while the compactness or softness of macromolecules has received less attention. Herein, we use Brownian dynamics simulations to study how the softness of crowders affects macromolecular diffusion. We find that in most cases, soft crowders slow down the diffusion less effectively than hard crowders like Ficoll. For instance, at a 30% occupied volume fraction, the diffusion in Ficoll70 is about 20% slower than in soft crowders of the same size. However, our simulations indicate that elongated macromolecules, such as double-stranded DNA pieces, can diffuse comparably or even faster in hard crowders. We relate these effects to the volume excluded by soft and hard crowders to different tracers. Our results show that the softness and shape of macromolecules are crucial factors determining diffusion under crowding, relevant to diverse intracellular environments.
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Affiliation(s)
- Edyta Słyk
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland.
- Department of Theoretical Chemistry, Institute of Chemical Sciences, Faculty of Chemistry, Maria Curie-Skłodowska University in Lublin, 20-031 Lublin, Poland
| | - Tomasz Skóra
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland.
| | - Svyatoslav Kondrat
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland.
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Institut für Computerphysik, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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26
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Zhou T, Xu P, Deng W. Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media. JOURNAL OF STATISTICAL PHYSICS 2022; 187:9. [PMID: 35250092 PMCID: PMC8883250 DOI: 10.1007/s10955-022-02904-8] [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: 11/17/2021] [Accepted: 02/16/2022] [Indexed: 06/14/2023]
Abstract
Based on the recognition of the huge change of the transport properties for diffusion particles in non-static media, we consider a Lévy walk model subjected to an external constant force in non-static media. Since the physical and comoving coordinates of non-static media are related by scale factor, we equivalently transfer the process from physical coordinate into comoving coordinate and derive the master equation governing the probability density function of the position of the particles in comoving coordinate. Utilizing the Hermite orthogonal polynomial expansions, some statistical properties are obtained, including the asymptotic behaviors of the first two moments in both coordinates and kurtosis. For some representative types of non-static media and Lévy walks, the striking and interesting phenomena originating from the interplay between non-static media, external force, and intrinsic stochastic motion are observed. The stationary distribution are also analyzed for some cases through numerical simulations.
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Affiliation(s)
- Tian Zhou
- Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 People’s Republic of China
| | - Pengbo Xu
- School of Mathematical Sciences, Peking University, Beijing, 100871 People’s Republic of China
| | - Weihua Deng
- Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 People’s Republic of China
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27
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Khatun S, Singh A, Shikha K, Ganguly A, Gupta AN. Plasmid DNA Undergoes Two Compaction Regimes under Macromolecular Crowding. ACS Macro Lett 2022; 11:186-192. [PMID: 35574767 DOI: 10.1021/acsmacrolett.1c00593] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The laser light scattering experiments were performed to explore the role of dextran (size (d): 2.6, 6.9, and 17.0 nm) in compacting the plasmids (pBS: 2.9 kbps; pCMV-Tag2B: 4.3 kbps; and pET28a: 5.3 kbps) in vitro in the volume fraction (ϕ) range 0.01 to 0.15 of the macromolecular crowder. Two compaction regimes were observed in terms of the radius of gyration (Rg) for plasmid-dextran combinations, wherein the plasmid diffusivity is governed by normal diffusion and subdiffusion, respectively. Generalized scaling, Rg ∼ ϕ-1/(1+x), where x represents the conformational geometry of plasmids, is reported. The plasmid conformation depends on the crowder's size, with larger conformational changes observed in the presence of smaller crowders. The second virial coefficient (A2) and translational diffusion coefficient (Dt) indicate that entropically driven depletion of crowders, excluded volume, and interplasmid repulsive interactions govern plasmids' conformational changes, validated herein from the scaling of Dt with molecular weight.
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Affiliation(s)
- Suparna Khatun
- Biophysics and Soft Matter Laboratory, Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
| | - Anurag Singh
- Biophysics and Soft Matter Laboratory, Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
| | - Kumari Shikha
- School of Bio Science, Indian Institute of Technology, Kharagpur 721302, India
| | - Agneyo Ganguly
- Department of Biotechnology, Indian Institute of Technology, Kharagpur 721302, India
| | - Amar Nath Gupta
- Biophysics and Soft Matter Laboratory, Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
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28
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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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29
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Liu J, Zhu P, Bao JD, Chen X. Strong anomalous diffusive behaviors of the two-state random walk process. Phys Rev E 2022; 105:014122. [PMID: 35193269 DOI: 10.1103/physreve.105.014122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
The phenomenon of the two-state process is observed in various systems and is increasingly attracting attention, such that there is a need for a theoretical model of the process. In this paper, we present a prototypal two-state random walk (TSRW) model of a renewal process alternating between the continuous-time random walk (CTRW) state and Lévy walk (LW) state. The jump length distribution of the CTRW state is assumed to be Gaussian whereas the time distributions of the two states are both considered to follow a power law. The diffusive behavior is analyzed and discussed by calculating the mean squared displacement (MSD) analytically and numerically. The results reveal that it displays strong anomalous diffusive behaviors caused by random motions of both states, i.e., two anomalous diffusion terms coexist in the expression of the MSD, and the time distribution which has the heavier tail determines their forms. Moreover, because the two diffusion terms originate from different mechanisms, we find that the diffusion can be characterized by either the term with the largest diffusion exponent or the term with the largest diffusion coefficient at long timescales, which shows very different properties from the single-state process. In addition, the two-state nature of the process of the particle moving in a velocity field makes the TSRW model applicable to describe it. Results obtained from the two-state model reveal that the diffusion can even exhibit subdiffusive behavior, which is significantly different from known results obtained using the single-state model.
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Affiliation(s)
- Jian Liu
- Department of Physics, Institute of Systems Science, Beijing Technology and Business University, Beijing 100048, China
| | - Ping Zhu
- Department of Physics, Institute of Systems Science, Beijing Technology and Business University, Beijing 100048, China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China
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30
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Yan Y, Xu W, Kumar S, Zhang A, Leng F, Dunlap D, Finzi L. Negative DNA supercoiling makes protein-mediated looping deterministic and ergodic within the bacterial doubling time. Nucleic Acids Res 2021; 49:11550-11559. [PMID: 34723343 PMCID: PMC8599721 DOI: 10.1093/nar/gkab946] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 09/28/2021] [Accepted: 10/04/2021] [Indexed: 11/14/2022] Open
Abstract
Protein-mediated DNA looping is fundamental to gene regulation and such loops occur stochastically in purified systems. Additional proteins increase the probability of looping, but these probabilities maintain a broad distribution. For example, the probability of lac repressor-mediated looping in individual molecules ranged 0–100%, and individual molecules exhibited representative behavior only in observations lasting an hour or more. Titrating with HU protein progressively compacted the DNA without narrowing the 0–100% distribution. Increased negative supercoiling produced an ensemble of molecules in which all individual molecules more closely resembled the average. Furthermore, in only 12 min of observation, well within the doubling time of the bacterium, most molecules exhibited the looping probability of the ensemble. DNA supercoiling, an inherent feature of all genomes, appears to impose time-constrained, emergent behavior on otherwise random molecular activity.
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Affiliation(s)
- Yan Yan
- Physics Department, Emory University, Atlanta, GA 30322, USA
| | - Wenxuan Xu
- Physics Department, Emory University, Atlanta, GA 30322, USA
| | - Sandip Kumar
- Physics Department, Emory University, Atlanta, GA 30322, USA
| | - Alexander Zhang
- Physics Department, Emory University, Atlanta, GA 30322, USA
| | - Fenfei Leng
- Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA
| | - David Dunlap
- Physics Department, Emory University, Atlanta, GA 30322, USA
| | - Laura Finzi
- Physics Department, Emory University, Atlanta, GA 30322, USA
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31
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Liu J, Zhang C, Bao JD, Chen X. Correlated continuous-time random walk in the velocity field: the role of velocity and weak asymptotics. SOFT MATTER 2021; 17:9786-9798. [PMID: 34657952 DOI: 10.1039/d1sm00995h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Within the framework of a space-time correlated continuous-time random walk model, anomalous diffusion of particles moving in the velocity field is studied in this paper. The weak asymptotic form ω(t) ∼ t-(1+α), 1 < α < 2 for large t, is considered to be the waiting time distribution. The analytical results reveal that the diffusion in the velocity field, i.e., the mean squared displacement, can display a multi-fractional form caused by dispersive bias and space-time correlation. The numerical results indicate that the multi-fractional diffusion leads to a crossover phenomenon in-between the process at an intermediate timescale, followed by a steady state which is always determined by the largest diffusion exponent term. In addition, the role of velocity and weak asymptotics is discussed. The extremely small fluid velocity can characterize the diffusion by a diffusion coefficient instead of diffusion exponent, which is distinctly different from the former definition. In particular, for the waiting time displaying a weak asymptotic property, if the anomalous part is suppressed by the normal part, a second crossover phenomenon appears at an intermediate timescale, followed by a steady normal diffusion, which implies that the anomalies underlying the process are smoothed out at large timescales. Moreover, we discuss that the consideration of bias and correlation could help to avoid a possible not readily noticeable mistake in studying the topic concerned in this paper, which may be helpful in the relevant experimental research.
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Affiliation(s)
- Jian Liu
- Department of Physics, Beijing Technology and Business University, Beijing, 100048, China.
- Institute of Systems Science, Beijing Technology and Business University, Beijing, 100048, China
| | - Caiyun Zhang
- Department of Physics, Beijing Technology and Business University, Beijing, 100048, China.
- Institute of Systems Science, Beijing Technology and Business University, Beijing, 100048, China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing, 100875, China
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, Beijing, 100875, China
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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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33
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Janczura J, Kowalek P, Loch-Olszewska H, Szwabiński J, Weron A. Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion. Phys Rev E 2021; 102:032402. [PMID: 33076015 DOI: 10.1103/physreve.102.032402] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2020] [Accepted: 07/27/2020] [Indexed: 12/20/2022]
Abstract
Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean-square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e., random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.
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Affiliation(s)
- Joanna Janczura
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Patrycja Kowalek
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Hanna Loch-Olszewska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Janusz Szwabiński
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Aleksander Weron
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
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34
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Speckner K, Weiss M. Single-Particle Tracking Reveals Anti-Persistent Subdiffusion in Cell Extracts. ENTROPY (BASEL, SWITZERLAND) 2021; 23:892. [PMID: 34356433 PMCID: PMC8303845 DOI: 10.3390/e23070892] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 07/06/2021] [Accepted: 07/09/2021] [Indexed: 01/08/2023]
Abstract
Single-particle tracking (SPT) has become a powerful tool to quantify transport phenomena in complex media with unprecedented detail. Based on the reconstruction of individual trajectories, a wealth of informative measures become available for each particle, allowing for a detailed comparison with theoretical predictions. While SPT has been used frequently to explore diffusive transport in artificial fluids and inside living cells, intermediate systems, i.e., biochemically active cell extracts, have been studied only sparsely. Extracts derived from the eggs of the clawfrog Xenopus laevis, for example, are known for their ability to support and mimic vital processes of cells, emphasizing the need to explore also the transport phenomena of nano-sized particles in such extracts. Here, we have performed extensive SPT on beads with 20 nm radius in native and chemically treated Xenopus extracts. By analyzing a variety of distinct measures, we show that these beads feature an anti-persistent subdiffusion that is consistent with fractional Brownian motion. Chemical treatments did not grossly alter this finding, suggesting that the high degree of macromolecular crowding in Xenopus extracts equips the fluid with a viscoelastic modulus, hence enforcing particles to perform random walks with a significant anti-persistent memory kernel.
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Affiliation(s)
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95447 Bayreuth, Germany;
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35
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Mahato J, Bhattacharya S, Sharma DK, Chowdhury A. Polarization-resolved single-molecule tracking reveals strange dynamics of fluorescent tracers through a deep rubbery polymer network. Phys Chem Chem Phys 2021; 23:10835-10844. [PMID: 33908423 DOI: 10.1039/d0cp05864e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Tracking the movement of fluorescent single-molecule (SM) tracers has provided several new insights into the local structure and dynamics in complex environments such as soft materials and biological systems. However, SM tracking (SMT) remains unreliable at molecular length scales, as the localization error (LE) of SM trajectories (∼30-50 nm) is considerably larger than the size of molecular tracers (∼1-2 nm). Thus, instances of tracer (im)mobility in heterogeneous media, which provide indicators for underlying anomalous-transport mechanisms, remain obscured within the realms of SMT. Since the translation of passive tracers in an isotropic media is associated with fast dipolar rotation, we propose that authentic pauses within the LE can be revealed by probing the hindrance of SM reorientational dynamics. Here, we demonstrate how polarization-resolved SMT (PR-SMT) can provide emission anisotropy at each super-localized position, thereby revealing the tumbling propensity of SMs during random walks. For rhodamine 6G tracers undergoing heterogeneous transport in a hydrated polyvinylpyrrolidone (PVP) network, analysis of PR-SMT trajectories enabled us to discern instances of genuine immobility and localized motion within the LE. Our investigations on 100 SMs in (plasticized) PVP films reveal a wide distribution of dwell times and pause frequencies, demonstrating that most probes intermittently experience complete translational and rotational immobilization. This indicates that tracers serendipitously encounter compact, rigid polymer cavities during transport, implying the existence of nanoscale glass-like domains sparsely distributed in a predominantly deep-rubbery polymer network far above the glass transition.
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Affiliation(s)
- Jaladhar Mahato
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
| | - Sukanya Bhattacharya
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
| | - Dharmendar K Sharma
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
| | - Arindam Chowdhury
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
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36
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Zhou T, Xu P, Deng W. Lévy walk dynamics in mixed potentials from the perspective of random walk theory. Phys Rev E 2021; 103:032151. [PMID: 33862717 DOI: 10.1103/physreve.103.032151] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Accepted: 03/14/2021] [Indexed: 11/07/2022]
Abstract
Lévy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in micro- and macrodynamics. From the perspective of random walk theory, here we investigate the dynamics of Lévy walks under the influences of the constant force field and the one combined with harmonic potential. Utilizing Hermite polynomial approximation to deal with the spatiotemporally coupled analysis challenges, some striking features are detected, including non-Gaussian stationary distribution, faster diffusion, still strongly anomalous diffusion, etc.
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Affiliation(s)
- Tian Zhou
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Pengbo Xu
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Weihua Deng
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
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37
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Kienle DF, Schwartz DK. Single molecule characterization of anomalous transport in a thin, anisotropic film. Anal Chim Acta 2021; 1154:338331. [PMID: 33736806 DOI: 10.1016/j.aca.2021.338331] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Revised: 02/01/2021] [Accepted: 02/14/2021] [Indexed: 01/07/2023]
Abstract
The diffusion of small, charged molecules incorporated in an anisotropic polyelectrolyte multilayer (PEM) was tracked in three dimensions by combining single-molecule fluorescence localization (to characterize lateral diffusion) with Förster resonance energy transfer (FRET) between diffusing molecules and the supporting surface (to measure diffusion in the surface-normal direction). Analysis of the surface-normal diffusion required model-based statistical analysis to account for the inherently noisy FRET signal. Combining these distinct single-molecule methods, which are inherently sensitive to different length-scales, permitted simultaneous characterization of severely anisotropic diffusion, which was more than three orders of magnitude slower in the surface-normal direction. We hypothesize that the anomalously slow surface-normal diffusion was related to the periodic distribution of charge in the PEM, which created electrostatic barriers. The motion was strongly subdiffusive, with anomalous temporal scaling exponents in lateral and normal directions, suggesting a connection to the transient, random fractal conformation of polymer chains in the film's matrix.
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Affiliation(s)
- Daniel F Kienle
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO 80309, USA
| | - Daniel K Schwartz
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO 80309, USA.
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38
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Levin M, Bel G, Roichman Y. Measurements and characterization of the dynamics of tracer particles in an actin network. J Chem Phys 2021; 154:144901. [PMID: 33858166 DOI: 10.1063/5.0045278] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.
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Affiliation(s)
- Maayan Levin
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Golan Bel
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel
| | - Yael Roichman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
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39
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Itto Y, Beck C. Superstatistical modelling of protein diffusion dynamics in bacteria. J R Soc Interface 2021; 18:20200927. [PMID: 33653112 PMCID: PMC8086855 DOI: 10.1098/rsif.2020.0927] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 02/04/2021] [Indexed: 01/18/2023] Open
Abstract
A recent experiment (Sadoon AA, Wang Y. 2018 Phys. Rev. E98, 042411. (doi:10.1103/PhysRevE.98.042411)) has revealed that nucleoid-associated proteins (i.e. DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion constant but also the anomalous diffusion exponent fluctuates for the various proteins. The distribution of displacements of such proteins is observed to take a q-Gaussian form, which decays as a power law. Here, a statistical model is developed for the diffusive motion of the proteins within the bacterium, based on a superstatistics with two variables. This model hierarchically takes into account the joint fluctuations of both the anomalous diffusion exponents and the diffusion constants. A fractional Brownian motion is discussed as a possible local model. Good agreement with the experimental data is obtained.
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Affiliation(s)
- Yuichi Itto
- ICP, Universität Stuttgart, 70569 Stuttgart, Germany
- Science Division, Center for General Education, Aichi Institute of Technology, Aichi 470-0392, Japan
| | - Christian Beck
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
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40
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Xu Y, Liu X, Li Y, Metzler R. Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes. Phys Rev E 2021; 102:062106. [PMID: 33466052 DOI: 10.1103/physreve.102.062106] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 10/22/2020] [Indexed: 01/03/2023]
Abstract
Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.
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Affiliation(s)
- Yong Xu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China
| | - Xuemei Liu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Yongge Li
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.,Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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41
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Liu J, Bao JD, Chen X. Correlated continuous-time random walk in a velocity field: Anomalous bifractional crossover. Phys Rev E 2021; 102:062122. [PMID: 33465995 DOI: 10.1103/physreve.102.062122] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 11/23/2020] [Indexed: 11/06/2022]
Abstract
The diffusion of space-time correlated continuous-time random walk moving in the velocity field, which includes the fluid flowing freely and the fluid flowing through porous media, is investigated in this paper. Results reveal that it presents anomalous diffusion merely caused by space-time correlation in the freely flowing fluid, and the bias from the velocity field only supplies a standard advection, which is verified by the corresponding generalized diffusion equation which includes a standard advection term. However, the diffusion in the fluid flowing through porous media, i.e., the mean squared displacement, can display a bifractional form of which one originates from space-time correlation and the other one originates from dispersive bias caused by sticking of the porous media. The fractional advection term emerging in the corresponding generalized diffusion equation confirms the results. Moreover, the coexistence of correlation and dispersive bias result in crossover phenomenon in-between the diffusive process at an intermediate timescale, but just as the definition of diffusion, the one owning the largest diffusion exponent always prevails at large timescales. However, since the two fractional diffusions originate from a different mechanism, even if it owns the smaller diffusion exponent, that one can dominate the diffusion if it fluctuates much stronger than the other one, which no longer obeys the previous conclusion.
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Affiliation(s)
- Jian Liu
- Department of Physics, Beijing Technology and Business University, Beijing, 100048, China Institute of Systems Science, Beijing Technology and Business University, Beijing, 100048, China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing, 100875, China
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, Beijing, 100875, China
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42
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Harusawa K, Watanabe C, Kobori Y, Tomita K, Kitamura A, Kinjo M, Yanagisawa M. Membrane Surface Modulates Slow Diffusion in Small Crowded Droplets. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:437-444. [PMID: 33351626 DOI: 10.1021/acs.langmuir.0c03086] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Membranes are ubiquitous structures in cells. The effects of membranes on various functional molecules have been reported, but their behaviors under macromolecular crowding and cell-sized confinement have not fully been understood. In this study, we model an intracellular environment by crowding micrometer-sized droplets and investigate the effects of membrane properties on molecular diffusion. The molecular diffusion inside small droplets covered with a lipid layer of phosphatidylcholine (PC) becomes slower compared with that of the corresponding bulk solutions under a crowding condition of polysaccharide dextran but not of its monomer unit, glucose. The addition of a poly(ethylene glycol) conjugated lipid (PEGylated lipid) to the PC membrane significantly alters the degree of slow diffusion observed inside small droplets of concentrated dextran. Interestingly, the change is not monotonic against dextran concentration; that is, the PEGylated membrane increases and decreases the degree of slow diffusion with increasing dextran concentration. We explain the nonmonotonic alternation from the increase in effective dextran concentration and the hindered temporal adsorption of dextran to the membrane. Because diffusion alteration by adding PEGylated lipid is observed for condensed small droplets of linear polymer PEG and hydrophilic protein bovine serum albumin, the phenomenon is general for other polymer systems as well. Furthermore, our findings may facilitate the understanding of intracellular molecular behaviors based on membrane effects as well as the development of numerous applications using polymer droplets.
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Affiliation(s)
- Kanae Harusawa
- Komaba Institute for Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
- Department of Applied Physics, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588, Japan
| | - Chiho Watanabe
- Komaba Institute for Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
| | - Yuta Kobori
- Komaba Institute for Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
- Department of Applied Physics, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588, Japan
| | - Kazuho Tomita
- Komaba Institute for Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
- Department of Applied Physics, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588, Japan
| | - Akira Kitamura
- Faculty of Advanced Life Science, Hokkaido University, Kita-21 Nishi-11 Kita-ku, Sapporo, Hokkaido 001-0021, Japan
| | - Masataka Kinjo
- Faculty of Advanced Life Science, Hokkaido University, Kita-21 Nishi-11 Kita-ku, Sapporo, Hokkaido 001-0021, Japan
| | - Miho Yanagisawa
- Komaba Institute for Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
- Department of Basic Science, The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan
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43
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Hubicka K, Janczura J. Time-dependent classification of protein diffusion types: A statistical detection of mean-squared-displacement exponent transitions. Phys Rev E 2021; 101:022107. [PMID: 32168604 DOI: 10.1103/physreve.101.022107] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2019] [Accepted: 01/23/2020] [Indexed: 01/26/2023]
Abstract
In this paper, we have proposed a statistical procedure for detecting transitions of the mean-square-displacement exponent value within a single trajectory. With this procedure, we have identified three regimes of proteins dynamics on a cell membrane, namely, subdiffusion, free diffusion, and immobility. The fourth considered dynamics type, namely, superdiffusion was not detected. We show that the analyzed protein trajectories are not stationary and not ergodic. Moreover, classification of the dynamics type performed without prior detection of transitions may lead to the overestimation of the proportion of subdiffusive trajectories.
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Affiliation(s)
- Katarzyna Hubicka
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Joanna Janczura
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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44
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Balcerek M, Burnecki K. Testing of Multifractional Brownian Motion. ENTROPY 2020; 22:e22121403. [PMID: 33322676 PMCID: PMC7764075 DOI: 10.3390/e22121403] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Revised: 12/09/2020] [Accepted: 12/10/2020] [Indexed: 12/12/2022]
Abstract
Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.
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45
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Szarek D, Sikora G, Balcerek M, Jabłoński I, Wyłomańska A. Fractional Dynamics Identification via Intelligent Unpacking of the Sample Autocovariance Function by Neural Networks. ENTROPY 2020; 22:e22111322. [PMID: 33287087 PMCID: PMC7712253 DOI: 10.3390/e22111322] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 11/18/2020] [Indexed: 12/20/2022]
Abstract
Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective; however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations.
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Affiliation(s)
- Dawid Szarek
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw, Poland; (D.S.); (G.S.); (M.B.)
| | - Grzegorz Sikora
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw, Poland; (D.S.); (G.S.); (M.B.)
| | - Michał Balcerek
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw, Poland; (D.S.); (G.S.); (M.B.)
| | - Ireneusz Jabłoński
- Department of Electronics, Wroclaw University of Science and Technology, B. Prusa 53/55, 50-317 Wroclaw, Poland;
| | - Agnieszka Wyłomańska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroclaw, Poland; (D.S.); (G.S.); (M.B.)
- Correspondence:
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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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Vojta T, Halladay S, Skinner S, Janušonis S, Guggenberger T, Metzler R. Reflected fractional Brownian motion in one and higher dimensions. Phys Rev E 2020; 102:032108. [PMID: 33075869 DOI: 10.1103/physreve.102.032108] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 07/24/2020] [Indexed: 02/01/2023]
Abstract
Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of large-scale computer simulations of FBM in one, two, and three dimensions in the presence of reflecting boundaries that confine the motion to finite regions in space. Generalizing earlier results for finite and semi-infinite one-dimensional intervals, we observe that the interplay between the long-time correlations of FBM and the reflecting boundaries leads to striking deviations of the stationary probability density from the uniform density found for normal diffusion. Particles accumulate at the boundaries for superdiffusive FBM while their density is depleted at the boundaries for subdiffusion. Specifically, the probability density P develops a power-law singularity, P∼r^{κ}, as a function of the distance r from the wall. We determine the exponent κ as a function of the dimensionality, the confining geometry, and the anomalous diffusion exponent α of the FBM. We also discuss implications of our results, including an application to modeling serotonergic fiber density patterns in vertebrate brains.
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Affiliation(s)
- Thomas Vojta
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Samuel Halladay
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Sarah Skinner
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Skirmantas Janušonis
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - Tobias Guggenberger
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany
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48
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Skóra T, Vaghefikia F, Fitter J, Kondrat S. Macromolecular Crowding: How Shape and Interactions Affect Diffusion. J Phys Chem B 2020; 124:7537-7543. [PMID: 32790396 DOI: 10.1021/acs.jpcb.0c04846] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
A significant fraction of the cell volume is occupied by various proteins, polysaccharides, nucleic acids, etc., which considerably reduces the mobility of macromolecules. Theoretical and experimental work so far have mainly focused on the dependence of the mobility on the occupied volume, while the effect of a macromolecular shape received less attention. Herein, using fluorescence correlation spectroscopy (FCS) and Brownian dynamics (BD) simulations, we report on a dramatic slowdown of tracer diffusion by cylindrically shaped double-stranded (ds) DNAs (16 nm in length). We find, for instance, that the translational diffusion coefficient of a streptavidin tracer is reduced by about 60% for a volume fraction of dsDNA as low as just 5%. For comparison, for a spherical crowder (Ficoll70) the slowdown is only 10% at the same volume fraction and 60% reduction occurs at a volume fraction as high as 35%. BD simulations reveal that this reduction can be attributed to a larger volume excluded to a tracer by dsDNA particles, as compared with spherical Ficoll70 at the same volume fraction, and to the differences in the tracer-crowder attractive interactions. In addition, we find using BD simulations that rotational diffusion of dsDNA is less affected by the crowder shape than its translational motion. Our results show that diffusion in crowded systems is determined not merely by the occupied volume fraction, but that the shape and interactions can determine diffusion, which is relevant to the diverse intracellular environments inside living cells.
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Affiliation(s)
- Tomasz Skóra
- Department of Complex Systems, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Farzaneh Vaghefikia
- I. Physikalisches Institut (IA), AG Biophysik, RWTH Aachen University, 52074 Aachen, Germany
| | - Jörg Fitter
- I. Physikalisches Institut (IA), AG Biophysik, RWTH Aachen University, 52074 Aachen, Germany.,Institut für Biologische Informationsprozesse (IBI-6), Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Svyatoslav Kondrat
- Department of Complex Systems, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.,Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.,Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Wang W, Cherstvy AG, Liu X, Metzler R. Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise. Phys Rev E 2020; 102:012146. [PMID: 32794926 DOI: 10.1103/physreve.102.012146] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 06/22/2020] [Indexed: 01/09/2023]
Abstract
Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x)=D_{0}|x|^{α}. Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble- and time-averaged mean-squared displacements couple the scaling exponents α of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y∼|x|^{1/(2/(2-α))}/t^{H} coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), P_{HDP-FBM}(y)=e^{-y^{2}}/sqrt[π]. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.
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Affiliation(s)
- Wei Wang
- College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China.,Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Xianbin Liu
- College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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50
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Shan Y, Xu BY, Li S, Fan Y, Liu YB, Zhang M, Ma QF, Gao JH, Lu J. Assessment of MRI-based anomalous diffusion changes in brain ischemic stroke with a fractional motion model. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 317:106795. [PMID: 32712547 DOI: 10.1016/j.jmr.2020.106795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Revised: 07/12/2020] [Accepted: 07/15/2020] [Indexed: 06/11/2023]
Abstract
The actual diffusion process in human brain has been shown to be anomalous comparing to that predicted with traditional diffusion MRI (dMRI) theory. Recently, dMRI based on fractional motion (FM) model has demonstrated the potential to accurately describe anomalous diffusion in vivo. In this work, we explored the potential value of FM model-based dMRI in quantificational identification of ischemic stroke and compared that with the traditional apparent diffusion coefficient (ADC). We included 23 acute stroke patients, 8 of whom finished a follow-up scan, and 22 matched healthy controls. The dMRI images were acquired by using a Stejskal-Tanner single-shot spin-echo echo-planar-imaging sequence (diffusion gradients were applied in three orthogonal directions with 25 non-zero b values ranging from 248 to 4474 s/mm2) at 3.0 T MRI. We calculated the coefficient of variation (CV) for FM-related parameters in stroke lesions, and compared the mean values for FM-related parameters and ADC by using two-sample t-tests. Correlation analysis was achieved using Pearson correlation coefficient test. In acute stroke lesions, CV for FM-related parameters showed significant increase compared with normal tissues (P < 0.01), while those of ADC didn't appear statistical difference. Mean values for FM-related parameters showed significant decrease in acute lesion (P < 0.01) and their changing pattern during follow-up was positively correlated with ADC (P < 0.005). Our results initially verified the utility of the FM-model in detecting ischemic stroke compared with traditional dMRI.
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Affiliation(s)
- Yi Shan
- Department of Radiology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China; Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, China
| | - Bo-Yan Xu
- Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics, Peking University, No. 5 Yiheyuan Road, Beijing 100871, China; Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, No. 5 Yiheyuan Road, Beijing 100871, China
| | - Shuang Li
- Department of Radiology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China; Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, China
| | - Yang Fan
- Beijing Intelligent Brain Cloud, Inc., Integrated Science Building, No. 5 Yiheyuan Road, Beijing 100871, China
| | - Yi-Bing Liu
- Department of Radiology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China; Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, China
| | - Miao Zhang
- Department of Radiology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China; Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, China
| | - Qing-Feng Ma
- Department of Neurology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China
| | - Jia-Hong Gao
- Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics, Peking University, No. 5 Yiheyuan Road, Beijing 100871, China; Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, No. 5 Yiheyuan Road, Beijing 100871, China; McGovern Institute for Brain Research, Peking University, No. 5 Yiheyuan Road, Beijing 100871, China
| | - Jie Lu
- Department of Radiology, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China; Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, China; Department of Nuclear Medicine, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing 100053, China.
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