1
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Zhao XB, Zhang X, Guo W. Diffusion of active Brownian particles under quenched disorder. PLoS One 2024; 19:e0298466. [PMID: 38437208 PMCID: PMC10911629 DOI: 10.1371/journal.pone.0298466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 01/24/2024] [Indexed: 03/06/2024] Open
Abstract
The motion of a single active particle in one dimension with quenched disorder under the external force is investigated. Within the tailored parameter range, anomalous diffusion that displays weak ergodicity breaking is observed, i.e., non-ergodic subdiffusion and non-ergodic superdiffusion. This non-ergodic anomalous diffusion is analyzed through the time-dependent probability distributions of the particle's velocities and positions. Its origin is attributed to the relative weights of the locked state (predominant in the subdiffusion state) and running state (predominant in the superdiffusion state). These results may contribute to understanding the dynamical behavior of self-propelled particles in nature and the extraordinary response of nonlinear dynamics to the externally biased force.
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Affiliation(s)
- Xiong-Biao Zhao
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming, China
| | - Xiao Zhang
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming, China
| | - Wei Guo
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming, China
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2
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Yu S, Chu R, Wu G, Meng X. A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution. Polymers (Basel) 2024; 16:524. [PMID: 38399901 PMCID: PMC10891538 DOI: 10.3390/polym16040524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Revised: 02/11/2024] [Accepted: 02/13/2024] [Indexed: 02/25/2024] Open
Abstract
In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.
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Affiliation(s)
- Shi Yu
- Department of Chemical Engineering, China University of Mining & Technology, Xuzhou 221116, China; (R.C.); (G.W.); (X.M.)
| | - Ruizhi Chu
- Department of Chemical Engineering, China University of Mining & Technology, Xuzhou 221116, China; (R.C.); (G.W.); (X.M.)
- Key Laboratory of Coal-Based CO2 Capture and Geological Storage, China University of Mining & Technology, Xuzhou 221116, China
| | - Guoguang Wu
- Department of Chemical Engineering, China University of Mining & Technology, Xuzhou 221116, China; (R.C.); (G.W.); (X.M.)
- Key Laboratory of Coal-Based CO2 Capture and Geological Storage, China University of Mining & Technology, Xuzhou 221116, China
| | - Xianliang Meng
- Department of Chemical Engineering, China University of Mining & Technology, Xuzhou 221116, China; (R.C.); (G.W.); (X.M.)
- Key Laboratory of Coal-Based CO2 Capture and Geological Storage, China University of Mining & Technology, Xuzhou 221116, China
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3
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Tang Y, Gharari F, Arias-Calluari K, Alonso-Marroquin F, Najafi MN. Variable-order porous media equations: Application on modeling the S&P500 and Bitcoin price return. Phys Rev E 2024; 109:024310. [PMID: 38491659 DOI: 10.1103/physreve.109.024310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 01/09/2024] [Indexed: 03/18/2024]
Abstract
This article reveals a specific category of solutions for the 1+1 variable order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO q-Gaussian functions, granting them significant versatility in their application to various real-world systems, such as financial economy areas spanning from conventional stock markets to cryptocurrencies. The VO q-Gaussian functions provide a more robust expression for the distribution function of price returns in real-world systems. Additionally, we analyzed the temporal evolution of the anomalous characteristic exponents derived from our study, which are associated with the long-term (power-law) memory in time series data and autocorrelation patterns.
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Affiliation(s)
- Yaoyue Tang
- Modelling and Simulation Research Group, The University of Sydney, Sydney NSW 2006, Australia
| | - Fatemeh Gharari
- Department of Statistics and Computer Science, University of Mohaghegh Ardabili, Ardabil 56199, Iran
| | - Karina Arias-Calluari
- School of Mathematics and Statistics, The University of Sydney, Sydney NSW 2006, Australia
| | | | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 11367, Iran
- Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA
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4
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Li J. Role of ergodicity, aging, and Gaussianity in resolving the origins of biomolecule subdiffusion. Phys Chem Chem Phys 2022; 24:16050-16057. [PMID: 35731614 DOI: 10.1039/d2cp01161a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The internal motions of biomolecules are essential to their function. Although biological macromolecules conventionally show subdiffusive dynamics, only recently has subdiffusion been associated with non-ergodicity. These findings have stimulated new questions in biophysics and statistical mechanics. Is non-ergodic subdiffusion a general strategy shared by biomolecules? What underlying mechanisms are responsible for it? Here, we performed extensive molecular dynamics (MD) simulations to characterize the internal dynamics of six different biomolecules, ranging from single or double-stranded DNA, a single domain protein (KRAS), two globular proteins (PGK and SHP2), to an intrinsically disordered protein (SNAP-25). We found that the subdiffusive behavior of these biomolecules falls into two classes. The internal motion of the first three cases is ergodic subdiffusion and can be interpreted by fractional Brownian motion (FBM), while the latter three cases involve non-ergodic subdiffusion and can be modeled by mixed origins of continuous-time random walk (CTRW) and FBM.
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Affiliation(s)
- Jun Li
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
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5
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Alcázar-Cano N, Delgado-Buscalioni R. Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels. SOFT MATTER 2022; 18:1941-1954. [PMID: 35191454 DOI: 10.1039/d1sm01713f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.
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Affiliation(s)
- Nerea Alcázar-Cano
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid and Condensed Matter Physics Center (IFIMAC), Madrid, Spain.
| | - Rafael Delgado-Buscalioni
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid and Condensed Matter Physics Center (IFIMAC), Madrid, Spain.
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6
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Zhao Y, Lu Y, Wang D. Tracking of Nanoparticle Diffusion at a Liquid-Liquid Interface Adsorbed by Nonionic Surfactants. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:12118-12127. [PMID: 34610245 DOI: 10.1021/acs.langmuir.1c01978] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Emulsions stabilized by both nanoparticles and surfactants often display longer shelf life than those stabilized by nanoparticles or surfactants alone. Although numerous works have been conducted to understand the effect of nanoparticles and surfactants on the variation of interfacial tension, little is known about interfacial diffusion when both nanoparticles and surfactants are present at interfaces. In this work, we used single-particle fluorescence tracking to study the lateral diffusion of individual hydrophobic nanoparticles at hexane-glycerol interfaces adsorbed by different amounts of nonionic surfactants. When the surfactant concentration is over a threshold, we found that the nanoparticle diffusion exhibits a two-regime behavior involving short-time Brownian and the emergence of subdiffusive, non-Gaussian, and dynamically anticorrelated diffusion in the long lag time regime. A stepwise analysis rationalized diffusion in different lag time regimes, leading to a mechanistic interpretation regarding the two-regime behavior. These results could provide insight into the understanding of the synergistic effect for the surfactant-assistant Pickering emulsion.
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Affiliation(s)
- Yuehua Zhao
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
- University of Science and Technology of China, Hefei 230026, P. R. China
| | - Yuyuan Lu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Dapeng Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
- University of Science and Technology of China, Hefei 230026, P. R. China
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7
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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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8
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Thermodynamic and Transport Properties of Tetrabutylphosphonium Hydroxide and Tetrabutylphosphonium Chloride-Water Mixtures via Molecular Dynamics Simulation. Polymers (Basel) 2020; 12:polym12010249. [PMID: 31968689 PMCID: PMC7023592 DOI: 10.3390/polym12010249] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Revised: 01/04/2020] [Accepted: 01/16/2020] [Indexed: 11/30/2022] Open
Abstract
Thermodynamic, structural, and transport properties of tetrabutylphosphonium hydroxide (TBPH) and tetrabutylphosphonium chloride (TBPCl)–water mixtures have been investigated using all-atom molecular dynamics simulations in response to recent experimental work showing the TBPH–water mixtures capability as a cellulose solvent. Multiple transitional states exist for the water—ionic liquid (IL) mixture between 70 and 100 mol% water, which corresponds to a significant increase in water hydrogen bonds. The key transitional region, from 85 to 92.5 mol% water, which coincides with the mixture’s maximum cellulose solubility, reveals small and distinct water veins with cage structures formed by the TBP+ ions, while the hydroxide and chloride ions have moved away from the P atom of TBP+ and are strongly hydrogen bonded to the water. The maximum cellulose solubility of the TBPH–water solution at approximately 91.1 mol% water, appears correlated with the destruction of the TBP’s interlocking structure in the simulations, allowing the formation of water veins and channeling structures throughout the system, as well as changing from a subdiffusive to a near-normal diffusive regime, increasing the probability of the IL’s interaction with the cellulose polymer. A comparison is made between the solution properties of TBPH and TBPCl with those of alkylimidazolium-based ILs, for which water appears to act as anti-solvent rather than a co-solvent.
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9
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Ubiquity of anomalous transport in porous media: Numerical evidence, continuous time random walk modelling, and hydrodynamic interpretation. Sci Rep 2019; 9:4601. [PMID: 30872610 PMCID: PMC6418150 DOI: 10.1038/s41598-019-39363-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Accepted: 01/23/2019] [Indexed: 11/08/2022] Open
Abstract
Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.
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10
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Coker HLE, Cheetham MR, Kattnig DR, Wang YJ, Garcia-Manyes S, Wallace MI. Controlling Anomalous Diffusion in Lipid Membranes. Biophys J 2019; 116:1085-1094. [PMID: 30846364 DOI: 10.1016/j.bpj.2018.12.024] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Revised: 11/21/2018] [Accepted: 12/14/2018] [Indexed: 12/24/2022] Open
Abstract
Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.
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Affiliation(s)
- Helena L E Coker
- Department of Chemistry, King's College London, London, United Kingdom; Chemistry Research Laboratory, University of Oxford, Oxford, United Kingdom
| | - Matthew R Cheetham
- Department of Chemistry, King's College London, London, United Kingdom; Chemistry Research Laboratory, University of Oxford, Oxford, United Kingdom
| | - Daniel R Kattnig
- Living Systems Institute & Department of Physics, University of Exeter, Exeter, United Kingdom
| | - Yong J Wang
- Department of Physics, King's College London, London, United Kingdom
| | | | - Mark I Wallace
- Department of Chemistry, King's College London, London, United Kingdom.
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11
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Alcázar-Cano N, Delgado-Buscalioni R. A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media. SOFT MATTER 2018; 14:9937-9949. [PMID: 30488923 DOI: 10.1039/c8sm01961d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This work numerically investigates the diffusion of finite inert tracer particles in different types of fixed gels. The mean square displacement (MSD) of the tracers reveals a transition to subdiffusive motion MSD ∼ tα as soon as the accessible volume fraction p in the gel decreases from unity. Individual tracer dynamics reveals two types of particles in the gels: mobile tracers cross the system through percolating pores following subdiffusive dynamics MSDmob ∼ tαmob, while a fraction ptrap(p) of the particles remain trapped in finite pores. Below the void percolation threshold p < pc all the particles get trapped and α → 0. By separately studying both populations we find a simple phenomenological law for the mobile tracers αmob(p) ≈ a ln p + c where c ≈ 1 and a ∼ 0.2 depends on the gel type. On the other hand, a cluster-analysis of the gel accessible volume reveals a power law for the trapping probability ptrap ∼ (p/pc)-γ, with γ ≃ 2.9. This yields a prediction for the ensemble averaged subdiffusion exponent α = αmob(1 - ptrap). Our predictions are successfully validated against the different gels studied here and against numerical and experimental results in the literature (silica gels, polyacrylamide gels, flexible F-actin networks and in different random obstacles). Notably, the parameter a ∼ 0.2 presents small differences amongst all these cases, indicating the robustness of the proposed relation.
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Affiliation(s)
- Nerea Alcázar-Cano
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Campus de Cantoblanco, and Condensed Matter Physics Center (IFIMAC), E-28049, Madrid, Spain.
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12
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Weatherill EE, Coker HLE, Cheetham MR, Wallace MI. Urea-mediated anomalous diffusion in supported lipid bilayers. Interface Focus 2018; 8:20180028. [PMID: 30443327 PMCID: PMC6227775 DOI: 10.1098/rsfs.2018.0028] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/08/2018] [Indexed: 12/16/2022] Open
Abstract
Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the time scale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous diffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatized with polyethylene glycol. Here, we extend this work, using urea to induce anomalous diffusion in SLBs. By tuning incubation time and urea concentration, we produce bilayers that exhibit anomalous behaviour on the same scale as that observed in biological membranes.
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Affiliation(s)
- E. E. Weatherill
- Department of Chemistry, Britannia House, King's College London, 7 Trinity Street, London SE1 1DB, UK
| | - H. L. E. Coker
- Department of Chemistry, Britannia House, King's College London, 7 Trinity Street, London SE1 1DB, UK
- Chemistry Research Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK
| | - M. R. Cheetham
- Department of Chemistry, Britannia House, King's College London, 7 Trinity Street, London SE1 1DB, UK
- Cavendish Laboratory, Department of Physics, NanoPhotonics Centre, University of Cambridge, Cambridge CB3 0HE, UK
| | - M. I. Wallace
- Department of Chemistry, Britannia House, King's College London, 7 Trinity Street, London SE1 1DB, UK
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13
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Cholesterol modulates acetylcholine receptor diffusion by tuning confinement sojourns and nanocluster stability. Sci Rep 2018; 8:11974. [PMID: 30097590 PMCID: PMC6086833 DOI: 10.1038/s41598-018-30384-y] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Accepted: 07/20/2018] [Indexed: 11/08/2022] Open
Abstract
Translational motion of neurotransmitter receptors is key for determining receptor number at the synapse and hence, synaptic efficacy. We combine live-cell STORM superresolution microscopy of nicotinic acetylcholine receptor (nAChR) with single-particle tracking, mean-squared displacement (MSD), turning angle, ergodicity, and clustering analyses to characterize the lateral motion of individual molecules and their collective behaviour. nAChR diffusion is highly heterogeneous: subdiffusive, Brownian and, less frequently, superdiffusive. At the single-track level, free walks are transiently interrupted by ms-long confinement sojourns occurring in nanodomains of ~36 nm radius. Cholesterol modulates the time and the area spent in confinement. Turning angle analysis reveals anticorrelated steps with time-lag dependence, in good agreement with the permeable fence model. At the ensemble level, nanocluster assembly occurs in second-long bursts separated by periods of cluster disassembly. Thus, millisecond-long confinement sojourns and second-long reversible nanoclustering with similar cholesterol sensitivities affect all trajectories; the proportion of the two regimes determines the resulting macroscopic motional mode and breadth of heterogeneity in the ensemble population.
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14
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Mardoukhi Y, Jeon JH, Chechkin AV, Metzler R. Fluctuations of random walks in critical random environments. Phys Chem Chem Phys 2018; 20:20427-20438. [PMID: 30043029 DOI: 10.1039/c8cp03212b] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.
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Affiliation(s)
- Yousof Mardoukhi
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
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15
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Zhokh A, Trypolskyi A, Strizhak P. Relationship between the anomalous diffusion and the fractal dimension of the environment. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.02.015] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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16
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Tuladhar R, Bologna M, Grigolini P. Non-Poisson renewal events and memory. Phys Rev E 2017; 96:042112. [PMID: 29347624 DOI: 10.1103/physreve.96.042112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Indexed: 06/07/2023]
Abstract
We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out-of-equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same nonexponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin recrossings and establishing the corresponding waiting time probability density function (PDF), ψ(t). In the former case, with no crucial events, ψ(t) is an exponential, and in the latter case, with crucial events, ψ(t) is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes.
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Affiliation(s)
- Rohisha Tuladhar
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
| | - Mauro Bologna
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 6-D, Arica, Chile
| | - Paolo Grigolini
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
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17
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Taheriyoun AR, Moghimbeygi M. Visual information and expert's idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation. Sci Rep 2017; 7:42482. [PMID: 28195153 PMCID: PMC5307349 DOI: 10.1038/srep42482] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 01/11/2017] [Indexed: 12/02/2022] Open
Abstract
An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.
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Affiliation(s)
- Ali R Taheriyoun
- Shahid Beheshti University, G.C., Department of Statistics, Tehran, 1983969411, Iran
| | - Meisam Moghimbeygi
- Shahid Beheshti University, G.C., Department of Statistics, Tehran, 1983969411, Iran
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18
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Stiehl O, Weiss M. Heterogeneity of crowded cellular fluids on the meso- and nanoscale. SOFT MATTER 2016; 12:9413-9416. [PMID: 27847940 DOI: 10.1039/c6sm01436d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Cellular fluids are complex media that are crowded with macromolecules and membrane-enclosed organelles on several length scales. Many studies have shown that crowding can significantly alter transport and reaction kinetics in biological but also in bio-mimetic fluids. Yet, experimental insights on how well bio-mimetic fluids can capture the complexity of cellular fluids are virtually missing. Therefore, we have combined fluorescence correlation spectroscopy (FCS) and fluorescence lifetime imaging microscopy (FLIM) to compare the spatial heterogeneities of biological and simple bio-mimetic crowded fluids. As a result, we find that these artificial fluids are capable of mimicking the average diffusion behavior but not the considerable heterogeneity of cellular fluids on the mesoscale (∼100 nm). On the nanoscale, not even the average properties are captured. Thus, cellular fluids feature a distinct, heterogeneous crowding state that differs from simple bio-mimetic fluids.
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Affiliation(s)
- Olivia Stiehl
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95440 Bayreuth, Germany.
| | - Matthias Weiss
- Experimental Physics I, University of Bayreuth, Universitätsstr. 30, D-95440 Bayreuth, Germany.
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Cherstvy AG, Metzler R. Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes. Phys Chem Chem Phys 2016; 18:23840-52. [DOI: 10.1039/c6cp03101c] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
We investigate the diffusive and ergodic properties of massive and confined particles in a model disordered medium, in which the local diffusivity fluctuates in time while its mean has a power law dependence on the diffusion time.
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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