A note on confined diffusion

Bickel, Thomas

doi:10.1016/j.physa.2006.11.008

Cited by 81 publications

(89 citation statements)

References 24 publications

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“…BARD analysis will provide probabilistic rankings of these models, but these probabilities can strictly only be interpreted in the context of the other models considered, and do not represent an absolute probability [55][56][57].…”

Section: Discussionmentioning

confidence: 99%

Inferring diffusion in single live cells at the single-molecule level

Robson

Burrage

Leake

2013

Phil. Trans. R. Soc. B

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The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single-molecule and single-cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared with competing single-molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level owing to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles; however, this generally requires more data points than is typical for single FP tracks owing to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes to discriminate multiple complex modes probabilistically. It is a computational approach that biologists can use to understand single-molecule features in live cells.

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Section: Discussionmentioning

confidence: 99%

Inferring diffusion in single live cells at the single-molecule level

Robson

Burrage

Leake

2013

Phil. Trans. R. Soc. B

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“…If α < 2, the probability distribution possesses power-law tails providing enhanced probability density in the wings of the distribution. P (z, t | z 0 ) is obtained as a solution to the diffusion equation with reflective boundaries as [11] …”

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confidence: 99%

Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics

Faux

McDonald

2017

Phys. Rev. E

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A model linking the molecular-scale dynamics of fluids confined to nano-pores to nuclear magnetic resonance (NMR) relaxation rates is proposed. The model is fit to experimental NMR dispersions for water and oil in an oil shale assuming that each fluid is characterised by three time constants and Lévy statistics. Results yield meaningful and consistent intra-pore dynamical time constants, insight into diffusion mechanisms and pore morphology. The model is applicable to a wide range of porous systems and advances NMR dispersion as a powerful tool for measuring nano-porous fluid properties.Understanding molecular-scale fluid dynamics in micro-and meso-porous materials is central to understanding a wide range of industrially-important materials and processes: rocks for petroleum engineering; zeolites for catalysis; calcium-silicate-hydrates for concrete construction; bio-polymers for food production to name but a few. A molecular-scale model of fluid in a pore is depicted in Fig. 1. In this general picture, one considers fluid within the body of the pore and a surface layer of fluid at the pore wall. The pore body fluid behaves much as a bulk fluid, free to diffuse in three dimensions with motion characterised by a correlation time τ b . The surface layer diffuses in just two dimensions (2D) with motion characterised by a slower correlation time τ . Molecular exchange is envisaged between the surface layer and the bulk fluid characterised by a desorption time τ d and a corresponding adsorption time linked to τ d by the requirements of mass balance. This model therefore simplifies the complex intra-pore dynamics of real fluids to three characteristic time constants,τ b , τ and τ d . Aspects of this general model, henceforth referred to as the 3τ model, are widely used throughout literature [1][2][3][4][5][6][7][8].Nuclear magnetic resonance (NMR) relaxation analysis is a uniquely powerful tool to access molecular correlation times of fluids in porous media [1][2][3][4][5][6][7][8][9]. It is rivalled only by small-angle scattering techniques, especially with neutrons, but has the advantage of being widely available using laboratory-scale equipment. Two NMR relaxation methods are especially valuable. NMR relaxation dispersion (NMRD) measurement of the frequency dependence of the nuclear (usually 1 H) spin-lattice relaxation time (T 1 ) of fluid molecules in the low-frequency range (kHz to MHz) is sensitive to fluid correlation times. Second, the T 1 -T 2 correlation experiment measures the ratio of T 1 to the nuclear spin-spin relaxation time T 2 . This is especially sensitive to different relaxation mechanisms.However, for the NMR methods to be useful, a model is required to link fluid molecular dynamics in pores to NMR relaxation rates. Several models have been proposed (for example, [1,2,6,7,10]) but that which builds most successfully on the general dynamics of the model illustrated in Fig. 1 in terms of fitting experimental data is due to Korb and co-workers [3-6, 10]. Korb's model reproduces the fundamental form ...

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“…Unrestricted free diffusion is then indicated by the linearity of the plot of MSD. In confined environment (i.e., disk of radius ), it has been demonstrated that MSD will saturate [237]:…”

Section: Spatio-temporal Detectionmentioning

confidence: 99%

A Guided Tour of Selected Image Processing and Analysis Methods for Fluorescence and Electron Microscopy

Kervrann

Sorzano

Acton

et al. 2016

IEEE J. Sel. Top. Signal Process.

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Abstract-Microscopy imaging, including fluorescence microscopy and electron microscopy, has taken a prominent role in life science research and medicine due to its ability to investigate the 3D interior of live cells and organisms. A long-term research in bio-imaging at the sub-cellular and cellular scales consists then in inferring the relationships between the dynamics of macromolecules and their functions. In this area, image processing and analysis methods are now essential to understand the dynamic organization of groups of interacting molecules inside molecular machineries and to address issues in fundamental biology driven by advances in molecular biology, optics and technology. In this paper, we present recent advances in fluorescence and electron microscopy and we focus on dedicated image processing and analysis methods required to quantify phenotypes for a limited number but typical studies in cell imaging.

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A note on confined diffusion

Cited by 81 publications

References 24 publications

Inferring diffusion in single live cells at the single-molecule level

Inferring diffusion in single live cells at the single-molecule level

Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics

A Guided Tour of Selected Image Processing and Analysis Methods for Fluorescence and Electron Microscopy

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