When Brownian diffusion is not Gaussian

Wang, Bo; Kuo, J.B.; Bae, Sung Chul; Granick, Steve

doi:10.1038/nmat3308

Cited by 513 publications

(678 citation statements)

References 59 publications

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“…4B), indicating that the MSD is also linear. The fact that mildly entangled fluids can give rise to "anomalous, yet Brownian" diffusion, with a non-Gaussian propagator and yet a linear MSD, ties in with recent observations that this type of behaviour is frequent in biological systems 83,84 . It remains nevertheless a surprising observation, because a linear MSD is often considered to be associated with a Gaussian propagator, and because most classical anomalous diffusion models predict an MSD deviating from linearity.…”

Section: The Anomalous Yet Brownian Motion Of Proteins In Crowded Dementioning

confidence: 80%

“…We also note that whether diffusion in complex media is characterized by Gaussian propagators is a current topic of interest [80][81][82] . However most of the data available so far has been obtained from single-particle experiments, and therefore is restricted to slow diffusion processes [83][84][85] .…”

Section: On the Importance Of Characterizing Complex Diffusion Procesmentioning

confidence: 99%

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Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

et al. 2016

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The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared displacement of the particles scales as r 2 ∝ t α with α < 1. Unfortunately, methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) probe diffusion only over a narrow range of lengthscales and cannot directly test the dependence of the mean-squared displacement (MSD) on time. Here we show that variable-lengthscale FCS (VLS-FCS), where the volume of observation is varied over several orders of magnitude, combined with a numerical inversion procedure of the correlation data, allows retrieving the MSD for up to five decades in time, bridging the gap between diffusion experiments performed at different lengthscales. In addition, we show that VLS-FCS provides a way to assess whether the propagator associated with the diffusion is Gaussian or non-Gaussian. We used VLS-FCS to investigate two systems where anomalous diffusion had been previously reported. In the case of dense cross-linked agarose gels, the measured MSD confirmed that the diffusion of small beads was anomalous at short lengthscales, with a cross-over to simple diffusion around ≈ 1 µm, consistent with a caged diffusion process. On the other hand, for solutions crowded with marginally entangled dextran molecules, we uncovered an apparent discrepancy between the MSD, found to be linear, and the propagators at short lengthscales, found to be non-Gaussian. These contradicting features call to mind the "anomalous, yet Brownian" diffusion observed in several biological systems, and the recently proposed "diffusing diffusivity" model.

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Section: The Anomalous Yet Brownian Motion Of Proteins In Crowded Dementioning

confidence: 80%

Section: On the Importance Of Characterizing Complex Diffusion Procesmentioning

confidence: 99%

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

et al. 2016

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“…The analysis of multi-probe spatial positions tracked over time provides important statistical information used in rendering super resolution microscopy images [1], investigating cellular transport mechanisms in biological systems [2,3], characterizing local rheological properties of heterogeneous fluids, soft matter or cross-linked polymer gels [4][5][6], and measuring the particle size distribution (PSD) of nanoparticles in suspension [7,8]. Empirical single particle tracking (SPT) trajectories are necessarily a superposition of thermal Brownian motion and particle localization errors.…”

Section: Introductionmentioning

confidence: 99%

Decorrelation correction for nanoparticle tracking analysis of dilute polydisperse suspensions in bulk flow

Hartman

Kirby

2017

Phys. Rev. E

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Nanoparticle tracking analysis, a multi-probe single particle tracking technique, is a widely used method to quickly determine the concentration and size distribution of colloidal particle suspensions. Many popular tools remove non-Brownian components of particle motion by subtracting the ensemble-averaged displacement at each time step, which is termed 'de-drifting'. Though critical for accurate size measurements, de-drifting is shown here to introduce significant biasing error and can fundamentally limit the dynamic range of particle size that can be measured for dilute, heterogeneous suspensions, such as biological extracellular vesicles. We report a more accurate estimate of particle mean-squared displacement, which we call Decorrelation Analysis, that accounts for correlations between individual and ensemble particle motion, which are spuriously introduced by de-drifting. Particle tracking simulation and experimental results show that this approach more accurately determines particle diameters for low concentration, polydisperse suspensions when compared with standard de-drifting techniques.

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“…Diffusion of colloidal beads along linear phospholipid bilayer tubes and in biofilament network [6], enhanced tracer diffusion in suspensions of microorganisms [7], liposomes in nematic solutions of aligned Factin filaments [8], nanoparticles in hard-sphere colloidal suspensions [9], colloidal hard discs in solid and hexatic phases [10] are examples showing such property. In some of these situations the deviation from Gaussian form is significant only at short times, while at longer times the PDF tends to the Gaussian form typical for the normal diffusion.…”

Section: Introductionmentioning

confidence: 99%

Nonscaling displacement distributions as may be seen in fluorescence correlation spectroscopy

Khadem¹,

Sokolov²

2017

Phys. Rev. E

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A continuous time random walk (CTRW) model with waiting times following the Lévy-stable distribution with exponential cut-off in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian diffusion. The distribution of the particle's displacements is explicitly time-dependent and does not scale. Since fluorescent correlation spectroscopy (FCS) is often used to investigate diffusion processes, we discuss the influence of this lack of scaling on the possible outcome of the FCS measurements and calculate the FCS autocorrelation curves for such equilibrated CTRWs. The results show that although the deviations from Gaussian behavior may be detected when analyzing the short-and long-time asymptotic behavior of the corresponding curves, their bodies are still perfectly fitted by the fit forms used for normal diffusion. The diffusion coefficients obtained from the fits may however differ considerably from the true tracer diffusion coefficients as describing the time dependence of the mean squared displacement.

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When Brownian diffusion is not Gaussian

Cited by 513 publications

References 59 publications

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

Decorrelation correction for nanoparticle tracking analysis of dilute polydisperse suspensions in bulk flow

Nonscaling displacement distributions as may be seen in fluorescence correlation spectroscopy

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