Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

Stauffer, Dietrich; Schulze, Christian; Heermann, Dieter W.

doi:10.1007/s10867-008-9075-2

Cited by 23 publications

(20 citation statements)

References 17 publications

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“…They observed Lévy flight like motion of the tracer. Superdiffusive motion was further seen in the simulations of a tracer particle diffusing in crowded environment of randomly moving barriers, 9 for diffusion in a 2D complex plasma 10 and for activated motion in live cells. 11 Recently, we 12 gave a model of "diffusing diffusivity" where diffusion coefficient is modeled as a Lévy flight process which eventually leads to superdiffusion for the particle's position.…”

Section: Introductionmentioning

confidence: 83%

Diffusing diffusivity: a new derivation and comparison with simulations

Jain

Sebastian

2017

J Chem Sci

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Many experiments are now available where it has been shown that the probability distribution function (pdf) for the position of a Brownian particle diffusing in a heterogeneous medium is not Gaussian. However, in spite of this non-Gaussianity, the mean square displacement (MSD) still remains Fickian, i.e., x 2 ∝ T. One possible explanation of this non-Gaussian yet Brownian behavior is that the diffusivity of the particle itself is "diffusing". Chubynsky and Slater (Phys. Rev. Lett. 113 098302 2014) proposed a model of "diffusing diffusivity" which they were able to solve analytically at small time scales, but simulations were performed for intermediate to large time scales. We present here a class of diffusing diffusivity models and show that the problem of calculating pdf for the position of diffusing particle is equivalent to calculating the survival probability of a particle undergoing Brownian motion in the presence of a sink. We give exact analytical results for all time scales and show that the pdf is non-Gaussian at short times which crosses over to a Gaussian at long times. The MSD is also shown to vary linearly with time at all times. We find that our results reproduce the numerical results of Chubynsky and Slater quite well.

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Section: Introductionmentioning

confidence: 83%

Diffusing diffusivity: a new derivation and comparison with simulations

Jain

Sebastian

2017

J Chem Sci

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“…Super-diffusion is faster than normal diffusion. As analyzed by Stauffer et al ( 2007 ), super-diffusion is theoretically possible in molecularly crowded environments. In biological systems, it can be the result of cellular transport processes and is observed if the diffusion is directed by a motor protein (Goychuk et al 2014 ).…”

Section: Introductionmentioning

confidence: 96%

Fractal model of anomalous diffusion

Gmachowski

2015

Eur Biophys J

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An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.

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“…It is worthwhile to underline that reports of anomalous transport connected to crowding are not limited to sub-diffusion. For example, Upadhaya and collaborators [28] have recorded superdiffusive behaviour in the motion of endodermal Hydra cells, which they traced back to long-range correlations within the scrutinized sample, while Stauffer and collaborators [29] proposed a minimalistic model of random barriers in a percolation network as a tool to mimic diffusion in a crowded environment.…”

Section: Introductionmentioning

confidence: 99%

Diffusion of tagged particles in a crowded medium

Galanti¹,

Fanelli²,

Maritan³

et al. 2014

EPL

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The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability distribution function of the tagged particles obeys to a nonlinear Fokker-Planck equation, where the drift and diffusion terms are determined self-consistently by the concentration of crowders in the medium. Transient sub-diffusive or super-diffusive behaviours are observed, depending on the selected initial conditions, that bridge normal diffusion regimes characterized by different diffusion coefficients. These anomalous crossovers originate from the microscopic competition for space and reflect the peculiar form of the non-homogeneous advection term in the governing Fokker-Planck equation. Our results strongly warn against the overly simplistic identification of crowding with anomalous transport tout court.

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Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

Cited by 23 publications

References 17 publications

Diffusing diffusivity: a new derivation and comparison with simulations

Diffusing diffusivity: a new derivation and comparison with simulations

Fractal model of anomalous diffusion

Diffusion of tagged particles in a crowded medium

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