Diffusing Diffusivity: Survival in a Crowded Rearranging and Bounded Domain

Jain, Rohit; Sebastian, K. L.

doi:10.1021/acs.jpcb.6b06094

Cited by 42 publications

(43 citation statements)

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“…However there are systems where although the diffusion is Fickian the distribution of displacement probability is non-Gaussian. This anomaly has been explained as an effect of different phenomena like weak ergodicity breaking 8 , decoupling of solutesolvent motion 2,3 and diffusing diffusivity 5,6 . In order to further understand this Fickian but non-Gaussian dynamics in this work we study a wide range of solutesolvent systems where the solute size is kept small so that it can explore the inter solvent cage and mimic the diffusion in a crowded environment.…”

Section: Discussionmentioning

confidence: 99%

“…Diffusion of smaller particles in a crowded medium is ubiquitous in nature and has huge industrial and academic relevance [1][2][3][4][5][6][7][8][9][10][11][12][13] . The diffusion of sodium chloride through granular soil bed is important in understanding the ground water contamination from solid waste landfills 14 .…”

Section: Introductionmentioning

confidence: 99%

“…It has been argued that this can lead to changing diffusivity of the solute as the solvent environment changes and has been termed as diffusing a) Electronic mail: mb.sarika@ncl.res.in diffusivity 5,6 . The diffusing diffusivity leads to Fickian but non Gaussian behaviour at short times, however the displacement distribution is shown to become Gaussian at longer times 2,3,5,6 . Note that in supercooled liquids, although there is no timescale difference between the solute and the solvent dynamics, a similar observation of Fickian but non-Gaussian distribution of displacement probability has also been observed.…”

Section: Introductionmentioning

confidence: 99%

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Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics

Acharya

Nandi

Bhattacharyya

2017

The Journal of Chemical Physics

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We present a study of the dynamics of small solute particles in a solvent medium where the solute is much smaller in size, mimicking the diffusion of small particles in crowded environment. The solute exhibits Fickian diffusion arising from non-Gaussian van Hove correlation function. Our study shows that there are at least two possible origins of this non-Gaussian behaviour. The decoupling of the solute-solvent dynamics and the intermittency in the solute motion, the latter playing a dominant role. In the former scenario when averaged over time long enough to explore different solvent environments the dynamics recovers the Gaussian nature. In case of intermittent dynamics the non-Gaussianity remains even after long averaging and the Gaussian behaviour is obtained at a much longer time. Our study further shows that only for intermediate attractive solute-solvent interaction the dynamics of the solute is intermittent. The intermittency disappears for weaker or stronger attractions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics

Acharya

Nandi

Bhattacharyya

2017

The Journal of Chemical Physics

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“…On the other hand, homogenization techniques were used to substitute piecewise constant reactivity κ(s) by an effective homogeneous reactivity [31][32][33][51][52][53][54][55][56][57][58]. More recent works investigated how the mean reaction time is affected by a finite lifetime of diffusing particles [59][60][61], by partial reactivity and interactions [63,64], by target aspect ratio [65], by reversible target-binding kinetics [66,67] and surface-mediated diffusion [68][69][70][71], by heterogeneous diffusivity [72], and by rapid re-arrangments of the medium [73][74][75]. Some of the related effects onto the whole distribution of reaction times were analyzed [76][77][78][79][80].…”

Section: Introductionmentioning

confidence: 99%

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

Grebenkov

2019

The Journal of Chemical Physics

108

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We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially reactive surface is expressed in terms of a much simpler propagator toward a homogeneous perfectly reactive surface. In other words, the original problem with general Robin boundary condition that includes in particular mixed Robin-Neumann condition, is reduced to that with Dirichlet boundary condition. Chemical kinetics on the surface is incorporated as a matrix representation of the surface reactivity in the eigenbasis of the Dirichlet-to-Neumann operator. New spectral representations of important characteristics of diffusion-controlled reactions, such as the survival probability, the distribution of reaction times, and the reaction rate, are deduced. Theoretical and numerical advantages of this spectral approach are illustrated by solving interior and exterior problems for a spherical surface that may describe either an escape from a ball or hitting its surface from outside. The effect of continuously varying or piecewise constant surface reactivity (describing, e.g., many reactive patches) is analyzed.

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“…Although a term of position-dependent diffusion coefficient appears in the FJ equation, it is used to describe the entropic effects of the boundary and does not focus on the intrinsic position-dependence of diffusion coefficients in a practical environment [30].Consider, for instance, a protein in a biological cell with a fixed geometrical shape and varied thickness as well as local porosity and crowding, its diffusivity is not spatially invariant, but depends on the position [11,31,32]. Additionally, some related experiments reveal that the diffusion coefficient may also depend on time [32][33][34][35]. Inter alia, many other systems, including the heterogeneity induced by macromolecular crowding in the cytoplasm and nucleoplasm or the accumulation of large cellular organelles in a perinuclear region [36], the intermittent motion of lipids in a protein-crowded membrane [37,38], and the scaling exponent of a virtual movement [39] also lead to similar effects.…”

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confidence: 99%

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Mei

et al. 2020

New J. Phys.

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This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D 0 ), as well as a low (D m ) and a high (D d ) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d , a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D m , a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two-or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.New J. Phys. 22 (2020) 053016 Y Li et al confined spaces, transport of particles in nanopores, zeolites and gel networks [8-10], or protein diffusion in the mammalian cell cytoplasm [11]. In many cases, such structured environments can be viewed as confined channels with different boundaries and properties [12][13][14]. The behaviours of systems in these confined channels have been studied by virtue of the analytical Fick-Jacobs (FJ) equation and numerical simulations of the dynamic equations [15][16][17][18][19][20]. Results for symmetric periodic channels indicate that the mean transport velocity may be proportional to large external forces in the confined environment [19][20][21][22]. For asymmetric channels, it was found that the shape of the confinement contributes to the moving direction and mean displacement [20,23], which can be applied to fine separation of mixtures and also the design of many devices [24,25]. Time-dependent and deformable boundaries were discussed to explore the activity in living cells [26,27]. In addition, the interaction...

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Diffusing Diffusivity: Survival in a Crowded Rearranging and Bounded Domain

Cited by 42 publications

References 28 publications

Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics

Fickian yet non-Gaussian behaviour: A dominant role of the intermittent dynamics

Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

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