Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Santos, Maike A. F. dos; Menon, L.

doi:10.3390/physics2040032

Cited by 13 publications

(8 citation statements)

References 81 publications

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“…(a-h) Dataset is identical to that shown in Fig. 1 c-f follows a long-tailed, log-scale distribution, consistent with Brownian motion in a heterogeneous environment (56,57). The distribution of apparent diffusivities exhibited a single peak (Fig.…”

Section: Cytoplasmic Diffusivity Spans Orders Of Magnitudesupporting

confidence: 71%

“…These data showed that variability in particle motion ranged over orders of magnitude; fits of particle and cell MSDs (Fig. 2c-d) showed that diffusivity follows a long-tailed, log-scale distribution, consistent with Brownian motion in a heterogeneous environment (Santos et al, 2020; Ślęzak and Burov, 2021). The distribution of apparent diffusivities exhibited a single peak (Fig.…”

Section: Resultsmentioning

confidence: 72%

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Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

Garner

Molines

Theriot

et al. 2022

Preprint

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The cytoplasm is a complex, crowded, actively-driven environment whose biophysical characteristics modulate critical cellular processes such as cytoskeletal dynamics, phase separation, and stem-cell fate. Little is known about the variance in these cytoplasmic properties. Here, we employed particle-tracking nano-rheology on genetically encoded multimeric 40-nm nanoparticles (GEMs) to measure diffusion within the cytoplasm of the fission yeast Schizosaccharomyces pombe. We found that the apparent diffusion coefficients of individual GEM particles varied over a 400-fold range, while the average particle diffusivity for each individual cell spanned a 10-fold range. To determine the origin of this heterogeneity, we developed a Doppelgänger Simulation approach that uses stochastic simulations of GEM diffusion that replicate the experimental statistics on a particle-by-particle basis, such that each experimental track and cell had a one-to-one correspondence with their simulated counterpart. These simulations showed that the large intra- and inter-cellular variations in diffusivity could not be explained by experimental variability but could only be reproduced with stochastic models that assume an equally wide intra- and inter-cellular variation in cytoplasmic viscosity. To probe the origin of this variation, we found that the variance in GEM diffusivity was largely independent of factors such as temperature, cytoskeletal effects, cell cycle stage and spatial locations, but was magnified by hyperosmotic shocks. Taken together, our results provide a striking demonstration that the cytoplasm is not “well-mixed” but represents a highly heterogeneous environment in which subcellular components at the 40-nm size-scale experience dramatically different effective viscosities within an individual cell, as well as in different cells in the population. These findings carry significant implications for the origins and regulation of biological noise at cellular and subcellular levels.Graphical abstract

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Section: Cytoplasmic Diffusivity Spans Orders Of Magnitudesupporting

confidence: 71%

Section: Resultsmentioning

confidence: 72%

Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

Garner

Molines

Theriot

et al. 2022

Preprint

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“…Based on the mathematical calculation (dos Santos & Menon Junior, 2020; Kim et al., 2017), the relative errors of porosity and effective diffusivity can be correlated through

n

(see Text S2 in Supporting Information S1 for a detailed derivation):

n\times {\varepsilon }_{V}=n\times {\varepsilon }_{\phi }={\varepsilon }_{{D}_{e}/{D}_{0}}.

…”

Section: Methodsmentioning

confidence: 99%

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

et al. 2022

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Clay rocks such as the Opalinus Clay (OPA) in Switzerland are considered as potential host rocks for deep geological disposal of nuclear wastes. Radionuclide migration in clay rocks is dominated by molecular diffusion highly dependent on the pore network geometries. In the sandy facies of OPA (SF-OPA), this pore network is critically modified due to compositional variability and owing to diagenetic reaction products, for example, carbonate and sulfide minerals (Philipp et al., 2017). Such spatial variability is responsible for heterogeneous diffusion patterns (Kulenkampff et al., 2015). At the continuum scale, the representative elementary volume (REV) is an important parameter for understanding and modeling the reactive transport (RT) of contaminants and radionuclides. An accurate estimation of the REV for diffusion is decisive for a meaningful continuum-scale simulation of radionuclide migration in heterogeneous clay rocks like SF-OPA, thus playing an important role in the safety analysis of deep geological repositories for nuclear waste.In continuum mechanics for a heterogeneous material, the REV is the smallest volume over which a measurement can be made to produce a representative value of the macroscopic property in three-dimensional space (3D) (Bear Abstract Accurate modeling and simulation of radionuclide migration in clay rocks such as the Opalinus Clay (OPA) play a key role in the safety assessment of deep geological repositories for nuclear wastes. At the continuum scale, the representative elementary volume (REV) is a fundamental constraint to quantify the effective diffusivity, which is a key parameter in reactive transport (RT) models. Therefore, an accurate estimation of the REV is essential for a meaningful continuum-scale RT simulation in heterogeneous clay rocks. This study presents a comprehensive analysis of the heterogeneities of porosity and effective diffusivity in clay rocks by using the classical sampling theory and pore-scale simulations. First, in this study, the two-dimensional representative elementary area is correlated with the REV for porosity via a characteristic length. Next, it is shown that the REV for diffusivity is larger than the REV for porosity. Moreover, these two REVs can be correlated using Archie's law. In such a way, the REV for diffusivity can be determined by the developed correlations through analyzing two-dimensional microstructures, thus significantly reducing the computational cost. Finally, the applicability of our approach for clay rocks is validated by experimental data on the diffusion of tritiated water in the heterogeneous sandy facies of OPA. From both the experimental data and the modeling prediction, the REV for diffusivity in the sandy facies of OPA is in the order of cubic centimeters. This study provides critical insights into the diffusion in heterogeneous clay rocks toward an enhanced predictability of radionuclide migration.Plain Language Summary Contaminant migration in clay rocks is dominated by molecular diffusion due to their low permeability....

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“…In fact, the derived equation (4.5) pushes the research not only towards the mathematical analysis of a novel family of equations as well as towards the development of solid and reliable numerical schemes for studying more realistic systems in multi-dimensional domains with real geometries and general initial and boundary condition but also towards the development of statistical methods and tools for properly taking into account a distribution of diffusion coefficients that can lead to different modelling approaches as those based on an heterogeneous ensemble of particles, e.g. the over-and under-damped ggBm [10,28,29,[35][36][37]48,71], or those based on diffusion in inhomogeneous random environments, e.g. the diffusing diffusivity approach [48,[72][73][74][75].…”

Section: Conclusion and Future Perspectivesmentioning

confidence: 99%

The Fokker–Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm

2022

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By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules’ displacement and we derive the corresponding Fokker–Planck equation. Molecules’ distribution emerges to be related to the Krätzel function and its Fokker–Planck equation to be a fractional diffusion equation in the Erdélyi–Kober sense. The irreducibility of the derived Fokker–Planck equation to those of other literature models is also discussed.

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Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Cited by 13 publications

References 81 publications

Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

The Fokker–Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm

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