Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes

Cherstvy, Andrey G.; Metzler, Ralf

doi:10.1063/1.4917077

Cited by 28 publications

(12 citation statements)

References 121 publications

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“…The primary focus of the current study is on the effects of resetting onto the TAMSD characteristics for stochastic processes of nearly ergodic (see Refs. [132][133][134][135] ) fractional BM (FBM) 42,[136][137][138][139][140][141][142][143][144] and of nonergodic heterogeneous diffusion processes (HDPs) 126,143,[146][147][148][149][150] as well as for a combination of FBM with varying Hurst exponent H 151,152 and HDPs with varying exponent of the power-law-like diffusivity γ 150 . Note that a "hybrid" process of SBM-HDP was also introduced 126 and recently applied to the experimental data 153 .…”

Section: Outline Of the Papermentioning

confidence: 99%

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Wang

Cherstvy

Kantz

et al. 2021

Preprint

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How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0|x|γ and of their "combined" process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle' displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for "confined" processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB~ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

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Section: Outline Of the Papermentioning

confidence: 99%

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Wang

Cherstvy

Kantz

et al. 2021

Preprint

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“…Material transport behavior with non-Gaussian increments has been observed and investigated in several non-living complex systems (46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)(62), ranging from glasses to granular matter and artificial F-actin networks, as well as for the dynamics of receptors on live cell membranes (41) and recently in living prokaryotic cell interiors (63) and in yeast (40). In those systems, non-Gaussian transport features have been rationalized by 1) sample-based variability, 2) rare occurring strong motion events, 3) aging, or 4) spatiotemporal heterogeneities of the medium.…”

Section: Cause Of Non-gaussian Dynamics In Passive Intracellular Transportmentioning

confidence: 99%

Heterogeneities Shape Passive Intracellular Transport

Witzel

Götz

Lanoiselée

et al. 2019

Biophysical Journal

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A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion that controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, non-biomotor-shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150-nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: 1) sample-based variability, 2) rarely occurring strong motion events, 3) ergodicity breaking/aging, and 4) spatiotemporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A, to our knowledge, novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, whereas cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.

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“…As these properties are likely affected by environmental conditions, e.g. temperature, it is reasonable to hypothesise that this process might lack robustness to some environmental stresses (Jeon et al, 2013;Cherstvy and Metzler, 2015), particularly since, in those conditions, other functions are likely to be more critical (Clegg et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Increased cytoplasm viscosity hampers aggregate polar segregation in Escherichia coli

Oliveira

Neeli-Venkata

Goncalves

et al. 2015

Molecular Microbiology

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SummaryIn Escherichia coli, under optimal conditions, protein aggregates associated with cellular aging are excluded from midcell by the nucleoid. We study the functionality of this process under sub-optimal temperatures from population and time lapse images of individual cells and aggregates and nucleoids within. We show that, as temperature decreases, aggregates become homogeneously distributed and uncorrelated with nucleoid size and location. We present evidence that this is due to increased cytoplasm viscosity, which weakens the anisotropy in aggregate displacements at the nucleoid borders that is responsible for their preference for polar localisation. Next, we show that in plasmolysed cells, which have increased cytoplasm viscosity, aggregates are also not preferentially located at the poles. Finally, we show that the inability of cells with increased viscosity to exclude aggregates from midcell results in enhanced aggregate concentration in between the nucleoids in cells close to dividing. This weakens the asymmetries in aggregate numbers between sister cells of subsequent generations required for rejuvenating cell lineages. We conclude that the process of exclusion of protein aggregates from midcell is not immune to stress conditions affecting the cytoplasm viscosity. The findings contribute to our understanding of E. coli's internal organisation and functioning, and its fragility to stressful conditions.

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Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes

Cited by 28 publications

References 121 publications

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Heterogeneities Shape Passive Intracellular Transport

Increased cytoplasm viscosity hampers aggregate polar segregation in Escherichia coli

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