Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

Cherstvy, Andrey G.; Nagel, Oliver; Beta, Carsten; Metzler, Ralf

doi:10.1039/c8cp04254c

Cited by 93 publications

(83 citation statements)

References 220 publications

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“…, as usual Q = F k k -for simplicity we may neglect the fluctuations counted in the next interval after the trapping events. Directly from (27) we see that S 2 has a geometric distribution. Any such variable can be expressed as an integer part of some exponentially distributed variable, E say, and therefore it has values between E and E−1.…”

Section: Short Memory Random Coefficient Ar(1)mentioning

confidence: 88%

“…Note that for fixed k the pair Φ k , Θ k may, and generally will be dependent. Averaging (27) yields…”

Section: Short Memory Random Coefficient Ar(1)mentioning

confidence: 99%

“…X see [23][24][25][26][27] as well as the extensive list of references in [28]. These 'Brownian yet non-Gaussian' processes along with a more general class of non-Gaussian PDFs, discussed in more detail below, are in the focus of this study.…”

Section: Introductionmentioning

confidence: 99%

“…is assumed to have the distribution as in(27) and be independent from F the exponents in a Taylor series yields an approximation for the codifference which depends only on the moments of Φ k and Θ k . Expansion up to first order, to calculating the covariance, so it is zero.…”

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confidence: 99%

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Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

2019

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Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models. We start from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.

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Section: Short Memory Random Coefficient Ar(1)mentioning

confidence: 88%

“…Note that for fixed k the pair Φ k , Θ k may, and generally will be dependent. Averaging (27) yields…”

Section: Short Memory Random Coefficient Ar(1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

2019

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“…Numerous studies have interestingly revealed anomalous diffusion or deviations from purely Brownian motion (15–26) thus making studies of probe particles in many biophysical systems an active area of research. Examples of systems where anomalous diffusion occurs include entangled F-Actin networks (17–19), living cells (20, 21), cytoplasm (22, 23), colloidal liquids (24, 25), and lipid membranes (26), among others. Anomalous diffusion, is often characterized analytically using fractional Brownian motion (fBm), which follows power law scaling of the form (13, 15), < Δ x 2 ( τ ) > ~ τ α .…”

Section: Introductionmentioning

confidence: 99%

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

Aure¹,

Bernido²,

Carpio-Bernido³

et al. 2019

Preprint

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1From observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an 2 analytical framework that allows determination of the probability density function (PDF) for 3 a stochastic process beyond fractional Brownian motion. Using passive microrheology via 4 videomicroscopy, mean square displacements (MSD) of tracer particles suspended in fibrin at 5 different ageing times are obtained. The anomalous diffusion is then described by a damped 6 white noise process with memory, with analytical results closely matching experimental plots 7 of MSD and PDF. We further show that the white noise functional stochastic approach 8 applied to passive microrheology reveals the existence of a gelation parameter µ which 9 elucidates the dynamics of constrained tracer particles embedded in a time dependent soft 10 material. This study offers experimental insights on the ageing of fibrin gels while presenting 11 a white noise functional stochastic approach that could be applied to other systems exhibiting 12 non-Markovian diffusive behavior. 13 14 15 16 17 18 19 20 21 22 23 24 25 1Fibrin is a protein polymer network that plays a crucial role in blood clotting, wound healing, 2 and other biological processes such as blood vessel formation and cell growth (1-6). Aside 3 from its importance in clinical applications, fibrin also finds an increasing role in tissue 4 regeneration and engineering (5,(7)(8). Thus, it is important to have a quantitative description 5 of the mechanics and complex structural formation of fibrin as a viscoelastic biomaterial (3, 6 9-11). Since not much is known about the diffusive behavior of probe particles in fibrin as its 7 structure evolves in time, we use passive microrheology via video microscopy to reveal the 8 gelation dynamics of fibrin by tracking the movement of probe particles suspended in its 9 network of protein polymers (12)(13)(14). Moreover, to elucidate how the structure of fibrin is 10 affected at different ageing times, we present a theoretical framework for the stochastic 11 fluctuations exhibited by the experimental observations. 12The diffusion of colloidal tracer particles in complex fluids is usually analyzed by 13 measuring the mean square displacement (MSD), < Δ 2 ( ) >, where brackets represent an 14 ensemble average and τ is the lag time between two positions taken by the particle in its 15 trajectory. Numerous studies have interestingly revealed anomalous diffusion or deviations 16 from purely Brownian motion (15-26) thus making studies of probe particles in many 17 biophysical systems an active area of research. Examples of systems where anomalous 18 diffusion occurs include entangled F-Actin networks (17-19), living cells (20, 21), cytoplasm 19(22, 23), colloidal liquids (24, 25), and lipid membranes (26), among others. Anomalous 20 diffusion, is often characterized analytically using fractional Brownian motion (fBm), which 21 follows power law scaling of the form (13, 15), < Δ 2 ( ) >~ . In particular, the motion of 22 the probe particles suspended in t...

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Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Di Bello,

Majumdar,

Marathe

et al. 2024

Annalen der Physik

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The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot‐noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite‐time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero‐mean kick distributions, including those leading to non‐Gaussian stationary statistics. For the case of Gaussian‐distributed active kicks, a re‐entrant behavior from non‐Gaussian to Gaussian stationary states and a heavy‐tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross‐correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot‐noise solely from the statistics the particle position.

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Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

Cited by 93 publications

References 220 publications

Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

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