Diffusive Search for Diffusing Targets with Fluctuating Diffusivity and Gating

Lawley, Sean D.; Miles, Christopher E.

doi:10.1007/s00332-019-09564-1

Cited by 33 publications

(27 citation statements)

References 54 publications

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“…where T 1,N := T N . While the distribution and statistics of a single FPT, τ 1 , are well understood in a variety of scenarios [26,27,28,29,30], studying the so-called extreme FPTs, T k,N , is notoriously difficult, both analytically and numerically [31,32,12,11,33,34]. The essential difficulty is that extreme FPTs depend on very rare events.…”

Section: Introductionmentioning

confidence: 99%

Distribution of extreme first passage times of diffusion

Lawley

2020

J. Math. Biol.

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Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.

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Section: Introductionmentioning

confidence: 99%

Distribution of extreme first passage times of diffusion

Lawley

2020

J. Math. Biol.

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“…This timescale has been estimated by calculating the mean first passage time (MFPT) of a given single searcher to a target. Indeed, many prior studies have calculated such MFPTs, especially for the case of a diffusing Brownian searcher and a small target, which is the so-called narrow escape problem [24,25,26,27,28,29,30,31,32,33,34]. However, a number of recent works have demonstrated that in many cellular systems, the relevant timescale is not the MFPT of a given single searcher but rather the MFPT of the fastest searcher out of many searchers [1,2,3,4,5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Approach to Extreme Statistics of Brownian Escape Times in Dimensions 1, 2, and 3

Lawley¹,

Madrid²

2020

J Nonlinear Sci

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First passage time (FPT) theory is often used to estimate timescales in cellular and molecular biology. While the overwhelming majority of studies have focused on the time it takes a given single Brownian searcher to reach a target, cellular processes are instead often triggered by the arrival of the first molecule out of many molecules. In these scenarios, the more relevant timescale is the FPT of the first Brownian searcher to reach a target from a large group of independent and identical Brownian searchers. Though the searchers are identically distributed, one searcher will reach the target before the others and will thus have the fastest FPT. This fastest FPT depends on extremely rare events and its mean can be orders of magnitude faster than the mean FPT of a given single searcher. In this paper, we use rigorous probabilistic methods to study this fastest FPT. We determine the asymptotic behavior of all the moments of this fastest FPT in the limit of many searchers in a general class of two and three dimensional domains. Our results correct and extend recent results on this problem.

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“…where σ is the standard deviation, µ is the mean and D = e µ+ σ 2 2 . Motivated by large amount of research in theoretical and experiment systems with fluctuating diffusivity [20,28,[38][39][40][41][42][43], we investigated the log-normal superstatistics of BM to describe Brownian yet non-Gaussian diffusion, and in the following we consider the log-normal superstatistics associated with scaled Brownian motions to include anomalous diffusion.…”

Section: Introductionmentioning

confidence: 99%

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Santos

Menon

2020

Physics

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Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory.

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Diffusive Search for Diffusing Targets with Fluctuating Diffusivity and Gating

Cited by 33 publications

References 54 publications

Distribution of extreme first passage times of diffusion

Distribution of extreme first passage times of diffusion

A Probabilistic Approach to Extreme Statistics of Brownian Escape Times in Dimensions 1, 2, and 3

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

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