Extreme statistics of anomalous subdiffusion following a fractional Fokker–Planck equation: subdiffusion is faster than normal diffusion

Lawley, Sean D.

doi:10.1088/1751-8121/aba39c

Cited by 12 publications

(4 citation statements)

References 76 publications

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“…[64] Within this context, the counter-intuitive result that subdiffusion increases the probability of finding a nearby target relative to Brownian diffusion has also been observed. [65,66] Indeed, it is speculated that crowding within cells and the induced subdiffusion enhance 7. The solid line and shaded area show the mean and uncertainty predicted by nonparametric regression using a Gaussian process.…”

Section: Dependence Of Mean Fpt On Subdiffusion Exponentmentioning

confidence: 99%

On the Effective Lifetime of Reversible Bonds in Transient Networks

Shanbhag

Ricarte

2023

Macro Theory & Simulations

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The renormalized bond lifetime model (RBLM) is a popular scaling theory for the effective lifetime of reversible bonds in transient networks. It recognizes that stickers connected by a reversible bond undergo many (J) cycles of dissociation and reassociation. After finally separating, one of these stickers finds a new open partner in time 𝝉 open via a subdiffusive process whose mean-squared displacement is proportional to t 𝜶 , where t is the time elapsed, and 𝜶 is the subdiffusion exponent. The RBLM makes convenient mathematical approximations to obtain analytical expressions for J and 𝝉 open . The consequences of relaxing these approximations is investigated by performing fractional Brownian motion (FBM) simulations. It is found that the scaling relations developed in the RBLM hold surprisingly well. However, RBLM overestimates both 𝝉 open and J, especially at lower values of 𝜶. For 𝜶 = 0.5, corresponding to the Rouse limit, it is found that 𝝉 open is overestimated by a factor of approximately 4x, while the approximation for J is nearly exact. The degree of overestimation worsens as 𝜶 decreases, and increases to 1-2 orders of magnitude at 𝜶 = 0.25, corresponding to the reptation limit. This has important ramifications for experimental studies that use RBLM to interpret rheology and dielectric spectroscopy observations.

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Section: Dependence Of Mean Fpt On Subdiffusion Exponentmentioning

confidence: 99%

On the Effective Lifetime of Reversible Bonds in Transient Networks

Shanbhag

Ricarte

2023

Macro Theory & Simulations

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“…Recently, it has been shown mathematically that extreme first passage time, the minimum time taken by a searcher in a group of searchers to reach a target, is lower in the case of sub-diffusive searchers compared with normally diffusing counterparts (59). This suggests that sub-diffusive behavior has a vital role to play in biological systems, where molecular encounters drive cellular processes.…”

Section: Discussionmentioning

confidence: 99%

What determines sub-diffusive behavior in crowded protein solutions?

Kompella,

Romano,

Stansfield

et al. 2024

Biophysical Journal

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“…Extreme FPTs for other types of search processes (i.e. non-diffusive) were considered in [59][60][61][62][63][64].…”

Section: Discussionmentioning

confidence: 99%

Extreme hitting probabilities for diffusion*

Linn¹,

Lawley²

2022

J. Phys. A: Math. Theor.

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A variety of systems in physics, chemistry, biology, and psychology are modeled in terms of diffusing ``searchers'' looking for ``targets.'' Examples range from gene regulation, to cell sensing, to human decision-making. A commonly studied statistic in these models is the so-called hitting probability for each target, which is the probability that a given single searcher finds that particular target. However, the decisive event in many systems is not the arrival of a given single searcher to a target, but rather the arrival of the fastest searcher to a target out of many searchers. In this paper, we study the probability that the fastest diffusive searcher hits a given target in the many searcher limit, which we call the extreme hitting probability. We first prove an upper bound for the decay of the probability that the searcher finds a target other than the closest target. This upper bound applies in very general settings and depends only on the relative distances to the targets. Furthermore, we find the exact asymptotics of the extreme hitting probabilities in terms of the short-time distribution of when a single searcher hits a target. These results show that the fastest searcher always hits the closest target in the many searcher limit. While this fact is intuitive in light of recent results on the time it takes the fastest searcher to find a target, our results give rigorous, quantitative estimates for the extreme hitting probabilities. We illustrate our results in several examples and numerical solutions.

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Extreme statistics of anomalous subdiffusion following a fractional Fokker–Planck equation: subdiffusion is faster than normal diffusion

Cited by 12 publications

References 76 publications

On the Effective Lifetime of Reversible Bonds in Transient Networks

On the Effective Lifetime of Reversible Bonds in Transient Networks

What determines sub-diffusive behavior in crowded protein solutions?

Extreme hitting probabilities for diffusion*

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