Anomalous persistence exponents for normal yet aging diffusion

Barbier-Chebbah, Alex; Bénichou, Olivier; Voituriez, Raphaël

doi:10.1103/physreve.102.062115

Cited by 11 publications

(7 citation statements)

References 48 publications

(45 reference statements)

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“…This subdiffusive regime shows that memory effects can have drastic consequences on space exploration, by changing the very dimension of trajectories, which qualitatively become more compact. (ii) Second, we argue theoretically that such ageing dynamics has important consequences on first-passage time statistics 55,56 , which is a key observable to quantify the efficiency of migratory patterns to find 'target' sites of interest in space 57,58 . In the simplest theoretical setting of a single target located in infinite space, first-passage statistics to the target are conveniently parametrized by the persistence exponent θ, which defines the long time asymptotics of the survival probability of the target S(t) ∝ t −θ59 .…”

Section: Isolated Cells Exhibit Regular Oscillationsmentioning

confidence: 96%

Cell migration guided by long-lived spatial memory

et al. 2021

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Living cells actively migrate in their environment to perform key biological functions—from unicellular organisms looking for food to single cells such as fibroblasts, leukocytes or cancer cells that can shape, patrol or invade tissues. Cell migration results from complex intracellular processes that enable cell self-propulsion, and has been shown to also integrate various chemical or physical extracellular signals. While it is established that cells can modify their environment by depositing biochemical signals or mechanically remodelling the extracellular matrix, the impact of such self-induced environmental perturbations on cell trajectories at various scales remains unexplored. Here, we show that cells can retrieve their path: by confining motile cells on 1D and 2D micropatterned surfaces, we demonstrate that they leave long-lived physicochemical footprints along their way, which determine their future path. On this basis, we argue that cell trajectories belong to the general class of self-interacting random walks, and show that self-interactions can rule large scale exploration by inducing long-lived ageing, subdiffusion and anomalous first-passage statistics. Altogether, our joint experimental and theoretical approach points to a generic coupling between motile cells and their environment, which endows cells with a spatial memory of their path and can dramatically change their space exploration.

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Section: Isolated Cells Exhibit Regular Oscillationsmentioning

confidence: 96%

Cell migration guided by long-lived spatial memory

et al. 2021

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“…This is straightforwardly confirmed in the case of the 1d SATW. It is clear that for T R dw , the confined SATW is equivalent to a simple random walk (in this regime all sites have been visited and V (n i ) = β for all sites), so that θ c = 1/2; in contrast, it was shown recently that in infinite space one has θ = e −β /2 [40]. In the case of the SERW, the above analysis shows that in the regime T 1, the process is also equivalent to a simple random walk, so that θ c = 1/2 ; in contrast, we find numerically θ = θ c .…”

Section: A Compact (Recurrent) Processesmentioning

confidence: 99%

“…As we recapitulate below, the analytical determination of d w remains a theoretical challenge ; so far it has been obtained analytically or numerically for different examples of V (n) and d, but even its numerical determination remains debated for attractive linear V (n) for d = 2. In turn, the aging properties of ∆ 2 (T, t) have not been studied until recently [40] and will be analyzed in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…In spite of their pivotal role in quantifying first-passage properties of random walks, determining analytically the exponents θ, ψ for general non Markovian, aging processes remains a theoretical challenge [52,54]. In particular, they remain unknown analytically for most examples of self-interacting processes, with the exception of [40] ; they will be analyzed numerically and analytically in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Self-interacting random walks : aging, exploration and first-passage times

Barbier-Chebbah¹,

Bénichou²,

Voituriez³

2021

Preprint

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Self-interacting random walks are endowed with long range memory effects that emerge from the interaction of the random walker at time t with the territory that it has visited at earlier times t < t. This class of non Markovian random walks has applications in a broad range of examples, ranging from insects to living cells, where a random walker modifies locally its environment -leaving behind footprints along its path, and in turn responds to its own footprints. Because of their inherent non Markovian nature, the exploration properties of self-interacting random walks have remained elusive. Here we show that long range memory effects can have deep consequences on the dynamics of generic self-interacting random walks ; they can induce aging and non trivial persistence and transience exponents, which we determine quantitatively, in both infinite and confined geometries. Based on this analysis, we quantify the search kinetics of self-interacting random walkers and show that the distribution of the first-passage time (FPT) to a target site in a confined domain takes universal scaling forms in the large domain size limit, which we characterize quantitatively. We argue that memory abilities induced by attractive self-interactions provide a decisive advantage for local space exploration, while repulsive self-interactions can significantly accelerate the global exploration of large domains.

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“…Persistence exponent for the diffusion equation has been a subject of interest to physicists [1]- [7] etc., researchers in mathematics and statistics [8] [9] etc. as well as experimentalists [10].…”

Section: Introductionmentioning

confidence: 99%

Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension

Sanyal¹

2021

JMP

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The persistence exponent o θ for the simple diffusion equation, with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field φ at a specified spatial coordinate remains positive throughout for a certain time t behaves as o t θ − for asymptotically large time t. The value of o θ , calculated here for any integer dimension d, is 4 o d θ = for 4 d ≤ and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values 0.12, 0.18, 0.23 o θ = for 1, 2, 3 d = respectively.

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Anomalous persistence exponents for normal yet aging diffusion

Cited by 11 publications

References 48 publications

Cell migration guided by long-lived spatial memory

Cell migration guided by long-lived spatial memory

Self-interacting random walks : aging, exploration and first-passage times

Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension

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