Random walks with random velocities

Zaburdaev, Vasily; Schmiedeberg, Michael; Stark, Holger

doi:10.1103/physreve.78.011119

Cited by 58 publications

(69 citation statements)

References 30 publications

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“…Regarding the distribution of speeds, we will consider here the simplest version of the model, in which the particle travels with constant speed v 0 during the motion periods. We think that the general model with an arbitrary distribution of velocities is also feasible analytically in the light of the velocity models proposed in [21]; that case, however, involves more complicated considerations, so we plan to deal with it in a separate forthcoming work.…”

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confidence: 99%

Persistent random motion: Uncovering cell migration dynamics

Campos

Méndez

Llopis

2010

Journal of Theoretical Biology

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In this paper we study analytically the stick-slip models recently introduced to explain the stochastic migration of free cells. We show that persistent motion of cells of many different types is compatible with stochastic reorientation models which admit an analytical mesoscopic treatment. This is proved by examining and discussing experimental data compiled from different sources in the literature, and by fitting some of these results too. We are able to explain many of the 'apparently complex' migration patterns obtained recently from cell tracking data, like powerlaw dependences in the mean square displacement or non-Gaussian behavior for the kurtosis and the velocity distributions, which depart from the predictions of the classical Ornstein-Uhlenbeck process.

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confidence: 99%

Persistent random motion: Uncovering cell migration dynamics

Campos

Méndez

Llopis

2010

Journal of Theoretical Biology

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“…The first term in the right-hand side of (6) stands for the initial conditions, while the second term contains the contribution from all particles that fly from any position of the domain to x, with Éðx; tÞ being the PDF that a single flight has length x and duration t. The function Éðx; tÞ is then related to the PDFs 'ðtÞ and hðvÞ through [15][16][17] Éðx; tÞ ¼ Z 1…”

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Optimal Intermittence in Search Strategies under Speed-Selective Target Detection

2012

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Random search theory has been previously explored for both continuous and intermittent scanning modes with full target detection capacity. Here we present a new class of random search problems in which a single searcher performs flights of random velocities, the detection probability when it passes over a target location being conditioned to the searcher speed. As a result, target detection involves an N-passage process for which the mean search time is here analytically obtained through a renewal approximation. We apply the idea of speed-selective detection to random animal foraging since a fast movement is known to significantly degrade perception abilities in many animals. We show that speedselective detection naturally introduces an optimal level of behavioral intermittence in order to solve the compromise between fast relocations and target detection capability.

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“…In our models, we fixed the swimming speed; an obvious extension is to replace this with a fluctuating quantity. Random velocities have been considered in the context of random walks [46], but have not been coupled with a model of rotational diffusion. This may further explain the departure of the experimental results from the run-only model predictions.…”

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confidence: 99%

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

Rosser

Baker

Armitage

et al. 2014

J. R. Soc. Interface.

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Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. Two further models incorporate stochastic reorientations, describing 'run-andtumble' motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.

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Random walks with random velocities

Cited by 58 publications

References 30 publications

Persistent random motion: Uncovering cell migration dynamics

Persistent random motion: Uncovering cell migration dynamics

Optimal Intermittence in Search Strategies under Speed-Selective Target Detection

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

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