Persistent random walk of cells involving anomalous effects and random death / Fedotov Sergei,Tan Abby,Zubarev Andrey // PHYSICAL REVIEW E. - 2015. - V. 91, l. 4.

ISSN/EISSN:

1539-3755 / 1550-2376

Type:

Article

Abstract:

The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Levy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residence (running) time. This assumption leads to the power law for the velocity switching time distribution. This describes the anomalous persistence of cell motility: the longer the cell moves in one direction, the smaller the switching probability to another direction becomes. We derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process. In the long-time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a Levy jump distribution. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death-rate-dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Author keywords:

REACTION-TRANSPORT SYSTEMS; TIME RANDOM-WALKS; FRACTIONAL DIFFUSION; RANDOM MOTION; MIGRATION; CHEMOTAXIS; EQUATION; MODELS; VELOCITIES; MOVEMENT

DOI:

10.1103/PhysRevE.91.042124

Web of Science ID:

ISI:000353142000003

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR 20
Publisher	AMER PHYSICAL SOC
Address	ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Language	English
Article-Number	042124
EISSN	1550-2376
Keywords-Plus	REACTION-TRANSPORT SYSTEMS; TIME RANDOM-WALKS; FRACTIONAL DIFFUSION; RANDOM MOTION; MIGRATION; CHEMOTAXIS; EQUATION; MODELS; VELOCITIES; MOVEMENT
Research-Areas	Physics
Web-of-Science-Categories	Physics, Fluids \& Plasmas; Physics, Mathematical
Funding-Acknowledgement	EPSRC {[}EP/J019526/1]
Funding-Text	This work was funded by EPSRC Grant No. EP/J019526/1 `Anomalous reaction-transport equations'. The authors thank Nickolay Korabel and Steven Falconer for very useful discussions.
Number-of-Cited-References	65
Usage-Count-Since-2013	10
Journal-ISO	Phys. Rev. E
Doc-Delivery-Number	CG2YL