Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102390
Title: Persistent random walk of cells involving anomalous effects and random death
Authors: Fedotov, S.
Tan, A.
Zubarev, A.
Issue Date: 2015
Publisher: American Physical Society
Citation: Fedotov S. Persistent random walk of cells involving anomalous effects and random death / S. Fedotov, A. Tan, A. Zubarev. — DOI 10.1103/PhysRevE.91.042124 // Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. — 2015. — Vol. 91. — Iss. 4. — 042124.
Abstract: The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy 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 Lévy 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. © 2015 American Physical Society.
Keywords: BALLISTICS
CELLS
CYTOLOGY
DIFFUSION
INTELLIGENT SYSTEMS
MONTE CARLO METHODS
RANDOM PROCESSES
STOCHASTIC MODELS
STOCHASTIC SYSTEMS
SWITCHING
TEMPERING
BALLISTIC TRANSPORTS
DECREASING FUNCTIONS
FRACTIONAL DERIVATIVES
MATERIAL DERIVATIVE
PERSISTENT RANDOM WALK
SWITCHING PROBABILITY
TRANSPORT PROCESS
UPPER AND LOWER BOUNDS
POPULATION STATISTICS
BIOLOGICAL MODEL
CELL DEATH
CELL MOTION
COMPUTER SIMULATION
DIFFUSION
FOURIER ANALYSIS
MONTE CARLO METHOD
NONLINEAR SYSTEM
STATISTICS
CELL DEATH
CELL MOVEMENT
COMPUTER SIMULATION
DIFFUSION
FOURIER ANALYSIS
MODELS, BIOLOGICAL
MONTE CARLO METHOD
NONLINEAR DYNAMICS
STOCHASTIC PROCESSES
URI: http://hdl.handle.net/10995/102390
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84929177765
PURE ID: 343898
cc8c36e8-d447-4842-ad9a-f23df7d7394d
ISSN: 15393755
DOI: 10.1103/PhysRevE.91.042124
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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