# Persistent random walk of cells involving anomalous effects and random death.

@article{Fedotov2015PersistentRW, title={Persistent random walk of cells involving anomalous effects and random death.}, author={Sergei P. Fedotov and Abby Tan and Andrey Yu. Zubarev}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2015}, volume={91 4}, pages={ 042124 } }

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…

## Figures from this paper

## 19 Citations

### Age representation of Lévy walks: partial density waves, relaxation and first passage time statistics

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

Lévy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there is a hyperbolic…

### Diffusion in an age-structured randomly switching environment

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

Age-structured processes are well-established in population biology, where birth and death rates often depend on the age of the underlying populations. Recently, however, different examples of…

### Non-linear continuous time random walk models

- Mathematics
- 2017

Abstract
A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional…

### Space-time fractional diffusion in cell movement models with delay

- BiologyMathematical Models and Methods in Applied Sciences
- 2019

Starting from a microscopic velocity-jump model based on experimental observations, this work includes power-law distributions of run and waiting times and investigates the relevant parabolic limit from a kinetic equation for resting and moving individuals.

### Aging in mortal superdiffusive Lévy walkers.

- PhysicsPhysical review. E
- 2017

The effects of aging on the motility of mortal walkers are examined, the means by which permanent stopping of walkers may be categorized as arising from "natural" death or experimental artifacts such as low photostability or radiation damage are discussed, and the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales is raised.

### Phase transitions in persistent and run-and-tumble walks

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2020

### Extended Poisson-Kac Theory: A Unifying Framework for Stochastic Processes with Finite Propagation Velocity

- MathematicsPhysical Review X
- 2022

Extended Poisson-Kac theory not only ensures by construction a mathematical representation of physical reality that is ontologically valid at all time and length scales, but also provides a toolbox of stochastic processes that can be used to model potentially any kind of finite velocity dynamical phenomena observed experimentally.

### Proliferating L\'evy Walkers and Front Propagation

- Mathematics
- 2015

We develop non-linear integro-differential kinetic equations for proliferating L\'{e}vy walkers with birth and death processes. A hyperbolic scaling is applied directly to the general equations to…

### Motility Switching and Front–Back Synchronisation in Polarised Cells

- MathematicsJ. Nonlinear Sci.
- 2022

The form of relevant macroscopic equations that describe the possible effects of synchronised movement in cells are clarified, and light is shed on the switching between normal and fractional diffusion.

### Reaction-anomalous diffusion processes for A+B⇌C

- ChemistryPhysica A: Statistical Mechanics and its Applications
- 2019

## References

SHOWING 1-10 OF 69 REFERENCES

### Random death process for the regularization of subdiffusive fractional equations.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The inclusion of the random death process in the random walk scheme is proposed, which is quite natural for biological applications including morphogen gradient formation and shows that this equation is structurally stable against spatial variations of the anomalous exponent.

### Fluid limit of the continuous-time random walk with general Lévy jump distribution functions.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x) and an integrodifferential equation describing the dynamics in the fluid limit is considered.

### Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

- Mathematics
- 2012

The criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain is found and the structural instability of fractional subdiffusive equation is shown with respect to the partial variations of anomalous exponent.

### Front propagation in reaction-dispersal models with finite jump speed.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

The continuous-time random walk and the Hamilton-Jacobi method are used to reach analytical expressions for the speed of traveling fronts in reaction-dispersal models and the possibility that several particle speeds are allowed, so different dispersal mechanisms can be considered simultaneously.

### FRACTIONAL DIFFUSION AND LEVY STABLE PROCESSES

- Mathematics
- 1997

Anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in ‘‘time’’ has been observed in all manner of physical and biological systems from…

### Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

A more general derivation valid under less stringent constraints than those found in the current literature is presented, e.g., for location-independent exponential evanescence.

### Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks

- MathematicsSIAM J. Appl. Math.
- 1997

The question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates of the myxobacteria.

### Towards deterministic equations for Lévy walks: the fractional material derivative.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A generalized dynamical formulation is derived for Lévy walks, in which the fractional equivalent of the material derivative occurs, which is expected to be useful for the dynamical formulations of LÉvy walks in an external force field or in phase space.

### Anomalous transport and nonlinear reactions in spiny dendrites.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

A mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites using two-state Markovian model with the transition probabilities depending on residence time variable and shows that the flux of particles between spines and parent dendrite is not local in time and space.