Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift–diffusion and long-range transport

Lin, Congping; Ashwin, Peter; Steinberg, Gero

doi:10.1140/epje/s10189-020-00007-4

Cited by 2 publications

(2 citation statements)

References 60 publications

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“…A possible biological mechanism underlying this self-reinforcement is given in Section VII of [10]. It would be interesting to extend this model to three dimensions, as was done for the diffusion-advection model for intracellular transport in [38].…”

Section: Stochastic Transport With Self-reinforcement and Mittag-leffler Distributed Rest Timesmentioning

confidence: 99%

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

et al. 2021

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We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

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Section: Stochastic Transport With Self-reinforcement and Mittag-leffler Distributed Rest Timesmentioning

confidence: 99%

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

et al. 2021

View full text Add to dashboard Cite

show abstract

“…It is now clear that the superdiffusion generated by this self-reinforcing mechanism [10] is fundamentally different to those generated by power-law flights in CTRW and Lévy walk formulations (a biological motivation is given in Section VII of [10]). It would be interesting to extend this model to three dimensions as it was done for the diffusion-advection model for intracellular transport in [37].…”

Section: Stochastic Transport With Self-reinforcement and Mittag-leff...mentioning

confidence: 99%

Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times

Han,

Alexandrov,

Gavrilova

et al. 2021

Preprint

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We introduce a persistent random walk model for the stochastic transport of particles involving selfreinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann-Liouville derivative. From Monte Carlo simulations, this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derive the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag-Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for application in stochastic biological transport.

show abstract

Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift–diffusion and long-range transport

Abstract: Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous driftdiffusion and long-range transport AUTHORS

Cited by 2 publications

References 60 publications

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

Anomalous stochastic transport of particles with self-reinforcement and Mittag-Leffler distributed rest times

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