TY - JOUR
T1 - Non-Markovian Persistent Random Walk Model for Intracellular Transport
AU - Korabel, Nickolay
AU - Al Shamsi, Hamed
AU - Ivanov, Alexey O.
AU - Fedotov, Sergei
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/10/15
Y1 - 2023/10/15
N2 - Transport of vesicles and organelles inside cells consists of constant-speed bidirectional movement along cytoskeletal filaments interspersed by periods of idling. This transport shows many features of anomalous diffusion. In this paper, we develop a non-Markovian persistent random walk model for intracellular transport that incorporates the removal rate of organelles. The model consists of two active states with different speeds and one resting state. The organelle transitions between states with switching rates that depend on the residence time the organelle spends in each state. The mesoscopic master equations that describe the average densities of intracellular transport in each of the three states are the main results of the paper. We also derive ordinary differential equations for the dynamics for the first and second moments of the organelles’ position along the cell. Furthermore, we analyse models with power-law distributed random times, which reveal the prevalence of the Mittag-Leffler resting state and its contribution to subdiffusive and superdiffusive behaviour. Finally, we demonstrate a non-Markovian non-additivity effect when the switching rates and transport characteristics depend on the rate of organelles removal. The analytical calculations are in good agreement with numerical Monte Carlo simulations. Our results shed light on the dynamics of intracellular transport and emphasise the effects of rest times on the persistence of random walks in complex biological systems.
AB - Transport of vesicles and organelles inside cells consists of constant-speed bidirectional movement along cytoskeletal filaments interspersed by periods of idling. This transport shows many features of anomalous diffusion. In this paper, we develop a non-Markovian persistent random walk model for intracellular transport that incorporates the removal rate of organelles. The model consists of two active states with different speeds and one resting state. The organelle transitions between states with switching rates that depend on the residence time the organelle spends in each state. The mesoscopic master equations that describe the average densities of intracellular transport in each of the three states are the main results of the paper. We also derive ordinary differential equations for the dynamics for the first and second moments of the organelles’ position along the cell. Furthermore, we analyse models with power-law distributed random times, which reveal the prevalence of the Mittag-Leffler resting state and its contribution to subdiffusive and superdiffusive behaviour. Finally, we demonstrate a non-Markovian non-additivity effect when the switching rates and transport characteristics depend on the rate of organelles removal. The analytical calculations are in good agreement with numerical Monte Carlo simulations. Our results shed light on the dynamics of intracellular transport and emphasise the effects of rest times on the persistence of random walks in complex biological systems.
KW - integro-differential equations
KW - intracellular transport
KW - subdiffusion
KW - superdiffusion
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UR - https://www.mendeley.com/catalogue/d2053f33-a62b-3e90-9807-8c35858cebb9/
U2 - 10.3390/fractalfract7100758
DO - 10.3390/fractalfract7100758
M3 - Article
AN - SCOPUS:85175143847
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 10
M1 - 758
ER -