Probability density of the fractional Langevin equation with reflecting walls

Vojta, Thomas; Skinner, Sarah; Metzler, Ralf

doi:10.1103/physreve.100.042142

Cited by 44 publications

(62 citation statements)

References 66 publications

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“…Direct simulations of macromolecular dynamics in confined domains can further enrich these studies; for example, in some simulations particles near the wall tend to stay near the wall (Chow and Skolnick, 2015), which may explain the tendency of serotonergic fibers to orient parallel to the edge immediately below the pia (for depths up to 25-50 µm; Figure 2). Finally, it has been recently demonstrated (Vojta et al, 2019) that the increased density close to a boundary arises from the non-equilibrium nature of FBM. A similar anomalous diffusion process in thermal equilibrium, modeled by the fractional Langevin equation, does not lead to accumulation at the boundary.…”

Section: Discussionmentioning

confidence: 99%

Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities

Janušonis

Detering

Metzler

et al. 2020

Front. Comput. Neurosci.

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All vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and vascular processes. Perturbations in the density of this matrix have been associated with a number of mental disorders, including autism and depression, but its self-organization and plasticity remain poorly understood. We introduce a model based on reflected Fractional Brownian Motion (FBM), a rigorously defined stochastic process, and show that it recapitulates some key features of regional serotonergic fiber densities. Specifically, we use supercomputing simulations to model fibers as FBM-paths in two-dimensional brain-like domains and demonstrate that the resultant steady state distributions approximate the fiber distributions in physical brain sections immunostained for the serotonin transporter (a marker for serotonergic axons in the adult brain). We suggest that this framework can support predictive descriptions and manipulations of the serotonergic matrix and that it can be further extended to incorporate the detailed physical properties of the fibers and their environment.

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Section: Discussionmentioning

confidence: 99%

Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities

Janušonis

Detering

Metzler

et al. 2020

Front. Comput. Neurosci.

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“…To properly simulate chromatin diffusion within the confines of the nucleus, we added an impassable boundary to serve as a nuclear membrane. Recent work on the behavior of FBM and the fractional Langevin equation in finite volumes of space showed that the presence of boundaries and the handling of those boundary conditions can affect the long-timescale distribution close to the edges of the domain ( Guggenberger et al, 2019 ; Vojta et al, 2020 ; Vojta et al, 2019 ; Wada and Vojta, 2018 ). These studies agree with our findings that in the sub-diffusive regime, depletion occurs at the boundary ( Figure 4—figure supplement 1C, D ).…”

Section: Methodsmentioning

confidence: 99%

Random sub-diffusion and capture of genes by the nuclear pore reduces dynamics and coordinates inter-chromosomal movement

Sumner

Torrisi

Brickner

et al. 2021

eLife

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Hundreds of genes interact with the yeast nuclear pore complex (NPC), localizing at the nuclear periphery and clustering with co-regulated genes. Dynamic tracking of peripheral genes shows that they cycle on and off the NPC and that interaction with the NPC slows their sub-diffusive movement. Furthermore, NPC-dependent inter-chromosomal clustering leads to coordinated movement of pairs of loci separated by hundreds of nanometers. We developed Fractional Brownian Motion simulations for chromosomal loci in the nucleoplasm and interacting with NPCs. These simulations predict the rate and nature of random sub-diffusion during repositioning from nucleoplasm to periphery and match measurements from two different experimental models, arguing that recruitment to the nuclear periphery is due to random sub-diffusion and transient capture by NPCs. Finally, the simulations do not lead to inter-chromosomal clustering or coordinated movement, suggesting that interaction with the NPC is necessary, but not sufficient, to cause clustering.

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“…This phenomenon is consistent with previous work at thermodynamic equilibrium. Related work involved fraction Brownian motion with the reflecting boundary condition can be found in [69,70]. However, it should be noted that the observed diffusion gradients come from particle-wall effects or the preciseboundary structure, which has a different regime with the temperature gradient.…”

Section: Steady State Probability Density Function (Pdf)mentioning

confidence: 99%

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Mei

et al. 2020

New J. Phys.

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This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D 0 ), as well as a low (D m ) and a high (D d ) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d , a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D m , a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two-or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.New J. Phys. 22 (2020) 053016 Y Li et al confined spaces, transport of particles in nanopores, zeolites and gel networks [8-10], or protein diffusion in the mammalian cell cytoplasm [11]. In many cases, such structured environments can be viewed as confined channels with different boundaries and properties [12][13][14]. The behaviours of systems in these confined channels have been studied by virtue of the analytical Fick-Jacobs (FJ) equation and numerical simulations of the dynamic equations [15][16][17][18][19][20]. Results for symmetric periodic channels indicate that the mean transport velocity may be proportional to large external forces in the confined environment [19][20][21][22]. For asymmetric channels, it was found that the shape of the confinement contributes to the moving direction and mean displacement [20,23], which can be applied to fine separation of mixtures and also the design of many devices [24,25]. Time-dependent and deformable boundaries were discussed to explore the activity in living cells [26,27]. In addition, the interaction...

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Probability density of the fractional Langevin equation with reflecting walls

Cited by 44 publications

References 66 publications

Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities

Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities

Random sub-diffusion and capture of genes by the nuclear pore reduces dynamics and coordinates inter-chromosomal movement

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

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