The narrow escape problem in a circular domain with radial piecewise constant diffusivity

Mangeat, Matthieu; Rieger, Heiko

doi:10.1088/1751-8121/ab4348

Cited by 11 publications

(11 citation statements)

References 46 publications

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“…We have studied this behavior in the Ref. [40] without a potential difference (β∆V = 0), and the main conclusions stay qualitatively the same for both attractive and repulsive cortex.…”

Section: Numerical Solutionsmentioning

confidence: 73%

“…We recently studied the impact of a heterogeneous diffusivity in Ref. [40] showing that without potential barrier no optimization of the MFPT can be observed, which motivated the study presented in this article. The mathematical model will be defined in Sec.…”

Section: Introductionmentioning

confidence: 78%

“…and (iii) the narrow escape limit for the two-shell geometry with heterogeneous diffusivity [40] when ∆V = 0:…”

Section: A Narrow Escape Limit In Two Dimensionsmentioning

confidence: 99%

“…and we mention two other interesting cases studied in 2d in Ref. [40]: (i) the narrow escape limit for the annulus geometry when ∆V → +∞:…”

Section: B Narrow Escape Limit In Three Dimensionsmentioning

confidence: 99%

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Narrow escape problem in two-shell spherical domains

Mangeat,

Rieger

2021

Preprint

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Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and microtubules, respectively. Recently it was reported that the mean first passage time (MFPT) for transport to a specific area on the cell membrane is minimal for an optimal actin cortex width. In this paper we ask whether this optimization in a two-compartment domain can also be achieved by passive Brownian particles. We consider a Brownian motion with different diffusion constants in the two shells and a potential barrier between the two and investigate the narrow escape problem by calculating the MFPT for Brownian particles to reach a small window on the external boundary. In two and three dimensions, we derive asymptotic expressions for the MFPT in the thin cortex and small escape region limits confirmed by numerical calculations of the MFPT using the finite element method and stochastic simulations. From this analytical and numeric analysis we finally extract the dependence of the MFPT on the ratio of diffusion constants, the potential barrier height and the width of the outer shell. The first two are monotonous whereas the last one may have a minimum for a sufficiently attractive cortex, for which we propose an analytical expression of the potential barrier height matching very well the numerical predictions.

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“…We have studied this behavior in the Ref. [40] without a potential difference (β∆V = 0), and the main conclusions stay qualitatively the same for both attractive and repulsive cortex.…”

Section: Numerical Solutionsmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 78%

“…and (iii) the narrow escape limit for the two-shell geometry with heterogeneous diffusivity [40] when ∆V = 0:…”

Section: A Narrow Escape Limit In Two Dimensionsmentioning

confidence: 99%

“…and we mention two other interesting cases studied in 2d in Ref. [40]: (i) the narrow escape limit for the annulus geometry when ∆V → +∞:…”

Section: B Narrow Escape Limit In Three Dimensionsmentioning

confidence: 99%

See 2 more Smart Citations

Narrow escape problem in two-shell spherical domains

Mangeat,

Rieger

2021

Preprint

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“…Previous research often investigated search problems in two‐dimensional space, largely motivated by animal foraging. Among others, this includes theoretical and computational studies of composite search strategies for hidden targets, [14,19–22] local search around a home base, [23,24] or finding a small orifice (narrow escape problem) [22,25–27] . Yet, microswimmers must usually search a three‐dimensional environment.…”

Section: Figurementioning

confidence: 99%

Composite Search of Active Particles in Three‐dimensional Space Based on Non‐directional Cues

2021

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We theoretically address minimal search strategies of self‐propelled particles towards hidden targets in three‐dimensional space. The particles can sense if targets are close, e. g., by detecting released signaling molecules, but they cannot deduce directional cues. We investigate composite search strategies, where particles switch between extensive outer search and intensive inner search; inner search is started when proximity of a target is detected and ends when a certain inner search time has elapsed. In the simplest strategy, active particles move ballistically during outer search, and transiently reduce their directional persistence during inner search. In a second, adaptive strategy, particles exploit a dynamic scattering effect by reducing directional persistence only outside a well‐defined target zone. These two search strategies require only minimal information processing capabilities, yet increase target encounter rates substantially. The optimal inner search time scales as power‐law with exponent −2/3 with target density, reflecting a trade‐off between exploration and exploitation.

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Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion

Voce,

Stevenson

2024

J. Phys. Chem. B

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The lateral mobility of molecules within the cell membrane is ultimately governed by the local environment of the membrane. Confined regions induced by membrane structures, such as protein aggregates or the actin meshwork, occur over a wide range of length scales and can impede or steer the diffusion of membrane components. However, a detailed picture of the origins and nature of these confinement effects remains elusive. Here, we prepare model lipid systems on substrates patterned with confined domains of varying geometries constructed with different materials to explore the influences of physical boundary conditions and specific molecular interactions on diffusion. We demonstrate a platform that is capable of significantly altering and steering the long-range diffusion of lipids by using simple oxide deposition approaches, enabling us to systematically explore how confinement size and shape impact diffusion over multiple length scales. While we find that a "boundary condition" description of the system captures underlying trends in some cases, we are also able to directly compare our systems to analytical models, revealing the unexpected breakdown of several approximate solutions. Our results highlight the importance of considering the length scale dependence when discussing properties such as diffusion.

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The narrow escape problem in a circular domain with radial piecewise constant diffusivity

Cited by 11 publications

References 46 publications

Narrow escape problem in two-shell spherical domains

Narrow escape problem in two-shell spherical domains

Composite Search of Active Particles in Three‐dimensional Space Based on Non‐directional Cues

Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion

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