Boundary homogenization for trapping by patchy surfaces

Berezhkovskii, Alexander M.; Makhnovskii, Yu. A.; Monine, Michael I.; Zitserman, V. Yu.; Shvartsman, Stanislav Y.

doi:10.1063/1.1814351

Cited by 139 publications

(179 citation statements)

References 15 publications

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“…A further discussion of this result and a comparison to other results in the literature, notably those in [2,3,34,51], are discussed in section 4. Finally, in section 7 we briefly summarize our main results and discuss a few open problems worthy of further study.…”

Section: R→∞ ∂ωRmentioning

confidence: 99%

“…More detailed studies [45,51,2,3,34] and fittings of the leakage parameter κ in a boundary homogenization procedure for nanotraps on either the sphere or on a flat plane are discussed in section 4. By taking the limit N 1 in our expression for the capacitance C 0 for a uniformly distributed configuration of nanotraps of a common radius σ, our result in section 4 for the low surface nanotrap coverage limit f = O(−σ 2 log σ) 1, and when cast in dimensional form, predicts that…”

Section: R→∞ ∂ωRmentioning

confidence: 99%

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First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

Lindsay¹,

Bernoff²,

Ward³

2017

Multiscale Model. Simul.

108

153

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Abstract. We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small absorbing pore radius, we derive and numerically verify a high order expansion for the capacitance of the structured target which incorporates surface effects and gives explicit information on interpore interaction through a Coulomb-type discrete energy with additional logarithmic dependencies. In the large N dilute surface trap fraction limit, a single homogenized Robin boundary condition ∂nv + κv = 0 is derived in which κ depends on the total absorbing fraction, the characteristic pore scale, and parameters relating to interpore interactions.

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Section: R→∞ ∂ωRmentioning

confidence: 99%

Section: R→∞ ∂ωRmentioning

confidence: 99%

First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

Lindsay¹,

Bernoff²,

Ward³

2017

Multiscale Model. Simul.

108

153

View full text Add to dashboard Cite

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“…The values used in the model are taken from [56] and are shown in Table 3. These were fitted by comparison of experimental data with compartmental simulations: more investigation on the correct values for spatial modeling is needed, for instance by following the approach of the homogenized 'effective' permeabilities proposed in [8]. NPC Table 3.…”

Section: Facilitated Translocation Through the Nuclear Envelopementioning

confidence: 99%

“…Our model couples diffusion equations such as (9) with the transport equation appearing in (8), which is only defined in the cytoplasm Ω c . In order to write all equations at once, we collect the advection and diffusion coefficients in, respectively, the tensor B ∈ [C 1 (0, T ; Ω)] n×d , whose rows are denoted by B i , i = 1, .…”

Section: The Pde Problem In Vector Formmentioning

confidence: 99%

A spatial model of cellular molecular trafficking including active transport along microtubules

Cangiani

Natalini

2010

Journal of Theoretical Biology

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To cite this version:A. Cangiani, R. Natalini. A spatial model of cellular molecular trafficking including active transport along microtubules. Journal of Theoretical Biology, Elsevier, 2010, 267 (4) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A SPATIAL MODEL OF CELLULAR MOLECULAR TRAFFICKING INCLUDING ACTIVE TRANSPORT ALONG MICROTUBULESA. CANGIANI * , R. NATALINI † Abstract. We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells. The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules. All parameters entering the models are thoroughly discussed. The model is tested by numerical simulations based on Discontinuous Galerkin finite element methods. The numerical experiments are compared to the behavior observed experimentally.

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“…This constraint arises because Eq. (2.2) was derived using the method of boundary homogenization, 13 which in this particular case is applicable only when the length of the wide sections is equal to or larger than its radius. 14 As follows from Eq.…”

Section: Preliminariesmentioning

confidence: 99%

Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force

Makhnovskii

Berezhkovskii

Antipov

et al. 2015

The Journal of Chemical Physics

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This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficientsmobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small. C 2015 AIP Publishing LLC. [http://dx

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Boundary homogenization for trapping by patchy surfaces

Cited by 139 publications

References 15 publications

First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

A spatial model of cellular molecular trafficking including active transport along microtubules

Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force

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