Quantifying intermittent transport in cell cytoplasm

Abstract

Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of intermittent dynamics, where the motion of a particle, such as a virus, alternates between pure Brownian and directed movement along microtubules. In this communication, we estimate the mean time for particle to attach to a microtubule network. This computation leads to a coarse grained equation of the intermittent motion in radial and cylindrical geometries. Finally, by using the degradation activity inside the cytoplasm, we obtain refined asymptotic estimations for the probability and the mean time a virus reaches a small nuclear pore.

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

“…We remark that in the context of the nuclear-pore structure, the nuclear radius is roughly 4 microns, and there are estimated to be approximately N = 2000 nanotraps, each of estimated radius 25 nanometers (cf. [29,41]). This yields that σ = 6.25 × 10 −3 , and a surface area fraction f of f = N σ 2 /4 ≈ 0.0195, providing only a small 2% coverage of the boundary of the nucleus by nanotraps.…”

“…It would be interesting to extend this analysis to compare the MFPT and standard deviation for a narrow capture process where there is a biased random walk or drift directed to the target site (cf. [28,29]). Our main focus was the derivation and numerical validation of an asymptotic expansion for the capacitance C 0 of the structured target in the limit σ 1 of small nanotrap radius for a finite collection of N circular nanotraps.…”

“…[28,29,22]). The cell nucleus is typically spherical or ellipsoidal in shape and occupies roughly 10% of the total cell volume.…”

“…The nuclear radius is roughly 4 microns, and there are estimated to be approximately N = 2000 nanotraps, each of estimated radius 25 nanometers (cf. [29,41]). This implies that roughly 2% of the boundary of the nucleus is covered by nanotraps.…”

“…For simplicity, we will neglect the often important effect of directed transport to the target site (cf. [28,29]) and instead assume that there is a simple Brownian motion to the target. The complicating factor in this problem is that the boundary ∂Ω ε of the target sphere is highly heterogeneous, of mixed DirichletNeumann type, and is assumed to consist of many small locally circular absorbing patches, or nanotraps, on an otherwise reflecting surface.…”