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Narrow escape problem in two-shell spherical domains.

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Summary
This summary is machine-generated.

Passive Brownian particles can achieve optimized intracellular transport, minimizing mean first passage time (MFPT) to cell membranes. This occurs with specific diffusion constants, potential barriers, and outer shell widths, mimicking active transport dynamics.

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Area of Science:

  • Cellular Biophysics
  • Theoretical Biology

Background:

  • Intracellular transport is spatially inhomogeneous, featuring accelerated diffusion near cell membranes and ballistic motion from the centrosome.
  • Active transport along actin filaments and microtubules creates complex cellular dynamics.
  • Previous studies indicated optimal actin cortex width minimizes mean first passage time (MFPT).

Purpose of the Study:

  • Investigate if passive Brownian particles can achieve optimized transport to cell membranes.
  • Analyze the narrow escape problem for Brownian particles in a two-compartment model.
  • Determine MFPT dependence on diffusion constants, potential barriers, and shell width.

Main Methods:

  • Modeling Brownian motion with differing diffusion constants and a potential barrier.
  • Deriving asymptotic expressions for MFPT in thin cortex and small escape region limits.
  • Numerical calculations using finite-element method and stochastic simulations.

Main Results:

  • Derived analytical expressions for MFPT in 2D and 3D, validated by numerical simulations.
  • Identified monotonous dependence of MFPT on diffusion constant ratio and potential barrier height.
  • Observed a minimum MFPT for a specific outer shell width under attractive cortex conditions.

Conclusions:

  • Passive Brownian motion can exhibit optimized transport dynamics similar to active transport.
  • The MFPT is influenced by diffusion properties, potential barriers, and cellular geometry.
  • An analytical expression for the potential barrier height was proposed, accurately predicting numerical results.