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Two-dimensional continuum percolation threshold for diffusing particles of nonzero radius.

Michael J Saxton1

  • 1Department of Biochemistry and Molecular Medicine, University of California, Davis, California, USA. mjsaxton@ucdavis.edu

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Summary
This summary is machine-generated.

Percolation thresholds for lateral diffusion are affected by tracer size, not just obstacle density. This study suggests percolation may not control plasma membrane diffusion, proposing a new experiment.

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Area of Science:

  • Biophysics
  • Cell Biology
  • Statistical Mechanics

Background:

  • Lateral diffusion in plasma membranes is crucial for cellular functions.
  • Cytoskeletal proteins impede membrane diffusion, creating obstructed diffusion scenarios.
  • Percolation theory is a key framework for understanding obstructed diffusion.

Purpose of the Study:

  • To determine percolation thresholds for tracers with non-zero radii in obstructed diffusion models.
  • To investigate the influence of obstacle size and repulsion on percolation thresholds.
  • To evaluate the relevance of percolation theory in controlling plasma membrane lateral diffusion.

Main Methods:

  • Generating random obstacle configurations using Brownian dynamics and Monte Carlo simulations.
  • Calculating percolation thresholds by solving bond percolation on Voronoi diagrams of immobilized obstacles.
  • Expressing thresholds as the maximum tracer diameter traversable through obstacles at a given density.

Main Results:

  • Thresholds for circular obstacles depend on excluded area, not solely obstacle concentration.
  • Results for overlapping obstacles align quantitatively with known analytical solutions.
  • Soft disk obstacles with 1/r(12) repulsion yield a ~20% lower percolating diameter than overlapping obstacles.
  • Percolation models predict high tracer radius sensitivity, not yet observed in plasma membrane studies.

Conclusions:

  • Percolation thresholds are sensitive to tracer size and obstacle properties.
  • The predicted strong dependence of percolation threshold on tracer radius is not typically observed in plasma membrane diffusion.
  • Percolation may not be the primary factor governing lateral diffusion in the plasma membrane.
  • A definitive experiment is proposed to further investigate this phenomenon.