Trapping of single diffusing particles by a circular disk on a reflecting flat surface. Absorbing hemisphere...

Area of Science:

• Biophysics
• Statistical Physics
• Physical Chemistry

Background:

• Advances in biophysics, including chemical sensing and cell signaling, present challenges for statistical theories of particle trapping.
• Understanding the trapping kinetics of single diffusing particles is crucial in various scientific domains.

Purpose of the Study:

• To develop an approximate method for analyzing the trapping kinetics of a single diffusing particle in a half-space bounded by a reflecting surface with an absorbing circular disk.
• To investigate the angular dependence of trapping kinetics and its simplification through approximation.

Main Methods:

• Proposed an approximation replacing the absorbing circular disk with an absorbing hemisphere of a specific radius.
• Transformed the essentially two-dimensional problem into an angular-independent, essentially one-dimensional problem.
• Derived an exact solution for the particle propagator (Green's function) based on the approximation.

Main Results:

• The absorbing hemisphere approximation yields an exact solution for particle propagator, characterizing trapping kinetics.
• Theoretical predictions show excellent agreement with 3D Brownian dynamics simulations when the particle starts far from the disk.
• The approximation's accuracy decreases when the starting point is close to the disk radius, with a ~10% error at two disk radii, rapidly improving with distance.

Conclusions:

• The absorbing hemisphere approximation provides a powerful and accurate method for studying particle trapping kinetics in confined geometries.
• The approach simplifies complex two-dimensional problems into manageable one-dimensional ones, offering significant analytical advantages.
• The study highlights the importance of initial particle position relative to the absorbing surface for accurate kinetic predictions.