Ligand binding in a spherical region randomly crowded by receptors

Area of Science:

• Biophysics
• Chemical Kinetics
• Physical Chemistry

Background:

• Standard mean-field theory accurately models bulk diffusion-controlled reactions.
• This theory, however, fails to describe ligand concentration near boundaries in 3D regions.
• Accurate modeling of boundary effects is crucial for understanding ligand-receptor interactions.

Purpose of the Study:

• To develop an improved theoretical framework for ligand-receptor binding in spherical 3D regions.
• To address the limitations of mean-field theory in diffusion boundary layers.
• To accurately quantify ligand concentration and binding flux near region boundaries.

Main Methods:

• Introduction of a complementary diffusion equation for the boundary layer.
• Development of an appropriate matching condition between bulk and boundary layers.
• Analytical derivation of ligand penetration length and time-dependent flux.

Main Results:

• The new boundary layer equation accurately models ligand concentration near the region boundary.
• The characteristic ligand penetration length was determined.
• The total time-dependent flux of ligand binding to receptors was calculated.

Conclusions:

• The proposed complementary diffusion equation enhances the predictive power of diffusion-controlled reaction theories.
• This approach provides a more accurate understanding of ligand-receptor dynamics in confined 3D spaces.
• The findings are applicable to various biological and chemical systems involving diffusion and binding.