Flux through membrane channel: linear transport vs. single-molecule approaches

Area of Science:

• Biophysics
• Physical Chemistry
• Computational Biology

Background:

• Accurately modeling molecular behavior at membrane channel openings is crucial for understanding flux.
• Existing methods face challenges in describing molecule interactions at the channel-bulk interface.
• Radiation boundary conditions were previously introduced to address this subtle step.

Purpose of the Study:

• To demonstrate the equivalence of a single-molecule approach using radiation boundary conditions with conventional transport theory.
• To validate the application of the one-dimensional Smoluchowski equation with these boundary conditions for flux calculations.
• To confirm the accuracy of modeling molecular trajectories at channel openings.

Main Methods:

• Utilizing the one-dimensional Smoluchowski equation to model molecular flux.
• Implementing "radiation boundary conditions" to describe molecule behavior at channel openings.
• Comparing the derived flux expression with results from linear transport theory.

Main Results:

• The single-molecule approach with radiation boundary conditions yields the same flux expression as linear transport theory.
• This confirms the validity of modeling molecule trajectories, including those escaping to infinity.
• The approach accurately accounts for the interplay between returning and escaping molecular trajectories.

Conclusions:

• The one-dimensional Smoluchowski equation combined with radiation boundary conditions provides a robust framework for calculating membrane channel flux.
• This method offers a consistent and accurate way to describe molecular behavior at channel-bulk interfaces.
• The findings bridge single-molecule dynamics with macroscopic transport phenomena.