Passage through a sub-diffusing geometrical bottleneck.

Area of Science:

• Chemical Physics
• Biophysics
• Physical Chemistry

Background:

• Kramers theory predicts reaction rates inversely proportional to medium viscosity (η).
• Experimental ligand-protein binding shows rates proportional to η^-ν (ν=0.4-0.8).
• Zwanzig's fluctuating gate model predicts η^-1/2 dependence, partially explaining observations.

Purpose of the Study:

• To generalize Zwanzig's model by incorporating subdiffusion of the opening.
• To explain the observed viscosity dependence of ligand-protein binding rates.
• To reconcile theoretical predictions with experimental findings in condensed media.

Main Methods:

• Developing a generalized Zwanzig model where the opening size undergoes subdiffusion.
• Solving the model to derive the rate dependence on viscosity.
• Comparing theoretical predictions with experimental data.

Main Results:

• The generalized model predicts reaction rates proportional to η^-ν, with ν ranging from 0.5 to 1.
• This viscosity dependence aligns with experimental observations of ligand-protein binding.
• Subdiffusion of the opening is key to explaining the observed rate behavior.

Conclusions:

• Subdiffusion in protein dynamics is crucial for understanding ligand binding rates.
• The generalized Zwanzig model provides a theoretical framework for observed viscosity dependencies.
• This work bridges the gap between Kramers theory and experimental ligand-protein binding kinetics.