Viscosity dependence of passage through a fluctuating bottleneck

Area of Science:

• Physical Chemistry
• Biophysics
• Chemical Kinetics

Background:

• Rate processes often involve passage through bottlenecks.
• Bottleneck size fluctuations can significantly impact reaction rates.
• Understanding these dynamics is crucial for various chemical and biological systems.

Purpose of the Study:

• To generalize models of rate processes through fluctuating bottlenecks.
• To investigate the relationship between bottleneck fluctuations, solvent viscosity, and passage rate.
• To provide an analytical and numerical framework for these phenomena.

Main Methods:

• Generalizing a rate process model with a power-law dependence on bottleneck radius (exponent α).
• Incorporating Langevin dynamics to govern coupled bottleneck fluctuations and medium motion.
• Employing numerical simulations and analytical explanations.

Main Results:

• Demonstrating a fractional power law dependence of the long-time decay rate on solvent viscosity for slow bottleneck fluctuations.
• The exponent of this power law is shown to be α/(α + 2).
• The model's predictions are consistent with experimental data for ligand binding to myoglobin.

Conclusions:

• The generalized model accurately describes rate processes influenced by fluctuating bottlenecks.
• The fractional power law dependence on viscosity offers a new insight into reaction dynamics.
• The findings have implications for understanding ligand binding and other chemical reactions with exponents between 0 and 1.