Reaction-path statistical mechanics of enzymatic kinetics

Area of Science:

• Biophysics
• Chemical Kinetics
• Statistical Mechanics

Background:

• Enzymatic reactions are crucial biological processes, often operating far from equilibrium.
• Understanding single-molecule enzyme kinetics requires advanced theoretical frameworks.
• The Michaelis-Menten mechanism serves as a fundamental model for enzyme catalysis.

Purpose of the Study:

• To introduce a novel reaction-path statistical mechanics formalism.
• To quantify the kinetics of single-molecule enzymatic reactions using large deviation principles.
• To analyze enzyme-substrate unbinding dynamics.

Main Methods:

• Developed a formalism based on the principle of large deviations.
• Defined reaction path entropy to construct a nonequilibrium ensemble.
• Utilized path-based partition functions and free energies from statistical mechanics.
• Applied large deviation theory under fixed observation time for unbinding rates.

Main Results:

• Calculated enzymatic reaction timescales without equilibrium boundary conditions.
• Quantified enzyme-substrate unbinding rates using the new formalism.
• Observed phase-separation-like, bimodal behavior in unbinding events at finite timescales.
• Demonstrated that this bimodal behavior vanishes in the long-time limit.

Conclusions:

• The reaction-path statistical mechanics formalism effectively quantifies nonequilibrium enzymatic kinetics.
• The study reveals novel insights into enzyme-substrate unbinding dynamics.
• The findings contribute to a deeper understanding of out-of-equilibrium processes in biological systems.