Single-molecule enzymology: stochastic Michaelis-Menten kinetics

Area of Science:

• Biochemistry
• Chemical Kinetics
• Statistical Mechanics

Background:

• Enzyme kinetics are typically described by deterministic models like Michaelis-Menten.
• Single-molecule studies reveal complex behaviors not captured by traditional models.
• Understanding stochasticity is crucial for a complete picture of enzyme function.

Purpose of the Study:

• To develop a stochastic model for single-molecule enzymatic reactions following Michaelis-Menten kinetics.
• To investigate the conditions under which oscillatory behavior emerges in non-equilibrium steady-state.
• To explore the role of enzyme conformation and substrate fluctuations in reaction dynamics.

Main Methods:

• Stochastic analysis incorporating enzyme dynamics and substrate turnover.
• Mathematical modeling of non-equilibrium steady-state conditions.
• Analysis of substrate survival probability and enzyme conformation time-correlations.

Main Results:

• The stochastic model predicts oscillatory behavior at appropriate substrate concentrations.
• Deterministic Michaelis-Menten kinetics emerge as a limit at high substrate concentrations.
• Fluctuations in enzyme conformation and substrate concentration contribute to complex kinetics.

Conclusions:

• Stochastic models are essential for accurately describing single-molecule enzyme kinetics.
• Oscillatory behavior in non-equilibrium steady-state is a key finding.
• Both enzyme and substrate stochasticity drive complex enzymatic reaction dynamics.