Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors

Area of Science:

• Biochemistry
• Chemical Kinetics
• Theoretical Chemistry

Background:

• Michaelis-Menten kinetics is fundamental to enzyme kinetics and metabolic processes.
• Understanding enzymatic reactions with inhibitory mechanisms is crucial for biological systems.

Purpose of the Study:

• To perform a stochastic analysis of Michaelis-Menten kinetics incorporating inhibitory mechanisms.
• To explore the application of Fock space formalism to inhibited enzymatic reactions.
• To characterize reaction dynamics and product formation times under inhibition.

Main Methods:

• Stochastic analysis of Michaelis-Menten kinetics.
• Application of Fock space formalism to reformulate the master equation.
• Examination of reversible inhibitions and inhibitor-activator duality.
• Calculation of the first product formation time distribution.

Main Results:

• Identified stiffness behavior in all examined inhibition scenarios.
• Demonstrated the capture of inhibitor-activator duality in partial inhibition.
• Observed an emergent intermediate timescale in product formation time distribution.
• Showcased the utility of Fock space formalism for low-copy-number reactions.

Conclusions:

• The Fock space formalism provides a powerful framework for analyzing inhibited enzymatic reactions.
• Inhibitory mechanisms introduce complex dynamics, including dual roles for inhibitors and novel timescales.
• The study offers new perspectives on the behavior of biochemical reactions under inhibition.