Integrated rate equations for enzyme-catalysed first-order and second-order reactions

Area of Science:

• Chemical Kinetics and Reaction Mechanisms
• Mathematical Modeling in Chemistry

Background:

• Understanding initial-rate kinetics is crucial for elucidating reaction pathways.
• Existing models may not comprehensively cover all relevant stoichiometric scenarios.

Purpose of the Study:

• To integrate generalized rate equations for hyperbolic initial-rate kinetics.
• To cover multiple reaction stoichiometries including equilibrium reactions.
• To provide regular and economical solutions for complex kinetic analyses.

Main Methods:

• Integration of generalized rate equations.
• Consideration of four key reaction stoichiometries: A <=> P, A <=> P + Q, A + B <=> P, and A + B <=> P + Q.
• Focus on hyperbolic initial-rate kinetics.

Main Results:

• Successful integration of generalized rate equations for the specified mechanisms.
• Demonstration of regular solutions for hyperbolic initial-rate kinetics.
• The derived solutions are computationally economical.

Conclusions:

• The integrated generalized rate equations offer a unified approach to analyzing hyperbolic initial-rate kinetics.
• The method provides efficient and reliable solutions across various common reaction stoichiometries.
• This work simplifies the kinetic analysis of complex chemical systems.