Phase-plane geometries in coupled enzyme assays

Area of Science:

• Biochemistry
• Chemical Kinetics
• Dynamical Systems Theory

Background:

• Enzyme activity determination often involves coupled indicator reactions.
• Traditional kinetic analysis relies on quasi-steady-state and reactant stationary state assumptions.
• Singular perturbation analysis simplifies complex enzyme reaction kinetics.

Purpose of the Study:

• To investigate the dynamical behavior of coupled enzyme-catalyzed reaction mechanisms.
• To analyze slow/fast dynamics using phase-plane analysis.
• To explore Sisyphus and Laelaps manifolds in enzyme kinetics.

Main Methods:

• Phase-plane analysis of coupled enzyme reactions.
• Identification and analysis of time-dependent slow manifolds (Sisyphus and Laelaps).
• Projection onto slow manifolds to derive reduced models.

Main Results:

• Characterization of Sisyphus and Laelaps manifolds in enzyme coupled reactions.
• Derivation of reduced models through projection onto slow manifolds.
• Geometric interpretation of slow/fast dynamics in reaction phase-planes.

Conclusions:

• Phase-plane analysis provides a powerful geometric approach to understanding coupled enzyme kinetics.
• The identified slow manifolds offer new perspectives on simplifying complex reaction dynamics.
• This work contributes to a deeper understanding of biochemical reaction mechanisms and their mathematical modeling.