Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation

Area of Science:

• Biochemistry
• Chemical Kinetics
• Mathematical Biology

Background:

• The Michaelis-Menten mechanism is fundamental in enzyme kinetics.
• Model reduction techniques, like the quasi-steady-state approximation (QSSA), simplify complex biochemical systems.
• Determining the precise conditions for QSSA validity is crucial for accurate biochemical modeling.

Purpose of the Study:

• To investigate the validity and accuracy of the standard quasi-steady-state approximation (sQSSA) in biochemical reactions.
• To compare the sQSSA with other quasi-steady-state reductions.
• To identify reliable biochemical conditions for ensuring the accuracy of the sQSSA.

Main Methods:

• Analysis of ordinary differential equations (ODEs).
• Singular perturbation theory.
• Comparison of different quasi-steady-state reduction methods.

Main Results:

• The ratio of initial enzyme concentration to Michaelis constant (e0/KM) indicates asymptotic accuracy but not overall validity.
• The standard QSSA's predominance depends on a small ratio of initial enzyme concentration to the Van Slyke-Cullen constant (e0/K).
• e0/K provides a more accurate measure of sQSSA validity than e0/KM.

Conclusions:

• The ratio e0/K is the most accurate metric for assessing the validity of the standard quasi-steady-state approximation.
• Understanding these ratios is key for reliable biochemical model reduction.
• This research refines the criteria for applying QSSA in enzyme kinetics.