Michaelis-Menten kinetics at high enzyme concentrations

Area of Science:

• Biochemistry
• Mathematical Biology
• Enzyme Kinetics

Background:

• The Michaelis-Menten model is fundamental in enzyme kinetics.
• Quasi-steady state approximations (QSSA) simplify complex reaction dynamics.
• Previous derivations of the total QSSA (tQSSA) had limitations in validity.

Purpose of the Study:

• To consistently derive the total quasi-steady state approximation (tQSSA) for the irreversible Michaelis-Menten scheme.
• To clarify the conditions for the uniform validity of the tQSSA and its linearized form.
• To extend the known domain of validity for the tQSSA.

Main Methods:

• Consistent mathematical derivation of the tQSSA.
• Analysis of initial transient self-consistency.
• Correction of criteria for linearized tQSSA validity.
• Derivation of uniformly valid approximate solutions.

Main Results:

• Self-consistency of the initial transient ensures uniform tQSSA validity.
• The tQSSA is broadly valid across a wide range of substrate and enzyme concentrations.
• The parameter domain for tQSSA validity overlaps with and extends beyond the standard QSSA.
• Corrected criteria and new approximations offer uniform validity in time.

Conclusions:

• The tQSSA provides a robust approximation for enzyme kinetics under diverse conditions.
• This work refines the understanding and application of tQSSA, enhancing its utility.
• The derived approximations offer improved accuracy and broader applicability in biochemical modeling.