Rate-limiting step: a quantitative definition. Application to steady-state enzymic reactions

Area of Science:

• Biochemistry and enzymology
• Chemical kinetics
• Enzyme kinetics

Background:

• The traditional definition of a rate-limiting step in enzyme kinetics has faced challenges due to inconsistencies observed in simulated isotopic experiments.
• Alterations to the conventionally identified rate-limiting step did not consistently impact the maximum velocity (Vmax) as predicted.
• This discrepancy questioned the generality and applicability of the existing concept of rate-limiting steps in enzymatic reactions.

Purpose of the Study:

• To propose a revised definition for the rate-limiting step that resolves inconsistencies with Vmax behavior in isotopic experiments.
• To retain the core concept of a rate-limiting step while ensuring its predictable impact on overall reaction velocity.
• To establish a framework for identifying the most sensitive step in linear reaction sequences.

Main Methods:

• Defined the rate-limiting step as the 'most sensitive' step in a steady-state linear reaction sequence, identified by its largest impact on overall velocity (v).
• Introduced the sensitivity function (SFj) and a normalized sensitivity index (SIj) to quantify the sensitivity of individual forward steps (kj).
• Described a procedure to approximate the sensitivity function using the Gibbs energy profile of the reaction.

Main Results:

• The 'most sensitive' step, determined by the sensitivity function and index, consistently predicts the effect of perturbations on overall velocity (v).
• An exact relationship was found between the sensitivity index of an isotopic step and the expressed fraction of the intrinsic isotopic effect.
• The Gibbs energy profile can be utilized to approximate sensitivity functions and identify the most sensitive step in a reaction sequence.

Conclusions:

• The proposed definition of the rate-limiting step as the 'most sensitive' step resolves previous inconsistencies in enzyme kinetics.
• This approach provides a robust method for identifying rate-limiting steps in both V and V/K systems using sensitivity analysis.
• The concept of a rate-limiting step should be based on sensitivity, not solely on minimal rate, for multistep enzymatic reactions.