Thermodynamic–kinetic link: The relationship connecting the equilibrium constant (Keq) with kinetic parameters (forward/reverse Vmax and Km values) is known as which equation?

Introduction:
Enzyme kinetics does not exist in isolation from thermodynamics. The Haldane relationship connects the equilibrium constant (Keq) of a reversible enzyme reaction to measurable kinetic constants, ensuring consistency between kinetic parameters and overall thermodynamic driving force.

Given Data / Assumptions:

• Reversible reaction S ⇌ P catalyzed by an enzyme.
• Kinetic parameters: Vmax,f, Vmax,r, Km,S, Km,P measured under initial-rate conditions.
• Equilibrium constant Keq is defined by standard thermodynamics.

Concept / Approach:
The Haldane equation links Keq to the ratio of kinetic constants. In simple forms (no complicating factors like multiple substrates or modifiers), Keq relates to (Vmax,f/Km,S)/(Vmax,r/Km,P), guaranteeing that kinetics does not violate thermodynamics.

Step-by-Step Solution:
Write a reversible Michaelis–Menten model for S ⇌ P.Express forward and reverse rates and their limiting Vmax values.Combine steady-state expressions to obtain Keq in terms of Vmax and Km parameters.Conclude that the thermodynamic Keq must equal the ratio implied by kinetic constants (Haldane relationship).

Verification / Alternative check:
Independent measurement of Keq (e.g., equilibrium composition) should match the value inferred from kinetic constants if the model and conditions are appropriate.

Why Other Options Are Wrong:
Michaelis–Menten equation: gives v as a function of [S], not the thermodynamic link.

Numerical solution approach: a method, not a named relationship.

Gibbs–Helmholtz equation: relates temperature dependence of free energy, not enzyme kinetic constants.

Common Pitfalls:

• Using irreversible fits to describe inherently reversible systems.
• Ignoring product inhibition which carries information about reverse parameters.

Final Answer:
Haldane equation