Enzyme kinetics: In pure noncompetitive inhibition of an enzyme-catalyzed reaction, what is the characteristic effect on the Michaelis constant (Km) and the maximum velocity (Vmax)?

Introduction:
Noncompetitive inhibition is a classic enzyme-kinetics concept tested to check understanding of how inhibitors alter apparent kinetic parameters. The focus is on distinguishing pure noncompetitive inhibition from competitive and uncompetitive mechanisms by evaluating what happens to the Michaelis constant (Km) and the maximum velocity (Vmax).

Given Data / Assumptions:

• Mechanism considered: pure noncompetitive inhibition (inhibitor binds equally well to E and ES at a site distinct from the active site).
• Steady-state Michaelis–Menten framework applies.
• Definitions: Km reflects substrate affinity; Vmax reflects catalytic capacity at enzyme saturation.

Concept / Approach:
In pure noncompetitive inhibition, the inhibitor does not change substrate binding equilibrium (so Km stays the same), but it removes a fraction of catalytically competent enzyme from acting, lowering the achievable maximal rate. Therefore, Vmax decreases while Km remains unchanged. Contrast this with competitive inhibition (Km increases, Vmax unchanged) and uncompetitive inhibition (Km decreases and Vmax decreases).

Step-by-Step Solution:
Start from v = (Vmax * [S]) / (Km + [S]).Introduce an inhibitor I that binds at an allosteric site to both E and ES with identical affinity (pure noncompetitive).The effective active enzyme concentration is reduced by factor 1/alpha where alpha = 1 + [I]/Ki.Thus the apparent maximal rate becomes Vmax,app = Vmax / alpha (so Vmax decreases as [I] increases).Because the relative binding of S to E is unaffected in the pure case, Km,app = Km (no change in substrate affinity).

Verification / Alternative check:
On a Lineweaver–Burk plot (1/v versus 1/[S]), noncompetitive inhibition shows lines with the same x-intercept (−1/Km) but higher y-intercepts (1/Vmax increases), confirming decreased Vmax with unchanged Km.

Why Other Options Are Wrong:
Increases Km and increases Vmax: inconsistent with any standard inhibition model; Vmax does not increase in inhibition.
Increases Km with no change in Vmax: describes competitive inhibition, not noncompetitive.
Decreases Km and decreases Vmax: describes uncompetitive inhibition, not noncompetitive.
Increases Vmax with no change in Km: inhibition does not increase Vmax.

Common Pitfalls:

• Confusing pure noncompetitive with mixed inhibition (where Km can change).
• Assuming any change in rate must alter Km; in noncompetitive, affinity is unaffected.
• Relying solely on qualitative graphs without remembering intercept relationships.

Final Answer:
Decreases Vmax with no change in Km