Allosteric enzymes like ATCase (aspartate transcarbamoylase) show sigmoidal (S-shaped) velocity-substrate curves rather than hyperbolic Michaelis-Menten kinetics. Which parameter, used in place of Km for allosteric enzymes, indicates the substrate concentration at which velocity is half-maximal?

• A Km is still valid for allosteric enzymes but is measured at a single fixed regulatory ligand concentration
• B Vmax/2 — this is the only valid measure of saturation for sigmoidal enzymes
• C Hill coefficient (n) — this replaces Km in all allosteric enzyme calculations
• D [S]0.5 (or K0.5) — since Michaelis-Menten kinetics do not apply and Km is undefined for cooperative enzymes ✓

Explanation

Allosteric (cooperative) enzymes violate Michaelis-Menten assumptions (a single substrate binding site with constant Km). Their sigmoidal v vs. [S] curves arise from positive cooperativity — binding of one substrate molecule increases affinity at other sites. For these enzymes, [S]0.5 or K0.5 is used for the substrate concentration at half-Vmax. The Hill coefficient (nH) quantifies the degree of cooperativity: nH=1 is non-cooperative (Michaelis-Menten), nH>1 is positive cooperativity, nH<1 is negative cooperativity. Hemoglobin has nH~2.8 for O2 binding, reflecting strong positive cooperativity.

Reference: Harper's Illustrated Biochemistry, 32nd ed.

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