Determining the Degree of Cooperativity in Enzymes: Which graphical method is appropriate?

Introduction:
Cooperativity describes how binding of one ligand molecule affects affinity for additional molecules, typical in multimeric proteins. This question asks for the plot used to quantify cooperativity.

Given Data / Assumptions:

• Multisubunit enzyme or protein exhibiting sigmoidal kinetics.
• Hill formalism applies for estimating the Hill coefficient nH.

Concept / Approach:

The Hill plot linearizes cooperative binding data by plotting log[θ/(1−θ)] versus log[S] (or log[L]), where θ is fractional saturation. The slope gives the Hill coefficient nH, indicating positive cooperativity (nH > 1), non-cooperative behavior (nH ≈ 1), or negative cooperativity (nH < 1).

Step-by-Step Solution:

Verification / Alternative check:

Non-linear regression with the Hill equation v = Vmax * S^nH / (K0.5^nH + S^nH) provides nH directly and serves as a numerical cross-check.

Why Other Options Are Wrong:

B: Koshland’s model explains mechanism but the suggested curve alone does not yield a simple numeric nH. C: Michaelis–Menten hyperbola applies to non-cooperative enzymes. D: Graphical determination is possible. E: Eadie–Hofstee is for MM kinetics, not specifically for cooperativity degree.

Common Pitfalls:

Over-interpreting nH as the exact number of binding sites; it is an empirical index of cooperativity strength.

Final Answer:

Hill plot