In Michaelis-Menten kinetics, Km equals (k-1 + k2)/k1. Which statement correctly reflects Km?

• A. Km = (k-1 + k2)/k1
• B. Km = k1/(k-1 + k2)
• C. Km = k2/k1
• D. Km = (k1 + k-1)/k2

Answer: (A)

Km is the substrate concentration at which the reaction rate is half of Vmax, for the classic enzyme mechanism E + S ⇌ ES → E + P. Applying the steady-state condition for the ES complex and solving for [ES] leads to the Michaelis form v = (Vmax[S])/(Km + [S]) with Vmax = k2[E]total and Km = (k-1 + k2)/k1. This shows why the expression Km = (k-1 + k2)/k1 is the correct reflection of Km. Intuitively, Km grows when ES tends to dissociate back to E and S (larger k-1) or when the conversion to product is slow (smaller k2), and it shrinks when association is very fast (larger k1). In limiting cases, if k2 ≪ k-1, Km ≈ k-1/k1; if k2 ≫ k-1, Km ≈ k2/k1.