Km is defined as substrate concentration at what fraction of Vmax?

Km is defined as substrate concentration at what fraction of Vmax?

• A. 1/2 Vmax
• B. 1/3 Vmax
• C. 2 Vmax
• D. Vmax

Answer: (A)

Km is the substrate concentration at which the reaction rate is half of Vmax. In Michaelis-Menten kinetics, v = (Vmax [S])/(Km + [S]). If you set [S] = Km, the equation becomes v = (Vmax Km)/(Km + Km) = Vmax/2, so the rate is exactly half of its maximum. This is why Km is described as the substrate concentration needed to reach half of Vmax and also why a smaller Km indicates higher enzyme affinity for the substrate. The other fractions presented don’t correspond to a substrate concentration that yields half of Vmax: achieving Vmax requires saturating the enzyme with substrate (in practice, [S] becomes very large, approaching, but never exactly reaching, Vmax), and a fraction like 1/3 Vmax would occur at a different [S] value than Km.

Km is the substrate concentration at which the reaction rate is half of Vmax. In Michaelis-Menten kinetics, v = (Vmax [S])/(Km + [S]). If you set [S] = Km, the equation becomes v = (Vmax Km)/(Km + Km) = Vmax/2, so the rate is exactly half of its maximum. This is why Km is described as the substrate concentration needed to reach half of Vmax and also why a smaller Km indicates higher enzyme affinity for the substrate. The other fractions presented don’t correspond to a substrate concentration that yields half of Vmax: achieving Vmax requires saturating the enzyme with substrate (in practice, [S] becomes very large, approaching, but never exactly reaching, Vmax), and a fraction like 1/3 Vmax would occur at a different [S] value than Km.