Which equation correctly represents the Michaelis-Menten model for velocity v as a function of substrate concentration [S]?

Which equation correctly represents the Michaelis-Menten model for velocity v as a function of substrate concentration [S]?

• A. v = (Vmax × [S]) / (Km + [S])
• B. v = (Km × [S]) / (Vmax + [S])
• C. v = Vmax − Km/[S]
• D. v = Vmax × [S] / (Km − [S])

Answer: (A)

Michaelis-Menten kinetics describe how enzyme velocity depends on substrate concentration, showing a hyperbolic rise that saturates at a maximum rate when the substrate is abundant. The correct form, v = (Vmax × [S]) / (Km + [S]), captures that behavior: at very low [S], velocity increases roughly linearly with [S] (slope Vmax/Km); when [S] is much larger than Km, the velocity approaches Vmax, reflecting enzyme saturation. Km represents the substrate concentration at which the velocity is half of Vmax. The other expressions don’t fit this behavior. They don’t reproduce the same saturation at high [S], or they predict nonsensical limits at low [S] (or involve undefined values when [S] surpasses Km).

Michaelis-Menten kinetics describe how enzyme velocity depends on substrate concentration, showing a hyperbolic rise that saturates at a maximum rate when the substrate is abundant. The correct form, v = (Vmax × [S]) / (Km + [S]), captures that behavior: at very low [S], velocity increases roughly linearly with [S] (slope Vmax/Km); when [S] is much larger than Km, the velocity approaches Vmax, reflecting enzyme saturation. Km represents the substrate concentration at which the velocity is half of Vmax.

The other expressions don’t fit this behavior. They don’t reproduce the same saturation at high [S], or they predict nonsensical limits at low [S] (or involve undefined values when [S] surpasses Km).