Michaelis-Menten

Meaning: The model describes enzymes following E + S ⇌ ES → E + P, using the initial rate before product builds up. At low [S] the rate rises nearly linearly with [S]; at high [S] the enzyme is saturated and the rate levels off at Vmax, giving a hyperbola. Km is the [S] at which v = ½Vmax; a lower Km often means tighter substrate binding.

Equation: v = Vmax[S] / (Km + [S]), where v is the initial rate (M/s), Vmax is the maximum rate (M/s), [S] is substrate concentration (M), and Km is the Michaelis constant (M). Also Vmax = kcat[E]total, with kcat in s⁻¹ and [E]total in M.

On the MCAT: Expect a rate versus [S] graph or a Lineweaver-Burk plot of 1/v versus 1/[S], where the y-intercept is 1/Vmax and the x-intercept is −1/Km. Inhibitors are identified by their effect: a competitive inhibitor raises apparent Km with Vmax unchanged, a pure noncompetitive inhibitor lowers Vmax with Km unchanged, and an uncompetitive inhibitor lowers both.

Common confusion: Km is a concentration, not a rate, and Vmax is only approached asymptotically as substrate increases. Adding more enzyme raises Vmax but leaves Km unchanged. Allosteric, cooperative enzymes give sigmoidal curves and do not fit this hyperbola.