1/Km
Summary
1/Km is the reciprocal of the Michaelis constant, the substrate concentration giving half of Vmax. A larger 1/Km usually signals higher apparent substrate affinity, though this is approximate. On a Lineweaver-Burk plot, the x-intercept is −1/Km.
Detail
Meaning: Km is the substrate concentration at which the reaction runs at half of Vmax, and 1/Km is its reciprocal. A large 1/Km usually means high apparent affinity for substrate, since little substrate is needed to reach half Vmax. This is approximate: Km equals the ES dissociation constant only when catalysis is much slower than substrate release. On a Lineweaver-Burk plot the line crosses the x-axis at −1/Km.
Equation: 1/v = (Km/Vmax)(1/[S]) + 1/Vmax, where v is initial rate (mol/(L·s)), [S] is substrate concentration (mol/L), Km is the Michaelis constant (mol/L) and Vmax is the maximum rate (mol/(L·s)). Setting 1/v = 0 gives 1/[S] = −1/Km (L/mol).
On the MCAT: Passages show double-reciprocal lines with and without an inhibitor. A competitive inhibitor raises apparent Km, so the x-intercept moves toward zero while the y-intercept (1/Vmax) stays fixed. A pure noncompetitive inhibitor keeps the x-intercept and raises the y-intercept. Uncompetitive inhibition gives parallel lines.
Common confusion: The x-intercept is −1/Km, not Km, so the sign and the reciprocal both matter. An intercept farther from zero means a smaller Km and tighter apparent binding.
Sources
- Lehninger Principles of Biochemistry
- Biochemistry (Berg, Tymoczko, Gatto, Stryer)
- Biochemistry (Voet and Voet)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.