Enzyme kinetics explorer (Michaelis–Menten)

The Michaelis constant Km is the substrate concentration at which the reaction runs at exactly half of Vmax. It is a rough measure of affinity: a low Km means the enzyme reaches half speed with very little substrate. Hexokinase has a Km of about 0.05 mM for glucose, so at the 5 mM glucose found in blood it runs at over 99% of Vmax; with Vmax = 100 µmol/min and Km = 2 mM, setting [S] = 2 mM gives exactly 50 µmol/min.

V = Vmax [S] / (Km + [S]) gives the initial reaction rate at a substrate concentration [S]. At low [S] the rate rises almost in proportion to substrate; at high [S] the active sites are saturated and the rate levels off at Vmax. At [S] = 10 × Km the enzyme runs at 10/11 of Vmax, about 91%, and reaching 90% of Vmax needs [S] = 9 × Km, which is 18 mM when Km = 2 mM.

A competitive inhibitor binds the active site, so it raises the apparent Km to Km(1 + [I]/Ki) but leaves Vmax unchanged: enough substrate can outcompete it. A noncompetitive inhibitor binds elsewhere and disables the enzyme whether or not substrate is bound, so it lowers the apparent Vmax to Vmax/(1 + [I]/Ki) and leaves Km unchanged. With [I] = Ki and [S] = Km, the competitive case doubles Km to 4 mM and drops the rate from 50 to 33.3 µmol/min, while the noncompetitive case halves Vmax and drops it to 25.