Michaelis–Menten kinetics

The dependence of an initial rate of reaction upon the concentration of a substrate S that is present in large excess over the concentration of an enzyme or other catalyst (or reagent) E with the appearance of saturation behaviour following the Michaelis-Menten equation: \[\nu=\frac{V\ \left[\text{S}\right]}{K_{\text{m}}+\left[\text{S}\right]}\] where v is the observed initial rate, V is its limiting value at substrate saturation (i.e. S ≫ K m), and Km the substrate concentration when v = V 2. The definition is experimental, i.e. it applies to any reaction that follows an equation of this general form. The symbols V max or v max are sometimes used for V. The parameters V and Km (the 'Michaelis constant') of the equation can be evaluated from the slope and intercept of a linear plot of v-1 vs. [S]-1 (a 'Lineweaver–Burk plot') or from slope and intercept of a linear plot of v vs. v/[S] ('Eadie–Hofstee plot'). A Michaelis–Menten equation is also applicable to the condition where E is present in large excess, in which case the concentration E appears in the equation instead of S. The term has sometimes been used to describe reactions that proceed according to the scheme: \[\text{E}+\text{S}\overset{k_{1}}{\underset{k_{-1}}\rightleftarrows }\text{ES}\overset{k_{\text{cat}}}{\rightarrow }\text{Products}\] in which case Km = (k-1 + kcat)/k1 (Briggs–Haldane conditions). It has more usually been applied only to the special case in which k-1 ≫ k cat and Km = k-1/k1 = Ks; in this case Km is a true dissociation constant (Michaelis–Menten conditions).
See also: rate-determining step
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1140 (https://doi.org/10.1351/pac199466051077)
PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 172 (https://doi.org/10.1351/pac199668010149)