The dependence of an initial @[email protected] upon the concentration of a @[email protected] S that is present in large excess over the concentration of an enzyme or other @[email protected] (or @[email protected]) E with the appearance of @[email protected] behaviour following the Michaelis-Menten equation: \[\nu=\frac{V\ \left[\text{S}\right]}{K_{\text{m}}+\left[\text{S}\right]}\] where \(\nu\) is the observed initial rate, \(V\) is its limiting value at substrate @[email protected] (i.e. \(\left[\text{S}\right]\gg K_{\text{m}}\)), and \(K_{\text{m}}\) the substrate concentration when \(\nu = \frac{V}{2}\). The definition is experimental, i.e. it applies to any reaction that follows an equation of this general form. The symbols \(V_{\max }\) or \(\nu_{\max }\) are sometimes used for \(V\). The parameters \(V\) and \(K_{\text{m}}\) (the '@[email protected]') of the equation can be evaluated from the slope and intercept of a linear plot of \(\nu^{-1}\) vs. \(\left[\text{S}\right]^{-1}\) (a '@[email protected]') or from slope and intercept of a linear plot of \(\nu\) vs. \(\frac{\nu}{\left[\text{S}\right]}\) ('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 \(\left[\text{E}\right]\) appears in the equation instead of \(\left[\text{S}\right]\). 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 \(K_{\text{m}} = \frac{k_{-1}+k_{\text{cat}}}{k_{1}}\) (Briggs–Haldane conditions). It has more usually been applied only to the special case in which \(k_{-1}\gg k_{\text{cat}}\) and \(K_{\text{m}} = \frac{k_{-1}}{k_{1}}=K_{s}\); in this case \(K_{\text{m}}\) is a true @[email protected] 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 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 172 [Terms] [Paper]