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:

$v = V S K m + S$ ,

where $v$ is the observed initial rate, $V$ is its limiting value at substrate saturation (i.e. $S ≫ K m$ ), and $K m$ 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 $K m$ (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:

$E + S ⇄ k −1 k 1 ES → k cat Products$

in which case $K m = k −1 + k cat k 1$ (Briggs–Haldane conditions). It has more usually been applied only to the special case in which $k −1 ≫ k cat$ and $K m = k −1 k 1 = K s$ ; in this case $K m$ is a true dissociation constant (Michaelis–Menten conditions).