Since the substrate concentration at Vmax cannot be measured exactly, enzymes can be characterized by the substrate concentration at which the rate of reaction is half its maximum.
This substrate concentration is called the Michaelis-Menten constant (KM) (also called Michaelis constant). This represents (for enzyme reactions exhibiting simple Michaelis-Menten kinetics) the dissociation constant of the enzyme-substrate (ES) complex. Low values indicate that the ES complex is held together very tightly and rarely dissociates without the substrate first reacting to form product.
Many enzymes obey Michaelis-Menten kinetics.
The derivation of Michaelis-Menten equation follows:
k1 -----> k2 E + S ES -----> E + P <----- k-1
E0 is the total or starting amount of enzyme. It is not practical to measure the amount of the enzyme substrate complex during the reaction, so the reaction must be written in terms of the total (starting) amount of enzyme, a known quantity.
The rate of production of the product (d[P]/dt) is often called 'V0', or 'reaction velocity'. Note that the term 'reaction velocity' is misleading and 'reaction rate' is prefered. The term 'k2[E0]' is often written as 'Vmax', the 'maximum velocity' or 'maximum rate'. Notice that if [S] is large compared to Km, [S]/(Km + [S]) approaches 1. Therefore, the rate of product formation is equal to k2[E0] in this case.
When [S] equals Km, [S]/(Km + [S]) equals 0.5. In this case, the rate of product formation is half of the maximum rate (1/2 Vmax). By plotting V0 against [S], one can easily determine Vmax and Km. Note that this requires a series of experiments at constant E0 and different substrate concentration [S].