Catalytic Efficiency and the Specificity of Enzyme Reactions: kcat/KM
The catalytic constant of an enzyme is defined as:
kcat = Vmax/[ET]
In the case of the simple example discussed above, kcat = k2.
(The units of kcat are time-1; typically, sec-1. Thus, if kcat = 1000 sec-1, the enzyme can convert 1000 molecules of substrate into product each second at saturating [S].)
Treating the enzyme catalyzed reaction as a simple second order reaction:
v = k[E][S]
Compare this equation to the Michaelis-Menten equation above. At very low substrate concentrations (ET =[E]), the Michaelis-Menten equation becomes:
v = k2 [ET][S]
= (kcat/KM)[E][S]
kcat/KM is the second order rate constant for this reaction. It represents the selectivity of the enzyme at limiting substrate concentrations. Selectivity can also be expressed as the ratio, Vmax/KM for a series of measurements where [ET] is constant.
Using the definitions of KM:
kcat/KM = k1k2/( k-1 + k2)
If the chemical reaction is rate-limiting (k-1>>k2) then: kcat/KM = k1k2/k-1 , and the observed reaction rate depends both on how well the substrate binds as well as the rate of catalysis.
If the chemical reaction is not rate-limiting (k-1<<k2) then: kcat/KM = k1 and the rate is only limited by how fast the substrate can diffuse into the active site.
