Question

Problem 3. Enzyme kinetics and

Human milk is Nature’s first and probably best functional food. The third most abundant component of mother’ milk comprises more than 100 sugar oligomers collectively referred to as human milk oligosaccharides (HMO) that select for beneficial bacteria and jump-start the gut microbiota of the infant. HMOs are assembled by adding β-(1→3)-linked repeating units of the disaccharide LNB (lacto-N-biose: Galactose-β-(1→3)-N-acetyl Glucosamine) to a lactose (Galactose-β-(1→4)-Glucose) at the reducing end. This motif can be fucosylated. e.g. the Lacto-N-difucohexaose I (LNDFI) shown below. A research group has recently discovered a new enzyme that is able to degrade LNDFI to lactose and to the Lewis b tetraose as shown below:

Lacto-N-difucohexaose (LNDFI) Lewis b tetraose Lactose Enzyme F - + Galactose (Gal) Fucose (Fuc) 5 3 2 Glucose (Glc) IN-acetyl glucosamine (GlcNAc) Figure 1. The hydrolysis of Lacto-N-difucohexagse I to LNB and lactose by the enzyme F. The key shows the monosaccharide composition and the linkages between the monosaccharides (e.g. 4 means that there is a 1-4 glycosidic linkage and all linkages are in the D-B configuration, except for fucosyl that is linked via a-L- linkages. The glycosidis bond that is cleaved is the D-B-(1.3)-bond between the GlcNAc and the Gal.

The kinetics of hydrolysis of this enzyme towards LNDFI were analysed by a coupled assay measuring the concentration of the lactose product. The initial rates are reported in Table 1.

D) Determine k_cat if [Enzyme F] = 20 nM

Answer 1

kcat is the called turnover number of the enzymatic reaction. It gives the number of molecules of substrate turned over into product per second.

The Michaelis-Menten equation will be used here to calculate Kcat. This equation is given by-

kcat = Vmax / [ET]

where Vmax = Maximum velocity

[ET] = Total enzyme concentration = 20 nM = 20 x 10-9  M  

Now, to calculate Vmax draw grapf between 1/ [LNDFI] and 1 / Vo . The graph is shown below-

Yuss 405 4.0 Wo 35 (slum 3.0 2-5 tost too 0.5 - 2 3 4 5 6 7 8 9 VENDE?] (mm)

Intercept on 1/Vo axis will give the value of 1 / Vmax

Intercept of graph on 1 / Vo axis = 0.65 = 1 / Vmax

Hence, Vmax = 1 / 0.65 = 1.538 uM/s = 1.538 x 10-6 M/s

Now. kcat = Vmax / [ET] = 1.538 x 10-6 / 20 x 10-9 = 0.0769 x 103 = 76.9 s-1