Question

An enzyme was found that catalyzes the reaction between students, S and academic success, P (for pass); the enzyme was called studyase.

An enzyme assay was run on studyase. 10μg of studyase (molecular weight 20,000D) was placed in a set of test tubes each of which contained 1mL of the substrate student at varying concentrations and the amount of product, academic success (P) was determined.

The following results were determined:

S, (mM)	Velocity, V (μmole/mL/sec)
1	12
2	20
4	29
8	35
12	40

Note 1mM = 1millimole/L = 1μmol/mL

Plot a Lineweaver-Burk plot of 1/V versus 1/S

Determine Vmax and Km for the enzyme studyase.

Calculate Kcat and the catalytic constant (kcat/km) for the enzyme. (find [E]_T as total μmoles/mL)

Another enzyme called partyase was analyzed and when 0.010 μmoles of this enzyme was assayed it was found to have a Vmax of about 50 μmol/mL/sec and a Km of 5 mM. Calculate Kcat and the catalytic constant for this enzyme.

i.Compare the 2 enzymes on the basis of affinity for the binding site and kinetic efficiency.

Answer 1

(a): Lineweaver - Burk plot:

(b): For the above graph,

1/Vmax = Y-intercept = 0.019

=> Vmax = 1/0.019 = 52.6 mM/s or micromol/mL/s (answer)

Km / Vmax = slope = 0.063 s

=> Km = 0.063 s x Vmax = 0.063 s x 52.6 mM/s = 3.314 mM (answer)

(c): Given mass of the enzyme studyase = 10 g

Molecular mass of studyase enzyme = 20000 g

moles of enzyme = mass / molar mass =  10 g / 20000 g/mol = 5x10^-4mol

volume of the solution = 1mL

Hence concentration of the enzyme, [E]t = 5x10^-4mol / 1mL = 5x10^-4mol/mL or 5x10^-4 mmol/L or  5x10^-4 mM

Kcat = Vmax / [E]t = 52.6 mM/s / 5x10^-4 mM = 105200 s-1 (answer)

Catalytic constant = Kcat / Km = 105200 s-1 / 3.314 mM = 31744 mM-1s-1 (answer)

(d): Concentration of partyase, [E]t = 0.010 ?moles/ 1mL = 0.010 ?M

Km = 5 mM

Vmax = 50 ?mol/mL/sec =  50 mM/s

Kcat = Vmax / [E]t = 50 mM/s / 5x10^-4 mM = 100000 s-1 (answer)

Catalytic constant = Kcat / Km = 100000 s-1 / 5 mM = 20000 mM-1s-1 (answer)

(e) Higher is the turn over number higher is the kinetic efficiency. Hence studyase has higher kinetic efficiency.