Question

Beta-galactosidase follows Michaelis-Menten kinetics. A 5 micromolar solution of beta-galactosidase catalyzes the formation of 0.8 mmoles ortho-nitrophenol s-1 when saturated with the substrate ortho-nitrophenyl-beta-galactoside. What is beta-galactosidase's kcat?

Answer 1

Answer : The beta-galactosidase's $K_{cat}$ is, $160s^{-1}$

Explanation :

Michaelis-Menten formula used :

$V_o=\frac{V_{max}}{K_{cat}}$

where,

$V_o$ = initial concentration = $5\mu mol=5\times 10^{-6}mol$

$V_{max}$ = maximum concentration = $0.8mmol.s^{-1}=0.8\times 10^{-3}mol.s^{-1}$

$K_{cat}$ = Michaelis-Menten constant = ?

Now put all the given values in the above formula, we get:

$5\times 10^{-6}mol=\frac{0.8\times 10^{-3}mol.s^{-1}}{K_{cat}}$

$K_{cat}=160s^{-1}$

Therefore, the beta-galactosidase's $K_{cat}$ is, $160s^{-1}$