Question

The study of an enzymatic action on a substrate (1-carboxy-1- glutamyl tyrosine) led to the value of Michaelis constant KM = 1.73x10–3 mol dm–3. In one experiment, in which 8.8x10–8 mol of the enzyme was added to 20 cm3 of solution containing 1.24x10–4 mol of substrate, it was found that a substrate conversion of 50 % was reached after 1.2 min. Calculate the turnover number and the catalytic efficiency of the enzyme.

Answer 1

K_M = 1.73*10^-3 moldm^-3

K_M is the substrate concentration at half of V_max^. Which was reached at 1.2 min.

20 cm^-3 = 20*10^-3 m^-3

Initial substrate concentration = 1.24*10^-4 /20*10^-3 = 6.2*10^-3

Hence,

Hence , V_max /2 = (6.2-10^-3 -1.73*10^-3) /1.2*60 = 0.062*10^-3 mol dm^-3s^-1 . 6.62*10^-4  moldms^-3s^-1

Or, V_max = 12.4*10^-5 moldm^-3s^-1

Again, V_max = K_cat [ E⁰] = K_cat* 8.8*10^-8/ 20*10^-3

Or, K_cat = 12.4*10^-5*20*10^-3/8.8*10^-8 = 28.18 s^-1

K _cat is called turnover number.

Catalytic efficiency = K_cat/ K_M = 28.18/1.73*10^-3

= 16290 .06 mol dm^-3s^-1 .