Question

An enzyme that degrades pheromone is isolated from the sensory hairs of the silk moth, Antheraea polyphemus. The kinetics of the reaction are studied at pH 7.2 using a fixed enzyme concentration and temperatures of 10 C to 40 C. The following table lists results for reaction velocity as a function of substrate concentration. (a) Determine vmax and km at Pheromone Concentration the four reaction temperatures. (umol/L) Initial Reaction Velocity (umol/L.sec) T=10C T=20C T=30C T=40C (b) Determine the Arrhenius 3.00E 5.50E 5.00E 7.70E- parameters (E and A) for this 0.5 06 06 06 06 enzyme reaction. 4.20E 9.70E 8.90E 1.40E- 06 06 06 05 6.10E 1.10E 1.30E 1.80E- 1.5 06 05 05 05 7.10E 1.60E 1.50E 2.10E- 2.2 06 05 OS 05 1.10E 1.90E 2.00E 3.50E- 5.5 05 05 05 05 1.20E 2.20E 2.90E 3.90E- 11 05 05 05 05 1

Answer 1

solut to at Tloc the plot of 1/ 105 vs)[s) is given below

A B с E F G H M N 1 0.5 3.3 2 1 4 1 3 4 3 5.1 4.2 6.1 7.1 y = 1.290x +0.792 R2=0.970 3.5 1.5 2.2 5 D 2 1 1 0.666 0.454 0.181 0.181 0.09 0.09 1/[s] 3 6 5.5 11 1.96 2.38 1.63 1.4 0.9 1.02 0.8 1.052 1/v *1045 2.5 7 5.5 9.8 (1/v) 1045 2 11 12 11 1.5 8 9 10 (s) 11 9.5 v*10^-6 1 0.5 12 0 13 14 0 0.5 1 1.5 2 2.5 15 1/[s] 16 17 18 19

Now Linear weaver Burk equation is v- Vnew & (5] - Vman (1) The best line Eamation a y = 1.290 x to 792. +0.791(2) we have ploted yas (110) 15. So best live carnation of lv usls] becomes G-1.290 105x + 0.192 * 105 (3) Comparing Eq 1 and 3 = 0.792 & 105 Vmax or&max= 1.264 165 MMI'S- Km/umax = 1.2904 105 or, km = 1.290 105 126 105 - 1.6254 MM a) 1:20 c the plot of (1/) + 10 vs 1 / [5] is given below

2 y = 0.682x+0.409 R?=0.978 1.8 1.6 1 2 1.81 2 1 1.08 3 1 1.03 4 0.666 0.909 5 0.454 0.625 6 0.181 0.66 7 0.181 0.52 8 0,09 0.45 9 0.09 0.47 10 1/[s] 1/v* 1045 11 0.5 5.5 1 9.2 1 9.7 1.5 11 2.2 16 5.5 15 5.5 19 22 11 21 v*10^-6 1.4 1.2 (1/v) 1045 1 0.8 0.6 0.4 [s] 0.2 12 13 14 0 0 0.5 1 1.5 2 2.5 15 16 1/[s] 17 18 19

ase or km = 0.682 + 1+ 2.ug 105=1.66402 klas line weaver - Dunk Equation a 음 Vmax & [s] Vmax) The best lire Equation is y=o.brat o yog (4) have poled a ys (1/4" 105, so beat line equation of llurs 1/[s] becomes = 0.682 * 158 0.400* 105 (5) Comparing sa lands ㅗ Vanas a Vnar=2.44€ 10 MM, it'st Im/max = 0.182 * 105 20-4094105 (11) + 5 vs 71 [s] is given bele at T=30°c a the plot of

B D E G Н K M N 0 P 0.5 1 4.2 9.5 8.9 13 1 1.5 2.5 2.38 1.05 1.12 0.76 1.02 0.52 0.38 0.344 0.4 1/V*10^5 2.2 5.5 9.8 19 y = 0.982x+0.268 R2 -0.935 А 1 2 2 1 3 1 4 0.666 5 0.454 6 0.181 7 0.181 8 0.09 9 0.09 10 1/[s] 11 12 13 2 5.5 1.5 11 11 26 29 25 v 10^-6 1/* 1045 . [s] 1 0.5 14 0 15 0 0.5 1 1.5 2 2.5 1/[s] 16 17 18 19

V The best line equation de Now line wearer-Burk Equation it Vman & (s]+ Viman (1) Y= 0.982 * +0.26816) platted equat of iv rs ills] becomes 4-6.982 105x +0.268105(1) Comparing Earl and] -0.268* 105 ay have () * 10, so best line y as Vmax or Vmax = 105 3-73 Myrist km/&max= 0.982 * 105 or. Km= 0.982 105 * 3.75 105 3.66286 My at T=40c the plot of (1/) * 105 vsics] is given below

А С D E F G H - J K L M N B 1.29 1 2 0.5 7.7 1.4 2 1 0.833 1 12 16 3 1 1 1.2 4 18 0.625 0.555 0.476 0.263 y = 0.533x + 0.209 R2 = 0.972 0.666 0.454 0.181 5 1.5 2.2 5.5 1 21 6 38 30 0.8 5.5 (1/v) *1045 11 39 0.6 7 0.181 8 0.09 9 0.09 10 1/[s] 11 12 0.333 0.256 0.277 1/V*10^5 11 36 v 10^-6 0.4 [s] 0.2 0 13 0 0.5 1 1.5 2 2.5 14 15 1/[s] 16 17 18

V Now linear Burk Xamaton & Km Vman & [s] + Vmax ) The best line - equation in V=0.533 X+0.298) plotted tas (1/0) 105, so best line equation of '/v for us 11CS] becomes y=0.533 105x+0-209 * 105 (9) as we have Comparing Earl and] = 0.209+ 105 Vmax ormar = 4:784 105MM tist km Jumax = 0.533 105 km = 0.533 1654 4.734 105=25550 MM 6 Arrhenian equation is Ea 1 - 1 In ke kis rate constant R: 8 319] wher Ea is activation at 0.5 MM substance concertoaton Talde (2283x, rate (R) =3.0*106 maits Ta=266 -293K, rake (R2) = 5.5 106pm tist now rate of the reaction is proportonal to Rate Constant R (T2 energy, RI So, or in (3.000 155 156 then in Ri (293 8.314 (-lab olin (315.5) Ea ㅗ 8-314 283 = Fd (-1.205 109 8.314 Ed (-1)054169 or Ea=8.3144 0.606 (1.205 104 or -0.606