Map Lehninger Principles of Biochemistry Nelson Cox MHE/Freeman by Sapling Leari

Question

Map Lehninger Principles of Biochemistry Nelson Cox MHE/Freeman by Sapling Learing For her undergraduate project, Jessica studied an enzyme that catalyzes the reaction A For substrate A, she determined that Km 3.0 M and kcat 20 min1. Jessica graduated and her project has been passed on to you. Unfortunately, Jessica was so busy that she sometimes forgot to record all of the details of an assay in her lab notebook. Your mentor suggests that you try to back calculate some of the missing concentration values. Assume that the enzyme follows Michaelis-Menten kinetics. In one experiment where A-4 mM, she found that the initial velocity, Vo was 324 nM min 1 in another experiment with [EJ = 0.4 ? . she found that Vo 6 HM min-1 What was the [A] she used in this experiment? b a What was the [Et] she used in this experiment? Number Number nM A 2.4 The compound Z was found to be a very strong competitive inhibitor of the enzyme, with an ? of 10 In an experiment with the same [El as in part (a), but Menten curve at low [Sj, the second order rate a different [A], an amount of Z is added that reduces the rate Vo to 162 nM min What was the [A] in this experiment? A measure of the catalytic efficiency of an enzyme is the initial slope of the Michaelis- constant kcat/Km. A "perfect" enzyme, limited only by diffusion, would have a value of 108 or 109 Ms-1 Calculate kcaKm for this enzyme Number Number A-3.0 1.667x 101 M-'s

Explanation / Answer

Enzyme activuty is measured using michellis mentan equation. Michellis mentan equation is

V = Vmax S/Km +S

V = intial velocity

Vmax = maximum velocity

Km = michellis mentan constant explain affinity of substrate toward enzyme

S= substrate concentration

Kcat is defined as maximum number of substrate molecule converted into product per unit tine by a single molecule of enzyme when it is in fully saturated state.

Kcat = Vmax/Et

Et = total enzyme cobcentration

a) in question 1 , we have to calculate total enzyme concentration. Given

V= 324 nm/ min

S = 4mM

Km = 3 uM

Kcat = 20 / min

We have to use michellis mentan equation to determine Vmax

V = Vmax S/ Km + S

Before putting values we have to unified all the units. Such as Km = 3 uM = 3*10^3 nM

S = 4mM = 4*10^6 nM

324 = Vmax 4*10^6/ 3*10^3 +4*10^6

Vmax = 324 x 4003000/4000000

Vmax = 324.24 nM / min

Et = 324/20 = 16.2 ~ 16 nM

So, here given answer is wrong the correct value of Et will be 16nM not 10.8

b) same equation used in question b, here we have to calculation concentration of substrate.

Vo = 6uM/min. Et = 0.4uM

6 = 20x 0.4 x S/ 3 +S

18 + 6S = 8S

2S = 18

S= 9 uM

c) in this question ans is correct . For competitive inhibition , michellis mentan equation will be

Vo = Vmax S/ Km a + S

a = alpha competitive inhibition value

Vo = 162nM/ min

a= 10 , Km = 3 uM , Et = 16 nM

162 = 20 x 16 x S/ 3*10^3*10 + S

486 x 10^4 + 162S = 320S

486*10^4 = 158 S

S = 3.07* 10^4 nM

S = ~ 3 uM

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