5. Papain is a cysteine protease of the peptidase C1 family that consists of a s

Question

5. Papain is a cysteine protease of the peptidase C1 family that consists of a single polypeptide chain with three disulfide bridges and a sulfhydryl group necessary for activity of the enzyme. It is extracted from papaya fruits and used widely in cooking as a meat tenderizer. A biochemistry graduate student performed preliminary Michaelis-Menten kinetics to measure the activity of the enzyme. During his experiment he varied the concentration of substrate and held the concentration of enzyme constant at 1.6x 107 M. Here is a plot of his data:

Explanation / Answer

a) calculate the slope first, by considering any 2 random points on the graph
[1/substrate, 1/vo]1 --------------> (12.5,10) (x1,y1)
[1/substrate, 1/vo]2 --------------> (21, 15) (x2,y2)
  slope = [y2 - y1 ] / [x2 - x1]  = [15-10] / [21-12.5] = 0.588235
from the graph 1/Vmax = 5 (mM min-1)-1
slope = Km / Vmax  
0.588235 = Km *  5 (mM min-1)-1
Km = 0.117647 mM min-1

b) 1 /Vmax = 5 (mM min-1)-1 [S] >>Km
Vmax = 0.2 mM min-1

c) Vmax = Kcat*Eo ,
   where Eo is the initial enzyme concentration = 1.6*10-7M = 1.6*10-7*106 mM =0.16mM
we can use the above equation since, all enzyme is bound to substrate.
   0.2 mM min-1 = Kcat * 0.16mM
   Kcat = 1.25 min-1

d)    = [S]/([S] + Km)
   [S] = 2.15 *10-4 M = 2.15*10-4*106 mM = 215 mM
     Km = 0.117647 mM min-1
      = 215 / (215 + 0.117647) = 0.999453

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