Efficiency of Enzyme Catalysis

1
Efficiency of Enzyme Catalysis

• For an example, in the reaction of decomposition
  of hydrogen peroxide, the activation energy Ea,o
  of the uncatalyzed reaction at 20oC is 18
  kcal/mol, whereas that for chemically catalyzed
  (Pt) and enzymatically catalyzed (catalase)
  decomposition are 13 kcal/mol (Ea,c) and 7
  kcal/mol (Ea, en), respectively.
• Compare the reaction rates at these three
  different conditions.

2
Efficiency of Enzyme Catalysis
2H2O2
2H2O O2

• The forward reaction rate r (moles/L-s),
• r kf(H2O2)
• k is the forward reaction rate constant, f(H2O2)
  is a function of substrate perioxide
  concentration.

3

• If k is represented by k0, kc, and ken ,
  respectively, for the uncatalyzed, chemically
  catalyzed (Pt) and enzymatically catalyzed
  reactions, the corresponding reaction rates (r0,
  rc, ren) can be expressed as follows
• r0 k0f(H2O2)
• rc kcf(H2O2)
• ren kenf(H2O2)

4

• The ratio of the chemically catalyzed rate to the
  uncatalyzed rate can be calculated by as follows
• rc /r0 kcf(H2O2)/k0f(H2O2)
• Similarly, The ratio of the enzymatically
  catalyzed rate to the uncatalyzed rate can be
  calculated by as follows
• ren /r0 kenf(H2O2)/k0f(H2O2)
• At 20oC, with the same initial concentration of
  reactant hydrogen peroxide, f(H2O2) remains the
  same for the above three process at initial
  conditions, the initial reaction rates vary with
  the rate constants.
• rc /r0 kc/k0
• ren /r0 ken/k0

5
Using Arrhenius Equations yields, rc /r0
kc/k0 (Aexp(-Ea,c/RT))/(Aexp(-Ea,o/RT)) re
n /r0 ken/k0 (Aexp(-Ea,en/RT))/(Aexp(-Ea,o/
RT)) Where Ea,o, Ea,c and Ea,en are activation
energy for uncatalyzed reaction, chemically
catalyzed and enzymatically catalyzed reactions,
respectively. A is a constant and remains same
for the specific system, the rate ratios could
be simplified to rc /r0 (exp(-Ea,c/RT))/(exp
(-Ea,o/RT)) ren /r0 (exp(-Ea,en/RT))/(exp(-E
a,o/RT))
6

• When T 20oC 27320 (K) 293 K,
• Ea,o 18 kcal/mol, Ea,c 13 kcal/mol (Ea,c) and
  
• Ea, en 7 kcal/mol, respectively.
• R 8.314 J mol-1K-1 , 1 cal 4.18 J.
• Then substituting the parameters in the rate
  ratio eqns. with these values, yields,
• rc /r0 (exp(-Ea,c/RT))/(exp(-Ea,o/RT))
• (exp(-130004.18/8.314293))/(exp(-180004.18/8.
  314293))
• ?
• ren /r0 (exp(-Ea,en/RT))/(exp(-Ea,o/RT))
• (exp(-70004.18/8.314293))/(exp(-180004.18/8.31
  4293)
• ?

7

• When T 20oC 27320 (K) 293 K,
• Ea,o 18 kcal/mol, Ea,c 13 kcal/mol (Ea,c) and
  
• Ea, en 7 kcal/mol, respectively.
• R 8.314 J mol-1K-1 , 1 cal 4.18 J.
• Then substituting the parameters in the rate
  ratio eqns. with these values, yields,
• rc /r0 (exp(-Ea,c/RT))/(exp(-Ea,o/RT))
• (exp(-130004.18/8.314293))/(exp(-180004.18/8.
  314293))
• 5.1X103
• ren /r0 (exp(-Ea,en/RT))/(exp(-Ea,o/RT))
• (exp(-70004.18/8.314293))/(exp(-180004.18/8.31
  4293)
• 1.4X108