ENZYMES
One of the fundamental conditions for life is that an organism must be able
to catalyze chemical reactions efficiently and selectively. Such functions are
performed in cells by highly specialized proteins called enzymes. Enzymes
CHAPTER 7
KINETICS AND ENZYMES
147
The cur9e for the charge-separated state, y′, can be written as a parabola that has been displaced
horizontally by a distance, d, and displaced vertically by the free-energy difference, ΔG°:
y′ = (x − d)
2
+ ΔG°
(db7.2)
When x is equal to d, then the initial curve has a value of λ. Thus, the final curve must
have a value of λ + ΔG° when x is equal to zero, yielding:
y ′ = λ + ΔG° = (0 − d)
2
+ ΔG°
λ = d
2
(db7.3)
At the crossing point, the two curves are equal so:
y = y′
(db7.4)
Finally, we also know that at the crossing point the y value is equal to the activation energy E A :
(db7.5)
Although these assumptions generally hold true in the normal region, they may not be applicable in the inverted region. Rather, the contribution of additional vibrational modes leads
to the rate becoming close to independent of the free-energy difference.
d = λ
x
G
=
+
°
λ
λ
Δ
2
2x
G
λ λ
= +
°
Δ
x
x
x
G
2
2
2
=
−
+ +
°
λ λ Δ
x
x
G
2
2
(
)
=
−
+
°
λ
Δ
E
G
A
(
)
=
+
°
λ
λ
Δ
2
4
y x
G
E A
=
=
+
°
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ =
2
2
2
λ
λ
Δ
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