BioPHYSICAL chemistry

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 cur 9 e 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 xis equal to d, then the initial curve has a value of λ. Thus, the final curve must

have a value of λ+ΔG° when xis 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 yvalue is equal to the activation energy EA:

(db7.5)

Although these assumptions generally hold true in the normal region, they may not be appli-

cable 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

2 xGλλ=+ °Δ

xxxG^22 =− 2 λλ++°Δ

xxG^22 =−()λ + °Δ

E

G

A

()

=

λ+°

λ

Δ^2

4

y x

G

== EA

⎛ +°

⎝

⎜⎜

⎞

⎠

(^2) ⎟⎟ =
2
2
λ
λ

Δ