Essential Cell Biology 5th edition

Free Energy and Catalysis
97
to the concentration of the product:
K = [AB]/[A][B]
The concentrations of both reactants are multiplied in the denominator
because the formation of product AB depends on the collision of A and
B, and these encounters occur at a rate that is proportional to [A] × [B]
(Figure 3–19). As with single-substrate reactions, ΔG° = –5.94 log K at
37°C. Thus, the relationship between K and ΔG° is the same as that
shown in Table 3–1.
The Equilibrium Constant Also Indicates the Strength of
Noncovalent Binding Interactions
The concept of free-energy change does not apply only to chemical reactions
where covalent bonds are being broken and formed. It is also used
to quantitate the strength of interactions in which one molecule binds to
another by means of noncovalent interactions (discussed in Chapter 2,
p. 48). Two molecules will bind to each other if the free-energy change for
the interaction is negative; that is, the free energy of the resulting complex
is lower than the sum of the free energies of the two partners when
unbound. Noncovalent interactions are immensely important to cells.
They include the binding of substrates to enzymes, the binding of transcription
regulators to DNA, and the binding of one protein to another to
make the many different structural and functional protein complexes that
operate in a living cell.
The equilibrium constant, K, used to describe reactions in which covalent
bonds are formed and broken, also reflects the binding strength of a
noncovalent interaction between two molecules. This binding strength
is a very useful quantity because it indicates how specific the interaction
is between the two molecules. When molecule A binds to molecule B
to form the complex AB, the reaction proceeds until it reaches equilibrium.
At which point the number of association events precisely equals
the number of dissociation events; at this point, the concentrations of
reactants A and B, and of the complex AB, can be used to determine the
equilibrium constant K (see Figure 3–19).
K becomes larger as the binding energy—that is, the energy released in
the binding interaction—increases. In other words, the larger K is, the
greater is the drop in free energy between the dissociated and associated
states, and the more tightly the two molecules will bind. Even a
association
rate
=
A + B
association
association
rate constant x concentration
of A
A
association rate = k on [A] [B]
B
x concentration
of B
dissociation
A B A + B
dissociation rate =
dissociation
rate constant
dissociation rate = k off [AB]
x concentration
of AB
AT EQUILIBRIUM:
association rate = dissociation rate
k on [A] [B] = k off [AB]
[AB] k on
= = K = equilibrium constant
[A] [B] k off
Figure 3–19 The equilibrium constant,
K, for the reaction A + B → AB depends
on the concentrations of A, B, and AB.
Molecules A and B must collide in order
to interact, and the association rate is
therefore proportional to the product of
their individual concentrations [A] × [B]. As
shown, the ratio of the rate constants k on
and k off for the association (bond formation)
and the dissociation (bond breakage)
reactions, respectively, is equal to the
equilibrium constant, K.