Molecular Biology of the Cell by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter by by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morg

PROTEIN FUNCTION
139
B B
A
A
the surfaces of molecules A and B,
and A and C, are a poor match and
are capable of forming only a few
weak bonds; thermal motion rapidly
breaks them apart
A
A
C
A
C
molecule A randomly encounters
other molecules (B, C, and D)
A
D
A
D
the surfaces of molecules A and D
match well and therefore can form
enough weak bonds to withstand
thermal jolting; they therefore
stay bound to each other
We can measure the strength with which any two molecules bind to each
other. As an example, consider a population of identical antibody molecules that
suddenly encounters a population of ligands diffusing in the fluid surrounding
them. At frequent intervals, one of the ligand molecules will bump into the binding
site of an antibody and form an antibody–ligand complex. The population of
antibody–ligand complexes will therefore increase, MBoC6 but not m3.42/3.39 without limit: over
time, a second process, in which individual complexes break apart because of
thermally induced motion, will become increasingly important. Eventually, any
population of antibody molecules and ligands will reach a steady state, or equilibrium,
in which the number of binding (association) events per second is precisely
equal to the number of “unbinding” (dissociation) events (see Figure 2–30).
From the concentrations of the ligand, antibody, and antibody–ligand complex
at equilibrium, we can calculate a convenient measure of the strength of binding—the
equilibrium constant (K)—(Figure 3–44A). This constant was described
in detail in Chapter 2, where its connection to free energy differences was derived
(see p. 62). The equilibrium constant for a reaction in which two molecules (A and
B) bind to each other to form a complex (AB) has units of liters/mole, and half
of the binding sites will be occupied by ligand when that ligand’s concentration
(in moles/liter) reaches a value that is equal to 1/K. This equilibrium constant is
larger the greater the binding strength, and it is a direct measure of the free-energy
difference between the bound and free states (Figure 3–44B). Even a change
1
2
3
(A)
dissociation
A B A + B
dissociation rate =
dissociation
rate constant
dissociation rate = k off [AB]
A + B
association rate =
association
association
rate constant
association rate = k on [A] [B]
AT EQUILIBRIUM:
× concentration
of AB
A B
× concentration
of A
association rate = dissociation rate
k on [A] [B] = k off [AB]
[AB] k on
= = K = equilibrium constant
[A][B] k off
× concentration
of B
The relationship between
standard free-energy
differences (ΔG°) and
equilibrium constants (37°C)
(B)
equilibrium
standard
constant
free-energy
difference
[AB] of AB minus
= K free energy
[A][B] of A + B
(liters/mole) (kJ/mole)
1
0
10 –5.9
10 2 –11.9
10 3 –17.8
10 4 –23.7
10 5 –29.7
10 6 –35.6
10 7 –41.5
10 8 –47.4
10 9 –53.4
10 10 –59.4
Figure 3–43 How noncovalent bonds
mediate interactions between
macromolecules (see Movie 2.1).
Figure 3–44 Relating standard
free-energy difference (ΔG°) to the
equilibrium constant (K). (A) The
equilibrium between molecules A and
B and the complex AB is maintained by
a balance between the two opposing
reactions shown in panels 1 and 2.
Molecules A and B must collide if they
are to react, and the association rate is
therefore proportional to the product of their
individual concentrations [A] × [B]. (Square
brackets indicate concentration.) As shown
in panel 3, the ratio of the rate constants
for the association and the dissociation
reactions is equal to the equilibrium
constant (K) for the reaction (see also p.
63). (B) The equilibrium constant in panel
3 is that for the reaction A + B ↔ AB, and
the larger its value, the stronger the binding
between A and B. Note that for every 5.91
kJ/mole decrease in standard free energy,
the equilibrium constant increases by a
factor of 10 at 37°C.
The equilibrium constant here has units of
liters/mole; for simple binding interactions
it is also called the affinity constant or
association constant, denoted K a . The
reciprocal of K a is called the dissociation
constant, K d (in units of moles/liter).