Bioinorganic Chemistry
649
substrate and possesses a much less open
binding site.
10
Other Factors
Numerous other factors affect metal ion
afFnities including size and number of
che
la
ter
ing
s
,p
re
sen
ceo
fo
the
rl
igand
s
,
noncovalent interactions among ligands,
ligand Feld strength (at most 10% of total
binding energy), and spin state (important
in heme proteins).
11
pH-dependent Stabilities
If at a given pH a ligand occurs in
a protonated form, competition develops
between metal ion and proton for a
basic ligand site. The concentration of
basic ligand available to the metal ion
drops in the presence of protonated ligand
species. Neutral solutions contain ligands
with protonated amine, phenolic, and
sulfhydryl groups. In these and other
cases, the tabulated stability constants
overstate the effective binding strength,
and its magnitude needs to be reduced to
reflect competition from the proton.
The tabulated stability constant
K
s
refers
to the following equilibrium:
M
+
L
−−−→
ML
K
s
=
[ML]
(
[M][L]
)
With a protonated ligand, however, the
relevant formation reaction becomes M
+
HL
ML
+
H
+
. There is the additional
acid–base equilibrium of the ligand.
HL
−−−→
H
+
+
L
K
a
=
(
H
+
)
[L]
[HL]
The fraction of the ligand in the basic form
available for metal ion binding is given by
α
=
[L]
(
[HL]
+
[L]
)
=
K
a
[
(
H
+
)
+
K
a
]
so that
0
<α<
1
.
The conditional, pH-dependent stability
constant is given by
K
c
=
α
K
s
,or
log
K
c
=
log
K
s
p
K
a
log[
(
H
+
)
+
K
a
]
±or pH
À
p
K
a
, as for carboxylates in
neutral solutions, the basic form of the un-
boundl
igandp
redom
ina
tesandlog
K
c
=
log
K
s
o
rpH
¿
p
K
a
,a
sf
o
ra
l
i
p
h
a
t
i
c
amines in neutral solutions, the unbound
ligand is predominantly protonated and
log
K
c
=
log
K
s
p
K
a
+
pH, and the con-
ditional constant shows a pH dependence.
When the pH is within 1.5 log units of p
K
a
,
thecomp
leteequationshou
ldbeused
.By
allowing for withdrawal of deprotonated
ligand from solution by protonation, the
value of the conditional stability constant
becomes less than the standard stability
constant,
K
c
K
s
. (The conditional con-
stant may exceed the tabulated constant for
cases in which a subsequent deprotonation
occurs from a complex.)
In Table 5, conditional stability con-
stants at pH 7.0 (represented as
K
7
)a
re
compared with the tabulated stability con-
stants (
K
s
) for three metal ions and four
unidentate ligands. The four ligands rep-
resent carboxylate, imidazole, sulfhydryl,
and aliphatic amine donors in biologi-
cal systems. ±or acetate, pH
=
7
À
p
K
a
,
α
=
1, virtually all ligand is in its basic, car-
boxylate form, and the conventional and
conditional stability constants are equal.
±or imidazole, 44% of the ligand is in
the basic form. ±or glutathione and am-
monia, only 1.2 and 0.47% respectively
of the ligands are in the basic form.
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