Bioinorganic Chemistry
651
12
Cooperativity
Life abounds in cooperative interactions
and would not exist, as we know it,
without them. For example, the important
enzyme that maintains the 20 000-fold
Ca
2
+
gradient across cell membranes
binds 2 Ca
2
+
or 2 protons so cooperatively
that it is not possible to resolve reliably the
successive stability constants. What is not
appreciated, and what makes meaningless
all calculations of the origin of life based
on random events, is the cooperation that
occurs in even the simplest systems. For
statistical reasons at least, and in the
case of charged ligands for electrostatic
reasons as well, we expect the successive
stability constants for ligand binding to
a metal ion to decrease as the number
of ligands increases. This decrease is
generally observed. Yet, there are simple
systems in which the second ligand is
bound more strongly than the ±rst.
Both the ammonia and imidazole com-
plexes of Ag
+
exhibit an inversion of the
usual stability order: for NH
3
,l
og
K
1
=
3
.
20 and log
K
2
=
3
.
83, while for imida-
zole, log
K
1
=
3
.
1andlog
K
2
=
3
.
8
.
Since
there is a statistical factor of 4 or 0.60
log units favoring
K
1
over
K
2
,th
eo
b
-
served inversion is actually 1.23 to 1.3
log units or a factor of about 20. This
result means that once the ±rst ammonia
molecule is bound, the second is bound
signi±cantly more strongly. Binding of two
ligands to Hg
2
+
and four to Zn
2
+
also ex-
hibits cooperative behavior. In these cases,
the explanation lies in a decrease in co-
ordination number upon ligand binding,
resulting in shorter and stronger bonds to
the remaining ligands.
In hemoglobin, the successive stability
constants for dioxygen binding to the four
iron-containing heme groups are coopera-
tive with
K
1
<
K
2
<
K
3
¿
K
4
.Inthiscase,
the inverse order is caused by interactions
among the
α
and
β
protein chains and
is of enormous physiological signi±cance.
The inverse order means that once the ±rst
dioxygen binds, the second, third, and es-
pecially the fourth are bound even more
avidly. As a result, wholly deoxygenated
and wholly oxygenated forms predomi-
nate.Theydosotosuchanextentthatthere
are only small amounts of species with
one, two, and three dioxygen molecules,
and the individual stability constants are
resolved with dif±culty though the over-
all product
K
1
K
2
K
3
K
4
is well known. In an
oxygen-rich environment such as the lung,
hemoglobin becomes wholly oxygenated,
wh
i
leinanoxygen
-poort
issue
,theen
t
ire
oxygen load undergoes ef±cient release.
13
Metal Ion Binding Characteristics
13.1
Amino Acids
Amino acids bind transition metal ions
more avidly with increasing pH since
the amino group suffers less competition
from the proton. The potentially tridentate
amino acids histidine and cysteine are
especially
strong
transition
metal
ion
binders. Alkali and alkaline earth metal
ions, Al
3
+
, and lanthanides bind only
weakly to amino acids.
13.2
Peptides
Owing to loss of basic carboxylate and
amino groups, peptides usually bind metal
ions more weakly than amino acids unless
the metal ion deprotonates the peptide
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