254
7 Respiratory Pigments
E + A ~ EA.
(7.1)
According to the mass effect theory, the binding
constant is
_ ~ [EA]
( )
Ka - r;;; [E] . [A] lImol.
7.2
Instead of the binding constant Ka, one can give
the inverse, i.e. the dissociation constant Kd = 1IKa
in molll. The first mathematical model for the
binding of A to a protein with n binding sites was
derived by Hill in 1909:
E + nA :;;::=: EAn
(7.3)
_ [EAn]
Ka - [E] . [A]n
(7.4)
Where Y is the completely occupied proportion of
the protein E, then
(7.5a)
Y
log 1 _ Y = n log [A] + log Ka· (7.5b)
According to the Hill equation (7.5b), log [Y/I-Y]
plotted against log [A] (a Hill plot) gives a
straight line whose slope n (the Hill constant) corresponds to the number of binding sites. However, this is not the case for either the tetrameric
haemoglobins or other respiratory pigments
(Fig. 7.3); more usually, the slope n gradually
decreases up to extreme values of log [A] and
never reaches a value on the curve equal to the
number of subunits. The Hill constant is usually
read at 50 % saturation, i.e. at 0 on the ordinate;
for the tetrameric human Hb A the value
obtained is 3.0. Equations (7.5a) and (7.5b)
assume that all the fl(s are bound simultaneously,
i.e. that only E or EAn exist. However, binding is
apparently also simultaneous if the affinity of E is
very low but is increased by the binding of an A.
All the following fl(s will bind rapidly, and cooperativity results. Thus, the Hill constant, n, does
not correspond to the number of binding sites but
is more a measure of the degree of interaction
between the subunits [13].
The model of Adair (1925) assigns a different
Ka value to each binding step. In this case, the O2binding curves may be described perfectly but the
individual Ka values cannot be directly measured.
The sequential model of Koshland (1958) assumes
that each subunit can exist in two states, T and R,
with different affinities. Somewhat simpler is the
model proposed by Monod, Wyman and Changeux in 1965 (MWC model); this assumes two
states, T and R, of the whole molecule with spontaneous transition between the two. The ratio of
the concentrations of the two forms in the
absence of the ligand A is given as L, and the
ratio of their binding constants as c:
L = [To]
(7.6)
Ro]
c = ~: .
(7.7)
Assuming a = [A]/KR' then
Y = Lca(1 + ca)n-l + a(1 + a)n-l (7.8)
L(1 + ca)n + (1 + a)n
A sigmoid binding curve then results only if n > 1,
L > 1 and c ~ 1 [13].
Instead of using oxygen, investigations of the
molecular mechanisms of ligand binding have
often made use of carbon monoxide, for which
vertebrate haemoglobins have a 60- to 550-fold
higher affinity. The CO complex can be dissociated by a light flash and this method therefore
allows measurements of the uptake kinetics in the
millisecond range. The alterations on haemoglobin structure after ligand binding are known
down to the atomic level, thanks largely to the
pioneering efforts of Perutz and coworkers
[131, 132]. The haemoglobin tetramer consists of
two a~ dimers, the chains of which are held together by so-called al~l contacts (packing contacts).
On the binding of a ligand, the al~l dimer rotates
150 relative to the a2~2 dimer, and shifts 0.1 nm;
responsible for this are the so-called al~2 contacts
(sliding contacts) between the two dimers.
Dimers and homotetramers are not cooperative.
In deoxygenated haemoglobin, the distance
between the ~-chains is increased so that anions,
such as organophosphates or chloride ions, can
bind to the positively charged side-chains. Substitutions in the al~2 contact region can reduce
cooperativity [131, 132].
In terrestrial vertebrates, the oxygenation of
haemoglobin is, as a rule, sufficiently accurately
described by the MWC model. Deoxygenated
haemoglobin is almost completely in the T state
and oxygenated haemoglobin in the R state; in
marine turtles, Hb02 has been found in the T
state [136]. The value of the Hill constant for the
haemoglobins of mammals is always in the region
n = 3.0; this is also true for most reptiles and
amphibians, which show values under 2.0 only at
low pH. Hill constants over 4.0, as are found in
all bird haemoglobins, the haemoglobins of Rana
catesbeiana and other frogs and several reptiles,
7 Respiratory Pigments
E + A ~ EA.
(7.1)
According to the mass effect theory, the binding
constant is
_ ~ [EA]
( )
Ka - r;;; [E] . [A] lImol.
7.2
Instead of the binding constant Ka, one can give
the inverse, i.e. the dissociation constant Kd = 1IKa
in molll. The first mathematical model for the
binding of A to a protein with n binding sites was
derived by Hill in 1909:
E + nA :;;::=: EAn
(7.3)
_ [EAn]
Ka - [E] . [A]n
(7.4)
Where Y is the completely occupied proportion of
the protein E, then
(7.5a)
Y
log 1 _ Y = n log [A] + log Ka· (7.5b)
According to the Hill equation (7.5b), log [Y/I-Y]
plotted against log [A] (a Hill plot) gives a
straight line whose slope n (the Hill constant) corresponds to the number of binding sites. However, this is not the case for either the tetrameric
haemoglobins or other respiratory pigments
(Fig. 7.3); more usually, the slope n gradually
decreases up to extreme values of log [A] and
never reaches a value on the curve equal to the
number of subunits. The Hill constant is usually
read at 50 % saturation, i.e. at 0 on the ordinate;
for the tetrameric human Hb A the value
obtained is 3.0. Equations (7.5a) and (7.5b)
assume that all the fl(s are bound simultaneously,
i.e. that only E or EAn exist. However, binding is
apparently also simultaneous if the affinity of E is
very low but is increased by the binding of an A.
All the following fl(s will bind rapidly, and cooperativity results. Thus, the Hill constant, n, does
not correspond to the number of binding sites but
is more a measure of the degree of interaction
between the subunits [13].
The model of Adair (1925) assigns a different
Ka value to each binding step. In this case, the O2binding curves may be described perfectly but the
individual Ka values cannot be directly measured.
The sequential model of Koshland (1958) assumes
that each subunit can exist in two states, T and R,
with different affinities. Somewhat simpler is the
model proposed by Monod, Wyman and Changeux in 1965 (MWC model); this assumes two
states, T and R, of the whole molecule with spontaneous transition between the two. The ratio of
the concentrations of the two forms in the
absence of the ligand A is given as L, and the
ratio of their binding constants as c:
L = [To]
(7.6)
Ro]
c = ~: .
(7.7)
Assuming a = [A]/KR' then
Y = Lca(1 + ca)n-l + a(1 + a)n-l (7.8)
L(1 + ca)n + (1 + a)n
A sigmoid binding curve then results only if n > 1,
L > 1 and c ~ 1 [13].
Instead of using oxygen, investigations of the
molecular mechanisms of ligand binding have
often made use of carbon monoxide, for which
vertebrate haemoglobins have a 60- to 550-fold
higher affinity. The CO complex can be dissociated by a light flash and this method therefore
allows measurements of the uptake kinetics in the
millisecond range. The alterations on haemoglobin structure after ligand binding are known
down to the atomic level, thanks largely to the
pioneering efforts of Perutz and coworkers
[131, 132]. The haemoglobin tetramer consists of
two a~ dimers, the chains of which are held together by so-called al~l contacts (packing contacts).
On the binding of a ligand, the al~l dimer rotates
150 relative to the a2~2 dimer, and shifts 0.1 nm;
responsible for this are the so-called al~2 contacts
(sliding contacts) between the two dimers.
Dimers and homotetramers are not cooperative.
In deoxygenated haemoglobin, the distance
between the ~-chains is increased so that anions,
such as organophosphates or chloride ions, can
bind to the positively charged side-chains. Substitutions in the al~2 contact region can reduce
cooperativity [131, 132].
In terrestrial vertebrates, the oxygenation of
haemoglobin is, as a rule, sufficiently accurately
described by the MWC model. Deoxygenated
haemoglobin is almost completely in the T state
and oxygenated haemoglobin in the R state; in
marine turtles, Hb02 has been found in the T
state [136]. The value of the Hill constant for the
haemoglobins of mammals is always in the region
n = 3.0; this is also true for most reptiles and
amphibians, which show values under 2.0 only at
low pH. Hill constants over 4.0, as are found in
all bird haemoglobins, the haemoglobins of Rana
catesbeiana and other frogs and several reptiles,