Báo cáo khoa học: Oxygen binding and its allosteric control in hemoglobin of the primitive branchiopod crustacean Triops cancriformis pdf

Oxygen binding and its allosteric control in hemoglobin of
the primitive branchiopod crustacean Triops cancriformis
Ralph Pirow
1
, Nadja Hellmann
2
and Roy E. Weber
3
1 Institute of Zoophysiology, University of Mu
¨
nster, Germany
2 Institute of Molecular Biophysics, Johannes Gutenberg University of Mainz, Germany
3 Zoophysiology, Institute of Biological Sciences, University of Aarhus, Denmark
The Branchiopoda are an ancient, primitive and,
except for the Cladocera, conservative group of crusta-
ceans [1]. The earliest known representatives were mar-
ine and occurred % 500 million years ago in the Upper
Cambrian [2]. Present-day branchiopods are predomin-
antly freshwater animals, and the fossil records indi-
cate that marine branchiopods invaded freshwater
habitats early in evolution. Two of the four extant
Keywords
allosteric control; Crustacea; hemoglobin;
oxygen binding
Correspondence
R. Pirow, Institute of Zoophysiology,
Hindenburgplatz 55, University of Mu
¨
nster,
D-48143 Mu
¨

nster, Germany
Fax: +49 251 8323876
Tel: +49 251 8323858
E-mail:
(Received 19 January 2007, revised 13 April
2007, accepted 8 May 2007)
doi:10.1111/j.1742-4658.2007.05871.x
Branchiopod crustaceans are endowed with extracellular, high-molecular-
mass hemoglobins (Hbs), the functional and allosteric properties of which
have largely remained obscure. The Hb of the phylogenetically ancient Tri-
ops cancriformis (Notostraca) revealed moderate oxygen affinity, coopera-
tivity and pH dependence (Bohr effect) coefficients: P
50
¼ 13.3 mmHg,
n
50
¼ 2.3, and u ¼ )0.18, at 20 °C and pH 7.44 in Tris buffer. The in vivo
hemolymph pH was 7.52. Bivalent cations increased oxygen affinity, Mg
2+
exerting a greater effect than Ca
2+
. Analysis of cooperative oxygen binding
in terms of the nested Monod–Wyman–Changeux (MWC) model revealed
an allosteric unit of four oxygen-binding sites and functional coupling of
two to three allosteric units. The predicted 2 · 4 and 3 · 4 nested struc-
tures are in accord with stoichiometric models of the quarternary structure.
The allosteric control mechanism of protons comprises a left shift of the
upper asymptote of extended Hill plots which is ascribable to the displace-
ment of the equilibrium between (at least) two high-affinity (relaxed) states,
similar to that found in extracellular annelid and pulmonate molluscan

Hbs. Remarkably, Mg
2+
ions increased oxygen affinity solely by displacing
the equilibrium between the tense and relaxed conformations towards the
relaxed states, which accords with the original MWC concept, but appears
to be unique among Hbs. This effect is distinctly different from those of
ionic effectors (bivalent cations, protons and organic phosphates) on anne-
lid, pulmonate and vertebrate Hbs, which involve changes in the oxygen
affinity of the tense and ⁄ or relaxed conformations.
Abbreviations
Hb, hemoglobin; i
r
, i
t
, interaction parameters of the cooperon model; K
i
, Adair constants of the i th oxygenation step; K
r
, K
s
, K
t
, oxygen-
binding constant for a particular conformation; K
ab
, oxygen-binding constant for a particular conformation; m, number of Mg
2+
-binding sites
per oxygen-binding site; MWC, Monod–Wyman–Changeux; n
50

, Hill’s cooperativity coefficient at half-saturation; P
50
, half-saturation oxygen
partial pressure; P
m
, median oxygen partial pressure; PO
2
, oxygen partial pressure; pK
ab
,pK value of an oxygenation-linked acid group for a
particular conformation; Q
ab
, q
ab
, magnesium and proton binding polynomials; q, size of the allosteric unit; rmse, root mean squared error;
SSR, sum of the squared residuals; s, number of functionally coupled basic allosteric units; s
Y
, standard error of Y; w, size of the basic
allosteric unit; x, oxygen partial pressure; Y,
^
Y , measured and predicted oxygen saturation; z, number of cooperons in a functional
constellation; z
ab
,Mg
2+
-binding constant of a particular conformation; ab (¼ tT, rT, tR, rR), particular conformation of the nested allosteric
model; u, Bohr factor.
3374 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
groups, the Conchostraca (clam shrimps) and the Not-
ostraca (tadpole shrimps), can be traced back to the

Devonian and the Late Carboniferous [3], respectively.
The transition from the marine to the physicochemically
more extreme inland water environments represented a
great challenge for the physiological systems involved
in regulating the internal milieu. Given the primitive
and conservative morphological characteristics of
many extant branchiopods, which seem to have chan-
ged little over long periods of time, it may be pre-
sumed that prehistoric adaptations to a highly variable
environment remained preserved and essentially unsup-
plemented by physiological ‘innovations’, allowing us
to gain insight into homeostatic mechanisms operative
in early crustaceans [4,5].
The tadpole shrimp Triops cancriformis (Notostraca)
is one of the ‘oldest’ extant branchiopods; it was found
to be inseparable from Triassic (250–205 million years
ago) fossils on the basis of morphological criteria [6].
Notostracans comprising the two genera Triops and
Lepidurus inhabit temporary water bodies that com-
monly exhibit extreme physicochemical conditions.
For desert ephemeral pools in south-western North
America, a typical branchiopod habitat, Scholnick [7]
reported large diurnal variations in oxygen tension
(40–200 mmHg), carbon dioxide tension (0.07–
3 mmHg), pH (7.5–9.0), and temperature (17–35 °C)
during summer months. Horne [8] similarly observed
large diurnal fluctuations in oxygen concentration
(1–6.5 mgÆL
)1
) and temperature (17–30 °C) in North

American ephemeral ponds typically inhabited by Tri-
ops longicaudatus. Notostracans seem to be well adapted
to varying oxygen conditions, as reflected by their
ability to maintain constant rates of oxygen consump-
tion even when the ambient oxygen concentration
decreases to critical levels of % 17% air saturation
(1.2–1.3 mgÆL
)1
)forLepidurus lemmoni at 12 °C [9] and
% 25% air saturation for T. cancriformis at 20 °C
(R. Pirow, unpublished data). Their oxyregulatory capa-
city is impressive given that notostracans appear to lack
extensive systemic (circulatory) regulatory capacities in
response to variations in ambient oxygen availability.
The open circulation of Triops lacks an arterial distri-
bution system [10] and tissue capillaries, so that regula-
tion of tissue oxygen supply by regional adjustments in
perfusion rate is scarcely possible. In addition, no ana-
tomical evidence has been found for a neuronal control
of cardiac output by the central nervous system [10,11].
Although the heart is able to respond to neurohormones
[12], it does not seem to be involved in the regulation of
circulatory oxygen transport, as no compensatory
adjustments in cardiac output were found in animals
challenged by progressive hypoxia [13].
As argued previously [14,15], the greater differenti-
ation and complexity of respiratory proteins in inverte-
brates than in vertebrates may compensate for the
lower morpho-functional organization at the organ
level in the former and represent a shift of the homeo-

static regulatory burden from the organ to the mole-
cular level compared with vertebrates. This view is
corroborated by the fact that exposure to hypoxic
conditions increases hemolymph hemoglobin (Hb)
concentrations in Triops spp. [16–18]. This homeostatic
response may be complemented by changes in the
functional properties of the protein.
The extracellular Hbs of invertebrates are commonly
high-molecular-mass complexes which exhibit high
variability in oxygen-binding properties and their sensi-
tivities to pH and ionic effectors [15]. So far, nothing
appears to be known about the allosteric control of
Hb–oxygen binding and its significance for the regula-
tion of internal oxygen conditions in branchiopod
crustaceans. This lack of knowledge contrasts with the
detailed information available on the structure of sev-
eral branchiopod Hbs [19,20]. To probe Hb function,
its molecular correlates and organismic regulation in
the phylogenetically ancient crustaceans, we investi-
gated the oxygen-binding characteristics, their sensitivi-
ties to pH, temperature and bivalent cations, and the
allosteric mechanisms controlling oxygen binding in
Hb from T. cancriformis.
Results and Discussion
Physicochemical characteristics of
Triops hemolymph
The in vivo pH of the hemolymph in the dorsal sinus
of T. cancriformis was 7.52 ± 0.02 (n ¼ 3 animals) at
20 °C. A markedly lower pH value of 7.1 (presumably
measured at 23 °C) has been given for T. longicaudatus

[21]. The hemolymph had an osmolality of 150 ± 19
mosmolÆkg
)1
(n ¼ 3). The chloride concentration was
58 meqÆL
)1
(mean of a triple determination of one
pooled hemolymph sample), which is comparable to
the concentrations reported for nonmolting T. cancri-
formis (40–57 meqÆL
)1
) [22] kept in distilled water and
for T. longicaudatus (56 mm) [23].
Oxygen affinity, cooperativity and pH
dependence
The Hb of dialyzed hemolymph showed a moderate
oxygen affinity (P
50
¼ 13.3 mmHg), cooperativity
(n
50
¼ 2.3), and pH sensitivity (Bohr factor u ¼
dLogP
50
⁄ dpH ¼ )0.18) at pH 7.44 (Tris buffer) and
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3375
20 °C (Fig. 1A,C). Raising the pH from 6.7 to 8.1

increased the n
50
from 1.9 to 2.9 and decreased the P
50
from 16.0 to 9.4 mmHg, respectively.
The oxygen-binding characteristics of purified Hb
(Fig. 1B,D) were comparable to those of dialyzed
hemolymph. The P
50
of purified Hb, for example, was
only 2–3% lower than that of dialyzed hemolymph
under the same buffer and temperature conditions
(Tris ⁄ Bis-Tris, pH 6.7–8.1, 20 °C). Experiments using
Hepes as an alternative buffer revealed a somewhat
higher P
50
than with Tris ⁄ Bis-Tris (Fig. 1D). At
pH 7.5, for example, which represents the in vivo pH
condition, the Hepes-buffered Hb showed a P
50
of
14.0 mmHg.
The oxygen-binding properties of whole hemolymph
were examined at three CO
2
levels at 20 °C (Fig. 2).
Strong alkalinization of hemolymph induced by CO
2
-
free conditions yielded an extreme affinity (P

50
¼
7.1 mmHg) and cooperativity (n
50
¼ 3.80) which excee-
ded the range of values obtained from Hepes-buffered
Hb at pH 6.7–8.3 (Fig. 1B,D). The exposure of whole
hemolymph to 1% and 2% carbon dioxide gave P
50
values of 13.4 and 16.5 mmHg, respectively, and n
50
values of 2.41 and 2.02, respectively. Essentially the
same P
50
⁄ n
50
combinations were observed for Hepes-
buffered Hb at pH 7.6 and pH 7.0 (Fig. 1B,D),
respectively. Analyses of buffer characteristics of
T. cancriformis hemolymph at 1% and 2% CO
2
revealed pH values of 7.63 and 7.36, respectively
(R. Pirow, unpublished data). These findings suggests
that the replacement of the native hemolymph environ-
ment by Hepes buffer does not significantly influence
the pH dependence of the oxygen-binding properties of
T. cancriformis Hb, at least in the physiological pH
range.
A comparison of oxygenation characteristics among
branchiopod Hbs (Table 1) reveals the lowest affinities

in the largest species, i.e. the notostracans (body length
10–100 mm [24]). This negative correlation extends to
the smallest branchiopods such as the cladocerans
(0.2–6 mm), which at high ambient oxygen tension rely
predominantly on simple diffusion. Several lines of
evidence [25–27], including the reduction in oxygen
uptake when Hb–oxygen binding is blocked by carbon
monoxide [28] and the striking induction of Hb under
hypoxia in euryoxic species such as Daphnia magna
(1–16 g HbÆL
)1
) [29], indicate that the high-affinity
Hbs of cladocerans (P
50
¼ 1.2–8.3 mmHg) function as
oxygen carriers mainly at low ambient oxygen tension.
Large branchiopods, in contrast, invariably require
convective transport of oxygen. The moderate oxygen
affinity (P
50
¼ 6.8–14 mmHg) and the high concentra-
tion of Hb (8–25 g HbÆL
)1
) [17,21] (this study) in Tri-
ops spp. suggest that the respiratory protein mediates
circulatory oxygen transport over a wide range of ambi-
ent oxygen tensions i n Notostraca. The remarkably
C
pH
6.5 7.0 7.5 8.0

log P
50
0.7
0.8
0.9
1.0
1.1
1.2
D
p
H
6.5 7.0 7.5 8.0
A
n
50
1.5
2.0
2.5
3.0
3.5
B
dialyzed hemolymph
purified Hb
20 °C Tris
10 °C Tris
20 °C Hepes
20 °C Tris
Fig. 1. pH-dependence of oxygen-binding properties of T. cancrifor-
mis Hb. Effects of pH on (A) Hill’s half-saturation cooperativity coef-
ficients (n

50
) and (C) half-saturation oxygen tensions (P
50
)at20°C
(circles) and 10 °C (squares) in Tris ⁄ Bis-Tris-buffered (dialyzed)
hemolymph. (B, D) Effects of pH on n
50
and P
50
of purified Hb in
Hepes buffer (diamonds) and Tris ⁄ Bis-Tris buffer (triangles) at
20 °C.
Oxygen partial pressure P
O2
(mmHg)
0 1020304 0
Fractional oxygen saturation Y
0.0
0.5
1.0
0 % CO
2
1 % CO
2
2 % CO
2
whole hemolymph
Fig. 2. Oxygen-binding curves of T. cancriformis Hb in whole hemo-
lymph at three different CO
2

concentrations and 20 °C.
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.
3376 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
large variability in P
50
observed in notostracan Hbs
(6.8–20 mmHg, pH 7.1–7.5, 20–23 °C) may reflect
genus ⁄ species-specific variation in oxygen tolerance
and temperature preference. In comparison with
Lepidurus spp., species of the genus Triops are generally
more warmth-demanding [6,24,30] and possess hemo-
globins of higher oxygen affinity. The moderate coop-
erativity (n
50
¼ 1.8–3.1, pH 6.7–8.3, 20 °C) and the
small Bohr effect (u ¼ )0.05 to )0.24, pH 7.0–8.0,
20 °C) found in T. cancriformis Hb conform with the
homotropic and heterotropic interactions reported for
other branchiopod Hbs. Prominent exceptions appear
to be cladoceran (D. magna and Moina macrocopa)
Hbs that seem to lack Bohr effects.
Effect of temperature on oxygen binding
The oxygenation of Hb is exothermic, and increasing
temperature lowers oxygen affinity directly by weakening
the bond between Hb and oxygen and indirectly via
the Bohr effect because of the associated pH decrease.
In T. cancriformis Hb, the increase in temperature
from 10 to 20 °C increased the P

50
from 6.5 to
13.3 mmHg at pH 7.44 (Fig. 1C). The pH-dependence
of n
50
was virtually unaffected by temperature
(Fig. 1A). The temperature-dependence of the P
50
val-
ues at pH 7.0 and pH 8.0 corresponded to the overall
heats of oxygenation of )51.3 and )45.6 kJÆmol
)1
,
respectively, which include the heat of oxygen dissolu-
tion and the heat of proton dissociation from oxygen-
ation-linked acid groups. The reduction in the overall
heat of oxygenation with increasing pH correlates with
an intensification of the Bohr effect at higher pH and
the endothermic nature of Bohr proton release [31]. In
the physiological context, the reduction in oxygen
affinity with increasing temperature may favor oxygen
delivery to the tissues in synchrony with temperature-
induced increases in oxygen consumption rates, but
Table 1. Oxygenation characteristics of branchiopod Hbs. Data from whole hemolymph (WH) were obtained under normocapnic conditions
(0.03% CO
2
). In cases where information on the experimental buffer conditions was lacking, the extraction buffer type is given together with
a question mark.
Group ⁄ species
P

50
(mmHg) n
50
T
(°C) pH Buffer
Bohr
factor u
b
DH
(kJÆmol
)1
) Reference
Anostraca
Artemia salina
(Hb-I) 5.3 1.6 25 8.5 Borate )0.09 )45 [65]
(Hb-II) 3.7 1.9 25 8.5 Borate )0.21 % )50
(Hb-III) 1.8 1.6 25 8.5 Borate )0.03 )23
Notostraca
T. longicaudatus 6.8 1.5 23 7.1 Phosphate )0.23 )31 [21]
T. cancriformis 13 2.3 20 7.4 Tris )0.18 )49 Present study
14 2.3 20 7.5 Hepes
Lepidurus bilobatus 20 2 20 7.2 Tris )0.13 )31 [66]
Lepidurus lynchi 21 3 20 8.0 Tris )0.19 [67]
Lepidurus couesi 22 3 20 8.0 Tris [67]
Conchostraca
Caenestheria inopinata 7.8 1.2 25 6.8 Phosphate )0.19 )37 [68]
Caenestheriella setosa 5.9 2.5 20 8.0 Tris )0.15 )21 [67]
Cyzicus hierosolymitanus 0.035 2.3 28 7.3 Tris ⁄ maleate [69]
Cladocera
Daphnia magna 3.5 20 7.2 Phosphate (?) $0 [70]

Daphnia magna
Pale 3.8 1.3 20 7.2 Phosphate [71]
Pale 8.3 20 WH [72]
Pale 7.7 1.6
a
25 7.2 Bis-Tris ⁄ propane [57]
Red 1.6 1.5 20 7.2 Phosphate [71]
Red 2.5 20 WH [72]
Red 2.6 1.8
a
25 7.2 Bis-Tris ⁄ propane [57]
Daphnia pulex
Hb-1 2.6 2.2 17 7.45 Tris (?) [73]
Hb-3 1.2 1.4 17 7.45 Tris (?) [73]
Moina macrocopa 2.1 20 7.2 Phosphate (?) $0 [70]
a
Calculated from the Adair constants;
b
dLogP
50
⁄ dpH.
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3377
may also compromise oxygen loading in warm hypoxic
water.
Effect of bivalent cations on oxygen binding
The addition of Mg
2+

and Ca
2+
increased the oxygen
affinity of T. cancriformis Hb at cation concentrations
higher than 5 mm (Fig. 3C,D). For example, increasing
the Mg
2+
concentration from 0 to 20 mm decreased
the P
50
from 14.6 to 11.4 mmHg at pH 7.1, and from
11.2 to 9.0 mmHg at pH 7.8. The effect of Ca
2+
was
smaller than that of Mg
2+
(Fig. 3C). The cations had
no strong effect on cooperativity (Fig. 3A,B); the indi-
vidual values of n
50
were % 2.2 (pH 7.1, BisTris), % 2.3
(pH 7.6, Hepes), and % 2.6 (pH 7.8, Tris ⁄ HCl).
Although the cation sensitivities were investigated by
adding chloride salts, the measured effects are probably
not attributable to the chloride counterions as Mg
2+
exerted a greater effect than Ca
2+
. The lack of a Cl
–

effect and the greater sensitivity of oxygen affinity to
Mg
2+
than Ca
2+
are moreover consistent with a previ-
ous study [21], which showed that univalent cations
such as Na
+
and K
+
(added as chloride salts) had no
significant effect on T. longicaudatus Hb. The differen-
tial effects of Mg
2+
and Ca
2+
show that specific prop-
erties of cationic effectors other than net ionic charge,
such as size and the stereochemical orientation of their
charges, influence oxygen affinity of Triops Hb.
Allosteric control mechanisms and their
physiological significance
To reveal the allosteric control mechanisms, high-reso-
lution oxygen-equilibrium curves of dialyzed hemo-
lymph (in Tris ⁄ Bis-Tris buffer) and purified Hb
(in Hepes buffer) were measured at different pH values
(pH 6.7–8.3) and Mg
2+
concentrations (0–100 mm).

As illustrated in the Hill-plot representation (Fig. 4),
all oxygen-binding curves virtually approach the same
asymptote of unity slope at low saturation (< 5%).
This convergence shows that the Adair constant
for the first oxygen-binding step (K
1
¼ 0.027–
0.030 mmHg
)1
) is independent of proton and Mg
2+
concentration. Increasing the Mg
2+
concentration
(0–100 mm) induced a left shift of the Hill plot in the
half-saturation range (Fig. 4C,D) without affecting the
affinity in the high-saturation range (> 95%), as
reflected by the almost constant Adair parameter for
the last oxygenation step (K
N
). K
N
assumed values of
0.86–0.95 mmHg
)1
at pH 7.50–7.60 (Hepes buffer) and
1.12–1.26 mmHg
)1
at pH 7.77–7.80 (Tris buffer). This
invariance of K

1
and K
N
reveals an apparently unique
heterotropic control mechanism for bivalent cations.
In contrast with the heterotropic interactions so far
described for annelid (Arenicola marina [32]), pulmo-
nate molluscan (Biomphalaria glabrata [33]) and ver-
tebrate [34] Hbs, where modulation of oxygen affinity
by ionic effectors invariably involves changes in K
1
and K
N
, increasing Mg
2+
concentrations raised the
oxygen affinity of T. cancriformis Hb without affecting
K
1
and K
N
.
The physiological significance, if material, of the
effects of bivalent c ations on Triops Hb is not clear. T he
cation concentrations in T. cancriformis hemolymph
(Ca
2+
, 1.6–3.1 mmolÆkg
)1
;Mg

2+
, 0.6–0.8 mmolÆkg
)1
;
R. Pirow, unpublished data) and T. longicaudatus
hemolymph (Ca
2+
, 0.8–1.7 mm;Mg
2+
, 0.6–0.9 mm)
[21,23] are more than one order of magnitude below
the values where the cations significantly increase oxy-
gen affinity. Moreover, raised ambient Mg
2+
concen-
trations are lethal to T. longicaudatus [35], and the
regulation of internal Mg
2+
concentrations in this spe-
cies breaks down when external levels exceed 14 mm,
although Na
+
,K
+
,Ca
2+
,Cl
–
and SO
4

2+
concentra-
tions continue to be regulated [35].
C
[M
g
2+
], [Ca
2+
] (m
M
)(m
M
)
12 5102050100
log P
50
0.7
0.8
0.9
1.0
1.1
1.2
D
[M
g
2+
]
12 5102050100
A

n
50
1.5
2.0
2.5
3.0
3.5
B
dialyzed hemolymph
purified Hb
Mg
2+
pH 7.8
Ca
2+
pH 7.8
Mg
2+
pH 7.1
Ca
2+
pH 7.1
Mg
2+
pH 7.6
Fig. 3. Effects of bivalent cations on oxygen-binding properties of
T. cancriformis Hb at 20 °C. Dependence of (A) n
50
and (C) P
50

on
Mg
2+
(circles) and Ca
2+
(squares) in Tris ⁄ Bis-Tris-buffered (dialyzed)
hemolymph at pH 7.1 (grey, filled symbols) and pH 7.8 (open sym-
bols), where the dotted lines extrapolate to the values in the
absence of bivalent cations at the same pH. (B, D) Effects of Mg
2+
on n
50
and P
50
of purified Hb in Hepes buffer (diamonds) at pH 7.6.
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.
3378 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
The proton and cation insensitivities at low satura-
tions contrast with the pH-dependent divergence of
oxygen-binding curves at high saturation (> 95%)
(Fig. 4A,B). Increasing pH enhanced the affinity for
binding the last oxygen molecule. Accordingly,
the Adair constant for the last oxygenation step
(K
N
) increased from 0.49 mmHg
)1
at pH 6.71 to

1.26 mmHg
)1
at pH 7.77 in Tris buffer in the absence
of Mg
2+
. In Hepes buffer, K
N
increased from 0.40 to
1.34 mmHg
)1
when the pH changed from 6.69 to 8.30.
This control mechanism, i.e. the left shift of the upper
asymptote of extended Hill plots, is similar to that
found in the extracellular annelid Hbs (Arenicola mar-
ina [32] and Lumbricus terrestris [36]) and pulmonate
molluscan Hb (Biomphalaria glabrata [33]). In water
breathers such as Arenicola that exploit the upper part
of the oxygenation curve maintaining a high ‘venous
reserve’ [37], a pronounced Bohr effect at high satura-
tion may be adaptive in favoring oxygen loading to
blood perfusing the respiratory structures [32]. This
characteristic contrasts with the tetrameric vertebrate
Hbs, where increases in the concentrations of protons
and anionic organic phosphates decrease Hb oxygen
affinity by lowering the binding constant for the low-
affinity (tense) state [38], which may favor oxygen
unloading in the tissues under varying oxygen demand.
The physiological significance of Hb in Triops has
been questioned on the basis of reports that some indi-
viduals lack Hb and because experiments with carbon

monoxide poisoning of Hb resulted in no depression
of the rate of oxygen consumption [21]. However,
these observations may merely indicate that the oxygen
requirements of the tissues may be satisfied by the oxy-
gen carried in physical solution in the hemolymph, at
least at rest and under normoxic conditions. Against
the background of the limited systemic (circulatory)
regulatory capacities in Triops, Hb becomes the key
control component of the oxygen-transport cascade
from environment to cell. Hb enables the animal
to maintain aerobic respiration under environmental
hypoxia by increasing the convective conductance for
oxygen in the circulatory system [39]. When oxygen
loading and unloading spans the steep part of the
oxygen-equilibrium curve, Hb also exerts a stabilizing
effect on the hemolymph oxygen tension (‘oxygen buf-
fering’) [40], thereby reducing the risk of oxidative
stress to the tissues. The oxyregulatory function of Hb
may be enhanced by the Bohr effect, which enables the
animal to optimize oxygen loading to the hemolymph
at the respiratory surfaces via hyperventilation and res-
piratory alkalosis under conditions of environmental
oxygen deficiency.
B
% Ox
y
Hb
99
98
95

90
70
50
30
10
5
2
–log K
N
D
log P
O2
0.0 0.5 1.0 1.5 2.0
% Ox
y
Hb
99
98
95
90
70
50
30
10
5
2
A
log [Y/(1–Y)]
-1
0

1
2
C
log P
O2
0.0 0.5 1.0 1.5 2.0
log [Y/(1–Y)]
-1
0
1
2
dialyzed hemolymph in Tris buffer purified Hb in Hepes buffer
–log K
1
pH 8.30
pH 7.50
pH 7.12
pH 6.69
pH 7.77
pH 7.44
pH 6.71
[Mg
2+
] pH
100 7.78
15 7.80
0 7.77
[Mg
2+
] pH

100 7.60
50 7.58
0 7.50
Fig. 4. Extended Hill plots of T. cancriformis
Hb at different pH values and different
Mg
2+
concentrations at 20 °C. Effects of pH
on Hb oxygen binding in Tris ⁄ Bis-Tris-buf-
fered hemolymph (A) and in Hepes-buffered
purified Hb (B) in the absence of Mg
2+
. The
lower row shows the influence of Mg
2+
concentration (values in mmolÆL
)1
)onHb
oxygen binding in Tris ⁄ Bis-Tris-buffered
hemolymph at pH 7.8 (C) and in Hepes-
buffered purified Hb at pH 7.5–7.6 (D). The
solid lines were fitted to the data by using
the 2 · 4 nested MWC model with one oxy-
genation-linked acid group and half a Mg
2+
-
binding site per oxygen-binding site. Dashed
lines with slopes of unity represent asymp-
totes approached by the curve furthest to
the left at very low and very high saturation.

The intercepts of these dashed lines
with the horizontal (dotted) line at log
[Y ⁄ (1–Y)] ¼ 0 correspond to the negative
logarithms of the Adair constants of the first
and last oxygenation step (K
1
and K
N
).
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3379
Structure–function relationships
The multimeric Hb of T. cancriformis is composed of
two subunit types, TcHbA (60–70%) and TcHbB
(30–40%), which have polypeptide masses of 35775
and 36055 Da, respectively; each carry two heme
groups and assemble into disulfide-bridged dimers that
comprise a homodimer of TcHbA and a heterodimer
[20]. These dimers assemble into three native isoforms,
one 16-mer and two 18-mer species. Only the larger
18-meric species seems to possess the heterodimer con-
taining subunit type TcHbB. Thus, several structural
levels are present: the first level is the di-domain sub-
unit, which carries two oxygen-binding sites (see
Fig. 6A). The next level is the disulfide-bridged dimer
D. As it seems unlikely that eight or nine copies of
these dimers oligomerize into a big lump, additional
substructures such as D

2
,D
3
or D
4
have to be taken
into account (Fig. 6A). These substructures carry 8, 12
and 16 oxygen-binding sites. In order to determine
whether the hierarchical structure plays a role in the
functional properties, and to obtain some indication of
which of the possible structural organizations might
occur, oxygen-binding data comprising six curves
(Fig. 4B,D) were analyzed in terms of different models
of cooperativity.
As the largest Hill coefficient determined empirically
from the oxygen-binding curves is 3.8 (whole hemo-
lymph at 0% CO
2
, Fig. 2), it does not seem necessary
to assume interactions beyond the dimer D, bearing in
mind, that each dimer D carries four oxygen-binding
sites. If this can be assumed, an analysis based on four
Adair constants should describe the data well. The
result of this analysis is shown in Table 2 together with
the results of the other models. The residual plots of all
models are shown in Fig. 5. In all cases, the sum of
squared residuals (SSR) is given for the simultaneous
analysis of all six binding curves, as in some cases
parameters are shared between individual binding
curves in order to reduce the number of free parameters

as well as the uncertainty in the remaining parameters.
In the Adair formalism none of the parameters are
shared between the curves, thus, the total set contains
24 free parameters. Despite this very large number of
parameters, the root mean squared error (rmse) is sig-
nificantly larger than that of most other models tested
(Table 2, model b). Furthermore, the residuals are not
randomly distributed (Fig. 5B), indicating systematic
deviations between the data and the fit. The obvious
next level to take into account is a functional coupling
of two dimers (Fig. 6A, substructure D
2
), involving an
interaction between eight oxygen-binding sites. This
Table 2. Comparison of the goodness of fit of different oxygen-binding models. Each model was applied to the set of six oxygen-equilibrium
curves of purified Hb shown in Fig. 4B,D. Shown are the total number of (shared and curve-specific) parameters, SSR, the degrees of free-
dom (DF), the root mean squared error (rmse ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
SSR=DF
p
), and the best-fit parameter values of each model. Shared parameters and curve-
specific parameters are given as single values and range of values, respectively. K values are in mmHg
)1
.
Model Number of parameters SSR DF rmse Best-fit values of model parameters
(a) Two-state MWC 9 (¼ 6 · 1 +3) 300 105 1.69 K
T
¼ 0.034 log L ¼ 5.2–6.6
with shared q K
R

¼ 1.820 q ¼ 4.6
(b) Tetramerous Adair equation 24 (¼ 6 · 4) 130 90 1.20
(c) Two-state MWC 14 (¼ 6 · 2 +2) 88 100 0.94 K
T
¼ 0.033 log L ¼ 4.6–6.5
with curve-specific q K
R
¼ 1.516 q ¼ 4.1–5.4
(d) Two-state MWC 19 [¼ 2 · (6 +2 + 1) +1] 80 95 0.92 species 1: species 2:
with two species and K
T
¼ 0.022 K
T
¼ 0.035
with species-specific q K
R
¼ 0.219
q ¼ 11.6
log L ¼ 2.4–6.9
species ratio ¼ 15 : 85
K
R
¼ 8.818
q ¼ 4.7
log L ¼ 8.4–10.0
(e) Three-state MWC 21 (¼ 6 · 3 +3) 42 93 0.67 K
S
¼ 0.026 log L ¼ 5.3–9.0
with curve-specific q K
T

¼ 0.074
K
R
¼ 1.546
log M ¼ 5.9–10.2
q ¼ 5.3–8.0
(f) 4 · 2 Cooperon model 14 (¼ 6 · 2 +2) 32 100 0.56 K
T
¼ 0.025 log L ¼ 8.3–10.8
z ¼ 4 dimeric cooperons K
R
¼ 1.448 i
T
¼ 4.6–11.3
with i
R
fixed to unity i
R
¼ 1 (fix)
(g) 4 · 2 Cooperon model 20 (¼ 6 · 3 +2) 20 94 0.46 K
T
¼ 0.026 log L ¼ 5.6–6.7
z ¼ 4 dimeric cooperons K
R
¼ 0.274 i
T
¼ 3.6–9.6
with curve-specific i
R
i

R
¼ 2.0–5.9
(h) 3 · 4 nested MWC (h ¼ 1, m ¼ 0.5) 15 20 99 0.45
(i) Octomerous Adair equation 48 (¼ 6 · 8) 11 66 0.40
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.
3380 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
leads to the octomerous Adair equation with 48 free
parameters. The agreement between the fit and the
data is very good (Table 2, model i) and the residuals
appear randomly distributed (Fig. 5I). The analysis
based on the Adair formalism gives an idea about the
minimal number of interacting binding sites, but does
not give any information about the number of confor-
mations (or substates) involved in the cooperative
mechanism or insights into any more complex interaction
pattern such as a hierarchical grouping of functional
units. In order to obtain this kind of information,
more specific models that take the structure of this Hb
into account are needed.
The simplest model to consider is the Monod–
Wyman–Changeux (MWC) model, which predicts two
conformations that are simultaneously adopted by a
molecule-specific number of binding sites, the allosteric
unit (Eqn 7, see Experimental procedures). We applied
this model in an approach where the binding constants
K
t
and K

r
are shared among the six binding curves,
and the allosteric equilibrium constant (L) is specific
for each curve. If one allows curve-specific values for
the size of the allosteric unit (q), a reasonably good fit
is obtained, but the values for q vary between
4.1 ± 0.2 and 5.4 ± 0.3 (means ± 95% confidence
interval) (Table 2, model c). If one fixes q to the same
value for all curves, a poor value for the rmse is
obtained (Table 2, model a) and the residuals are non-
randomly distributed (Fig. 5A), indicating that the
MWC model does not reflect the complexity of the
oxygen-binding process for Triops Hb.
At the next level of complexity, we allowed one
more conformation for the allosteric unit within the
framework of the MWC model, and employed a three-
state model (Eqn 8). In this case, the value for the size
of the allosteric unit (q) is still highly variable, ranging
from 5.3 to 8.0 (Table 2, model e), disfavoring this
model too. Alternatively, we extended the simple
MWC model to take a possible heterogeneity in the
cooperative interactions because of the different sizes
of the oligomers (16-mers and 18-mers; Fig. 6A) into
account. This extension is based on superimposition of
two binding curves corresponding to two types of mole-
cules, each having an oxygen-binding characteristic
that obeys the MWC formalism (Eqn 9). The size of
the allosteric unit (q) is allowed to differ between these
two types, but for each molecule species, q is shared
among the binding curves obtained at different effector

concentrations (Table 3, model d). The agreement
between the fit and the data is much better than that
obtained for a single molecule species with shared q.
However, in total, the agreement is still not as good as
I
Fractional ox
yg
en saturation Y
0.0 0.2 0.4 0.6 0. .0
A
Residuals
-0.05
0.00
0.05
2-state MWC (shared q)
B
C
Residuals
-0.02
0.00
0.02
D
E
Residuals
-0.02
0.00
0.02
F
Residuals
-0.02

0.00
0.02
G
H
Fractional ox
yg
en saturation Y
0.0 0.2 0.4 0.6 0.8 1.0
Residuals
-0.02
0.00
0.02
0.0
pH 8.30 (0)
pH 7.12 (0)
pH 6.69 (0)
pH 7.60 (100)
pH 7.58 (50)
pH 7.50 (0)
tetramerous Adair
2-state MWC (curve-specific q
-state MWC (2 species)
3-state MWC (curve-specific q)
4×2 cooperon (i
R
= 1) 4×2 cooperon (curve-specific i
R
)
3×4 nested MW
ctomerous Adair

1.0
Fig. 5. Comparison of the (unweighted) resi-
duals of the fit provided by the different
oxygen-binding models (see Table 2). (A)
Two-state MWC with shared q. (B) Tetra-
merous Adair equation. (C) Two-state MWC
with curve-specific q. (D) Two-state MWC
with two species and species-specific q. (E)
Three-state MWC with curve-specific q. (F)
4 · 2 cooperon model consisting of four
dimeric cooperons with i
R
fixed to unity. (G)
4 · 2 cooperon model consisting of four
dimeric cooperons with curve-specific i
R
. (H)
3 · 4 nested MWC with one oxygenation-
linked acid group and half a Mg
2+
-binding
site per oxygen-binding site. (I) Octomerous
Adair equation.
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3381
in the case of the octomerous Adair model, and the
distribution of residuals is clearly not random
(Fig. 5D). The two species as identified by this

approach are present in a ratio of 15 : 85, indicating
that the main part of the oxygen-binding curve is dom-
inated by one species. Altogether, these results indicate
that models allowing hierarchical functional properties
need to be applied.
The cooperon model includes both KNF-type and
MWC-type interactions [41,42]. It describes a basic
dimeric cooperon (the ab dimer in the case of verteb-
rate Hb), in which cooperative interactions are allowed
according to the induced-fit mechanism. The change in
the binding affinity for the second oxygenation step
compared with the first is quantified via a parameter i.
A value for i larger than unity indicates positive coop-
erativity, and a value smaller than unity indicates neg-
ative cooperativity. The dimeric cooperon is nested
into a higher-level oligomer formed by a number of z
cooperons, which are regulated according to the MWC
mechanism. Thus, for each conformation r and t, a
specific interaction parameter (i
r
and i
t
) is considered.
We applied this model by equating the dimeric cooper-
on with the di-domain subunit of the T. cancriformis
Hb (Fig. 6A). The resulting fit describes the data
somewhat better than the three-state model, with the
additional plus that the values for the parameters do
not violate model-inherent assumptions. The best fit
for this model was achieved for a variant where four

dimeric cooperons form an oligomeric structure, which
functions according to the MWC model. Such a
functional constellation is accommodated by the
substructure D
2
(Fig. 6A). Similar to the results for
vertebrate Hb, there is no need to include KNF-type
interactions in the R-state: the agreement between fit
and data is quite good for a fixed value of i
r
¼ 1
(Fig. 5F; Table 2, model f). The value for the inter-
action parameter i
t
is effector-dependent and ranges
between 4.6 and 11.3. The rmse can be further reduced
by allowing curve-specific values for i
r
(Fig. 5G;
Table 2, model g). When this is done, the value for i
r
ranges between 2.0 and 5.9, with i
t
assuming values
between 3.6 and 9.6. Thus, the KNF-type interaction
predicts a positive cooperativity for the T and the R
state at the level of the di-domain subunit of T. cancri-
formis Hb.
An alternative description of hierarchical interac-
tions provides the nested MWC model [43,44]. Here,

two levels of allosteric units, which both function
according to the MWC model, are embedded into each
other. This model has been successfully applied to
describe the allosteric interactions in hierarchically
structured, multimeric proteins such as arthropod
hemocyanins [45,46], annelid Hbs [47], and chaperonin
GroEL [48]. The nested MWC model was fitted to the
data using different combinations of the size (w) of the
basic allosteric unit and the number (s)ofw-sized
basic allosteric units. In order to keep the number of
free parameters as small as possible, the influence of
effectors such as protons and Mg
2+
was directly inclu-
ded in the model (Eqns 14–16, 18–20). The results
obtained for different combinations of s and w are
shown as contour maps (Fig. 7), which also visualize
the influence of variations in the numbers of Mg
2+
-
binding sites (m) and proton-binding sites (h) per
oxygen-binding site.
di-domain subunit
disulfide-bridged dimer D
possible sub-structures
possible stoichiometries of native Hb isoforms
D
2
D
3

D
4
(D )
42
(D )
24
(D )
33
(D ) D
24
(D)D
42
16-mer:
18-mer:
l
R
rR
rR
tR
tR
tT
tT
rT
rT
l
T
L
A
B
Fig. 6. Possible stoichiometries of Hb quaternary structure and

scheme of the nested MWC model. ( A) T. cancriformis Hb consists
of di-domain subunits, which carry two heme groups and form
disulfide-bridged dimers. Three possible assemblies of dimers (D
2
,
D
3
and D
4
) have been suggested as building blocks of the native
16-meric and 18-meric Hb isoforms [20]. (B) Nested 2 · 4 MWC
model showing the conformational states (tR, rR, rT and tT) and
transitions for a nested, basic allosteric unit containing w ¼ 4 oxy-
gen-binding sites. A number of s ¼ 2 copies of the basic allosteric
unit assemble into a larger structure. This s · w assemblage can
adopt two overall conformations, R and T, which impose con-
straints on the conformations of the constituent basic allosteric
units. The conformational equilibria are described by the allosteric
constants l
R
, l
T
, and L.
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.
3382 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
These contour maps suggest that the size of the basis
allosteric unit is a functional tetramer (i.e. w ¼ 4),
which is accommodated by the disulfide-bridged,

dimeric structure D of the T. cancriformis Hb
(Fig. 6A). The higher-level allosteric unit seems to con-
sist of a number of s ¼ 2–3 functional tetramers. A
number of s ¼ 2 would correspond to the substructure
D
2
, whereas s ¼ 3 would refer to the D
3
(Fig. 6A). D
4
as functionally operative substructure can be ruled out
on the basis of the SSR (Fig. 7). The details of
the contour maps vary somewhat with changing
number of binding sites for protons and Mg
2+
, but
the principal behavior is maintained. The lowest values
for SSR were obtained for (s · w) combinations of
2 · 4 and 3 · 4 with one (h ¼ 1) oxygenation-linked
acid group and half (m ¼ 0.5) a Mg
2+
-binding site per
oxygen-binding site. For both combinations, 2 · 4 and
3 · 4, the oxygen-binding and allosteric-equilibrium
constants (Table 3, Fig. 6B) showed the typical pattern
(K
tT
<K
tR
<K

rR
<K
rT
and L<<l
R
<l
T
) found in anne-
lid Hbs (Macrobdella decora [47]) and arthropod
hemocyanins [45,46].
On the basis of the parameters of the 2 · 4 nested
MWC model, conformational distributions were calcu-
lated for three different situations. Under the condi-
tions used for the measurement of oxygen-binding
curves, the conformation tT is not strongly populated
(Fig. 8A–C). Thus, neither protons nor Mg
2+
displace
the conformational distribution sufficiently towards the
tT state to visibly shift the lower asymptote of the Hill
plot. This also explains the relatively large errors in
the parameter describing the effector binding in the tT
Size of the basic allosteric unit w
3456
Number of coupled allosteric units s
4
3
2
1
1/4 1/2 1

Number (m) of Mg
2+
-binding sites per heme
Number (h) of proton-binding sites per heme
SSR
20 30 40
2
1
1
2
–
Fig. 7. Gallery of error contour maps showing the dependence of
SSR on different parameter combinations. The s · w nested MWC
model was globally fitted to a set of six oxygen-equilibrium curves
of purified Hb in Hepes buffer (Fig. 4B,D). Error contour maps
were calculated for nine different combinations of the number of
proton-binding sites (h) and magnesium-binding sites (m) per oxygen-
binding site. Each error contour map shows (in a grey-scale repre-
sentation) the SSR in relation to the size of the basic allosteric unit
(w) and the number of coupled allosteric units (s). The combination
of h ¼ 0.5 and m ¼ 0.25 yielded the error contour map with the
lowest SSR (¼ 17.8) which occurred at s ¼ 2.1 and w ¼ 4.5. The
best fit using integer-sized (s · w) combinations gave the 3 · 4
model (SSR ¼ 20.3) in the presence of presence of one (h ¼ 1)
oxygenation-linked acid group and half (m ¼ 0.5) a Mg
2+
-binding
site per oxygen-binding site. The 68.3% (i.e. one standard devi-
ation) confidence region of this best-fit integer-sized parameter
combination lies within the SSR contour of 22.3. This confidence

region excludes the 4 · 4 combination (SSR ¼ 34.6) but includes
the 2 · 4 combination (SSR ¼ 22.1). The confidence region also
includes all combinations of m and n (SSR < 21.9), for which the
3 · 4 nested model was tested. Note that the error contour maps
are truncated at SSR levels higher than 40.
Table 3. Best-fit parameter combinations of the nested MWC
model. The best fit of oxygen-binding data from T. cancriformis Hb
gave a model that assumed a basic allosteric unit with w ¼ four
oxygen-binding sites and a functional coupling of s ¼ two to three
allosteric units. The parameters refer to the presence of one oxy-
genation-linked acid group and half a Mg
2+
-binding site per oxygen-
binding site. Given are the oxygen-binding constants (K
ab
), the pK
ab
values, and the Mg
2+
-binding constants (z
ab
) for the four conforma-
tions (ab ¼ tT, rT, tR, rR). The allosteric equilibrium constants (l
T
°,
l
R
°, L°) refer to the reference condition at pH 6.5 and zero Mg
2+
concentration. The SSR was taken as a measure of the goodness

of fit. The degrees of freedom (DF) represent the number of data
points minus the number of fitted parameters. Parameter values
are given as mean ± 95% confidence interval, either in absolute
terms or as a percentage.
Parameter
s · w
2 · 43· 4
K
tT
(mmHg
)1
) 0 ± 0.0100 0.0073 ± 0.0070
K
rT
(mmHg
)1
) 1.41 ± 6% 1.38 ± 7%
K
tR
(mmHg
)1
) 0.028 ± 6% 0.029 ± 2%
K
rR
(mmHg
)1
) 0.181 ± 15% 0.337 ± 10%
pK
tT
7.97 ± 2% 7.40 ± 36%

pK
rT
7.65 ± 1% 7.63 ± 1%
pK
tR
8.16 ± 1% 8.15 ± 1%
pK
rR
7.95 ± 1% 7.84 ± 1%
z
tT
(mM
)1
) 0.016 ± 50% 0 ± 0.147
z
rT
(mM
)1
) 0.023 ± 20% 0.024 ± 18%
z
tR
(mM
)1
) 0.009 ± 33% 0.011 ± 25%
z
rR
(mM
)1
) 0.025 ± 21% 0.028 ± 18%
log l

R
° 2.08 ± 12% 2.99 ± 6%
log l
T
° 4.66 ± 9% 3.12 ± 8.18
log L° )6.70 ± 6% )7.30 ± 6%
SSR 22.1 20.3
DF 99 99
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3383
state. In contrast, the upper asymptote of the Hill plot
is shifted by changes in pH, and the preferential bind-
ing of protons to rR rather than to rT is reflected by
the pK values (pK
rT
<pK
rR
). The presence of Mg
2+
does not lead to shifts in the Hill-plot asymptotes, a
phenomenon that is explained by the very similar val-
ues for the Mg
2+
-binding constants z
rR
and z
rT
. Thus,

the effector-induced phenomena visualized by the Hill
plot are reflected in the conformational distribution
and can be rationalized by the values for the effector
binding constants.
From the detailed analysis of oxygen-binding curves
measured at different effector concentrations, some
information about the functional properties can be
gained. Firstly, the functional coupling extends beyond
the disulfide-bridged dimer D. Secondly, the structural
hierarchy is mirrored in the functional properties, and
a certain complexity in the binding process involving
several conformational substates is present. No indica-
tion of negative cooperativity (for example in the
values for i
r
and i
t
) could be found. Thus, if any
heterogeneity is present at the subunit level, it is not
sufficient to influence the results of the analysis. A lack
of significant functional heterogeneity despite the exist-
ence of different subunit types is known for other
proteins such as the hemocyanins [49–51].
Both the cooperon model and the nested MWC
model identify substructure D
2
(Fig. 6A) as a possible
higher-level allosteric unit. However, D
3
may also be

an allosteric unit, as indicated by the results of the nes-
ted MWC model. Thus, for the 16-mer, a (D
2
)
4
confi-
guration can be proposed. For the 18-mer, we cannot
finally decide between (D
2
)
4
Dor(D
3
)
3.
One can ima-
gine that a mixture of the 2 · 4 and the 3 · 4 nested
MWC model applies, representing the mixture of
16-meric and 18-meric Hb molecules, but it might be
difficult to imagine two different oligomerization
patterns arising from only one subunit type. The other
possibility that has also to be taken into account is
that a 9th dimer D is attached to the 16-meric (D
2
)
4
configuration to yield the 18-meric structure (D
2
)
4

D.
Actually, a hybrid model consisting of a 2 · 4 nested
MWC model and the Hill equation, the latter descri-
bing the oxygen binding of the attached 9th dimer in
an effector-independent manner, gave an SSR similar
to that of the 3 · 4 nested MWC model. The parame-
ters of this hybrid model (data not shown) typically
differed by less than 10% from those obtained for the
pure 2 · 4 nested MWC model.
Although the physiological significance of the pres-
ence of 16-mers and 18-mers remains unresolved, the
Hb of the branchiopod crustacean T. cancriformis
at constant pH 7.6
pH
6.5 7.0 7.5 8.0
log [ , L]
-8
-6
-4
-2
0
Mg
2+
-free conditions
log [l
R
, l
T
]
1

2
3
4
5
[Mg
2+
] (mM)
12 5102050100
log l
T
log l
R
log L
log
C
P
O2
(mmHg)
0.1 1 10 100 1000
Fraction
0.0
0.5
1.0
A
Fraction
0.0
0.5
1.0
B
Fraction

0.0
0.5
1.0
D
tT
tR
rR
rT
Y
Fig. 8. Conformational distributions (A–C) and effector sensitivities of the allosteric equilibrium constants of the 2 · 4 nested MWC model
(D). The conformational distributions as a function of oxygen partial pressure (PO
2
) were calculated for three different conditions (Hepes buf-
fer and 20 °C): at pH 7.60 and 100 m
M Mg
2+
(A), and in the absence of Mg
2+
at pH 8.30 (B) and pH 6.69 (C). The conformational states are:
tT (dotted lines), tR (dashed lines), rR (solid lines), and rT (dotted ⁄ dashed lines). Oxygen saturation (Y) is given by circles. (D) Dependence of
the allosteric equilibrium constants (l
T
, l
R
, L, L) on pH under Mg
2+
-free conditions (left) and on Mg
2+
concentration at constant pH 7.6 (right).
Error bars represent the standard errors of the allosteric equilibrium constants for the reference state at pH 6.5 and zero Mg

2+
concentra-
tion.
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.
3384 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
presents another example of an invertebrate Hb in
which the cooperative interactions do not extend over
the whole structural hierarchy of the multimeric mole-
cule but remain confined to a lower structural level, as
in the case of the giant Hb of the leech [47]. However,
the existence of hierarchical functional properties indi-
cates that a certain plasticity is important for this
animal.
Experimental procedures
Hemolymph extraction and characterization
Tadpole shrimps, T. cancriformis, were raised in the labor-
atory as previously described [20]. Animals with a carapace
length of 11–16 mm, weighing 0.2–0.5 g, were used for the
experiments. The hemolymph was sampled directly from
the dorsal sinus after piercing of the cuticle between the
head shield and the dorsal shield with a fine needle [23] and
aspirating it into thinly drawn-out glass capillaries. Samples
from individual animals were stored separately on ice.
Those lacking brownish tinges (which may indicate the
presence of met-Hb) were then pooled for analysis. In vivo
hemolymph pH was measured by aspirating hemolymph
directly from the dorsal sinus into the capillary pH elec-
trode (Radiometer BMS 2 Mk 2, Copenhagen, Denmark)

without contact with air [33]. Hemolymph osmolality was
measured in three individual organisms using a cryoscopic
osmometer (Osmomat 030; Gonotec, Berlin, Germany).
The chloride concentration was measured in a pooled sam-
ple of hemolymph using a CMT 10 chloride titrator (Radio-
meter). The heme concentration was determined from the
a-absorption peak of oxygenated Hb at 576 nm using a
millimolar absorption coefficient of 10.4 LÆmmol
)1
Æcm
)1
determined for T. cancriformis Hb (R. Pirow, unpublished
data). Hb concentration (mg proteinÆmL
)1
) was deduced
from heme concentration by assuming that the T. cancrifor-
mis Hb is composed of 37-kDa subunits each carrying two
heme groups [20].
Preparation of dialyzed hemolymph
Dialyzed hemolymph solutions were prepared from two
pooled samples (500 lL each) of pure hemolymph drawn
from 60 animals. Hemolymph cells were removed by cen-
trifugation (7000 g, 10 min) at 4 °C. To remove possible
cofactors to Hb–oxygen binding, the Hb-containing super-
natant was repeatedly dialyzed against 0.01 m Tris ⁄ HCl
buffer (pH 7.5 at 5 °C) using 4 mL centrifugal filter devices
with a molecular mas cut-off of 30 kDa (Amicon Ultra-4;
Millipore, Schwalbach, Germany). Any cofactor that may
have been present was thereby diluted to less than 1.2% of
its native concentration. The retentate was finally concen-

trated to the initial hemolymph sample volume (500 lL).
The dialyzed samples had heme concentrations of 1.21 and
1.36 mm, which corresponded to Hb concentrations of 22
and 25 gÆL
)1
. The samples were divided into separate 30 lL
aliquots, which then were either frozen at ) 20 °C or stored
on ice until oxygen-binding measurements.
Preparation of purified Hb
Two purified Hb solutions were prepared from pooled
hemolymph samples (60 and 80 lL), each drawn from three
animals. Each sample was transferred to a mixture com-
posed of 100 lL Tris ⁄ HCl buffer (0.01 m, pH 7.4 at 4 °C)
and 30 lL stock (7 · conc.) solution of a protease-inhibitor
cocktail (complete, Mini; Roche Diagnostics GmbH,
Mannheim, Germany). Hemolymph cells were removed by
5-min centrifugation (table-top centrifuge 5410; Eppendorf,
Hamburg, Germany) and subsequent filtration (0.45 lm,
4-mm syringe filters; Nalgene, Rochester, NY, USA). The
cell-free sample (% 200 lL) was then injected on to a
Superdex 200 column (10 · 300 mm; Pharmacia, Uppsala,
Sweden) equilibrated with 10 mm Tris ⁄ HCl buffer (pH 7.4
at 4 °C) as previously described [20]. Gel filtration pro-
duced a single, slightly asymmetric elution peak, and the
Hb was contained in three successive 0.5-mL fractions.
These fractions were pooled, and the Hb was concentrated
using centrifugal filter devices with a molecular mass cut-
off of 100 kDa (Microcon YM-100; Millipore). The purified
Hb solutions had a final heme concentration of 1 mm
which corresponded to a Hb concentration of 19 gÆL

)1
. The
samples were kept on ice until oxygen-binding measure-
ments.
Oxygen-binding curves
The various types of Hb-containing samples (whole hemo-
lymph, dialyzed hemolymph, purified Hb) were investigated
in two campaigns using different experimental set-ups.
Oxygen-binding curves of dialyzed hemolymph were
recorded at different pH values obtained by adding (to a
30-lL aliquot of Hb stock solution) BisTris buffers
(pH 6.7–7.3) and Tris buffers (pH 7.4–8.1) to a final buffer
concentration of 0.1 m and distilled water to a final sample
volume of 100 lL. pH measurements were carried out in
duplicate, at the same temperature as the oxygen-equilib-
rium measurements, using % 50-lL subsamples and the
above-described pH meter. The effects of inorganic bivalent
ions on oxygen binding were examined by adding accurate
volumes of standard (40 mm, 100 mm,1m) solutions of
MgCl
2
and CaCl
2
. In addition to the experiments with dia-
lyzed Hb, three oxygen-binding curves of a pooled sample
of whole hemolymph were recorded at 0%, 1%, and 2%
CO
2
. Oxygen equilibria were determined on 3–6-lL sub-
samples using a modified gas diffusion chamber [32,52]

linked to cascaded gas mixing pumps (Wo
¨
sthoff, Bochum,
R. Pirow et al. Allosteric control of O
2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3385
Germany). Oxygen tension in the equilibration gas mixtures
was increased stepwise by mixing air with highly pure
(> 99.998%) nitrogen or oxygen. Oxygen saturation was
evaluated from absorbance relative to the values for the
fully oxygenated and fully deoxygenated samples, i.e. those
equilibrated with pure oxygen and nitrogen, respectively.
Oxygen-binding curves of purified Hb were recorded at
20 °C at different pH values obtained by adding (to a 5-lL
aliquot) BisTris buffers (pH 6.7–7.3), Tris buffers (pH 7.4–
8.2), and Hepes buffer (pH 6.7–8.3) to a final buffer
concentration of 0.1 m and distilled water to a final sample
volume of 10 lL. The sample pH was measured at 20 °C
using a micropH-electrode (MI-415; Microelectrodes Inc.,
Bedford, MA, USA). The effect of Mg
2+
ions was exam-
ined by adding accurate volumes of standard (0.5 and 1 m)
solutions of MgCl
2
. Oxygen equilibria were determined on
10-lL subsamples using a gas diffusion chamber linked to a
Wo
¨

sthoff gas mixing pump which mixed air with pure
nitrogen. Oxygen saturation was evaluated from absorbance
relative to the values obtained for the samples equilibrated
with air and nitrogen, respectively. As deduced from earlier
experiments, the Hb is practically saturated with oxygen
at normoxic conditions. Possible errors introduced by a
slightly incomplete saturation when equilibrating with air
were taken into account by an adjusting parameter for nor-
malization to 100% saturation. This parameter remained
above 0.97 in all cases.
The possibility of met-Hb formation during the oxygen-
equilibrium measurements was checked at the end of the
experiment by recording absorbance spectra of the recov-
ered Hb sample. The met-Hb content was derived from
the peak wavelength of the Soret peak using a calibration
curve, which was generated from different linear combina-
tions of the absorption spectra of fully oxygenated Hb
(peak wavelength 415.7 nm) and fully oxidized Hb
(404.3 nm). Gaussian curve-fitting was used to determine
the exact position of the Soret peak. The recovered Hb
samples had a met-Hb content of 4.1 ± 2.4% (mean ±
SD, n ¼ 19).
Determination of oxygen-equilibrium parameters
Oxygenation data based on at least five equilibrium steps
between 0.05 and 0.95 fractional saturation (Y) were con-
verted into Hill plots {log [Y ⁄ (1–Y)] against log PO
2
, where
PO
2

is the oxygen partial pressure} for the estimation of
the half-saturation oxygen tension (P
50
) and Hill’s coopera-
tivity coefficient (n
50
) as described [53]. The median oxygen
partial pressure (P
m
) as a measure of the overall affinity
[54] was derived from the geometric mean of the calculated
Adair constants (see below). The overall heat of oxygen-
ation (D H
app
), i.e. the total net heat released per mol of
oxygen that combines with Hb [55], was calculated from
oxygen equilibria measured at 10 °C and 20 °C at fixed pH
according to:
DH
app
¼ R
D ln P
m
1=T
2
À 1=T
1
ð1Þ
where R is the gas constant and T
1

and T
2
are the absolute
temperatures (283 and 293 K, respectively).
Analysis of oxygen-binding curves
Precise equilibrium measurements for extended Hill plots
that emphasize extreme (low and high) oxygen saturation
values were carried out as previously described [53]. Six
equilibrium curves (Fig. 4B,D), which were measured under
four pH conditions and at three Mg
2+
concentrations in
Hepes buffer, were analyzed using different models for
cooperativity. The binding polynomial (B
mod
) for each
model (Adair, MWC, three-state, cooperon, nested MWC)
is given below. From B
mod
, the degree of saturation (
^
Y)is
obtained by differentiation according to:
^
Y ¼
1
N
xoB
mod
=ox

B
mod
ð2Þ
where x represents the oxygen partial pressure and N is the
number of interacting binding sites.
For some models, the six binding curves were analyzed
simultaneously, with some of the parameters shared
between the curves. This means, that the values of these
particular parameters were forced to be the same for all six
binding curves. This strategy allows the number of free
parameters to be reduced. A comparison of the results of
all models tested is given in Table 2. Curve fitting was per-
formed using the ‘lsqnonlin’ function contained in the opti-
mization toolbox of Matlab 7.0 (MathWorks, Inc.) using
weights obtained as described below. The dependence of
the standard error (s
Y
) on the measured saturation level (Y)
is represented by a parabolic curve [56] based on experi-
mental data (Fig. 9):
S
Y
¼ 0:0443Yð1 À YÞþ0:0005 ð3Þ
The SSR was then calculated according to:
SSR ¼
X
k
i¼1
ðY
i

À
^
Y
i
Þ
2
s
2
Y
i
ð4Þ
where Y
i
and
^
Y
i
are the measured and predicated satura-
tions of the ith point, and k is the number of data points.
Adair equation
To determine the minimum number of interacting binding
sites necessary to describe the data, the binding curves were
analyzed by a tetramerous and octomerous Adair equation
[54,56]. The native Hb isoforms of T. cancriformis contain
32 and 36 oxygen-binding sites [20], respectively, but often
it is not mandatory to assume that all binding sites of large
respiratory proteins are coupled in a cooperative manner.
Allosteric control of O
2
binding in crustacean Hb R. Pirow et al.

3386 FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS
The octomerous Adair equation proved to be appropriate
to (phenomenologically) describe the oxygen binding of the
related D. magna Hb [57,58], which also contains 32 oxy-
gen-binding sites [59]. The binding polynomial for the
Adair equation is given by [54]:
B
Adair
¼ 1 þ
X
N
i¼1
N
i

x
i
Y
i
j¼1
K
j
ð5Þ
where K
j
denotes the intrinsic association equilibrium
(‘Adair’) constant for the jth binding step. The median oxy-
gen partial pressure (P
m
) that is required to analyze the

effects of temperature and pH on the overall oxygen affin-
ity was calculated from the geometric mean of the Adair
constants [54]:
P
m
¼
Y
N
i¼1
K
i
!
À
1
N
ð6Þ
MWC model and three-state model
The MWC model [60] is based on two conformations
(r and t), which are in equilibrium (L) and have different
binding affinities for the ligand (K
r
, K
t
). The number of
molecules that are coupled so that they always adopt the
same conformation is defined by the size of the allosteric
unit (q):
B
MWC
¼

ð1 þ K
r
xÞ
q
þ Lð1 þ K
t
xÞ
q
1 þ L
ð7Þ
A linear extension of this model is the three-state model
[61] which allows a third conformation (s):
B
3-state
¼
ð1 þ K
r
xÞ
q
þ L
s
ð1 þ K
s
xÞ
q
þ L
t
ð1 þ K
t
xÞ

q
1 þ L
s
þ L
t
ð8Þ
For a situation where two molecule species with oxygen-
binding characteristics obeying the MWC formalism are
present as fractions q and 1–q, the saturation function
(Y
2-MWC
) is given by:
Y
2-MWC
¼ qY
1
þð1 À qÞY
2
ð9Þ
The individual saturation functions Y
1
and Y
2
are derived
from B
MWC
with species-specific values for K
r
, K
t

, and L.
Cooperon model
The cooperon model [41,42] describes a situation, where
two binding sites are coupled via an induced-fit (KNF)
mechanism [62]. This mechanism leads to a binding affinity
for the second binding step which is altered by a factor i
compared with the first binding step. This KNF-coupled
dimer is nested into a higher-level allosteric unit (of size z),
which functions according to the MWC model:
B
cooperon
¼
ð1 þ 2K
r
x þ i
r
K
2
r
x
2
Þ
z
þ Lð1 þ 2K
t
x þ i
t
K
2
t

x
2
Þ
z
1 þ L
ð10Þ
Nested MWC model
Oxygen-binding curves were also analyzed in terms of the
nested MWC model [43,44], which takes hierarchies within
the quaternary structure of multimeric proteins into
account. In this model it is assumed that a number of w
binding sites are functionally coupled to form an allosteric
unit which, in accordance with the standard MWC model
[60], can adopt two basic conformations (r and t). A num-
ber of s copies of these basic allosteric units assemble into
a larger allosteric unit containing q ¼ s · w oxygen-
binding sites. This s · w structure can adopt two overall
conformations (R and T) which impose constraints on the
conformations of the constituent (nested) w-sized allosteric
units. When the s · w structure is in the R-state, the nes-
ted w-sized allosteric units can adopt two conformations,
B
Fractional ox
yg
en saturation (Y)
0.0 0.2 0.4 0.6 0. .0
Standard deviation (s
Y
) of Y
0.00

0.01
0.02
A
Standard deviation (s
Y
) of Y
0.00
0.01
0.02
pH 8.30
pH 7.50
pH 7.12
pH 6.69
mean S
Y
curve fit
Fig. 9. (A) Standard deviation (S
Y
) of fractional oxygen saturation (Y)
as a function of Y. Individual S
Y
profiles were obtained under differ-
ent pH conditions and derive from the oxygen-equilibrium data of
two separate Hb preparations; the respective oxygen-equilibrium
curves are shown in Fig. 4B. (B) Average standard deviation (cros-
ses) of the data shown in (A). The solid line was fitted to the data
by Eqn (3). This bell-shaped curve was further used to generate
a weight function for the least-squares curve-fitting analysis of
oxygen-equilibrium curves.
R. Pirow et al. Allosteric control of O

2
binding in crustacean Hb
FEBS Journal 274 (2007) 3374–3391 ª 2007 The Authors Journal compilation ª 2007 FEBS 3387
rR and tR. Two alternative conformations, rT and tT, are
available when the overall conformation is T (Fig. 6). The
equilibrium between the unliganded R
0
and T
0
states of
the overall conformation is described by the equilibrium
constant L ¼ [T
0
] ⁄ [R
0
]. The allosteric equilibrium con-
stants l
R
and l
T
correspond to the concentration ratio of
the unliganded states of the basic allosteric unit, l
R
¼
[tR
0
] ⁄ [rR
0
] and l
T

¼ [tT
0
] ⁄ [rT
0
]. The binding polynomial
for an individual oxygen-binding site of a nested w-sized
allosteric unit in a given conformation ab (¼ tT, rT, tR,
rR) is given by:
B
ab
¼ 1 þ K
ab
x ð11Þ
where K
ab
refers to the binding constant for a particular
conformation. The binding polynomial for the s · w struc-
ture, i.e. the assembly of s copies of nested w-sized allosteric
units, can be given by [47]:
B
nMWC
¼ B
w
rR
þ l
R
B
w
tR
ÀÁ

s
þ K B
w
rT
þ l
T
B
w
tT
ÀÁ
s
ð12Þ
with
K ¼ L
ð1 þ l
R
Þ
s
ð1 þ l
T
Þ
s
¼
½rT
0

s
½rR
0


s
ð13Þ
This particular form allows us to include the binding prop-
erties of effectors explicitly into a saturation function (see
below). The latter equation shows that the s-th root of L
describes the allosteric equilibrium between the two relaxed
conformations available to the basic allosteric unit in the
unliganded state.
The influence of effectors such as protons and Mg
2+
on
the allosteric equilibrium constants (l
R
, l
T
, L) was taken
into account by implementing the corresponding effector-
binding functions. This approach successfully describes pro-
ton binding [59] and urate binding [63] in hemocyanins.
Here, we assume the simplest effector-binding model with h
identical proton-binding sites and m identical Mg
2+
-bind-
ing sites per oxygen-binding site. It is assumed that the
binding of protons and Mg
2+
occurs independently. Given
a nested s · w structure, the dependence of the allosteric
equilibrium constants on magnesium concentration is des-
cribed by [59]:

l
R
¼ l
Ã
R
ðQ
tR
=Q
rR
Þ
wm
ð14Þ
l
T
¼ l
Ã
T
ðQ
tT
=Q
rT
Þ
wm
ð15Þ
K ¼ K
Ã
ðQ
rT
=Q
rR

Þ
swm
ð16Þ
with
Q
ab
¼ 1 þ z
ab
½Mg
2þ
ð17Þ
where l
R
*, l
T
*, and L* represent the allosteric equilibrium
constants in the absence of magnesium at a given pH. Q
ab
and z
ab
refer to the Mg
2+
-binding polynomial and the
Mg
2+
-binding constant of a particular conformation
(ab ¼ tT, rT, tR, rR), respectively. The dependence of the
allosteric equilibrium constants on pH in the absence of
Mg
2+

is given by:
l
Ã
R
¼ l

R
ðq
tR
=q
rR
Þðq

rR
=q

tR
Þ
ÂÃ
wh
ð18Þ
l
Ã
T
¼ l

T
ðq
tT
=q

rT
Þðq

rT
=q

tT
Þ
ÂÃ
wh
ð19Þ
K
Ã
¼ K

ðq
rT
=q
rR
Þðq

rR
=q

rT
Þ
ÂÃ
swh
ð20Þ
with

q
ab
¼ 1 þ 10
pK
ab
ÀpH
ð21Þ
where l
R
°, l
T
°, and L° represent the allosteric equilibrium
constants in the absence of Mg
2+
at pH 6.5 (reference con-
dition), whereas q
ab
and pK
ab
refer to the proton-binding
polynomial and the pK value of the oxygenation-linked
acid group for the particular conformation. q
ab
° refers to
the reference state at pH 6.5 and zero Mg
2+
concentration.
Parameter constraints included the following lower and
upper boundary values: K
ab

>0,z
ab
> 0, and pK
ab
¼ 6–9.
Uncertainties in best-fit parameter values are given as 95%
confidence interval. The confidence interval of L was calcu-
lated from best-fit values and the standard errors of l
T
, l
R
,
and L according to the law of error propagation [64].
Statistical analysis
Unless otherwise stated, data are expressed as mean ± SD
with n indicating the number of observations. A compar-
ison of curve-fitting results was performed via F-statistics
using a confidence level of 68.3% (i.e. one standard devi-
ation). The F-statistics predicted the increase in the vari-
ance (or the SSR) of a fit that is associated with one
standard deviation of the parameter.
Acknowledgements
The technical assistance of Anny Bang, Ina Buchen,
and Marita Koch is gratefully acknowledged. We wish
to thank three anonymous reviewers for their
constructive criticism and helpful comments on the
manuscript. This work was supported by the Danish
Natural Science Research Council.
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