Bivalent cations increased oxygen affinity, Mg2+ exerting a greater effect than Ca2+.. Analysis of cooperative oxygen binding in terms of the nested Monod–Wyman–Changeux MWC model reveale
Trang 1the primitive branchiopod crustacean Triops cancriformis Ralph Pirow1, Nadja Hellmann2and Roy E Weber3
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: pirow@uni-muenster.de
(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: P50¼ 13.3 mmHg,
n50¼ 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, Mg2+ exerting a greater effect than Ca2+ 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, Mg2+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; ir, it, interaction parameters of the cooperon model; Ki, Adair constants of the i th oxygenation step; Kr, Ks, Kt, oxygen-binding constant for a particular conformation; K ab , oxygen-binding constant for a particular conformation; m, number of Mg2+-binding sites per oxygen-binding site; MWC, Monod–Wyman–Changeux; n50, Hill’s cooperativity coefficient at half-saturation; P50, half-saturation oxygen partial pressure; Pm, median oxygen partial pressure; PO2, oxygen partial pressure; pKab, 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; sY, 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 , Mg2+-binding constant of a particular conformation; ab (¼ tT, rT, tR, rR), particular conformation of the nested allosteric model; u, Bohr factor.
Trang 2groups, 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 (17–35C)
during summer months Horne [8] similarly observed
large diurnal fluctuations in oxygen concentration
(1–6.5 mgÆL)1) and temperature (17–30C) 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 concentraconsump-tion
decreases to critical levels of 17% air saturation
(1.2–1.3 mgÆL)1) for Lepidurus lemmoni at 12C [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 verteinverte-brates 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 condiregula-tions 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 (n¼ 3 animals) at
20C A markedly lower pH value of 7.1 (presumably measured at 23C) has been given for T longicaudatus [21] The hemolymph had an osmolality of 150 ± 19 mosmolÆkg)1 (n¼ 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 (P50¼ 13.3 mmHg), cooperativity (n50¼ 2.3), and pH sensitivity (Bohr factor u ¼ dLogP50⁄ dpH ¼)0.18) at pH 7.44 (Tris buffer) and
Trang 320C (Fig 1A,C) Raising the pH from 6.7 to 8.1
increased the n50from 1.9 to 2.9 and decreased the P50
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 P50of 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 P50 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 P50 of
14.0 mmHg
The oxygen-binding properties of whole hemolymph
were examined at three CO2 levels at 20C (Fig 2)
Strong alkalinization of hemolymph induced by CO2
-free conditions yielded an extreme affinity (P50¼
7.1 mmHg) and cooperativity (n50¼ 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 P50
values of 13.4 and 16.5 mmHg, respectively, and n50 values of 2.41 and 2.02, respectively Essentially the same P50⁄ n50 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% CO2 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 (P50¼ 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 (P50¼ 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 in Notostraca The remarkably
C
pH
P50
0.7
0.8
0.9
1.0
1.1
pH
A
n50
1.5
2.0
2.5
3.0
3.5
B
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 (n50) and (C) half-saturation oxygen tensions (P50) at 20 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.
0.0 0.5 1.0
whole hemolymph
Fig 2 Oxygen-binding curves of T cancriformis Hb in whole hemo-lymph at three different CO 2 concentrations and 20 C.
Trang 4large variability in P50 observed in notostracan Hbs
(6.8–20 mmHg, pH 7.1–7.5, 20–23C) may reflect
genus⁄ species-specific variation in oxygen tolerance
and temperature preference In comparison with
Lepidurusspp., 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 (n50¼ 1.8–3.1, pH 6.7–8.3, 20 C) and the
small Bohr effect (u¼)0.05 to )0.24, pH 7.0–8.0,
20C) 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 20C increased the P50 from 6.5 to 13.3 mmHg at pH 7.44 (Fig 1C) The pH-dependence
of n50 was virtually unaffected by temperature (Fig 1A) The temperature-dependence of the P50 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 dissociadissolu-tion 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
P50 (mmHg) n50
T
Bohr factor u b
DH (kJÆmol)1) Reference Anostraca
Artemia salina
Notostraca
Conchostraca
Cladocera
Daphnia magna
Daphnia pulex
a Calculated from the Adair constants; b dLogP 50 ⁄ dpH.
Trang 5may also compromise oxygen loading in warm hypoxic
water
Effect of bivalent cations on oxygen binding
The addition of Mg2+and Ca2+increased the oxygen
affinity of T cancriformis Hb at cation concentrations
higher than 5 mm (Fig 3C,D) For example, increasing
the Mg2+ concentration from 0 to 20 mm decreased
the P50from 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 Ca2+ was
smaller than that of Mg2+ (Fig 3C) The cations had
no strong effect on cooperativity (Fig 3A,B); the
indi-vidual values of n50were 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 Mg2+
exerted a greater effect than Ca2+ The lack of a Cl–
effect and the greater sensitivity of oxygen affinity to
Mg2+than Ca2+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 Mg2+and Ca2+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 Mg2+ 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 (K1¼ 0.027– 0.030 mmHg)1) is independent of proton and Mg2+ concentration Increasing the Mg2+ 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 (KN) KN assumed values of 0.86–0.95 mmHg)1at 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 K1 and KNreveals 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 K1 and KN, increasing Mg2+ concentrations raised the oxygen affinity of T cancriformis Hb without affecting
K1and KN The physiological significance, if material, of the effects of bivalent cations on Triops Hb is not clear The cation concentrations in T cancriformis hemolymph (Ca2+, 1.6–3.1 mmolÆkg)1; Mg2+, 0.6–0.8 mmolÆkg)1;
R Pirow, unpublished data) and T longicaudatus hemolymph (Ca2+, 0.8–1.7 mm; Mg2+, 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 Mg2+ concen-trations are lethal to T longicaudatus [35], and the regulation of internal Mg2+concentrations in this spe-cies breaks down when external levels exceed 14 mm, although Na+, K+, Ca2+, Cl– and SO42+ concentra-tions continue to be regulated [35]
C
P50
0.7
0.8
0.9
1.0
1.1
A
n50
1.5
2.0
2.5
3.0
3.5
B
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 n50and P50of purified Hb in Hepes buffer (diamonds) at pH 7.6.
Trang 6The 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
(KN) 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 Mg2+ In Hepes buffer, KN increased from 0.40 to
1.34 mmHg)1when 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
99 98 95 90 70 50 30 10 5 2
–log KN
D
log PO2
0.0 0.5 1.0 1.5 2.0
99 98 95 90 70 50 30 10 5 2
A
-1 0 1 2
C
log PO2
0.0 0.5 1.0 1.5 2.0
-1 0 1 2 dialyzed hemolymph in Tris buffer purified Hb in Hepes buffer
–log K1
pH 8.30
pH 7.50
pH 7.12
pH 6.69
pH 7.77
pH 7.44
pH 6.71
[Mg2+] pH
100 7.78
15 7.80
0 7.77
[Mg2+] 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-bufBis-Tris-buf-fered
purified Hb (B) in the absence of Mg2+ The
lower row shows the influence of Mg 2+
concentration (values in mmolÆL)1) on Hb
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 (K1and KN).
Trang 7Structure–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 D2, D3 or D4 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% CO2, 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 D2), 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.
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
K R ¼ 1.546
log M ¼ 5.9–10.2
q ¼ 5.3–8.0
Trang 8leads 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
Kt and Kr 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 oxygen saturation Y
A
-0.05 0.00 0.05
2-state MWC (shared q)
B
C
-0.02 0.00
E
-0.02 0.00 0.02
F
-0.02 0.00
H
Fractional oxygen saturation Y
-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
3-state MWC (curve-specific q)
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 iR (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.
Trang 9in 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 (ir and it) 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 D2 (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 ir¼ 1 (Fig 5F; Table 2, model f) The value for the inter-action parameter it is effector-dependent and ranges between 4.6 and 11.3 The rmse can be further reduced
by allowing curve-specific values for ir (Fig 5G; Table 2, model g) When this is done, the value for ir ranges between 2.0 and 5.9, with it 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-formisHb
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) of w-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 Mg2+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 Mg2+ -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
16-mer:
18-mer:
rR
rR
tR
tR
tT tT
rT
rT
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 (D2,
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.
Trang 10These contour maps suggest that the size of the basis
allosteric unit is a functional tetramer (i.e w¼ 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 s¼ 2–3 functional tetramers A
number of s¼ 2 would correspond to the substructure
D2, whereas s¼ 3 would refer to the D3 (Fig 6A) D4
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 Mg2+, 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 (m¼ 0.5) a Mg2+-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 (KtT<KtR<KrR<KrT and L<<lR<lT) 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 Mg2+ 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
4
3
2
1
-binding sites per heme
SSR
2
1
1
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-oxygen-binding constants (Kab), the pKab values, and the Mg2+-binding constants (z ab ) for the four conforma-tions (ab ¼ tT, rT, tR, rR) The allosteric equilibrium constants (l T ,
lR, 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