The efficiency in O2 transport of an O2 carrier is best expressed by the slope of O2 equilibrium curve (dS/dP), where S and P denote the fractional O2 saturation of the carrier and the partial O2 pressure, respectively. The aim of this study is to characterize the O2 binding to arthropod hemocyanins (Hcs) in term of the O2 transport efficiency, and for that purpose we have reexamined the previously published O2 equilibrium data and their mathematical interpretations. Examination of the data for 6- and 12-meric Hcs from lobsters (Panulirus japonicus, Procambarus clarkii) revealed the relationship Pdmax < P50 ≈ Pnmax, where Pdmax, P50 and Pnmax denote the P at which dS/dP is maximized, P at half-saturation and P at which the Hill coefficient is maximized, respectively. On the other hand, 48-meric Hcs from horseshoe crabs (Tachypleus gigas, and Limulus polyphemus) gave the relationship Pdmax ≤ P50 < Pnmax, when the O2 binding is cooperative. The results indicate that Hc functions most effectively at P values lower than that expected from the maximal degree of cooperativity, similarly to the previous results obtained for human hemoglobin (Hb) [6]. The profile of dS/dP vs. P curves for lobster Hcs was similar to that of Hb, showing a single maximum and a relatively symmetric shape. On the other hand, the curves for horseshoe crab Hcs showed multiple maxima tailing in the low P range, indicating that the O2 transport efficiency is high even under hypoxic circumstances. As far as the O2 transport efficiency is concerned, horseshoe crab Hcs are regarded as unique, and the features seem to reflect their uniqueness in the molecular architecture and the mode of allosteric transition.
INTRODUCTION
Hemocyanin (Hc) is a copper-containing O2 carrier found in the hemolymph of many arthropods and mollusks. In arthropod Hcs, molecular mass of the subunit is about 75 kDa, and the whole molecules are composed of 6, 12, 24 or 48 subunits. The 6-meric unit is regarded as the “binding block”, and the size of the molecule is controlled by the “linker” subunits, which bridge between the structural units. Under the physiological conditions they show cooperativity in the O2 binding, which enables efficient loading and unloading of O2. Their O2 equilibria have been described on the basis of allosteric model of Monod et al. [13], but various extensions of the model have been introduced to describe them system-atically [1, 3, 7, 14, 15]. Although the cooperativity of Hc has often been discussed in analogy to that of Hb, they have several different features, which presumably arise from their different molecular architectures and subunit interactions.
The magnitude of cooperativity in an O2 carrier has usually been discussed in terms of the slope of the Hill plot (n), but the efficiency of O2 transport is best expressed by the slope of O2 equilibrium curve, dS/dP (S′), where S and P stand for the O2 saturation of the O2 carrier and the partial pressure of O2, respectively. The quantity, S′, directly relates to the amount of O2 loaded or unloaded on a small change in P. Figure 1 shows the S vs. P and S′ vs. P curves for cooperative (Hb) and non-cooperative (Mb) O2 binding. The curves for Hb were obtained from the experimentally obtained Adair constants [5]. The curves for the noncooperative binding (such as the binding to Mb) were calculated numerically on the assumption of the hyperbolic binding function. The S′ vs. P curve for Hb is characterized by a relatively symmetric shape with a single maximum, while the non-cooperative binding is characterized by a monotonously decreasing curve without any maximum. Our preceding study [6] showed that in human Hb the relation Pdmax < P50 < Pnmax holds generally, where Pdmax, P50 and Pnmax are P at which S′ is maximized, P at the half-saturation and P at which n is maximized, respectively. The result indicates that Hb transports O2 most effectively at P lower than that expected from the maximal degree of cooperativity. In Hb the S value giving the maximum S′ (S′max) was about 0.38 irrespectively of the experimental conditions.
Fig. 1
O2 equilibrium and transport efficiency of human Hb and a non-cooperative carrier. Hb at pH 7.4, 0.1 M Cl−, 2 mM DPG (P50 = 14.0 Torr), calculated from the Adair constants [5]. Non-cooperative O2 binding, calculated for P50 = 14.0 Torr. The dashed and solid lines show the S vs. P and S′ vs. P curves, respectively.
The aim of this study is to examine the O2 transport efficiency of arthropod Hcs in comparison with that of Hb. We have reexamined the O2 equilibrium data and cooperativity models previously presented for Hcs of two Decapoda species (spiny lobster Panulirus japonicus and crayfish Procambarus clarkii) and two Xiphosura species (horseshoe crabs, Tachypleus gigas and Limulus polyphemus). Panulirus has 6-meric Hc, while Procambarus contains 6-meric and 12-meric Hc molecules that are not interchangeable [10]. The horseshoe crab Hcs are 48-meric and are characterized by high Hill coefficients (n = 3 to 5) [3]. In this study we have found distinct differences in the O2 transport efficiency profile between the lobster and horseshoe crab Hcs, which seems to reflect the differences in the mechanism of the allosteric transitions.
MATERIALS AND METHODS
For the calculation of ΔS vs. P plots we have used previously published O2 equilibrium data for Hcs of Panulirus japonicus (spiny lobster)[7], Procambarus clarkii (crayfish) [10] and Tachypleus gigas (horseshoe crab) [8]. The O2 equilibrium data were smoothed by a moving average method. Then the change in S was calculated from the smoothed data and expressed as ΔS per 1 Torr. In addition, we also calculated the theoretical S′ vs. P curves on the basis of the fitted mathematical models. In the preceding paper [6] on Hb, we have calculated the O2 transport efficiency on the basis of Adair equation. In Hc, however, the order of the equation is too high (6 or more), and it is generally difficult to obtain a statistically significant set of values for the Adair constants. We therefore decided to apply the previously published results of model fitting studies. For arthropod Hcs a considerable number of theoretical studies have been published, but for the present purpose it is important whether the mathematical model can reproduce the O2 equilibrium of the Hc in question with a sufficient accuracy, rather than whether it is theoretically valid. On this criterion we selected the following O2 binding model and calculated the S′ vs. P plots, as described below, using the reported parameter values. The used models were :the three-state model for Panulirus Hc [7], the two-state model for Procambarus and Tachypleus Hcs [8, 10] and the “interacting cooperative unit (ICU)” model for Limulus Hc [3].
According to the theory of Wyman [18] S is calculated from the binding polynomial B as:
where m is the number of interacting subunits. The function B depends on the mathematical model. From Eq. (1), S′ is given as and S′0 (S′ at P = 0) is obtained as
The S′0 value corresponds to the affinity of the carrier for the first ligand (O2) molecule.
In the original model of Monod et al. [13] an allosteric equilibrium was assumed between two different affinity states (R and T), but the model was extended to three affinity states by Minton and Imai [12] to apply to the O2 binding to Hb. The binding polynomial for the two-state model is written as
and S′0 is calculated as For the three-state model, and where KR, KT and KS are the O2 equilibrium constants for the states R, T and S, respectively. L and M are the allosteric equilibrium constants ([T]/[R] and [S]/[R], respectively). It should be noted that all the four parameters (m, L, KR and KT) in Eq. (4) must be variable when the two-state model was applied to the O2 binding to Procambarus and Tachypleus Hcs [8, 10].
Brouwer and Serigstad [3] proposed the “interacting cooperative unit (ICU)” model to describe the O2 equilibrium of Limulus Hc. In this model an equilibrium is assumed between the functional m-mer and 2m-mer, in each of which an additional equilibrium is assumed to exist between the states R and T. The binding polynomial is written as
and where K′R and K′T are the O2 association constants for the cooperative units composed of 2m subunits in the states R and T, respectively. The equilibrium constants, L, I, and L1, are defined as [Tm]/[Rm], [R2m]/[Rm], and [T2m]/[R2m], respectively.
The numerical calculation was performed with programs compiled with MS-FORTRAN on an NEC 9801 model DA personal computer.
RESULTS
Figure 2A and 2B show the S vs. P and ΔS vs. P plots calculated from the O2 equilibrium data for Panulirus Hc and Procambarus 12-mer Hc [7, 10]. The ΔS vs. P plots for the lobster Hcs showed a single maximum and a relatively symmetric shape, which closely resemble those for human Hb (Fig. 1). In Procambarus Hc, the n values for the 6-mer were somewhat lower than those for the 12-mer [10], but no substantial difference was observed in the profile of S′ vs. P plots (data not shown).
Fig. 2
O2 equilibrium and ΔS vs. P plot of decapod Hcs. The open and closed symbols show the O2 equilibrium and ΔS vs. P plots, respectively. (A) Panulirus Hc [7]. (square) Cooperative O2 binding at pH 7.5 in the presence of 10 mM CaCl2 (P50 = 20.6 Torr). (triangle) Non-cooperative O2 binding to EDTA-treated Hc at pH 9.5 (P50 = 17.6 Torr). (B) Procambarus Hc 12-mer [10]. (square) Cooperative O2 binding in physiological saline at pH 7.5 (P50 = 4.33 Torr). (triangle) Non-cooperative O2 binding at pH 9.5 in the presence of 1 mM EDTA (P50 = 12.49 Torr). (C) Tachypleus Hc [8]. (square) Cooperative O2 binding in physiological saline at pH 7.33 (P50 = 5.54 Torr). (triangle) Non-cooperative O2 binding at pH 9.03 in the presence of 1 mM EDTA (P50 = 1.47 Torr).
Figure 2C shows the S vs. P and ΔS vs. P plots for Tachypleus Hc obtained from the O2 equilibrium data. Under the physiological conditions, however, its ΔS vs. P plot was considerably different from those for the lobster Hcs and human Hb described above. Its shape was broader and asymmetric, spreading to the lower P range.
When Hcs from three species dissociated into the subunits by treatment with EDTA, it shows a hyperbolic O2 binding curve characteristic of the non-cooperative ligand binding as shown in Figure 1.
Figure 3A shows the S vs. P and S′ vs. P curves for Panulirus and Procambarus Hcs which were obtained mathematically on the basis of cooperativity models. The S′ vs. P curves for Panulirus Hc were computed on the three-state model with the parameter values fitted to the data shown in Figure 2A [7]. The S′ vs. P curves for Procambarus Hc were obtained on the basis of the two-state model with the four variable parameters (m, L, KR and KT) [10]; the parameter values fitted to the data shown in Figure 2B were used for the computation. As expected from the goodness of the fit, the calculated S′ curves well reproduced the observation (Fig. 2A and 2B).
Fig. 3
O2 equilibrium and transport efficiency of Hcs calculated on the basis of the cooperativity models. The dashed and solid lines show the S vs. P and S′ vs. P curves, respectively. (A) (P.j.) S and S′ for Panulirus Hc, calculated on the basis of the three-state model with the parameter values fitted to the O2 equilibrium data shown in Fig. 2A (m = 6, L = 2.97 × 106, M = 2.99 × 104, KT = 0.008 Torr−1, KR = 0.6 Torr−1, and KS = 0.0624 Torr−1) [7]. (P.c.) S and S′ for Procambarus Hc 12-mer, calculated on the basis of the two-state model with the parameter values fitted to the O2 equilibrium data shown in Fig. 2B (m = 5.22, L = 6.53 × 103, KT = 0.0702 Torr−1, and KR = 1.32 Torr−1) [10]. Scales of abscissa, for Procambarus (top) and Panulirus (bottom) Hcs. (B) (T.g.) S and S′ for Tachypleus Hc, calculated on the basis of the two-state model with the parameter values fitted to the O2 equilibrium data shown in Fig. 2C (m = 4.61, L = 1.81 × 107, KT = 0.101 Torr−1 and KR = 7.94 Torr−1) [8]. (L.p.) S and S′ for Limulus Hc, calculated on the ICU model with the parameter values fitted to the O2 equilibrium data at pH 7.4 in the presence of 10 mM Ca2+ (L = 1.546 × 103, L1 = 6.418 × 109, I = 3.972 × 10−7, KT = 16.08 Torr−1, K′T = 7.23 Torr−1, KR = K′R = 0.61 Torr−1) [3].
Figure 3B shows the S vs. P and S′ vs. P curves for Tachypleus and Limulus Hcs. The S′ vs. P curve for Tachypleus Hc was obtained on the basis of the two-state model with four parameter values fitted to the data shown in Figure 2C [8], and it showed a good agreement with the observed data. The curve for Limulus Hc was computed according to the ICU model together with fitted parameter values that were presented by Brouwer and Serigstad [3]. Similarly to the results on Tachypleus Hc, the S′ vs. P curve for Limulus Hc was characterized by multiple peaks and rather an asymmetric shape.
Figure 4 shows the Pdmax and Pnmax values as a function of P50 under various conditions where the Hcs show the cooperativity in O2 binding. The data points were obtained mathematically on the basis of the cooperative models using fitted parameter values, as described in Methods. As judged from the goodness of the models, the error arising from the model fitting is estimated to be small and thus negligible. In Panulirus and Procambarus Hcs, as shown in Figure 4A, the Pnmax value was generally close to the P50 value, but both values were significantly greater than the corresponding Pdmax value. In the horseshoe crab Hcs, on the other hand, the Pdmax values were nearly equal to or smaller than the corresponding P50 values, while the Pnmax values were considerably greater than the P50 values (Fig. 4B). In this respect, horseshoe Hcs were also different from the vertebrate Hb and lobster Hcs.
Fig. 4
Relationship between Pdmax, Pnmax and P50 in the cooperative O2 binding to Hcs. Open symbols, Pnmax; cross and plus symbols, Pdmax. (A) Lobster Hcs. (circle and cross) Panulirus Hc, (square and plus) Procambarus Hc 12-mer and 6-mer. (B) Horseshoe crab Hcs. (circle and plus) Tachypleus Hc, (square and cross) Limulus Hc. The values for Pdmax, Pnmax and P50 were obtained from the mathematical models fitted to the O2 binding (see Methods).
Figure 5 shows the maximum S′(S′max) values and S′ values at P = 0 (S′0) as functions of Pdmax for Hb and Hcs under the conditions where they bind O2 cooperatively. The plot for Panulirus Hc (and Procambarus Hc, though data are not shown) was very similar to that for Hb; both S′max and S′0 changed greatly with the change in Pdmax (and consequently with P50). Limulus Hc was also unique on this point, and S′max was almost constant in spite of the wide variation of Pdmax (Fig. 5A). As seen in Figure 5B, the S′0 for Limulus Hc was independent of Pdmax, though the plot was more scattered. In Tachypleus Hc, the significant difference was not observed between the S′max and S′0.
Fig. 5
S′max and S′0 values plotted as functions of Pdmax. (plus) Human Hb, (cross) Panulirus Hc, (closed triangle) Tachypleus Hc and (closed circle) Limulus Hc. The values were calculated on the basis of the fitted mathematical models (see Methods). The plots for human Hb were calculated on the basis of the Adair equation presented by Imai [5].
DISCUSSION
The results shown in Figure 4 show that the function dS/dP is generally maximized at P lower than that giving the maximum slope of the Hill plot (Pdmax < Pnmax). This means that the O2 transport efficiency is maximized at P lower than that expected from the magnitude of the cooperativity. This was also true for human Hb [6], though some differences were observed in their relative magnitudes. In Hb the relationship Pdmax < P50 < Pnmax was found for all the cases examined [6], but lobster (Panulirus and Procambarus) Hcs gave the relationship Pdmax < P50 ≈ Pnmax, whereas horseshoe crab (Limulus and Tachypleus) Hcs gave the relationship Pdmax ≤ P50 < Pnmax.
In Procambarus Hc the Hill coefficient (n) for the 12-mer is significantly higher than that for the 6-mer [10], but in this study no significant difference was found in the S′ vs. P plot. Apparently, the association to 12-meric structure seems to have little effect on the O2 transport efficiency. It will be of interest to examine further the S′ profiles of other 12-meric and 24-meric Hcs such as those of crabs and spiders.
The results of the present study show that the lobster Hcs resemble human Hb in a sense that the S′ vs. P curves give a single and relatively symmetric peak, and also that the S′0 values are relatively low. On the other hand, curves for the horseshoe crab Hcs are characterized by multiple peaks or shoulders tailing toward the low P region (Fig. 3B). In addition, in the case of Limulus Hc, the maximum transport efficiency, S′max, was independent of Pdmax, while the S′0 values were relatively high irrespectively of Pdmax (Fig. 5). The present results indicate that distinct differences exist between the lobster and horseshoe crab Hcs in the O2 binding profile, which may be ascribed to the difference in the cooperativity mechanism.
The S′0 values for horseshoe crab Hcs were generally higher than those for lobster Hcs and Hb (Fig. 5B). This is because horseshoe crab Hcs bind O2 almost noncooperatively when P is low; previous studies [3, 8] have shown that the slope of Hill plot remains close to unity even up to S = 0.3 in many cases examined. Therefore in the low P range the profile of the S′ vs. P plot is analogous to that of Mb (Fig. 1), and the S′ value increases rapidly as P approaches to 0, as exemplified in the diagram for Tachypleus Hc (Fig. 3B). In terms of the allosteric model this property is explained by a relatively low ratio of KR/KT and a large allosteric constant (L) [3, 8]. The protein molecule is confined in the state T at low P, and relatively a high P value is required for the allosteric transition to take place.
According to Brouwer and Serigstad [3], the O2 binding to Limulus Hc can be described by the ICU model. In this model it is assumed that an equilibrium exists between the functional 6-mer and 12-mer, which undergo different allosteric transitions (T6↔R6 and T12↔R12). By numerical examination of the model it was found that P values giving the maxima and shoulders in the S′ vs. P curve correspond to those at which the T/R transitions take place in the functional 6-mer and 12-mer (data not shown). If the two switchover points are close in position, then maxima may apparently fuse into a single peak. Thus in the framework of the ICU model, the uniqueness of horseshoe crab Hc is explained by the presence of different functional species that make different allosteric transitions. More generally, the heterogeneity in the S′ profile of horseshoe crab Hcs possibly arises from the huge molecular construction which allows many kinds of cooperative interactions. In the case of Tachypleus Hc, only a single peak was observed in the S′ vs. P diagram under the conditions examined (Fig. 3B), and its O2 equilibra could be fitted by the two-state model with m as an adjustable parameter (Eq. 4) [8].
Apart from such an allosteric model, it is also possible that in the horseshoe crab Hcs the subunit heterogeneity contributes to the functional heterogeneity. Horseshoe crab Hcs are composed of 6 or more different subunits, of which O2 affinities differ by several folds [2, 9, 16], and this also can cause the heterogeneity in the O2 binding.
In the O2 carriers including vertebrate Hb and arthropod Hcs, it seems to be a general rule that they are most adapted to O2 concentration lower than normal. This means that they are designed to function best in hypoxia, such as occurring under vigorous exercise. Particularly in arthropods, blood O2 levels are strongly dependent on ventilatory and circulatory states [17], and the O2 affinity of arthropod Hcs is modulated by various inorganic and organic ions such as H+, Ca2+, lactate and urate ions [17]. In crustacean Hcs, the O2 affinity is increased by lactate, which is accumulated in the hemolymph under hypoxia or after physical exercise. Horseshoe crab Hcs lack such a lactate sensitivity, but this is covered by a large reverse Bohr effect [11]. At the lower end of the physiological pH, however, the reverse Bohr effect diminishes, and under severe hypoxic conditions the effect can not increase the O2 affinity enough to meet the O2 requirement [4]. The results of the present study show that the horseshoe crab Hcs still maintain a high O2 transport efficiency in a wide range of P, particularly at a low P, independently of the functional modulators. This seems to be a new way of adaptation to ambient hypoxia and may be unique to O2 carriers having large molecular constructions such as those found in horseshoe crab Hcs. It would be therefore interesting and worthwhile to examine the O2 transport efficiency of other carriers in relation to their physiological function and mechanism of the cooperativity.
Acknowledgments
The authors wish to thank Dr. S. Akiyama (Niigata University) for many helpful comments.
