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* Structural and Computational Biology Programme, European Molecular Biology Laboratory, Heidelberg, Germany; Institute of Biophysics and Physical Biochemistry, University of Regensburg, Germany; and Physical Chemistry, Institute of Chemistry, University of Graz, Austria
Correspondence: Address reprint requests to Dr. Angelika Krebs, Structural and Computational Biology Programme, European Molecular Biology Laboratory, Meyerhofstrasse 1, D-69117 Heidelberg, Germany. Tel.: 49-6221-387256; Fax: 49-6221-387306; E-mail: krebs{at}embl-heidelberg.de.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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3.5 MDa. By small angle x-ray scattering (SAXS), Eudistylia vancouverii chlorocruorin and Macrobdella decora hemoglobin were investigated in solution. On the basis of the experimental SAXS data, three-dimensional models were established in a two-step approach (trial and error and averaging). The main differences between the complexes concern the structure of their central part and the subunit architecture. Usage of our SAXS models as templates for automated model generation (program DAMMIN) led to refined models that fit perfectly the experimental data. Special attention was paid to the inhomogeneous density distribution observed within the complexes. DAMMIN models without a priori information could not reproducibly locate low-density areas. The usage of templates, however, improved the results considerably, in particular by applying electron microscopy-based templates. Biologically relevant information on the presence of low-density areas and hints for their presumable location could be drawn from SAXS and sophisticated modeling approaches. Provided that different models are analyzed carefully, this obviously opens a way to gain additional biologically relevant structural information from SAXS data. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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; Kapp et al., 1990; Qabar et al., 1991; Lamy et al., 1996; for a recent review, see Weber and Vinogradov, 2001). The hemoglobin of the earthworm Lumbricus terrestris (Lumbricus Hb) is the most extensively studied annelid hemoglobin. The complex has an overall D6 symmetry (Royer and Hendrickson, 1988; Boekema and van Heel, 1989). Due to considerable differences in the mass estimations, the exact stoichiometry of the components was unclear for a long time (Martin et al., 1996b; Zhu et al., 1996). Two models have been proposed to explain the architecture of Lumbricus Hb: The first model comprises 24 octameric subassemblies of globin chains and 24 linker chains (Ownby et al., 1993). In the second, the so-called "bracelet model" (Vinogradov et al., 1986, 1991; Martin et al., 1996a,b), 12 dodecameric 200-kDa subunits, each composed of three monomeric and three trimeric heme-containing globin chains, and 36 heme-deficient linker chains form the HBL complex with a total mass of 3.5 MDa.
For Lumbricus Hb, several three-dimensional (3D) reconstructions from cryoelectron microscopy have been presented (Schatz et al., 1995; de Haas et al., 1997; Taveau et al., 1999; Mouche et al., 2001). Recently the crystal structure at 0.55 nm resolution was published (Royer et al., 2000), revealing an organization of 144 oxygen-binding hemoglobin subunits and 36 nonhemoglobin linker subunits, similar to the bracelet model. Thus, in the case of Lumbricus Hb, the picture of its structure has obtained a very detailed level over the years.
Less structural information is available for other related oxygen-carrying proteins. Bracelet architectures, similar to Lumbricus Hb, have been suggested for Macrobdella decora hemoglobin (Macrobdella Hb; de Haas et al., 1996a) and for Eudistylia vancouverii chlorocruorin (Eudistylia Chl; de Haas et al., 1996b), although the exact number of globin and linker chains is still unknown. These studies show subunits that appear somewhat hollow in the center (hollow globular substructures), similar to the subunits of Lumbricus Hb (Schatz et al., 1995; de Haas et al., 1997; Taveau et al., 1999; Mouche et al., 2001).
The investigation of the 3D structure of the giant annelid hemoglobins is essential for a better understanding of their complex architecture and functionality. In this context, small angle x-ray scattering (SAXS) is a potent tool for studying the solution structure of such giant proteins at low resolution (Kapp et al., 1990; Krebs et al., 1996, 1998). In this study, we used the SAXS technique to investigate Eudistylia Chl and Macrobdella Hb and to determine their radius of gyration, RG, molar mass, M, maximal diameter, dmax, hydrated volume, V, and shape. The experimentally obtained data were simulated by 3D models consisting of a large number of small spheres. These SAXS models were constructed by trial and error in a two-step procedure leading to consensus models. In addition, SAXS models were also created by using the advanced modeling procedure implemented in the program DAMMIN (Svergun, 1999, 2000) in several alternatives (cf. Zipper et al., 2004). All models were compared on the basis of their fit with the experimental data; for a visual comparison they were displayed as surface-rendered densities. Furthermore, the models were used as bases for the prediction of hydrodynamic parameters.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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), were provided by S. N. Vinogradov (Department of Biochemistry and Molecular Biology, Wayne State University, Detroit, MI). For SAXS experiments, highly concentrated solutions of the oxygenated proteins were dialyzed against 0.1 M Tris/HCl buffer, 1 mM EDTA, pH 7.0. A dilution with dialysis buffer led to final protein concentrations between 5 and 80 mg/ml.
SAXS experiments were carried out at 4°C by means of a Kratky compact camera (A. Paar, Graz, Austria), using copper radiation (wavelength 
= 0.154 nm) from a conventional x-ray tube, and a proportional counter. Scattering measurements were performed in the angular range of 2
= 0.7–57 mrad, corresponding to h values of 0.029–2.3 nm–1 (h = (4
/)sin; is half the scattering angle). Both proteins were investigated under the same conditions, and the data were evaluated in the same way as reported previously for Lumbricus Hb (Krebs et al., 1996), to establish a founded basis for the comparison of the low-resolution structures of these HBL complexes.
All scattering curves were measured repeatedly. With each protein, two independent series of experiments were performed, each comprised measurements at four different concentrations between 5 and 15 mg/ml in the angular range below 7 mrad and measurements at high concentrations (67 or 80 mg/ml) over the full range mentioned above. A minimum of three scattering curves was recorded for each protein concentration in each series. The measured intensities were corrected for background scattering, and the low-concentration data were extrapolated to zero concentration before the necessary corrections for the beam geometry were applied. This desmearing procedure was performed by means of the program ITP (Glatter, 1977) and led to scattering curves, I(h), and pair-distance distribution functions, p(r) (Glatter and Kratky, 1982). The molecular parameters RG and dmax were determined from the p(r) functions, M from the absolute scattering intensity at zero angle, and V from Porod's invariant. To obtain representative patterns of the proteins, the scattering curves, p(r) functions, and molecular parameters of each complex were averaged over the repeated measurements; only averaged data are discussed in the following. The calculated limits of error in Fig. 1 and Table 1 reflect the reproducibility of the data rather than their absolute accuracy.
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). Alternatively, models were generated by an advanced modeling approach (program DAMMIN; Svergun, 1999, 2000), an automated procedure based on simulated annealing, which uses compactness and connectivity constraints and, optionally, a priori structural information. To speed up the computations, the program uses spherical harmonics to calculate the model intensity. The input of experimental data occurs via a GNOM file (Semenyuk and Svergun, 1991). This modeling approach was applied either without a priori structural information (ab initio modeling) or by using templates derived from the original SAXS consensus models or from 3D electron microscopy (EM) reconstructions (de Haas et al., 1996a,b). The templates were produced by a similar procedure as described previously (Zipper et al., 2004). For generating templates from the 3D EM reconstructions, a rescaling step was performed to obtain the proper angular position of the first submaximum in the scattering curve of the basic EM model (cf. Krebs et al., 1998); an additional upscaling of the coordinates of the EM templates by a factor of 1.05 was applied in some cases to reduce the effects of DAMMIN's peripheral penalty.
Calculations of scattering curves and p(r) functions from the coordinates of the spheres were performed with several programs based on Debye's formula and other algorithms outlined in Glatter (1980) and Glatter and Kratky (1982). For the trial-and-error models, the radius of the spheres was chosen so that a continuum was simulated by an appropriate overlap of the spheres. For the Debye calculation of scattering curves from the DAMMIN models, the size of the spheres was reduced to optimize the comparison with the curves provided directly by DAMMIN (Zipper et al., 2004). In general, the p(r) functions of models were calculated by Fourier transformation of the scattering curves. Hydrodynamic parameters (sedimentation coefficient s and translational diffusion coefficient D) of the models were predicted by application of the program HYDRO (García de la Torre et al., 1994, 2000).
The program RASMOL (Sayle and Milner-White, 1995) was adopted for the primary graphical representation of all models obtained. Surface representations of the models were applied to allow a closer comparison of the structural features of the various protein models. For this purpose, electron density maps were generated from the coordinates of the spheres with programs from the CCP4 package (Collaborative Computational Project, Number 4, 1994). Threshold levels were chosen in a way that all models represented the same volume. The electron densities were displayed by VOLVIS (Research Foundation of the State University of New York).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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); the differences in their intensities, however, suggest some differences in the protein architecture. Resulting SAXS parameters, e.g., RG, dmax, V, and M, are listed in Table 1, together with the corresponding data for Lumbricus Hb (Krebs, 1996; Krebs et al., 1996, 1998). Our experimental values for RG and dmax of Macrobdella Hb are compatible with those of 10.5 (±0.2) nm and 28.0 (±0.5) nm, respectively, found in previous SAXS studies (Kapp et al., 1990), whereas our value for V is considerably smaller than the volume of 7500 (±300) nm3 reported earlier; our value for M is similar to that of 3500 (±300) kg/mol found previously (Schmuck, 1989). For Eudistylia Chl, SAXS reference data are not available in the literature. SAXS models were built from identical spheres of radius rb = 0.66 nm. Experimental values for RG and dmax and the shapes of the I(h) and p(r) patterns were used as selection criteria for modeling based on an assumed HBL structure. For our models, a two-step approach turned out to be useful. In the first step, a number of different models were developed by trial and error. None of these models provided a perfect fit to the experimental scattering curve. In the second step, a consensus model was constructed by averaging the best-fitting models of the first step. Due to this averaging, the initially identical spheres were replaced with spheres of individual statistical weightings. These weightings were derived from the frequency of occupancy of given positions in the various models. The highest weighting was given to positions that were occupied in all models and the lowest to positions occupied only in a single model. By this procedure, the original two-level density distributions of the individual models (with a value of 1 corresponding to matter and 0 corresponding to void) were transformed into a multilevel density distribution reflecting different levels of probability of the positions in the resulting consensus model. In this context, it has to be noted that in the interior of the consensus model inhomogeneities in its density distribution can only occur if the distributions of the individual models themselves are inhomogeneous.
The resulting consensus models for Eudistylia Chl and Macrobdella Hb are shown in Fig. 2, A and B. The models of both complexes are composed of 12 identical subunits in an eclipsed HBL structure, and in the center of each model an additional central unit is assumed. The different weighting of the spheres is expressed by different shades of gray: dark is used for spheres with the highest weighting, and the light spheres indicate areas of less probability. Essential structural parameters are given in Tables 1 and 2, together with the corresponding data for Lumbricus Hb.
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, 2000). For this purpose, appropriate templates were established from the consensus models according to the following procedure. First the selected model was superimposed in six rotation states. A subsequent data-reduction step (Zipper and Durchschlag, 2000) using a hexagonal lattice of definite cell size (1.6 nm) led to an intermediate template. Finally one-twelfth of the reduced structure was used to create the final template with exact D6 symmetry as required by DAMMIN (for a detailed description see Zipper et al., 2004). In this procedure, the different weightings of the spheres of the consensus models were not considered, but all spheres were treated as identical. Thus the templates, defining the search space for the subsequent DAMMIN approach, were made up from the entire set of occupied positions in the SAXS models underlying the consensus models, without preferring any particular model configuration. When performing the data reduction step, the resulting spheres were placed either at the centers of the hexagonal lattice cells or at their local centers of gravity as calculated from the mass distribution in each cell. The latter variant yielded templates of a more realistic appearance, however, resulted in considerable amounts of overlapping spheres (see Fig. 2, C and E), whereas the approach using hexagonal lattice points is devoid of overlapping.
Top and side views of selected SAXS-biased DAMMIN models of Eudistylia Chl (D) and Macrobdella Hb (F) are also shown in Fig. 2. These models were created using the SAXS templates (C and E) with overlapping spheres placed at local centers of gravity. The comparison of the templates with the resulting models suggests that the main structural features of the templates were only moderately altered by the DAMMIN procedure. The most obvious changes concern the reduced mass density in the central region of both models (marked by black circles). Similar changes were observed with models that were biased by templates consisting of spheres placed exactly at hexagonal lattice points (data not shown).
Surface rendering of the DAMMIN models shown in Fig. 2 visualizes the effects of the applied procedure even more impressively. Though the similarity of the rendered SAXS-biased DAMMIN models in Fig. 3 b (A–D, Eudistylia Chl; E–H, Macrobdella Hb) with the underlying SAXS consensus models (Fig. 3 a) is evident, in the center of both HBL complexes less density is assumed by the DAMMIN models, and the subunits appear to be more hollow than in the SAXS consensus models (cf. the top views (A and B; E and F), and the central slabs (D and H) in a and b of Fig. 3). Moreover, the SAXS-biased DAMMIN models fit the experiment much better; their scattering curves (Fig. 4, A and C, green circles with error bars) match the observed data in the angular range h < 1.7 nm–1 perfectly, whereas the fit by the initial SAXS models (green lines) is less satisfactory. The fit of the experimental p(r) functions is nearly perfect (Fig. 4, B and D). The model parameters, as shown in Table 2, are also in agreement with the observations.
Ab initio DAMMIN models
DAMMIN models were also created without using templates, to check the influence of these constraints. By this approach, the low-resolution shape and internal structure of the hemoglobins were restored ab initio, exploiting the experimental SAXS curves without any a priori information or with no constraint other than the assumption of D6 symmetry. In accordance with previous observations, only the latter variant resulted in models of physical relevance (Zipper and Durchschlag, 2003; Zipper at al., 2004). Nevertheless, many of the models generated this way represented unrealistic structures and were therefore discarded, although in all cases the experimental scattering curve was fitted perfectly. Models were considered as unrealistic if their appearance deviated substantially from that suggested by EM, e.g., because of the occurrence of central protuberances, isolated spheres, or sphere-like overall shapes. Some typical examples of discarded models are outlined in Fig. 5, to illustrate the philosophy of the applied selection criteria.
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,b) were chosen for a more detailed analysis. For Eudistylia Chl and Macrobdella Hb, 11 different ab initio DAMMIN models were used to create averaged ab initio models, similar to the creation of the consensus SAXS models shown in Fig. 2, A and B. To accumulate structural information that is represented more often in the models, spheres that were not present in at least from two to five models were omitted in the averaging process. All other spheres were weighted according to their frequency of occupancy.
Various averaged ab initio DAMMIN models of Eudistylia Chl and Macrobdella Hb and their structural and hydrodynamic parameters have been presented elsewhere (Zipper et al., 2004). In this article, we analyze the corresponding surface representations (Fig. 6 a). In agreement with the SAXS consensus and SAXS-biased DAMMIN models (Fig. 3), the representations of the averaged ab initio DAMMIN models also show little density in the central unit (Fig. 6 a, arrows), but unlike the aforementioned models they give, at first sight, no hint for cavities in the 12 subunits. A careful analysis, however, reveals that this is mainly caused by the special process of averaging: most of the ab initio models selected for averaging actually possess small holes in their subunits, but the positions of these holes are quite different in the various models; therefore the averaging procedure results in a blurred density distribution without pronounced minima in the subunits. Owing to the averaging procedure, the distance distribution functions p(r) of the averaged models (Fig. 4, B and D, red lines) differ significantly from the p(r) functions of the original models (red circles with error bars) that simulate the experimental p(r) functions (black lines) almost perfectly. Therefore the averaging procedure also deteriorates the fit of the scattering curves: the curves of the original ab initio DAMMIN models, which were used for averaging, fit the experimental curves within the limits of error up to h = 1.7 nm–1 (Fig. 4, A and C, red circles with error bars and black lines), whereas the curves that were calculated from the averaged structures (red lines) deviate remarkably.
EM-biased DAMMIN models
For comparison, we include DAMMIN models that were created making direct use of the precise structural information available from 3D EM reconstructions. The EM density data of Eudistylia Chl and Macrobdella Hb were provided by F. de Haas and J.-C. Taveau (Laboratoire de Biochimie Fondamentale, University François Rabelais, Tour, France) (for details of the reconstructions, see de Haas et al., 1996a,b). A total of 18 EM-biased models were calculated for each protein, all of them fitting the experimental data very well (blue circles with error bars in Fig. 4), and the averaged structures are given in Fig. 6 b in surface representation (the original models can be found in Zipper et al., 2004). These models clearly show hollow subunits, similar to the original EM reconstructions (de Haas et al., 1996a,b), even after averaging. This demonstrates that DAMMIN neither fills the holes given by the templates nor does it shift their position (which would lead to a blurred electron density distribution, similar to the situation observed for the averaged ab initio models shown in Fig. 6 a). In addition, the subunits in the EM-biased DAMMIN models seem to be more hollow than assumed by the SAXS and SAXS-biased models. The density in the central unit appears to be comparable with the SAXS-biased DAMMIN models.
Mass fraction in the central region
All models presented above exhibit a low-density area in the center. To establish a founded basis for a quantitative comparison, the fraction of mass contained in the central region of each individual model was derived from the number of spheres whose centers are located within a radial distance of 4.1, 4.9, and 5.7 nm, respectively, from the center of the model. The data obtained for models belonging to the same type (trial-and-error SAXS models; SAXS-biased, ab initio, and two variants of EM-biased DAMMIN models) were averaged to yield mean mass fractions and the corresponding standard deviations. In the case of models representing averaged structures (SAXS consensus and averaged DAMMIN models), mean mass fractions were also calculated directly from the numbers and statistical weightings of the spheres; if all spheres were taken into account, the same mean values resulted as from the procedure described before, and only slightly different values were obtained if the spheres with the lowest weighting were neglected. To eliminate the trivial effect of the volume, the data shown in Fig. 7 have been normalized to the volume of the sphere with a radius of 4.9 nm; by this normalization procedure, the plotted data become representative of the mean density in the central region. For comparison, the results obtained for Lumbricus Hb are included in Fig. 7.
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; Zipper et al., 2002). This approach was quite challenging considering the large number of beads involved and the inhomogeneous density distributions in the consensus models (for Lumbricus Hb, the model presented in Krebs et al., 1998, was used). To take the density distributions adequately into account, the different weightings of the initially equal-sized spheres had to be expressed by different bead volumes. This implied the use of different radii, whereas the coordinates of the spheres were not altered. The results of the hydrodynamic predictions are included in Table 2. |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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) points at the presence of low-density areas in all complexes and suggests the occurrence of structural differences. Areas of low density in protein complexes are often of biological and structural interest. Therefore we paid special attention to their modeling, although this process proved to be quite demanding. DAMMIN analyses of the experimental scattering curves, using templates based on the SAXS consensus models, improved these models considerably. Although the SAXS-biased DAMMIN models essentially retain the gross-structural features of the consensus models (Fig. 3), slight deviations from the original structure occur both in the central unit and the 12 subunits. These changes appear to be responsible for the significantly improved fit to the experimental data (Fig. 4, green circles with error bars). The results concerning the low-density areas in these DAMMIN models are remarkable because the templates used to generate the models were based on all of the spheres of the respective consensus model but did not contain any information about the different weightings of these spheres.
DAMMIN analyses performed without the usage of templates were challenging because of the problem of uniqueness. The creation of DAMMIN models without any a priori information led to generally unrealistic models (irregular globular shapes and peripheral cavities). The restriction of the DAMMIN procedure to models with D6 symmetry, without using templates, turned out to be a major improvement and led to a variety of models (see Zipper et al., 2004). About 50% of these ab initio models looked quite realistic and were selected for a further analysis; unrealistic models (Fig. 5) were discarded. However, the diversity of the selected structures did not allow choosing a unique model. Therefore an averaging procedure was applied, similar to the creation of the SAXS consensus models. Model averaging is a legitimate procedure to accumulate overall information and to cope with the problem of uniqueness as recently addressed by Volkov and Svergun (2003). The observed loss of information concerning the existence of holes in the subunits as a consequence of averaging indicates that the DAMMIN procedure, though being capable of detecting ab initio inhomogeneities in the density distribution of the complexes, has difficulties in locating them with a sufficient degree of reliability because of the limited resolution of the SAXS experiments and the usage of three-dimensionally averaged information from specimens in solution.
Obviously, SAXS alone cannot precisely locate low-density areas in these protein complexes, and structural information on a high-resolution level cannot be expected. Therefore, an improvement was attempted by DAMMIN analyses importing a priori structural information from 3D EM reconstructions through appropriate templates. This tactic turned out to be a highly promising way, by combining structural data from different methods and at unequal levels of resolution. The resulting EM-biased DAMMIN models are of higher quality and relevance for the solution structure than the models originating merely from SAXS studies and fit the experimental SAXS data much better than EM-based models that were established without the application of the DAMMIN program as in a previous study on Lumbricus Hb (Krebs et al., 1998).
The central unit
The high similarity of the experimental SAXS data of Eudistylia Chl and Macrobdella Hb (Fig. 1) suggests that their solution structures can only differ slightly. From our trial-and-error and consensus SAXS models, we conclude that major structural differences occur in the central region of the complexes. According to our data (Table 1, number of high-weight spheres in the central unit), Macrobdella Hb has a very small central unit, whereas the central mass of Eudistylia Chl seems to be more similar to that of Lumbricus Hb. The mean values of the mass fractions in the central region of the SAXS models and the SAXS-biased DAMMIN models up to the chosen radii are in full accord with these findings; the normalized mass fractions presented in Fig. 7 reflect the differences between the models impressively and allow a direct comparison of the mean densities in the central region. A smaller central mass in Macrobdella Hb also follows from the mass fractions obtained from the EM-biased models. All of these results are in good agreement with the observed differences in the structure of the central units in 3D EM reconstructions (de Haas et al., 1996a,b). The finding that the analyzed ab initio DAMMIN models yield mass fractions for Macrobdella Hb that are closer to the values for Lumbricus Hb than for Eudistylia Chl is less important in view of the large standard deviations of these results, corroborating the problem of uniqueness.
A very small and subtle central subunit was first described by Ohtsuki and Crewe (1983), after the results of earlier SAXS experiments (Pilz et al., 1980) that already postulated a central subunit in the center of Lumbricus Hb. The first EM reconstruction of Lumbricus Hb reached a resolution of 3 nm (Schatz et al., 1995). In the center of the molecule, a doughnut shape of 5 nm height and 12 nm diameter was found; it exhibited a central hole 2.5 nm wide, which was close to the resolution limit achieved in that study. This additional subunit was assumed to accommodate 12 linker chains. From the crystallographic reconstruction to 0.55 nm, we know that indeed only linker chains are present toward the center (Royer et al., 2000). Very unexpected in this context was the finding that 12 triple-stranded coiled-coil helices are present in this area. Thus emanating from each one-twelfth subunit are three 4.5-nm long rods consistent with coiled-coil 
-helices. A hole of 4.5 nm diameter in the center of the molecule and the region where only the triple-stranded linker helices are present constitute a low-density area with 10–12 nm diameter in the center of Lumbricus Hb.
At a resolution of 3.5 nm, EM reconstructions of the Chl from the polychaete E. vancouverii show little density (a flat hexagonal mass) in the center (de Haas et al., 1996b). By contrast, the central region of Macrobdella Hb contains a hexagonal toroid at a resolution of 4 nm (de Haas et al., 1996a). The structural role of the toroid was assumed to be a pier to which two bracelets are fixed by 12 connections. In the polychaete worm Arenicola marina, the central subunit appears as an ellipsoid in EM reconstructions at 2.5 nm (Jouan et al., 2001).
Hollow globular subunits
In EM reconstructions, the subunits themselves are found to be hollow (de Haas et al., 1996a,b). The SAXS consensus models show slight density variations in the subunits but to a much lesser extent than observed in the EM reconstructions. A refinement of the SAXS consensus models by DAMMIN makes their subunits much more hollow (see Fig. 3). Of the ab initio DAMMIN models, which were generated without bias, some assume filled subunits without density variation, whereas others definitely possess holes in their subunits, at positions that are different for each model. Accordingly, averaging the structures of the ab initio models leads to a nearly complete loss of information concerning density variations in the subunits (see Fig. 6 a). If internal cavities are part of the structure of a template imported by DAMMIN as a priori structural information, such holes are not filled up but are rather enlarged by DAMMIN. This is the case with the SAXS-biased and, even more expressed, with the EM-biased DAMMIN models (see Figs. 3 b and 6 b).
Oblate anisometry
Apart from the aforementioned differences in the central units, dissimilarities between Eudistylia Chl, Macrobdella, and Lumbricus Hb are also suggested by their different experimental volumes V, which are reproduced almost perfectly by all modeling approaches applied, and also by a critical analysis of the data obtained for the dimensions of the proteins in the three directions of space (see Tables 1 and 2). The comparison of the values for dz, the dimension in z direction, gives some hint that the height of Eudistylia Chl might be lower than that of the other proteins under investigation; however, the considerable limits of error of some dz values do not allow a founded decision. Similarly, the comparison of the radii of gyration in the three directions of space, Rx, Ry, and Rz, is not conclusive in most cases because of the too large uncertainties of the quantities to be compared. Only the modeling approach making use of EM-based templates with the beads on local centers of gravity is able to unveil significant differences in the mass distribution of Eudistylia Chl and Macrobdella or Lumbricus Hb. According to the results obtained by this approach, the ratio Rz/Rx of the axial radii of gyration, a measure of the oblate anisometry, is 0.621 ± 0.003 for Eudistylia Chl, 0.648 ± 0.006 for Macrobdella Hb, and 0.665 ± 0.005 for Lumbricus Hb. The comparison of these values with the corresponding ratios for the used EM templates (Eudistylia Chl template, 0.753; Macrobdella Hb template, 0.731; and Lumbricus Hb template, 0.714) convincingly shows that the ratios given above present real results of the DAMMIN analysis of the experimental scattering curves and are not imported from the templates. Similar differences in the particle dimensions and volume between Eudistylia Chl and Lumbricus Hb as observed by us were also suggested by EM studies (Qabar et al., 1991).
Hydrodynamic parameters
As follows from Table 2, the parameters D and s predicted for the consensus models of Eudistylia Chl and Macrobdella Hb are quite similar to the values anticipated for the corresponding Lumbricus Hb model. While predicted D values for Lumbricus Hb are in the range of the experimental data found in the literature, the values predicted for s exceed the experimental ones slightly (cf. Table 2 legend).
The prediction of D values for the various DAMMIN models led to nearly identical results for the three proteins (Table 2). With each of the different types of DAMMIN models (SAXS-biased, ab initio, and EM-biased) the D values predicted for the three proteins always agree within the limits of error (1% in most cases). Slightly larger differences can be observed, on the other hand, between the predictions for different types of DAMMIN models. Ab initio models show the lowest D values, whereas EM-biased models, with the beads on centers of gravity, give the highest values; the differences do not exceed, however, a few percent. It must be borne in mind that for the prediction of D values the molar mass M and the partial specific volume 
of the proteins are not used. For the prediction of s values, on the other hand, both M and are required. Usage of the same M and values for all three proteins leads to very consistent results for s (Table 2). At least for Macrobdella Hb, this approach is in good agreement with data reported for M and (Weber et al., 1995). On the other hand, lower s values for Eudistylia Chl and Macrobdella Hb would be obtained by the usage of our experimentally observed M values (Table 1) for these proteins. In the extreme case of Eudistylia Chl, the s values predicted this way would be even lower than the very low experimental value (cf. Table 2). For Lumbricus Hb, the predictions for D from the DAMMIN models are in accord with values from the literature, whereas the predicted s values are slightly larger than the observed values.
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CONCLUSIONS |
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; Zipper and Durchschlag, 2003). |
ACKNOWLEDGEMENTS |
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This work was supported by the Austrian Academy of Sciences (to A.K.) and the Austrian "Fonds zur Förderung der wissenschaftlichen Forschung" (to A.K. and P.Z.).
Submitted on December 2, 2003; accepted for publication April 12, 2004.
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