Quanternary structure of multihexameric arthropod hemocyanins

Micron,Vol. 25, No. 4, pp. 387-418, 1994

Pergamon

Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0968~,328/94 $26.00 0968--4328(94)00020--4

Quaternary Structure of Multihexameric Arthropod Hemocyanins* MARIN

VAN

HEEL

and PRAKASH

DUBE

Fritz Haber Institute of the Max Planck Society, Faradaywe# 4 4 , D-14195 Berlin, Germany

Abstract--Arthropod hemocyanins are large oligomeric oxygen-transporting proteins with molecular weight ranging from 450 k D a in the spiny lobster (Panulirus interruptus) up to more than 3.6 m D a in the horseshoe crab (Limuluspolyphemus). Hemocyanins from different species consist of one or multiple copies of a hexameric building block (of 450 kDa) and are sufficiently large to be easily visualized in the electron microscope. Arthropod hemocyanins were a m o n g the first macromolecules studied by multivariate statistical image analysis techniques. We present an overview of the different characteristic molecular images of various multihexameric (1 x 6, 2 × 6, 4 × 6, and 8 x 6) assemblies as these occur in electron-microscopical preparations. We also model the different assemblies in three dimensions by merging multiple copies of the X-ray-diffraction electron density of the single hexameric hemocyanin of Panulirus interruptus. By making correct enantiomeric decisions while merging the densities at the various levels of assembly and by fine-tuning the assembly parameters used, a good match can be obtained between the microscopical images and twodimensional projections calculated from the three-dimensional (3D) model densities. Knowledge of the quaternary structures of this intricate hierarchical family of oligomers is essential for understanding the allosteric interactions associated with their strong oxygenbinding cooperativity.

Key words: Hemocyanin structure, electron microscopy, image processing, model building, assembly parameters.

CONTENTS I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Subunit heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Application of 'MSA' to hemocyanin structure and early models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. The present work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Sample preparation and electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Particle selection and preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Alignment using multiple reference images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Multivariate statistical analysis and classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Resolution in the characteristic views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Model building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The hexameric structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. The 2 x 6-meric structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. The 4 × 6-meric structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. The flip and flop views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The 45 ° view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. The 2 x 6-mer arrangement within the 4 × 6-mer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 x 6-mer assembly parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. The 8 x 6-merit structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Characteristic views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. The 8 x 6-mer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Interpretation of the molecular profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Pentagonal views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Cleft views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Cross and bow-tie views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. The flip-flop views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

* This paper is dedicated to Erni van Bruggen on the occasion of his retirement in January 1994. 387

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M. van Heeland P. Dube I. INTRODUCTION A. General

Hemocyanins are oligomeric oxygen-carrier proteins occurring freely dissolved in the hemolymph of arthropods and molluscs. The oxygen-binding site in hemocyanins consists of a dinuclear copper(III) causing the typical blue coloration of the hemolymph (van Holde and Miller, 1982; Ellerton et al., 1983). Like vertebrate hemoglobins, hemocyanins exhibit a high degree of cooperativity in oxygen binding and a pronounced Bohr effect (cf. van Bruggen et al., 1981). Hemocyanins of arthropods and of molluscs have a very different quarternary organization, as is evident from electron micrographs of such samples (cf. Salvato and Beltramini, 1990). In contrast to the multi-hexameric organization of arthropod hemocyanins (for a recent review see Markl and Decker, 1992), the large multimeric molluscs hemocyanins have an overall cylindrical shape and molecular weights of up to 9 mDa. The smallest arthropod hemocyanin--a single hexamer with a molecular weight of 450 kDa--is found in the spiny lobster (Panulirus interruptus). Its six polypeptides, each containing ,~ 660 amino acids and a dinuclear-copper binding site, are arranged as a trigonal antiprism with approximate 32 point-group symmetry (Volbeda and Hol, 1989). Such a hexameric structure is considered to represent the 'basic building block' in larger multihexameric hemocyanin molecules found in other species (van Bruggen et al., 1980; Magnus et al., 1991). For example, the hemocyanin molecule of the crayfish Astacus leptodactylus is dihexameric (2 ×6-mer), that of the tarantula Eurypelma californicum consists of four hexameric (4 x 6-mer) units and the native hemocyanin of the horseshoe crab Limulus polyphemus (Fig. 1) consist of eight hexamers (8 x 6-mer). In general, crustacean hemocyanins are either 1 x 6-mers or 2 x 6-mers, whereas in chelicerata they also occur as 4 x 6-mers or 8 x 6-mers (van Bruggen et al., 1981). There are some exceptions, however: in the crustacean Callianassa and Uniramus the hemocyanin molecules are 4 x 6-meric and 6 x 6-meric, respectively (van Bruggen et al., 1981; Cavellec et al., 1990). Note also that the 2 × 6-meric structure studied in this paper (a substructure of the large 4 x 6 and 8 x 6 meric hemocyanins) differs in inter-hexameric organization from the native 2 x 6-merie hemocyanins of other arthropod (Bijlholt and van Bruggen, 1986; de Haas et al., 1991). A major achievement in understanding arthropod hemocyanins was the elucidation of the structure of the hexameric molecule of Panulirus interruptus by X-ray crystallography. The electron density map of this molecule was first calculated to a resolution of 5 A and later refined to 3.2 A (van Schaick et al., 1982; Gaykema et al., 1984; Volbeda and Hol, 1989; see Fig. 2). Each of the six bean-shaped polypeptide chains was found to be folded into three structurally distinct domains. Domain #1 (175 residues) has a larger globular part containing six ~helices and a smaller part consisting of one or-helix and one fl-strand. Domain #2, containing 220 residues, is arranged as seven ct-helices (four of which surround the dinuclear copper site at the centre) and two antiparallel fl-

sheets. Domain #3 is the largest domain with 260 residues and contains a seven-stranded antiparallel fl-barrel and many long polypeptide loops with six a-helices and two antiparaUel fl-strands. These six polypeptides (arranged in 32 point-group, i.e. as two layers of three 'beans') were shown to have more intense contacts between neighboring subunits of the two trimers ('up-down' contacts) than between the subunits within the trimer ('lateral' contacts). This molecule was thus thought to be a trimer of tight dimers rather than a dimer of trimers (Linzen et al., 1985; Volbeda and Hol, 1989). Most of the residues participating in the 'up-down' inter-dimer contacts are provided by domain 2 of each polypeptide, and the amino acid sequence of this part is shown to be quite well conserved in various hemocyanins (Linzen et al., 1985; Volbeda and Hol, 1989). More recently, however, after solving the structure of a deoxygenated version of the Limulus II subunit, the hexamer is considered to function rather as a dimer of trimers in cooperative oxygen binding (Magnus et al., 1991; Hazes, 1993; Hazes et al., 1993). B. Subunit heterogeneity The multi-hexameric hemocyanins, such as that of Limulus polyphemus, can be dissociated into their monomeric constituent polypeptides by EDTA dialysis (Sullivan et al., 1974) and may be reassembled in a slow but completely reversible manner by supplementing with calcium ions (Schutter et al., 1977; Bijlholt et al., 1979, 1982a). Reassembly can only take place if all of the different polypeptides are simultaneously present in the solution. For example, the dissociated subunits of Limulus can be separated into five chromatographic 'zones' (Sullivan et al., 1974), each of which plays a specific role during reassembly: zones V and lI are important to form structures larger than 1 x 6-mers; zones IV and III are necessary to form 8 x 6-mers from four 2 x 6-mers (Bijlholt et al., 1979). Such reassembly behavior was later found also for Eurypelma hemocyanin (Decker et al., 1980) and other crustacean and cheliceratan multihexameric hemocyanins (Markl et al., 1979a,b; Lamy et al., 1979, 1980; Markl and Kempter, 1981; StScker et al., 1988). The Eurypelma californicum 4 × 6-meric hemocyanin molecule is composed of seven types of subunits (a through g) which are all present in four copies with the exception of subunits b and c of which there are only two (the stoichiometry of the 4 × 6-mer is thus 4a, 2b, 2c, 4d, 4e, 4f and 49). The difference in the subunits' immunological and electrophoretic patterns is due to major differences in their amino acid sequences (Markl et al., 1979c). All seven subunits are necessary to form the complete and stable 4 × 6-meric assembly. The two 2 x 6meric halves of the 4 × 6 are considered to be identical and have the same subunit composition as the whole molecule. The individual hexamers, however, are not identical since these contain either a copy of subunit b or one copy of subunit c. The subunits b and c show a strong association which is disruptible only by a high concentration of EDTA or 4M Urea. This b-c heterodimer plays a

Structure of Muttihexameric Hemocyanins very i m p o r t a n t role in v a r i o u s assemblies. It serves as a core in forming the i n t e r - h e x a m e r i c link within the Eurypelma half-molecules, a n d also forms the central c o n n e c t i o n between the two d o d e c a m e r i c halves of the 4 x 6 - m e r ( M a r k l et al., 1982). R e a s s e m b l y of these structures does n o t o c c u r if the b - c dimers are replaced by artificial b - b o r c-c dimers. S u b u n i t a shows a s t r o n g affinity t o w a r d s the b--c c o m p l e x , a n d if s u b u n i t # is also

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present the h e x a m e r i c a n d h e p t a m e r i c structure are formed. A d d i t i o n o f s u b u n i t f into the r e a s s e m b l y s o l u t i o n leads to the f o r m a t i o n of 2 x 6-meric structures, b u t 4 x 6-mers are f o r m e d only when all the subunits are present ( M a r k l et al., 1982). Similar o b s e r v a t i o n s were m a d e for the 4 x 6-meric h e m o c y a n i n of Androctonus which c o n t a i n s eight i m m u n o l o g i c a l l y different subunits a n d a central dimeric structure called 'fraction l ' - - w h i c h

Fig. 1. A limestone fossil of Limulus (Mesolimulus walchii) found in Maxberg, Germany (scale bar: 10 cm) with an estimated age of 140 million years. The tracings of the last movements of the animal prior to petrifieation have been perfectly preserved in this intriguing document. The evolutionary age of the species is estimated to be ~600 million years, with little somatic difference over the past 150 million years with respect to the present day species. The adult Limulus polyphemus reaches a size of about 50 cm.

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is equivalent to the b-c compex ofEurypelma (Lamy et al., 1980). These studies revealed a specific stoichiometric relationship among the subunits of multi-hexameric hemocyanins and indicated the importance of this stoichiometry for generating stable and functional molecules after biosynthesis of the individual polypeptides. Subunit heterogeneity is, therefore, established to be a general characteristic of these hemocyanins and, depending upon the species, some 3-15 types of subunits have been found (Markl et al., 1979a,b; Van Holde and Miller, 1982; Ellerton et al., 1983). The specific interactions between the individual monomers in forming larger multimeric assemblies within one species indicated a structural correspondence between specific monomers of different species. Using subunits from three different cheliceratan hemocyanins--Limulus, Eurypelma and Androctonus, van Bruggen et al. (1980) even obtained interspecies hybrid 4 x 6- and 8 x 6-meric structures. N o t only is the structural integrity maintained through heterogeneous subunits, the allosteric oxygen binding in hemocyanins is also directly dependent upon specific interactions a m o n g the various subunits. In the dissociated Limulus hemocyanin a different oxygen affinity

exists in each fraction (Sullivan et al., 1976). Similarly, in Eurypelma hemocyanin, the individual subunits as well as the dimeric b-c complex failed to exhibit any cooperative oxygen binding at all, whereas in the whole hemocyanin molecule a very high Hill coefficient ( n i l = > 7 ) was observed (Savel-Niemann et al., 1988). In Androctonus hemocyanin, a Hill coefficient of 9.25 was measured for the whole 4 × 6-meric at pH 7.5, but its dissociated subunits again failed to show any cooperativity (Lamy et al., 1980). Concurrent to the work cited above, a wealth of new amino acid sequence data on m a n y arthropod hemocyanin subunits is being revealed, elucidating evolutionary and structural relations between these hemocyanins and their different chains (Bak et al., 1986; Bak and Beintema, 1987; N a k a s h i m a et al., 1986; Jekel et al., 1988; Neuteb o o m et al., 1990; Sonner et al., 1990). In spite of a good degree of homology in primary structure (expecially around the oxygen-binding domain and at the site of intersubunit contacts) and of a general similarity in the hydrophobic or hydrophilic micro-environment of the amino acids (Linzen et al., 1985), a diversity between individual subunits has been noted which is manifested as

Fig. 2. The structure of the Panulirus interruptushemocyanin was determined by X-ray crystallography (cf. Volbeda and Hol, 1989). Shown here is the top half of the hexameric structure, three subunits related by the 3-fold axis of this approximate 32 point-group symmetryoligomer.Within each subunit, three domains can be recognized. Domain #1 is shown in ribbon representation,domain #2 is marked by an 'arrowed' Ca-tracing incorporating cylindrical helices and domain #3 is shown as a continuous Cct-tracingwithout arrows. The helix 1.2 of the domain #I (whichis missingin cheliceratan hemocyanin)and helix 3.3 of domain #3 (probably important in interhexameric bonding in multi-hexamericassembly)are marked by arrowheads. Filled circles show the location of copper ions and open circles represent disulfide bonds. An outer boundary is marked to indicate the overall quarternary structure of the half molecule. The figure is taken from Volbeda and Hol (1989).

Structure of MultihexamericHemocyanins pronounced immunogenic characteristics of various subunits (Linzen, 1983; Lamy et al., 1983a; Markl, 1986; Markl et al., 1986; St/Scker et al., 1988). C. Application of'MSA" to hemocyanin structure and early models Another development which contributed significantly to our knowledge of arthropod hemocyanin structures was the introduction of multivariate statistical analysis (MSA) techniques to electron microscopical image processing (van Heel and Frank, 1980, 1981; van Heel, 1984, 1989). This technique combined the alignment of molecule images (cf. Frank et al., 1981) and multivariate statistical analysis methods ('correspondence analysis', Benzrcri, 1980; Lebart et al., 1984). Alignment of molecular images allows averaging to be applied so as to reduce the random noise while boosting the common signal. Through alignment and averaging one can obtain good noise-free images of biological macromolecules from very noisy electron micrographs. With mixed populations of images, however, the concept of averaging has to be applied carefully: one needs to first recognize (by pattern recognition techniques) the different types of molecular images present in the mixed data set prior to averaging. In the very first papers presenting the basic MSA technique (van Heel and Frank, 1980, 1981), a study of the 4 x 6-meric Limulus half-molecule was used to exemplify the new methods. The molecule was found to have two different faces ('flip' and 'flop') and to exhibit two stable 'rocking' positions on the carbon support film in each of these orientations, which led to the conclusion that the four hexamers of the structure were not coplanar. The next study using these techniques elucidated that the quarter-molecule of Limulus (a 2 x 6-mer) shows only two different faces on the support film (van Heel, 1981; van Heel and Keegstra, 1981). The same MSA approach revealed flip-flop and rocking behavior for the 4 x 6-meric hemocyanins of Andoctonus and Eurypelma (Bijlholt et al., 1982b). The MSA image-processing results for the 4 x 6-mers from these three different species studied were indistinguishable. The first models proposed for the 4 x 6-meric hemocyanins (Lamy et al., 1981; Markl et al., 1981) were based on combining: (a) the structure of the hexameric 'building block' (van Schaick et al., 1982) with (b) the preliminary model of the 4 x 6-meric structure determined by imageprocessing techniques (van Heel and Frank, 1980, 1981); (c) the assembly behavior of monomeric components from Eurypelma hemocyanin (Markl et al., 1981) and (d) immuno-electron microscopic observations on the Androctonus and Eurypelma hemocyanin (Lamy et al., 1981). However, since at that time the absolute handedness of even the hexameric building block (from X-ray diffraction analysis) was not known, the final enantiomeric choices for constructing a 2 x 6-mer or a 4 x 6-mer could not yet be made. Moreover, in the paper by van Heel and Frank (1981) all illustrations depicted the molecules ' . . . as seen through the supporting carbon

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film ...'. In explaining the general idea of rocking and flip-flop, a schematic drawing for the 4 x 6 assembly was presented which matched the ('mirrored') images in that paper. Unfortunately, this schematic drawing was interpreted as being a structural model for the 4 x 6-meric hemocyanins to localize specific subunits based on immuno-electronmicroscopic experiments. Whereas the immuno-microscopy experiments were well performed and added significantly to our understanding of these complex structures, the subunit localization in both the A ndroctonus (Lamy et al., 1981) and Eurypelma (Markl et al., 1981)4 x 6-mers remained, at best, rather speculative. The interpretations of such immuno-microscopical experiments cannot be simply mirrored to fit different enantiomeric versions of the 4 × 6-mer. The 45 ° view of the 4 x 6-meric Limulus half-molecule (van Heel et al., 1983) provided the first direct evidence (and not indirectly through its rocking behavior) for the non-coplanar nature of the 4 x 6-meric structure. Also, the 2 x 6-meric halves of the 4 x 6-mer were so clearly distinguishable in this view that the handedness of the 4 x 6-mers--given that of the 2 x 6-mers--became evident. The 4 x 6-meric models that had been used for interpreting the immuno-labelling experiments turned out to have been an incorrect enantiomer, and a reinterpretation of the immuno-electronmicroscopic work for the 4 x 6-mers of all three species became necessary. A model of the Limulus 8 x 6-meric structure consisting of two copies of the incorrect 4 x 6-mer thus also needs reconsideration (Lamy et al., 1982, 1983b). The controversy about the enantiomeric choices culminated in a lively debate at the Leeds conference in 1982 (van Heel et al., 1983) between Jean Lamy and one of the authors (MvH), moderated by Ernst van Bruggen. The issue was not resolved at the time, but at the next conference on Invertebrate Oxygen Carriers at the Evangelische Akademie in Tutzing (Germany) in 1985, Jean Lamy conceded that their earlier models had been incorrect enantiomers (Lamy, 1986). Using the structural arguments presented by van Heel et al. (1983) for the choice of enantiomer in constructing a 2 × 6-mer (see also van Heel, 1984), models for the Androctonus hemocyanin (Lamy et al., 1985a,b, 1986; Boisset et al., 1990), and for Eurypelma hemocyanin (Savel-Niemann et al., 1988), incorporating the right enantiomeric form of dodecameric half with correct subunit organization in 4 × 6-mer, were proposed. When building 3D models of the multi-hexameric hemacyanins, enantiomeric decisions need to be made at each level of the hierarchical assembly. At the hexamer level itself there are already two possibilities, one being the mirror version of the other. This handedness problem was solved in 1982 in an early stage of the X-ray analysis of the Panulirus hemocyanin crystals (van Schaick et al., 1982). At the next level of hierarchical organization, the 2 x 6mer, two different ways of rotating one hexamer relative to the other are possible given the overall shape of this molecule in electron micrographs (typical EM images of the 2 x 6-meric molecules show side-to-side contacts between two hexamers; van Bruggen et al., 1981). Using

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the knowledge that the 'bridge' connections (Lamy et al., 1981; Markl et al., 1982) that hold together the 4 × 6meric structure are located on a long edge of the 2 x 6mer, there are four different 2 × 6-mer edges that could be responsible for this binding. Since the hexamers in the 4 x 6-mer are not co-planar (van Heel and Frank, 1980, 1981) the 4 x 6 - m e r can be assembled using either a positive or a negative rocking angle as well as with a positive or a negative flip-flop shift. Thus, there are at least some 2 x 4 × 2 x 2 = 32 different possibilities to assemble a 4 x 6-meric structure. The total number of possibilities for the assembly of the 8 x 6-meric structure from two 4 x 6-mer assemblies is again larger by at least a factor of 4. Determination of the correct handedness of all multi-hexameric structures is essential for interpreting the positions of the antigenic epitopes on the hemocyanins in immuno-electronmicroscopic experiments. For building good models of the multi-hexameric hemocyanins not only the right enantiomers must be selected, but also correct assembly parameters such as relative rotation angles and shifts must be applied and a correct size for the basic hexamer be used. In the models of the Androctonus 4 x 6-mer proposed by the Lamy group, a too flat hexameric building block was used (height-towidth ratio of only 0.67, instead of 0.9), due to which a wrong direction for the rocking angle was derived originally a n d - - i n a later stage---extra 'protein material' was postulated so as to obtain an acceptable spatial organization for the two 2 x 6-mers (Lamy et al., 1981, 1985a; Sizaret et al., 1982). Two of the four models for the 4 x 6-mer considered in their work (cf. model T and 'IV' of Fig. 3 in Lamy et al. 1985b) are thus a priori inconsistent with the known shape of the hexamer. Although there still is no biochemical evidence for the existence of this additional 'material', the issue has not yet been settled (Lamy et al., 1986; Boisset et al., 1990).

D. The present work In this paper, the characteristic views of the single hexamer (Panulirus interruptus), the 2 x 6-mer (dissociated Limulus hemocyanin), the 4 x 6-mer (dissociated Limulus hemocyanin), and the 8 x 6-mer (whole Limulus hemocyanin) are studied in negative-stained preparations by means of the MSA image-processing techniques. The various views obtained are compared with projections of the 3D model densities created from multiple copies of the X-ray electron densities of the single hexamer (van Schaick et al., 1982). Model building of progressively larger arthropod hemocyanin assemblies, while maintaining compatibility with the characteristic views found in the electron microscope, allows us to find translational assembly parameters to a precision of about +__6 / k and rotational parameters to about + 2 °. The precision of the approach decreases somewhat for the 8 × 6-mer due to the accumulation of the errors made in assembling the 2 × 6mer and the 4 × 6-mer models. Even there, however, this positional precision is nevertheless much better than the reproducible resolution found in the processed electron microscopic images, an effect comparable to finding

atomic coordinates to a precision of 0.3 A in an X-ray map with only 3 A resolution. The assembly parameters obviously only make sense in an enantiomerically correct structure, and we thus seek to answer these questions, including the question of whether a 'flip-to-flip' or a 'flopto-flop' interface joins the two 4 × 6-meric halves of the 8 × 6-meric Limulus polyphemus hemocyanin. The new Limulus II structure (Magnus et al., 1991; Hazes et al., 1993) deviates in details from the Panulirus interruptus structure we use for our model building; this fact only has consequences for the model of the 2 x 6 - m e r as is discussed below.

II. MATERIALS AND M E T H O D S

A. Sample preparation and electron microscopy Whole blood from Limulus polyphemus was Millipore filtered and diluted to a concentration of ~0.1 mg protein/ml with 10 mM Tris. HCI, pH 7.4 containing 5 m s CaCI 2. This solution was prepared fresh and used as such for microscopy of the whole 8 × 6-meric structure. To study the 4 × 6-meric and 2 × 6-meric dissociation products, this solution was dialyzed against 10 mM Tris.HCl+ 10 mM EDTA, pH 8.5. It was observed that after about 2 hr of dialysis, the 8 × 6-meric hemocyanin assembly completely dissociates into single hexamers. At different stages of dialysis aliquots were taken to monitor the degree of dissociation microscopically. Schutter et al. (1977) reported that dialysis of the 8 × 6-meric hemocyanin solution at pH 5.5 and 7.5 with EDTA led to a preponderence of 2 × 6-mers and 4 × 6-mers, respectively. A sequential dissociation to the next lower assembly of the hemocyanin should be expected by alkaline hydrolysis, SH-reagent treatment or by dialysis in the presence of EDTA. However, it was difficult to arrest the dialysis process so as to obtain relatively homogeneous stages of dissociation. EM grids were thus prepared from the solution which contained both 4 × 6-mers and 2 × 6-mers. Since it was rather easy to separate the different assemblies in the micrographs visually prior to the image processing, no efforts were undertaken to further purify the dissociation products. Freshly carbon-coated 400-mesh copper grids were used for the specimen preparation. In some cases, the carbon films required one or two days of aging to reach optimal adsorption properties. Samples of 5 pl were applied to the grid, and the excess fluid was blotted off after 2 min. Uranyl acetate (1%; centrifuged at 20,000 rpm to remove any crystals) was then applied to the grids, and excess fluid blotted away after about a minute and a half. Without introducing further washing steps the grids were air-dried and observed in a Philips EM300 or CM12 microscope at 80 kV. Areas of interest were imaged at 70,000 magnification using an underfocus of 3-5 Scherzer units. The micrographs (AGFA Scientia 23-D56 photographic film) were exposed for 1 sec and then developed in full strength Agfa G170p developer for 5 min.

Structure of MultihexamericHemocyanins

B. Image processing After visual selection of the micrographs based on a good distribution, they were inspected in an optical diffractometer, and micrographs suffering from astigmatism or drift were discarded. The good micrographs were digitized using a DATACOPY 610F linear CCD densitometer mounted on a standard 6 x9 cm enlarger equipped with a direct-current-driven halogen lamp for illumination, at a sampling step of 25.5 ~t or 3.6 A on the specimen scale. The digitized images were then transferred from the densitometer PC to a duster of Vax/VMS computers (Digital Equipment Corp.) including various 3100s and one Alpha workstation for further processing. All image processing was performed using the IMAGIC software system (van Heel and Keegstra, 1981) in its current enhanced form--IMAGIC-V (Image Science Software GmbH).

1. Particle selection and preprocessing The digitized micrographs typically contained some 50-100 molecular images which were selected interactively on the screen of an X-windows workstation. Overlapping molecules or molecules touching each other were excluded from processing. The selected molecules were extracted in a frame of 96 x 96 pixels for the 8 x 6mers and of 64 x 64 pixels for 4 x 6-mers and 2 x 6-mers. All molecular images extracted from different micrographs were placed in a single IMAGIC image file. (IMAGIC image files may contain ten thousands of smaller images; this organization is essential for the processing of large numbers of small molecular images.) Thus, 2700 molecular images of the 8 x 6-mers, 1080 of the 4 x 6-mers, and 1067 of the 2 x 6-mers were obtained. Molecular images in electron micrographs are very noisy for a number of reasons: Poisson noise associated with the statistical nature of the electron exposure, the irregular structure of the supporting carbon foil, and granularity of the staining material. In contrast to what one might intuitively think, it is mainly the low-frequency noise in the images which interferes most with the subsequent processing. These very low spatial frequencies are associated with large-scale effects such as stain gradients and inhomogeneous illumination, effects which are not related to the structure studied yet may have a strong influence on the correlation-function based alignment procedures. It is thus important to suppress these disturbing low spatial frequencies in the images by filtering in Fourier space, and the low spatial frequencies corresponding to image details larger than the characteristic size of the molecules are thus reduced to a fraction (0.1 or 0.5 %) of their original values. The low frequencies are not entirely removed, hence they may be restored at a later stage, if necessary. The very high-frequency components, beyond the expected maximum resolution in the data, are also largely associated with noise and may be filtered out, but this filtering is less essential than the suppression of the lowfrequency components. By our convention, the contrast

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in the digitized micrographs is chosen such that protein is light and the surrounding stain is dark. Finally, a circular mask with a diameter of approximately 1.5 times the linear size of the molecules is applied to all images to remove unwanted background. The image variance within this mask was normalized to an arbitrary value of 100 and the average density within the mask set to zero.

2. Alignment using multiple reference images Prior to any averaging (summing) operation, the noisy images need to be aligned relative to each other. However, in an image data set of randomly oriented individual macromolecules, the alignment may be a problem because of the presence of different types of molecular views which cannot be brought into register by simple 'inplane' rotations and translations, i.e. by correlation alignments, because they are fundamentally different views of the molecule corresponding to different orientations of the molecule relative to the plane of the support film ('out-of-plane' rotations). Such different views need to be treated largely separately. From the filtered data set, several (typically three to five) different molecular profiles are selected to be used as reference images for the initial round of multi-reference alignment procedures (van Heel and Strffler-Meilicke, 1985). These reference images are contoured individually and the density values outside the mask set to zero. To center these reference images, the area inside the contour is geometrically centered with respect to the center of the image frame. A threshold is applied to the densities within the contour (below which the densities are set to the threshold value), to reduce the influence of strong negative stain accumulations on the alignment procedure. To avoid bias towards any given handedness (cf. Boekema et al., 1986), each reference image in the procedure is always used twice; once in its original form and once mirrored horizontally. All reference images are also aligned relative to each other at various stages of the procedures. The filtered image data set is aligned both rotationally and translationally relative to each of the reference images. At the end of the first iteration of alignments relative to each noisy reference, the 20 aligned images with highest cross-correlation coefficient relative to that reference (CCC: the normalized peak in the cross-correlation function relative to each reference image) are summed. These averages, being much less noisy than the first raw reference images, are then used as references for a second round of alignments. From all these alignments, one proceeds with that aligned version of each original image which is associated with the highest CCC relative to one of the references.

3. Multivariate statistical analysis and classification The use of different references to align a mixed population of molecular images is only part of the solution. We also need to recognize ('classify') the different views in the data set by pattern-recognition

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techniques prior to any averaging operation. Multivariate cloud in the compressed hyperspace will ideally show a set statistical analysis (MSA) in the form of eigenvector data of clearly separate clusters of images, each cluster compression (van Heel and Frank, 1981; Lebart et al., corresponding to one of the preferred orientations of the 1984) and unsupervized automatic classification (van structure. However, clusters of points in a 5-20-dimenHeel, 1984, 1989) are used to detect and separate the sional space may not always be easy to visualize and to different views present in the data set. comprehend. In favorable cases the distribution of image The aligned molecular images, each consisting of points in the compressed dataspace can become transn x n = m pixels, are first represented as a single point in an parent when the points are projected onto planes spanned m-dimensional ('hyper') space. The position of the point by the directions of two specific eigenvector axes. The in this space is determined by the grey value of the pixels of resulting two-dimensional patterns may already reveal the corresponding image. The grey values of the raw clear clustering (Figs. 4 and 9). image thus serve as the coordinates along each of the Reliable automatic classification techniques remain, n × n = m unit vectors spanning this space. The point in however, indispensable for separating the clusters present hyperspace is entirely equivalent to the image itself as in the multi-dimensional cloud in an objective and described by the pixel densities arranged in the original reproducible way. We favor a hierarchical ascendant two-dimensional molecular image. A set of images classification (HAC) scheme (cf. Lebart et al., 1984; van translates to a set of points in the hyperspace or a 'cloud'. Heel, 1984) with a moving-elements relaxation (van Heel, The closer two points of the cloud are to each other within 1989) for the automatic partitioning of the data cloud into this m-dimensional space, the more similar the corres- groups of very similar images. In the HAC process, each ponding images. image of the data set is first considered to be a class by The coordinate system in the m-dimensional space is itself. Classes are then merged if that merging is associated then rotated such that the new (also orthogonal) coordi- with the lowest possible increase in the intraclass variance nate system is optimally adapted in a least-squares sense ('added intraclass variance' or AIV, also known as Ward to the shape of the data cloud (Benz~cri, 1973; Lebart et criterium; Ward, 1982) at that level of the procedure. This al., 1984; Borland and van Heel, 1990). The first axis of merging process is continued until all images are finally this new coordinate system typically (depending on the grouped together in one huge class; the full history of the metric used) accounts for the fact that the center of the merging procedure is meanwhile stored in a so-called cloud does not coincide with the origin of the coordinate classification 'tree'. The classification tree is cut at a level system and does not always bear significant information. corresponding to the number of classes requested by the The second axis, orthogonal to the first, then describes the user. At this stage the clustering is refined by extracting most important direction of differences between the each member image from its class and allowing the images. The third axis (orthogonal to the first two) image to move to another class if this transfer leads describes the next most important direction of differences to a reduction of the variance contribution of that within the data set of images, etc. With each new axis, the image (moving-elements-refinement). Such refinement is significance of the inter-image variance described reduces performed iteratively for all images until no further (eigenvalues) and after some 5-20 eigenvectors the inter- migrations occur and the total partition stabilizes. The image differences represent noise rather than interesting moving-elements-refinement algorithm typically leads to structural information and may be discarded. an overall reduction of the intra-class variance by about Instead of describing the images by their 64 x 64 or 10% whereby about 2(P40% of the images change their 96 x 96 pixel densities, after this data compression they class assignments. are described by their 5-20 main eigenvector coordinates The images belonging to each of the classes obtained only. A comparison between two images thus reduces to are summed into class averages which have a largely the order of 5-20 multiplications and additions, a improved signal-to-noise ratio as compared to the raw reduction in computational requirements by orders of images. Since good noise-free images form ideal reference magnitude. When using chi-square metrics (Benzrcri, images (Saxton and Frank, 1977) the results of the first 1973) or modulation distance metrics (Borland and van round(s) of classification(s) are typically used as new Heel, 1990) for the eigenvector-eigenvalue analysis, the reference images for new round(s) of alignments. This first axis of the new coordinate system corresponds to the iterative multi-reference alignment process, of which the center of the data cloud and describes the total average of classifications are an integral part, is continued until the the aligned images. The calculation of the eigenvectors results stabilize and no further characteristic molecular (also called eigenimages since they have the character of views emerge (van Heel and Strffler-Meilicke, 1985). images) is normally restricted to a narrow region ('MSAMASK') drawn interactively around the total sum of all 4. Resolution in the characteristic views images in the data set so as to reduce the influence of the background. The resolution in the average images obtained after the A reduction of the total amount of data by restricting classification step is assessed on the basis of the S-image ourselves to main eigenvectors of the system facilitates the criteria (Sass et al., 1989). This method is a more understanding of the data set considerably. If the data set, appropriate measure of intra-class similarity than the for example, consists of a number of preferred or 'stable' phase residual (Frank et al., 1981) or the Fourier ring orientations of the molecule on the support film, the data correlation (Saxton and Baumeister, 1982; van Heel et

Structure of MultihexamericHemocyanins al., 1983), techniques which are rather aimed at measuring the cross-resolution between two individual images. Classes with a relatively poor resolution may correspond to mixtures of images containing misaligned images, damaged molecules, or rare molecular views. Classes with a good statistical resolution are the characteristic views emerging from the analysis. We try, as much as possible, to include rare molecular views as reference images during the multi-reference alignment in order to extract as many different views as possible from the data set. Rare views may be very important for the interpretation of the structure and deserve special attention.

C. Model buildin# The electron density distribution of the single hexameric Panulirus hemocyanin at 5 A resolution (van Schaick et al., 1982) has been used for all model building procedures. To obtain identical monomers, the density map was first averaged over all six subunits, and the missing low frequencies (due to the presence of a beam stop in the X-ray diffractometer) were 'restored' by thresholding the data at zero density. Finally, the high spatial frequencies in the data (above 1/20 A) were filtered out so as to make the data more comparable to the electron microscopic projection images. Models of the multi-hexameric assemblies are generated by first merging two copies of the hexamers to obtain a 2 x 6-mer. Two copies of this 2 x 6-mer are then merged to make a 4 x 6-mer; and finally, merging two 4 x 6-mers yields the 8 x 6-meric assembly. Before merging two copies of lower assemblies to construct the next larger one, these copies are first brought into correct spatial orientation by rotations and shifts in 3D space, and are then merged such that the highest of the two densities prevails in the resulting model. The 3D density distribution of Panulirus was originally sampled on a 1.5 A grid in a volume of 96 x 96 x 96 sampling points. For the present work the hexameric unit is sampled down by averaging to a 48 x 48 x 48 grid, leading to a 2 x 6-mer model of 48 x 48 x 96, to a 4 x 6-mer model of 48 x 96 x 96, and an 8 x 6-mer model of 96 x 96 x 96 sampling points. Each of the model assemblies is constructed using a range of assembly parameters, i.e. using a range of different relative rotation angles and shifts. The projections of these models in many different (Euler angle) directions are compared directly with the results obtained from the electron microscopy analysis to find the best assembly parameters. The final models of the different hemocyanin assemblies are presented in two different forms: as a straightforward projection through the 3D density distribution in directions specified by three Euler angles--~, fl and ~-and as a stereographic projection or surface representation (van Heel, 1983; Saxton, 1985) in which the surface of the 3D molecular volume, as defined by a certain threshold value, is depicted (surface rendering). Galleries of such views are displayed preferably such that every pair of neighbor images forms a stereo pair.

395 III. RESULTS

A. The hexameric structure The single hexameric hemocyanin molecule from Panulirus interruptus shows two discernible orientations (see review by van Bruggen et al., 1981). In the top view, the molecule appears roughly hexagonal; this a projection along the 3-fold axis of the hexameric structure. The other view is clearly a side view of the structure with a roughly rectangular shape with two 'sharp' and two 'fuzzy' edges which is the side view of the molecule (van Bruggen et al., 1981). From a single electron micrograph, 145 individual molecular images of the hexagonal view were selected for processing. The aligned images were analyzed by MSA and automatic classification (see Materials and Methods section). The number of dasses was chosen to be 20. In the resulting class averages of the hexagonal view, all images looked alike and differed mainly in their relative staining. The most compact class (most similar image members) of the hexagonal views was selected for a closer comparison with the X-ray data (Fig. 3). A number of details emerged in the EM class averages which can readily be compared to the X-ray structure. The first detail is an area in the 'beans', close to the 3-fold axis, in which a number of ~-helices run more or less parallel to that axis (see Fig. 2: domain #2, containing the di-copper oxygen-binding site). In projection along this 3fold axis, these high-density areas form a distinct bright spot some 18 A away from the 3-fold axis (Fig. 3g,j). This spot is also clearly visible in the EM result (Fig. 3h,i). Another detail which can be seen with both techniques is an area of domain #3 with a high density of/~-barrel (Volbeda and Hol, 1989) with the shape of an arrowhead. This detail is on the outside of the hexameric structure and can clearly be seen on the surface representations (stereo of top view) of the hexamer (Fig. 3c,d; see also arrows in Fig. 3f,g). Since, in projection, corresponding arrowhead areas in 'beans' of the upper half and of the lower half of the hexamer overlap, this detail is dearly visible in the full projection through the X-ray electron densities of the hexamer (Fig. 3g) as well as in the EM projections through the hexamer (Fig. 3h,i). The X-ray data of the hexameric molecule extended over about 63 sections (on the 1.5 A grid in 96 x 96 x 96 sampling volume) along the 3-fold axis. By excluding the central 24 sections from the calculation of the projection, the contributions of the top and the bottom of the molecule can be emphasized as a crude approximation for a preferential staining of the outer parts of the protein. It is interesting to see that with this rough stain-penetration model, the projection (Fig. 3j) changes such that the arrowhead areas appear now to be connected by one 'bridge' to the central part of the structure just as in the EM average (Fig. 3i). The EM average (Fig. 3h,i) is not as symmetric as the Xray projection (Fig. 3g) of the molecule. Three of the dark 'clefts' in the EM averages (Fig. 3h,i) are darker than the other three. Projecting a 32 point-group density along the 3-fold axis (i.e. perpendicular to 2-fold axis) should lead to a 3 m symmetric projection (mirror symmetry around the

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Fig. 3. The Panulirus interruptus hexameric hemocyanin, a~l: Stereographic representations of electron density distribution of hemocyanin as determined by X-ray analysis (van Schaick et al., 1982). The molecule consists of six bean-shaped subunits arranged in 32 point-group which beans can clearly be recognized in these stereographic images (van Heel, t983) derived from a low-pass filtered version of the 5 A raw X-ray map (van Schaick et al., 1982). In the a-b stereo pair, the direction of view is along a 2-fold axis, i.e. perpendicular to the 3-fold axis of the structure, c~l: Stereo pair along the 3-fold axis of the hexamer. In this surface representation the 'arrowheads'--the domain #3 containing fl-barrels--are visible (see mark in Fig. 3c). Only the three 'beans' close to the observer are visible. The arrowhead domains being at the surface are well accessible to the negative stain in electron microscopical preparations (see below), e: Projection through the lower half (lower three monomers) of the X-ray electron density map of the hexameric molecule, f: Projection through the top half (top three monomers) of X-ray electron density of the hexamer. The E-barrel of domains #3 forming the arrowheads are marked, g: Projection through the full molecule, or-helicesclose to 3-fold axis (three high-density areas near the centre of the image) are clearly visible. The arrowhead domains of the top and the lower half of the molecule overlap (marked by arrowheads), h: Electron microscopical average of P. interruptus hemocyanin molecules. This average has many details in common with the X-ray density projections (e-f). The high-density or-helices area at the center of the molecule and the arrowhead domain connected by a 'bridge' can be recognized. The EM average resembles the top half (f) of the X-ray structure more than the lower half (e), which suggests that the top half (away from the carbon foil) of the molecule is stained slightly more than the side oriented towards the support film. i: Same electron microscopical average as in h but this image has additionally been high-pass filtered in order to emphasize the high-frequency image details, j: Projection through the full X-ray density distribution of the molecule (as in g) excluding the central sections of the electron density. The full density extended to 63 sections, of which the central 24 were excluded. The arrowheads are now connected by one high-density bridge with the central part of the molecule, just as is the case in the electron microscopical averages (h-i). This suggests that the negative stain in the EM preparation is concentrated more on the outer surfaces of the molecule.

Structure of MultihexamericHemocyanins projected 2-fold axes). Small differences thus apparently exist in the amount of staining of the top and the bottom halves of the structure. Comparison of the EM averages (Fig. 3h,i) with the X-ray half-projections (Fig. 3e,f) shows that in this preparation, the EM data look more like Fig. 3f, i.e. the top half of the molecule. Thus, the top side of the hexamer facing away from the carbon foil is apparently stained somewhat more strongly by uranyl acetate than the carbon-foil of the structure (see also de Haas et al., 1994). Preferential top side staining has been previously reported in other specimens (cf. Mandelkow and Mandelkow, 1981). The larger, multi-hexameric assemblies studied in our present work do show a conventional 'carbon-foil-side' preferential staining. The use of preferential staining behavior as a structural argument is thus tricky and should be avoided. Only structure characteristics which are invariant to preferential staining effects are used in the present work for making the enantiomeric decisions. B. The 2 x 6-meric structure

The whole native hemocyanin molecules of the chelicerata species Limulus (8 x 6-mer), Androctonus (4 x 6mer) and Eurypelma (4 x 6-mer) dissociate into their dodecameric constituents in alkaline pH (cf. van Bruggen et al., 1981) or by EDTA dialysis (Schutter et al., 1977; Bijlholt et al., 1979). In electron micrographs, the dodecameric assembly shows a rectangular and a circular half (van Heel and Keegstra, 1981; Bijlholt et al., 1982a). This indicates that the inter-hexameric connection is located on the sides of the roughly cylindrical hexamers and that the 3-fold axes of the hexamers are approximately at a right angle to each other. From the electron micrographs of dissociated Limulus hemocyanin (a small section of one is shown in Fig. 4a), 1067 molecules were selected, pretreated, aligned, and subsequently analyzed by the MSA data compression and automatic classification procedure. The classification procedure was performed using the image coordinates along the first eight eigenvectors. The images were classified into eight classes, the averages of which are shown on the borders of Fig. 4c. It is apparent from inspection of the various classes and from the good separation between the images in the upper left and the lower left of the MSA map, that there are two main orientations of the molecule (van Heel and Keegstra, 1981). The total average of the images in the left upper half ('type A') and of the left lower half of the map ('type B') are the main result of this analysis. These two classes are interpreted as the face-up and face-down versions of the same structure. As was the case with 4 x 6meric structure (van Heel and Frank, 1981), the two classes are not exactly each other's mirror image due to preferential staining effects. A significant number of the molecules of the 2 x 6-mer (right panel in Fig. 4c) did not show the typical type 'A' or 'B' structure. These images most likely represent intermediate edge-on views of the 2 x 6-meric assembly which had not been detected in earlier studies. Although the data set of 690 particles is

397

about five times larger than the data sets used in previous studies (van Heel and Keegstra, 1981; Lamy et al., 1986) this data set still does not contain enough of these rare molecular views to give them a good statistical significance. That only two and not four stable positions were found (the 2 x 6-meric structure has four flat sides at approximately right angles from each other, see Fig. 5) is strong evidence for the presence of a 2-fold axis at the interface between the hexamers which renders the four sides of the 2 x 6-mer pairwise identical. The 2-fold axis (Fig. 7) is perpendicular to the long axis of the assembly and is at an angle of about 45 ° with the local 3-fold axes of the hexamers (half the 90 ° angle between the 3-fold axes of the two hexamers). This 2-fold axis is not absolutely exact due to the heterogeneity of the monomers (see Introduction) and the point-group symmetry of the 2 x 6-mer is thus only approximately 2 (also known as C2: cyclical 2). The fact that two and not just one single class emerged from the analysis implies that none of the local 2-fold axes of the hexamers coincides with one of the 2-fold axes of the other hexamer (and with the long axis of the 2 x 6-mer). If that had been the case, the point-group symmetry of the 2 x 6mer would have been 222 (also known as D2: dihedral 2) and all of its flat surfaces would have been structurally equivalent. Let us now compare the flat hexameric half of the 2 x 6mer EM averages with the results of analysis of the single hexamers. The arrowheads that are pronounced in the single hexameric images (Fig. 3i) are also a predominant feature in the flat hexameric half of the 2 x 6 molecule (see arrows in Fig. 5a). The three most pronounced clefts between beans are the same as noted for the single hexamers, indicating, again, that the top side of the flat hexamer is stained slightly preferentially. Note that the triangle formed by the arrowheads in the flat hexameric half of the 2 x 6-mer has none of its sides running exactly parallel to the long axis of the double-hexameric structure; the long axis of the 2 x 6-met makes an angle of 24 ° ( + 2 °) with the closest local 2-fold axis of the hexamers (see Fig. 6). The other (rectangular) half of the 2 x 6-merit structure corresponds to a side projection through the single hexamer. Such side projections through the X-ray data are visible in the projections through the 2 x 6 model (Fig. 5b,c; in Fig. 3a surface representation of the side view is presented). An important detail in the rectangular half of the 2 x 6 projections is a dark oblique'cleft' at the center of the rectangle (see arrowheads in Fig. 5a), with two bright 'blobs' on each side. This blob~left-blob detail, which can readily be recognized in both the EM averages and in the model projections, has a specific orientation relative to the long axis of the 2 x 6-meric structure. Based on the averaged EM images, one can now make the enantiomeric decision for the 2 x 6 structure. The handedness of the 2 x 6-meric structure is determined by whether one hexamer is rotated over + 90 ° or over - 9 0 ° relative to the other hexamer in the assembly (Fig. 6). Model densities of both enantiomeric versions were built and projected (Fig. 5b,c) in the four directions (90 °

398

M. van Heel and P. Dube

the 'far' and in the 'near' sides overlap. Comparison of the relative orientation of these two stain-invariant structural details allows the enantiomeric decision for the 2 x 6-mer to be made. These structural characteristics are different for the + 90 ° ('right'; Fig. 5b), and for the - 9 0 ° ('wrong'; Fig. 5c) enantiomeric versions of the structure. The

intervals) corresponding to the EM images (Fig. 5a). As mentioned before, the three arrowheads in the fiat hexamer form a stain-invariant detail and the same is true for the blob~left-blob (BCB) detail in the rectangular half (hexameric side view) of the 2 x 6-mer. This is due to the fact that in the hexamer comparable BCB structures in

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C Fig. 4. Analysis of the 2 × 6-meric structure, a: Section of one of the electron micrographs of negatively stained preparation of the 2 × 6-meric molecules (dissociated Limulus 8 x 6 hemocyanin) used in the analysis (scale bar: 20 nm). b: Some molecular images (from a total of 690) after the pretreatment and alignment procedures (scale bar: 10 rim). c: MSA m a p of the population of 2 x 6 molecules obtained by projecting the data cloud in hyper space onto two eigenvector axes (axis 2 vs axis 3). The m a p shows a separation of the molecular images depending on their orientation on the carbon foil. The left part of the m a p is separated into two main clusters, 'A' (upper half) and 'B' (lower half). The right part of the m a p is somewhat diffuse and contains molecular views (right panel) in various unstable intermediate orientations between the stable A and B positions (Scale bar: 10 nm).

Structure of Multihexameric Hemocyanins

relative orientation of the details in the EM averages can only be matched by the + 90 ° model. The handedness of the 2 x 6-mer is therewith determined unambiguously. Even a mirror inversion of the EM images would not change this interpretation. Two further rotations are possible in the assembly of this structure. The first is a rotation of the 3-fold axes of the hexamers towards the long axis of the 2 × 6 structure. If such a rotation is present it must be less than a few degrees. The remaining rotation possibility is that of a small rotation additional to the + 90 ° or - 9 0 ° handedness rotation of the assembly. We have the impression that such additional rotation is small although we speculate that this type of rotation may be the mechanism of allosteric action for the 2 x 6-meric assembly (see discussion). Note that the two hexamers in the 2 x 6-meric assembly (Fig. 6) fit snugly into each other: the interface

399

between the hexamers is a narrow gap with an almost constant width. Such nice fits were never found in wrong enantiomeric versions of the 2 x 6-mer model structure. The only place where the two hexamers get 'too close for comfort', is an area (visible in Fig. 7, locations 7 and 13) where the protein sequence of Panulirus is 21 amino acids longer than the corresponding cbelicerata sequence (helix 1.2 marked by arrows in Fig. 2 is absent in ehelicerata spp.; Linzen et al., 1985), and where the Panulirus hexamer thus has too much material to be a perfect model for the chelicerate structures. Recently, the X-ray structure of a chelicerate hexamer, consisting of only the Limulus II component, became available (Hazes et al., 1993), which indeed has this helix missing and which thus will be a better model for future work. We now need to take a closer look at the 2 x 6 model (Fig. 7a) and its projections (Fig. 7b) since these images

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Fig. 5. The 2 x 6 EM results compared to the 2 x 6 model, a: Averages of the 2 x 6-mer images from two main classes (A and B views; see main text) corresponding to four stable positions of the molecule on the support film. Details seen in the averages of the single hexamer (Fig. 3) can also be recognized in the flat hexameric half of the 2 x 6 averages. In particular the arrowhead domains (marked by arrows) are clearly discernable (of. Fig. 3i). One of the local 2-fold axes of the hexameric halves makes an angle of 24 ° with the long axis of the structure (see Fig. 6). The rotational increment between these projections is 90 ° . These views are two-by-two identical (though rotated over 180 ° in the plane of the paper) due to the 2-fold symmetry axis of the 2 x 6 structure. As was the case for the single hexamer, the flat hexameric halves of these images show a slight preferential top side staining. The rectangular half of the 2 x 6-met view does not change much with preferential top or bottom staining since in this projection direction comparable features ('Blob-Cleft-Blob' or BCB; see arrowheads) in the upper half and in the lower half of the structure overlap (compare Fig. 7a-7 and 7a-19). The BCB detail is thus staininvariant as are the arrowhead details; the relative orientation of arrowheads and the BCB detail provide the absolute handedness of the 2 × 6-mer. b: The 'right' enantiomeric model structure is projected in the four different flat directions, to simulate the behavior of the 2 x 6-meric assembly in the electron microscopical preparations. The rdative orientation of the arrowhead details and the BCB detail correspond to that of the EM averages. The projection direction in this image is not exactly perpendicular to the long axis of the 2 x 6 (5° off) since the stable position of the 2 x 6-mer is slightly tilted due to the three-dimensional shape of the molecule, c: Projections of the model density of the 'wrong' enantiomeric alternative are inconsistent with the averaged EM images independent of possible preferential staining effects.

400

M. van Heel and P. Dube

provide us with the arguments needed to determine the correct 4 x 6-mer assembly. While determining the correct enantiomeric form of the 2 x 6-meric structure, we have defined the A and B views of the 2 x 6-mer. Electron microscopic views are projections through the total threedimensional volume; we also need to name the A and B 'faces' (surfaces of the three-dimensional structure) of the 2 x 6-mer. In the A view, we define the A face of the 2 x 6mer to be oriented towards the observer while the B face interacts with the supporting carbon foil. Equivalently, in the B-type view, a B face is oriented towards the observer while an A face is touching the carbon foil. With one 2fold axis at the inter-hexameric boundary of the 2 x 6-mer, three structurally different edges exist between these A and B faces: the A-A and the B-B edges (both internally symmetric while intersected by the approximate 2-fold axis), and the A-B edge of which two are present in the 2 x 6 structure. Especially important in interpreting the 4 x 6 images are the 2 x 6 views in Fig. 7a,b in which the 2 x 6 is in a 45 ° orientation relative to the viewer (locations 4, 10, 16 and 22). C. The 4 x 6-meric structure 1. The flip and flop views

The study of the 4 x 6-meric hemocyanin structures was closely associated with the development of multivariate image-processing techniques in electron microscopy (van Heel and Frank, 1980, 1981; Bijlholt et al., 1982b). In these first MSA papers, the four hexamers constituting the 4 x 6 structure were found to not all lie in the same plane, as indicated by the 'rocking' behavior of the molecule on the support film (see Fig. 8). Of the four hexamers, one was systematically found to show a lower contrast and

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this effect was believed to be caused by one hexamer not being in direct contact with the support film and thus being less well embedded in the negative stain material. Moreover, two fundamentally different views were found corresponding to a face-down and face-up orientation of the molecule, named 'flip' and 'flop' views (van Heel and Frank, 1981). With the cleft between the two dodecamers in the microscopical images aligned vertically (Figs 8, 11), the right dodecamer can be shifted upwards relative to the left one (flip view) or downwards (flop view). An asymmetry thus exists in the molecule between its top and its bottom surface. The orientation of the 'rocking direction' relative to the cleft in both the flip and the flop views of the molecule (van Heel and Frank, 1981), actually already determines the overall handedness of the 4 x 6 unambiguously (van Heel et al., 1983). However, this handedness reasoning is based on assumptions about the interaction of the molecule with the staining material: the three hexamers in close contact with the carbon support film must be contrasted more strongly than the fourth hexamer. In this particular case, such reasoning appears safe enough since an assumption of top side preferential staining would lead to the ad absurdum conclusion that only one hexamer is in direct contact with the support film and three are floating above the carbon layer. Yet, such argumentation is dependent on the behavior of the staining material and is thus avoided here. 2. The 45 ° view

An orientation of the 4 x 6 structure different from the flip and flop views was found in the high-stain areas of the same micrographs which had been used for the analysis of the flip and flop views of 4 x 6-mer. This new view was named '45 ° view' (van Heel et al., 1983); in this position, the molecule lies on one of the fiat sides of the dodecamers on the outside of the 4 x 6-mer, i.e. on one of the fiat sides facing away from the central cleft (Fig. 9b). This entirely different projection of the 4 x 6 structure provides valuable information on the magnitudes of the rocking angle and flip-flop shift, as we will see below. Moreover, the details in the 45 ° views can be directly linked to the 2 x 6meric projections discussed above which then leads to a direct coupling of the handedness of the 2 x 6-mer to that of the 4 x 6-mer. From the negatives of the 4 x 6-mer preparation, 45 ° views were selected interactively and pretreated as described in the Materials and Methods section. All 225 molecules selected were processed by multi-reference alignment, MSA data compression, and automatic classification. Interestingly, the analysis resulted in just two main classes of 45 ° views (Fig. 9d). A third cluster corresponds to images which were obviously aligned incorrectly. The fact that the four different fiat 2 x 6-mer surfaces on the outer side of the 4 x 6 structure lead to only two stable positions or classes of 45 ° views indicates the presence of a 2-fold axis in the 4 x 6-mer which renders the four outer dodecamer surfaces two-by-two equivalent. Since in the flip-flop analysis an asymmetry between the

Structure of Multihexameric Hemocyanins

two faces of the molecule has been found (van Heel and Frank, 1981), this 2-fold axis cannot lie in the plane of the molecule but, instead, be perpendicular to that plane. In the averages of the 45 ° views, the 2 x 6-meric structures can readily be recognized (compare right panel of Fig. 9d

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with the left panel of Fig. 4c). One lightly stained dodecamer lies, under an angle, over a more intensively stained dodecamer. The same type of 'stain-dependent' handedness reasoning as applied above to the flip-flop views of the 4 x 6-mer could be applied to the 45 ° view: if

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402

M. van Heel and P. Dube

the lightly stained dodecamer is away from the support film, the handedness of the 4 x 6 structure can be determined unambiguously. However, we again choose to avoid the use of stain-dependent arguments in our structural reasoning. 3. The 2

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6-met arrangement within the 4 x 6-mer

The rare side views of the 4 x 6-mer in which the molecule stands perpendicular to the plane of the support film look like two squares which slightly overlap in one corner (Bijlholt et al., 1982b; see also Fig. 9a, double arrows). The connection between the two 2 x 6-mers within the 4 x 6-mer is thus located at the edges of the dodecamers. There are three possible choices for these connecting edges (the A-A, the B-B or the A-B edge) since there are only three types of structurally different edges in the 2 x 6-mer. Connections between different types of edges are unlikely since that could lead to linear polymerization of the dodecamers, which is never observed. If the interdodecameric connections consisted

of A-B edges, the same polymerization argument would apply since the outer edges of the 4 x 6-mer would then also consist of A-B edges due to the 2-fold symmetry of the dodecamer. Moreover, if A-B edges would form the connection, the resulting 4 x 6-mer would also have a wrong enantiomeric form and be incompatible with the EM projection. In such a construction the edges of the 2 x 6-meric halves in contact with the support film would be either A-A or B-B edges which are intersected by the local 2-fold axis of the dodecamer. This, in turn, would mean that the dodecameric projections within the 4 x 6-mer should show local 2-fold symmetry (compare a combination of Fig. 7b-10 and 7b-22 with Fig. 10, left row). The dodecameric halves, rather, show a local mirror symmetry (more like a combination of Fig. 7b-4 and 7b-16 with Fig. 10, left row) consistent with a projection perpendicular to the local 2fold axis of the dodecamer. The interface between the two dodecamers thus must consist of either A - A or B-B edges (Fig. 5a). The 4 x 6mer projection in the 45 ° position solves this problem: the B - C - B detail in the 2 x 6-meric halves of the 45 ° uniquely shows that B-B edges form the inter-dodecameric interface (compare Fig. 10, middle and right row, with Fig. 5a). Moreover, only the B-B edge connection leads to a 4 x 6mer model which, in projection, resembles the dodecamer projections in the flip and flop views of the 4 × 6-mer. 4 . 4 x 6-mer assembly parameters

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Fig. 8. Schematicdrawing of the non-planar arrangement of the hexamers within the 4 x 6-merit structure. The molecule in this drawing is represented as lying between the observer and the carbon support (plane of the page). The hexamers are shown as balls and the inter-dodecamericbinding is represented by narrow bridges. The face-up and face-down position of the molecule produces 'flip' and 'flop' views. In both these positions the moleculeis able to 'rock'. In the flop view,the structure can rock around one long diagonal axis (L) and in the flip view along the short diagonal (S). This model explains the stain imbalance between juxtaposed hexamers in both the face-up or face-down orientation. The figure is adapted from van Heel and Frank (1981). Note that the micrographs in van Heel and Frank (1981) were printed in an unusual (mirrored) way, and the authors clearlystated that fact. The originalillustration--from which this figure was derived--thus showed the molecule with a mirrored handedness.

It is interesting to note that in the 4 x 6 structure, in contrast to early models (Lamy et al., 1981, 1982), the local 2-fold axes of the two 2 x 6-mers do not coincide. H a d they coincided, then we would have had two 2-fold axes perpendicular to each other and the overall pointgroup symmetry would have been 222 (D2) rather than 2 (C2). This would have meant that the flat top and bottom parts of the assembly would have been identical and that there would thus have been no flip-flop difference (no flip-flop shift), and there would also only have been one type of 45 ° view. Whereas the flip and flop views of the 4 x 6-mer allow for the flip-flop shift to be measured conveniently, the 45 ° view provides more direct information about the rocking angle. The assembly parameters (a flip-flop shift of 17 A + 5 A, and a rocking angle of 2 × 6 ° = 12 ° + 3 °) used for building the best models of the 4 x 6-meric structure are illustrated in Fig. 11. In the EM projections of the 4 × 6-mer the interdodecameric contacts appear to take place through two high-density 'bridges' (Fig. 12, left panel). These bridgelike structures of the 'bridged-tetramer' were proposed to represent a small molecular mass protein or an extended polypeptide chain in subunits forming inter-dodecameric contacts in a model for Androctonus 4 x 6-meric hemocyanin by the L a m y group (Lamy et al., 1985a; Boisset et al., 1990). However, when the model for the 4 x 6-mer is projected (Fig. 12)in directions corresponding to the EM flip and flop views, the bridge-like structures appear quite naturally and thus do not require the postulation of any extra protein 'material'.

Structure of Multihexameric Hemocyanins

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d Fig. 9. Analysis of 4 x 6 hemocyanin in the 45 ° view. a: The preferred orientation of the 4 x 6 structure with respect to the support film is highly correlated to the local stain concentration in the preparation. In areas of the grid with lower stain concentration the molecule tends to be in the normal fiat (flip or flop) position. The 45 ° position is found preferably in high-stain areas of the grid (see arrows). The rare vertical orientation of the 4 x 6 structure in which the molecule stands with its cleft perpendicular to the carbon support is marked by double arrows (scale bar: 20 nm). b: Schematic drawing of the 45 ° stable position of the 4 x 6 structure with respect to carbon foil as seen in the direction along the cleft between the two dodecameric halves of the assembly, c: Some of the 4 x 6 molecules in 45 ° position (from a total of 263 molecules) after the multi-reference alignment procedure. (Scale bar: 20 nm.) d: MSA map (axis 2 vs 3) of the 4 x 6 structure in 45 ° position. The class averages obtained are shown on the edge of the map and indicate a good separation of the data into two characteristic views. The group on the left side contains mainly a set of systematically misaligned images. The 4 x 6 molecule is thought to exhibit only two main types of 45 ° views. The four different fiat 2 x 6 surfaces on the outer side of the 4 x 6-mer are two-bytwo related by the 2-fold axis of the structure. Within each of the two main classes of 45 ° views, a 'rocking' type of variation was found, indicating the relative instability of this view.

403

404

M. van Heel and P. Dube

As was the case for the 2 x 6-meric structure, we need to distinguish the 4 x 6-mer views (projection through the three-dimensional structure) and faces (surfaces of the three-dimensional structure) for the sake of understanding the 8 x 6 assembly. In the flip view we define the flip face of the 4 x 6-mer to be oriented towards the observer while the flop face rests on the carbon support, away from the observer. In the flop view, this means the flop face is towards the observer while the flip face touches the supporting carbon foil. Note that the earlier definition of the flip and flop faces, based on an incorrect enantiomer (Lamy et al., 1982), could, in principle, be transferred to the correct enantiomeric 4 x 6 form (Bijlholt, 1986; Lamy, 1987). In retrospect, however, we think this transferring led to an awkward combination of views and faces; the flip

face w a s - - i n the old definition--at the back of the assembly when looking at the molecule in the flip view orientation.

D. The 8 x 6-meric structure 1. Characteristic views

In micrographs of negatively stained Limulus hemocyanin some six different typical profiles of the 8 x 6-mer can readily be recognized (van Bruggen et al., 1981; L a m y et al., 1986). Examples of such views are mounted on the lower edge of Fig. 13. F r o m 30 micrographs (part of one shown in Fig. 13a), 2800 individual molecular images were extracted and processed. Three of the typical views

Fig. 10. Differencebetween the projection imagesof the 'right' (top row) and the 'wrong' (bottom row) enantiomericmodelsofthe 4 × 6 structure (#I: flop view; #2 and #3:45 ° views).In the middle row the corresponding average imagesfrom the EM work are shown. Note that the 'bridges' in this structure which is also known as the 'bridged-tetramer' (seeleft panel) occur quite naturally if the model structure is projected approximately along its 2-fold axis: no additional protein material needs to be postulated to account for these bridges.

Structure of Multihexameric Hemocyanins

were used as references for a first round of alignments and MSA analysis, which yielded improved versions of all six typical views. These were then used (together with their mirror views) as references for subsequent rounds of multi-reference alignment. In a final classification, a total of 75 classes was calculated. The averages of these classes themselves can be further grouped into about eight major characteristic views, shown in Fig. 14. Among the different molecular views, the most eyecatching one is certainly the pentagonal view (Fig. 14a,b) in which one can directly discern the 45 ° view of the 4 x 6meric constituents (halves) of the 8 x 6-mer. The pentagonal view can thus be straightforwardly interpreted as consisting of one lower 4 x 6-mer in 45 ° position (visible in the central and in the right part of the molecule; Fig. 14a,b) and another 4 x 6-mer, also in approximate 45 ° position, placed on top of the first one. The lower 4 x 6mer is well embedded in the negative stain material whereas the upper one appears to be contrasted to a lesser extent (Fig. 15). The differences between the pentagonal view averages (Fig. 14a,b) indicate some variations in the projection directions or 'rocking behavior' around the long axis of the 2 x 6-mer which lies in direct contact with the support film (Lamy et al., 1982). These variations in the adsorption during the preparation of the molecules onto the grid correspond to an angular range of about 10°, as can be estimated by comparison to the projections of the model structure (see below). Variations in orientations around a stable average position were reported for different specimens prepared with the negative stain technique (Bijlholt

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Fig. 11. Assembly parameters for the 4 x 6 structures. The distance between the two 2 x 6-merit halves of the molecule was found to be 108 A (__+5 A). The total flip-flop shift is found to be 17A ( + 5 A ) . The rocking angle was found to be 6 ° leading to a total angle of t2 ° between the long axes of the 2 x 6-meric constituents of the 4 x 6. For the correct enantiomeric choice see Fig. 10.

405

et al., 1982b; Lamy et al., 1982; van Heel and StrfflerMeilicke, 1985; Harauz et al., 1987). 2. The 8 x 6-mer model

One of the main questions to be answered while building a model for the 8 x 6-mer from two copies of 4 x 6-mer is whether to join the 4 x 6-mers with their flip or their flop faces. A joining of different faces (flip-to-flop) is unlikely since this would lead to linearly polymerized assemblies, which are not observed. The two other important assembly parameters for constructing the 8 x 6-mer are the distance and the staggering angle (Fig. 16) between the two 4 x 6-mers. In all models of the 8 x 6-mer, the two 2-fold axes of the 4 x 6-mers were chosen to be coaxial, leading to 8 x 6-mer models with 222 (D2) point-group symmetry. In our analyses we never have seen indications for the overall structure to belong rather to point-group symmetry 2 (C2) as is case of the 2 x 6-mer (approximate C2) and the 4 x 6-mer (exact C2). However, the subunit stoichiometry for a 222 point-group oligomer requires the structure to contain at least four copies of each type of monomer, which seems to be contradicted by the findings of Lamy et al. (1983) for the subunits I and IIA. To find the assembly parameters for the 8 x 6-meric hemocyanin different flip-to-flip and flop-to-flop models were constructed using a range of different staggering angles and various inter-4 x 6-meric distances. The two models whose projections match best with the corresponding EM views are: an 8 x 6-mer model with flip-toflop contact with staggering angle of 2 x 16° = 32 ° and one with flop-to-flop contact with a 42 ° staggering angle. The best-fit distance between the centers of the two 4 x 6-mers is 102 A for both models. Although rather similar, the projections of these two types of models cannot be identical, and the study of the more subtle details in the projection images could help in making a choice between these models. Both the flip-to-flip and flop-to-flop models are shown in greater detail in Fig. 17 and Fig. 18, as surface representations and as projections through the full threedimensional density of the models. The surface representations (Fig. 17a, Fig. 18a) of the structures reveal the outer shape of the assembly which, in turn, helps us understand why certain views are well represented in the micrographs. Particularly helpful ,in localizing 'threepoint' stable support surfaces on the outside of the structure is a simplified version of the surface rendering (van Heel, 1983) in which the grey-scale of the image is purely dependent on the distance to the observer (Fig. 19). All these overview pictures cover the full asymmetric triangle for the 222 (D2) symmetry point-group. For a 222 point-group structure this unique part of the unit sphere covers one-fourth of the 'globe'. All images within these pictures refer to the same Euler directions: the direction of view of, say, image #12 in Figs 17, 18 and 19, are thus identical. The images cover the full asymmetric triangle using an angular increment of 22.5 ° in both directions. As a consequence of this choice of angular interval the top

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M. van Heel and P. Dube

row (#1-#8) in these pictures show the same 'north-pole' view each rotated over increments of 22.5 ° . The viewing directions in these images is from the 'north-pole' (fl = 0 °, images #1-#8) to the equator ( ~ = 9 0 °, #33-#40) and extending in the azimuthal direction from ( 7 = 0 ° ) to (7= 180°). Note that, in projection (Figs 17b, 18b), the directions beyond 7 > 90 ° are related by mirror symmetry to the directions 7 < 90 °. Projections related by this mirror symmetry can be interpreted as the front and the back projection through the same structure. In particular, if a given projection is frequent in electron micrographs, say #15 in Fig. 17b, that observation can then be related to the back surface (image #11 in Fig. 17a and Fig. 19), the molecule offering a three-point stable contact to the supporting carbon foil. The 8 x 6-mer model has 222 point-group symmetry and thus has three different 2-fold axes. Projections through the density distribution in any direction perpendicular to one of these 2-fold axes will exhibit mirror symmetry (a general property of even-fold axes). Since the vertical (Z) axis of the model coincides with a 2-fold axis of the structure, for example, all equatorial projections

exhibit mirror symmetry (cf. Fig. 17b, #33-#40). The projections along the three 2-fold axes of the molecule are, at the same time, projections in directions perpendicular to the other 2-fold axes simultaneously; these special projections thus exhibit mm symmetry (Fig. 17b #1-#8, #33, #37). The corresponding surface views in Fig. 17a exhibit only 2-fold symmetry, since here one is looking at the opaque outer surface of the three-dimensional data and not projecting through it.

3. Interpretation of the molecular profiles a. Pentagonal views. The pentagonal profiles (Fig. 14a,b) of the 8 x 6 - m e r roughly correspond to the equatorial orientation shown in Figs 17b, 18b (image #27), which positions correspond to the Euler angle direction (fl= 90 °, 7 = 450) • In this orientation, however, the molecule would not be in a stable position because the flat outerside of 2 x 6-mer at the back of the structure (Figs 17a, 19 image #39) is not approximately parallel to the support film. Stability can be achieved by tilting some

Fig. 12. a: Viewsof the 4 x 6 modelstructure rotating fromthe 0° position (direction of viewalong the 2-foldaxis of the 4 × 6 structure) to the 45° position. The top row showsthe stereographicrepresentations of the surface(neighboringimagingformingstereo pairs), the second row the correspondingprojections through the model structures, and the third row depicts the associated EM averages. The viewingdirection in the EM averagesdeviates slightlyfrom those in the first two rows due to the interaction of the structure with the supporting carbon foil. b: The model,its projection, and the correspondingEM averageof the 4 x 6 structure in the vertical orientation in which the cleft of the molecule stands perpendicular to the carbon support.

Structure of Multihexameric Hemocyanins

10 ° out of the equator plane (to fl = 80 °, between image #35 and image #27). The effect of this tilt on the back 2 x 6 is illustrated in Fig. 19 when moving up from image #39 towards image #31. The best match between model projections and the EM pentagonal view (Fig. 14a) was found for fl = 80 °, ~ = 45 ° (Fig. 20, #5). b. Cleft views. The EM views in Fig. 14c,d show a d a r k central cleft. These views correspond to projections of the model in directions around (fl= 90 °, ), = 90°), i.e. projections along the separation plane between the two 4 x 6mers constituting the 8 x 6-mer. The cleft views in Fig. 14d exhibit even approximate mm symmetry so that these

407

correspond to projection directions very close to the 2-fold axis of the point-group 222 structure. The views of Fig. 14c correspond to a projection direction about 15 ° away from this 2-fold axis; best fit at fl = 76 °, ~ = 85 ° (Fig. 20, #4). In these projection directions, the 4 x 6-mers of the 8 x 6-mer are projected side-ways in a projection direction never observed in EM preparations of individual 4 x 6-mers due to instability of the corresponding molecular position. c. Cross and bow-tie views. The next two types of microscopical views (shown in Fig. 14e,f) correspond to projection directions close to the Z axis of the model

Fig. 13. A section of a typical electron micrograph of negative stained hemocyanin molecules of Limulus polyphemus (a) used in the analysis (scale bar: 50 nm). Contaminating hemaglutinin molecules, present in the hemolymph and believed to play a role in the immune defence of this species, are depicted as small ring-like structures (top views) or as bilobed rods (side views). In Fig. 13b-g six typical 8 × 6 molecule profiles are shown which can already be distinguished visually in the micrographs. The average linear size of the hemocyanin molecule was found to be ~ 220 A.

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a

b

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d

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h

Fig. 14.

Structure of Multihexameric Hemocyanins

409

(fl = 30 °, ? = 130°). This three-point contact to the support film is in fact so stable that it constitutes the third largest image population within the total 8 x 6-mer data set.

Fig. 15. Schematic model of the 8 x 6-meric hemocyanin to explain the main pentagonal view. Each rectangle represents a 2 x 6-mer viewed along its long axis. The lower 4 x 6-mer-viewed more or less along its cleft--rests on the carbon support filmin the 45° position. The top 4 x 6-mer is not in direct contact with the support film and is thus stained to a lesser extent. This drawing is oversimplified,since the two clefts in the 4 x 6-merit halves are not parallel to each other in the real structure.

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d. The flip-flop views. We know from the rocking behavior of the 4 x 6-mer that both the flip and the flop faces of the molecule c a n - - a f t e r tilting with respect to the 2-fold axis of the 4 x 6-mer--provide a three-point stable support on the substrate. Since one of these faces is also available on the outside of the 8 x 6-mer one would expect it to also provide a stable position of the 8 × 6-mer. The 2fold axes of the 4 x 6-mers in the 8 x 6-mer coincide with the (fl=90 °, ? = 0 °) direction in Figs 17a and 18a. Projections about 20 ° away (at fl = 70 °, y = 8 ° ) from this 2fold axis best reproduce the views depicted in Fig. 14g,h which also have an overall pentagonal shape (Bijlholt, 1986). These views, although clearly defined in terms of internal consistency (S-image; Sass et al., 1989), are not very abundant in the present data set. This view, corresponding to the most abundant view in 4 x 6 preparations, exhibits no easily recognizable details of the 4 x 6 and 2 x 6 substructures. A direct interpretation of this view without the help of model building is clearly very difficult.

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Fig. 16. Schematic drawing illustrating the 'staggering' angle between the clefts of the lower and upper 4 x 6-mers. The staggering angle depicted in this flip-to-flip example is 2 x 16°= 32°. The other important parameter is the distance 'd' between the 24-merswithin the 48-mer(the distance betweenthe clefts of the constituent 4 x 6-mers)which was found to be 102 A (+5 A). structure (fl=0°; Figs 17b, 18b). In this projection direction, the clefts of the 4 x 6-meric constituents of the 8 x 6-mer are in an orientation close (ignoring the 'staggering angle') to the projection direction which corresponds to vertical adsorption of the 4 x 6-mer on the carbon support (Fig. 12b). The cross view (Fig. 14e) corresponds closely to the projection along the Z axis and thus exhibits m m symmetry. The view is not very frequent in the data set: in this particular orientation the 8 x 6-mer touches the carbon support film at only two symmetryrelated points (Fig. 19, #1-#8; Fig. 20, #1); the molecule thus tends to 'fall' away from the 2-fold axis towards a more stable rocking position with a three-point contact to the support film (Fig. 19, #11, Fig. 20, #2). The resulting 'bow-tie' views (Fig. 14f), characterized by 'one half consisting of two high densities with a squarish shape and another half with ill-defined fuzzy structure' (Lamy et al., 1982), are thus associated with the Euler directions

IV. D I S C U S S I O N Multivariate statistical image-processing techniques in electron microscopy w e r e - - m o r e than a decade a g o - first applied to the 4 x 6-meric Limulus polyphemus halfmolecule, and, by elucidating the flip--flop and rocking properties of the assembly, contributed significantly to our structural understanding of multi-hexameric hemocyanins. These MSA techniques, which have brought an advanced level of objectivity to the study of noncrystallized samples of biological macromolecules, continue to give new clues on the structure of these macromolecular assemblies and their interaction with the supporting carbon foil and staining material. Noncrystallized single macromolecules have a wide degree of orientational freedom on electron microscopical preparations. All the various stable positions which the molecule can assume on the support film can be recognized and noise-free averages of these views obtained after multi-reference alignment and automatic classification procedures (van Heel and Stfffier-Meilicke, 1985). The noise-free characteristic views resulting from these exhaustive search procedures provide valuable three-dimensional information about the macromolecules even without an explicit three-dimensional reconstruction. We were fortunate enough to have had the X-ray structure of the hexamer of Panulirus interruptus----or,

Fig. 14. (opposite)A galleryofdifferentcharacteristicmolecularviewsof the 8 × 6-merichemocyaninresulting from the MSA analysis. The pentagonal views(a, b) are projectionsthrough the moleculewhen it lies on one flat surfaceofa 2 × 6-mer on the carbon foil (Fig. 15). The interpretation of the other views(c h) in terms of projection directionsis not simpleand needs to be done in conjunction with the 8 × 6-mer model. The resolution of the images is around 20--30A, as determined by the S-imagecriterion (Sass et al., 1989).

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O*

22,5"

~5"

67,5*

90*

O,

22.5*

t.5*

67.5*

90* =

0*

22.5*

t,5 °

67.5 °

900

112.5 °

135 °

157.5 °

Fig. 17. The best-fit 'flip-to-flip' model for theLimulus polyphemus hemocyanin was constructed with a staggering angle of 2 x 16° = 32 ° and an inter-24-mer distance of 102/~. Two of the outer surfaces of the 8 x 6-mer are the flop faces of the 4 x 6-mers; the flip-faces are oriented towards each other in the center of the assembly. The three-dimensional Limulus model is shown as surface representation (a) and as projections through the three-dimensional density distribution (b). The projection directions in both parts of this illustration are one-by-one the same. Shown here are the views corresponding to one asymmetric 'triangle' of the point-group 222 structure extending from the 'north-pole' (Euler angle fl = 0 °, # 1-8) to the equator (fl = 90 °, #33-#40) and extending in the azimuthal direction from (Euler angle y = 0 °) to (7 = 180°) • Note that, in projection (Fig. 17b) the projection directions beyond (y > 90 °) are related by mirror symmetry to the directions (y > 90 °). The third Euler angle ~t= 0 ° is chosen zero here, it merely leads to a rotation of the images around their center (cf. Fig. 20).

Structure of Multihexameric Hemocyanins

rather, the low-resolution electron densities derived from the X-ray diffraction experiments--available in an early stage of the analysis (van Heel et al., 1983; Bijlholt, 1986), and we could thus model the three-dimensional structure of the multi-hexameric hemocyanins using the known basic building block. The complementarity of electron

411

microscopy and X-ray crystallography is very rewarding and helps us formulate and determine the handedness and assembly parameters of this hierarchy of structures. Although electron microscopy of negatively stained specimens is tyically limited in resolution to about 20 A,, the precision of positional information attained by this

0 °

22.5 °

1,5 °

67.5 °

90 °

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22.5 °

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67.5"

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0°

22.5 °

1,5 °

67.5 °

90 °

112.5 °

135 °

157.50

Fig. 18. The best-fit 'flop-to-flop' model for the Limulus polyphemus hemocyanin was constructed with a staggering angle of 2 x 21 ° = 42 ° and an inter-24-mer distance of 102 A ( + 5 A). Two of the outer surfaces of the 8 x 6-mer are the flip faces of the 4 x 6mers; the flop-faces are oriented towards each other in the center of the assembly. (For an explanation of the organization of this figure see legend of Fig. 17.)

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hybrid approach is around 5 A. The approach is applicable to various oligomeric systems for which the Xray electron density of the monomer(s) is available such as actin (see Kabsch et al., 1990; Holmes, et al., 1990; Milligan et al., 1990; Stewart et al., 1993). Electron microscopical projections of three-dimensional structures are, in principle, devoid of handedness: a given three-dimensional projection fits just as well to the correct three-dimensional structure as to its mirrored version. Handedness information must thus be introduced externally or from explicit tilt experiments in which one follows how a given projection of the structure changes as a function of the tilt angle. This problem has long since been recognized in, for example, studies of icosahedral viruses (Klug and Finch, 1965). Sometimes one can indirectly determine the handedness of the specimen by studying the interaction of the specimen with the negative-staining material. In their study of the h u m a n wart virus, Klug and Finch (1965) first determined from stereo views of their 530 A diameter objects that these viruses were preferentially stained at the carbon foil interface, and they then used this information to determine the absolute handedness of their specimen. As was discussed above, the absolute handedness of the 4 x 6-meric hemocyanins could be determined from the staining pattern (rocking behavior) around the molecules. However, an a priori assumption that the staining of a macromolecule is preferentially on the carbon-foil side would have led to incorrect conclusions for the single hexamer and for the dodecamer since these turned out to

have top side preferential staining. (We may actually be witnessing a preferential 'destruction' of the carbon-foil side of the molecule due to strong interaction forces, rather than a preferential top side staining effect.) In our handedness analysis we thus avoided arguments which depend on the behavior of the staining material altogether but rather, used the handedness of the X-ray structure as external standard. A correct handedness and subtle determination of the assembly parameters resulted in models which are capable of reproducing the observed characteristic electron microscopical views with a high degree of accuracy. It is interesting to note that all outer surfaces of the threedimensional assemblies which could represent a major three-point contact or fiat surface to the supporting carbon foil do indeed correspond to preferred orientations as shown in the micrograph (Figs 19, 20). The match between model projections and EM averages is particularly good for the 2 x 6 and the 4 x 6 structures where incorrect earlier models can be dismissed. In the model for the 4 x 6-mer derived from our experiments, the existence of this central dimeric unit (b-c in Eurypelma nomenclature) was not assumed a priori but, rather, found independently using image analysis arguments exclusively. The 'bridges' between the dodecamers, built by these b-c dimeric units, do not require the postulation of additional protein material but appear quite naturally in the projections of the correct 4 x 6-mer model corresponding to the EM flip and flop views. The situation is less clear for the full 8 x 6-meric Limulus

Fig. 19. A purely depth-queued representation of the 8 × 6-mer model structure in which the grey scale value in each pixel is proportional to the distance from the hypothetical support film.This picture illustrates the exterior surfaceof the structure that could create a stable interaction with the carbon support film. Our analysis revealed that all three-point or fiat outer surfaces given indeed rise to stable positions of the molecule. All major characteristic views of the 8 × 6-mer can be interpreted in terms of such stable interactions with the support film; for further details see Fig. 20.

Structure of Multihexameric Hemocyanins

polyphemus hemocyanin. The analysis of this structure has reduced the n u m b e r of possible three-dimensional structures to just two: a flip-to-flip structure in combination with a 2 x 16 ° = 32 ° staggering angle, and a flop-toflop structure with a 2 x 2 1 ° = 42 ° staggering angle, both models with a distance between the two 4 x 6-mers of 102 A. Given the n u m b e r of theoretical possibilities this m a y be quite an achievement, yet it remains frustrating that this choice does not uniquely determine the inter 4 x 6mer contact face within the 8 x 6. (There appears to be a slightly better m a t c h with the E M data for the flip-to-flip model; Fig. 20.) Moreover, since the Limulus subunits on the flip and the flop faces of the 4 x 6 half-molecules in the current interpretation (Fig. 21) are the same, the elegant a n t i b o d y experiments by L a m y et al. (1982, 1985b) and reassembly experiments by Bijlholt et al. (1979) c a n n o t be called u p o n for additional external argumentation. Thus we c a n n o t yet distinguish between two preliminary models p r o p o s e d previously (Bijlholt et al., 1983; Bijlholt, 1986). Nevertheless, the model p r o p o s e d by the groups of L a m y and F r a n k ( L a m y et al., 1982, 1983b) is inconsistent

413

with our findings (their model was withdrawn after conceding it was based on an incorrect 2 x 6 model (Lamy et al., 1985a). A new model was proposed by L a m y et al. (1985b, 1987) in which, however, the 4 x 6 structure used to construct the 8 x 6-mer exhibits no flip-flop shift. The reason why we c a n n o t yet quite distinguish between the flip-to-flip model and the flop-to-flop model is partially due to the roundish shape of this point-group 222 assembly and partially due to the accumulation of errors in the model-building procedure. The 8 x 6 model is the result of merging two hexamers into one dodecamer, then merging two dodecamers into a 4 x 6-mer and finally merging two 4 x 6-mers into the 8 x 6-merit full Limulus hemocyanin. Errors in the assembly parameter which occur while building the smaller aggregates m a y accumulate in the 8 x 6-mer and m a y thus degrade the quality of the model. Thus there is need for an explicit threedimensional reconstruction of the whole Limulus hemocyanin. Such a three-dimensional reconstruction of the 4 x 6 - m e r i c Androctonus h e m o c y a n i n was recently reported (Boisset et al., 1990) using the r a n d o m conical

Fig. 20. The main characteristic views of the 8 x 6-mer in negatively stained electron microscopical preparations (some images from Fig. 14) together with the corresponding 'best fit' projection views of the model structures. Also shown are the 'back-side' surface corresponding to the view indicating stable support surfaces. The exhaustive study of the characteristic views of the 8 x 6 structure in the micrographs can directly be correlated to the available 'stable' outer surfaces of the three-dimensional structure. The Euler angles used for creating this illustration result from a refined version of Figs 1%19, created with a 5° interval for covering the asymmetric triangle of the 222 point-group symmetry. Even in these refined views it remains difficult to distinguish the flip-to-flip model views (second line from the top) from the corresponding flop-to-flop views (fourth line from top). The Euler angles used to create this illustration are: column #1, the 'cross' view (~t= 0°, fl = 90°, ? = 0°); column #2, the 'bow-tie' view (~ = 50°, fl = 30°, 7 = 130°);column #3 the 'flip-flop' view (~ = -90 °, fl = 70°, 7 = 8°); column #4, the "cleft'view (~ = 93°, fl = 76°, 7 = 85°); and column #5, the 'pentagonal' view (ct=0°, fl=80 °, 7=45°).

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tilt reconstruction technique proposed by Radermacher et al. (1987, 1988). This technique, however, relies on the existence of a preferred attachment orientation of the molecule on the support film. The preparation technique needs to optimize this aspect. Strong interaction between specimen and carbon foil, however, leads to artefacts such as 'flattening'; this is specifically true for the double carbon foil technique used in that work. Thus, in spite of the reconstruction clearly reflecting the well known flip-flop and to a lesser extent the rocking properties of the structure, it was not possible to derive quantitative numbers for the assembly parameters for the 4 x 6-mer. Our specimens, when tilted in the microscope (results not shown), also look rather fiat. However, we did not need to account for any structural deformation ('squashing') to match the model projections with the EM averages. This implies t h a t - - t o a first approximation-our microscopical two-dimensional projections of the three-dimensional structure remain undistorted. The shrinking in our specimens appears to be mainly in the direction perpendicular to the carbon foil ('Z'-direction flattening) which process does not distort the twodimensional projection image very much. This justifies the hope that we m a y - - i n the future--achieve threedimensional reconstructions using the angular reconstruction technique (van Heel, 1987) of negatively stained specimens without worrying too much about Z-direction flattening. Currently, an angular reconstitution threedimensional reconstruction of Limulus polyphemus hemocyanin is underway using the vitreous ice embedding technique (Adrian et al., 1984; Dobochet et al., 1987). It is hoped that this study will provide additional justification for such negative-stain-based reconstruction procedures. As was discussed earlier, the subunit heterogeneity of arthropod hemocyanins is essential not only for maintaining the structural integrity of these assemblies, but also for transferring the local aUosteric changes within the larger structure during cooperative oxygen binding. In many immuno-electronmicroscopy experiments (Lamy et al., 1981; Markl et al., 1981; Sizaret et al., 1982; Lamy et al., 1990), the relative positions of the various subunits within the 4 x 6-meric Androctonus and Eurypelma hemocyanins, and in the 4 x 6-meric Lirnulus half-molecule, were studied. We have recompiled the results from those experiments (Lamy et al., 1986; Savel-Niemann et al., 1988) into what was found to be the correct form of the 4 x 6-mer (Fig. 21). Taken into account are the direct immunological experiments as well as the reassociation and hybrid reassociation experiments (van Bruggen et al., 1980; Decker et al., 1980). The one remaining interpretational ambiguity---of which we are aware--is that of the orientation of the central dimeric unit (b--c in Eurypelma nomeclature) with respect to the flip-flop shift of the 4 x 6mer (Fig. 11). We do not yet know whether in the flip view (right half up), for example, to the top-right element of the central b~c tetramer really is a c (as is in Fig. 21b) or

whether it is a b. (We are not aware of studies aimed at determining this relative orientation.) In dissociation and reassociation experiments on Limulus hemocyanin, fractions III and IV were found to be indispensable for achieving structures larger than the 4 x 6 - m e r (Bijlholt et al., 1979, 1982a). It is thus reasonable to assume that contacts between these types of subunits hold together the 8 x 6, and that proximity between these subunits could help us decide whether the flip-to-flip or the flop-to-flop model would be more plausible. It is interesting to note that with the subunit assignments shown in Fig. 21, both with the flip-to-flip and with the flop-to-flop we have a proximity between subunits IV of the front 4 x 6 and the subunits IV of the back 4 x 6-mers. A similar proximity relation exists in both models between subunits IliA and subunit IIIB of the juxtaposed 4 x 6-mer. In other words, both models are compatible with the subunit assignments with the 4 x 6 and both models allow for inter-4 x 6 interactions of the type suggested by the reassembly experiments. Although these observations do not allow us to distinguish between the two different 8 × 6 models, they do provide evidence for this specific type of subunit interaction within the 8 x 6, as opposed to various other conceivable inter-4 x 6 connections which would all be consistent with the reassembly experiments. One of the main goals of the studies on chelicerate hemocyanins is to understand how their intricate hierarchical structure achieve such a high co-operativity of oxygen binding (particularly for Androctonus and Eurypelma). Although this is certainly not the final word on the issue, we cannot resist the temptation to speculate about the mechanism of action of this nested allosteric system (Decker and Sterner, 1990). The 2 × 6 - m e r has an approximate local 2-fold axis intersecting the A-A and B-B edges of the dodecamer. In our current 2 × 6 model (Fig. 6), the two 3-fold axes of the two hexamers make an angle of approximately 90 ° with each other. In a recent publication Hazes et al. (1993) suggested that the difference between the oxygenated and the deoxygenated versions of the single hexamer is mainly a rotation over 3 ° of the upper trimer relative to the lower trimer. From a preliminary mechanical model for the interactions within the 2 x 6-mer (not shown) we have the impression that such a rotation within each hexamer translates to a rotation of the two hexameric 3-fold axes relative to each other by approximately the same angle. In other words, this suggests that the oxy-deoxy conformational changes would be a change in the approximately 90 ° rotation angle which exists between the hexamers of the 2 x 6-mer. Such rotation within the 2 x 6 structure could then lead to a change in the rocking angle of the 4 × 6-mer (Fig. 11) of comparable magnitude. We have chosen to wait, and make speculations about the allosteric interactions within the 8 x 6-mer only after the flip-to-flip vs flop-to-flop ambiguity has been solved.

Fig. 21. (opposite)An interpretation of the subunit locations based on immuno-labellingexperimentsin the 4 x 6-mericstructure in the right enantiomeric form. The surface representation of both 'flip' (left panel) and 'flop' view (right panel) are used for easy orientation. (a) Androctonus australis, (b) Eurypelma californicum and (c) Limulus polyphemus half-molecule.

Structure of Multihexameric Hemocyanins

Fig. 21.

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CONCLUSIONS Modern multivariate statistical image-processing techniques are very powerful tools for studying electron microscopical images of large oligomeric assemblies such as the members of the hierarchical family of arthropod hemocyanins. Model building of the various multihexameric assemblies, based on the X-ray electron density of the Panulirus interruptus hemocyanin, helps us understand the various levels of the structural hierarchy and allows us to determine precisely the assembly parameters of the various hemocyanins. The handedness and assembly parameters of the 2 x 6 and 4 x 6 oligomers could be determined uniquely and thus the subunit assignments for the various 4 x 6-meric hemocyanins became more reliable. The interpretation of the 8 x6-meric Limulus polyphemus hemocyanin is more elaborate because of the overall shape of this structure and because of the summation of errors in the model building of this hierarchical structure. As yet, it is difficult to distinguish between a flip-to-flip model with a staggering angle of 2×16°=32 ° and a flop-to-flop structure with a 2 × 21°=42 ° staggering angle. We expect to settle the issue in a forthcoming three-dimensional reconstruction of this hemocyanin based on vitreous ice embedded specimens using the angular reconstitution approach. Preliminary results from this forthcoming analysis indicate that the flip-to-flip model is probably the correct enantiomeric form of the 8 x 6 structure. Acknowledoements--We thank Joseph Bonaventura of Duke University for the kind gift of Limulus polyphemus hemolymph; Wil Gaykema and Wim Hol for making available the 5 A electron density map of the hemocyanin of Panulirus interruptus used for the model building. Ernst van Bruggen and Martha Bijlholt were involved in the early stages of this project; Wilma Schutter provided the micrograph of Panulirus hemocyanin used. We thank Elmar Zeitler for long-term support of this project. Michael Sehatz and Rail Schmidt contributed to the development and maintenance of the various modules of IMAGIC-5 software system. Edith Kitzelmann, Matina Gerdsmeyer and Sonja Herrmann are acknowledged for excellent technical assistance. PD was financially supported by Stipends from the Max-Planck-Gesellschaft and the Deutsche Forschung Gemeinschaft (Grant number: HE 2162 1-1).

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