SYMMETRY OF THE SURFACE, AND STRUCTURE OF THE CENTRAL CORE OF HUMAN LDL PARTICLES, ANALYZED BY X-RAY SMALL ANGLE SCATTERING
Although there exists a widely accepted model of the general structure of the LDL particle, there are still some important open questions, the most interesting being the three dimensional structure of the apoB molecule. There is very little knowledge of the exact conformation of this large polypeptide chain, containing many hydrophobic residues. Despite this hydrophobicity it was shown by several techniques (MABs, NMR, FTIR) that many domains of this protein are localized at the particle surface or are at least accessible to the solvent. An elaborate evaluation of X-ray scattering data from three LDL subtractions shows that a) The apoB molecule has to cover at least 47% of the surface of small LDL particles, and 37% of the surface of large LDL. b) Most of the mass of the apoB molecule is located within a small shell of 2.2nm width directly at the particle surface.
c) There is no evidence for symmetries other than spherical, which means, that there are no marked 'spikes' of protein at the surface.
An other uncertain point is the organization of the central cholesterol ester (CE) core below the phase transition temperature. Our X-ray data confirms those models in which the cholesterol moieties of the CE-molecules are located at two concentric shells of 3.2 and 6.4 nm radius. In contrast to previous models we propose, based on detailed space filling calculations, that the CE molecules are arranged .in an alternating orientation in such a way that about half of the acyl chains of the CE-molecu!es in each shell point towards the center of the particle, the other half pointing to the surface. This model facilitates an interdigitation of acyl chains of cholesterol esters with each other and with surface phospholipids. The interdigitation of acyl chains of core and surface lipids has also been proposed in the case of HDL and protein free models of LDL, and seems to be a general feature of lipoprotein structure.
Our current knowledge on the molecular structure of low density lipoproteins (LDL) originates to a large extent from X-ray and neutron small-angle studies that have been published by several groups. For references see 1 2 3 4 • In all of these studies evaluation theories assuming mono disperse, radially symmetric particles were used. Only Luzzati et al.6 considered deviations from spherical symmetry. While still assuming monodispersity, deviations from spherical symmetry turned out to be essential in Luzzati's interpretation of the data. Our evaluation theory 8 7 predicts the exact scattering intensity of a "polydisperse ensemble, of quasi radially symmetric particles", and consequently needs neither to assume monodispersity nor perfect radial symmetry. It has to be emphasized that assuming monodisperse particle populations is in obvious contrast to biochemical and metabolic features of lipoproteins.
In this paper we address mainly two questions: the structure of the apoB molecule and the structure of the central lipid core. Differences between LDL subtractions are discussed in detail in4 • The aim of our study was to find a model of the LDL structure which reproduces the scattering intensity of the sample within the experimental error (noise band) of the X-ray scattering data. None of the models published up to now has been shown to be consistent with this requirement. Since both, polydispersity and deviations from radial symmetry are quantitatively treated in our model, our method is well suited for investigating the question of whether the assumption of a multipole component, as proposed by6•8
is in fact necessary to explain the experimental data. In addition, our approach allows to give an estimate of the random errors of the resulting electron density profiles. New aspects arise from the precisely determined electron density profiles and from the fact that we determined the electron density profiles of three different LDL subtractions. Based on our molecular model and chemical analysis, we present a detailed comparison of volumes, areas, and radii given by the electron density profiles to the space requirement of the molecular components.
MATERIALS AND METHODS
Samples
Serum was obtained from freshly drawn blood (50 ml without anticoagulant) of male, clinically healthy donors. LDL (d = 1.006-1.063 g/ml) was isolated by standard methods8 • LDL subtractions were prepared as described previously4 • After centrifugation the material of subtractions LDL-1 (d=1.006-1.031 g/ml), LDL-3 (d=1.034-1.037 g/ml), and LDL-6 (d=1.044-1.063 g/ml) was dialyzed against a buffer containing 0.196 mol/kg NaCI, 0.5 g/1 NaN3 and 0.1 g/1 EDTA. An immersible CX-30000 ultrafilter (Milliporel was used to concentrate the samples to total cholesterol concentrations of up to 50 mg/ml.
Chemical analysis
In all subtractions total cholesterol, free cholesterol, triacylglycerol (all Boehringer, Mannheim), and phospholipids (bioM6rieux, Nurtingen) were determined. CE concentrations were calculated as (total cholesterol - free cholesterol) x 1.68. All tests were standardized according to the manufacturers' instructions. ApoB concentrations were determined by kinetic rate nephelometry using an automated Beckman ICS Analyzer II. This test was carefully standardized using amino acid analysis (for details see4). The given protein concentrations therefore represent amino acid concentrations and do not include the carbohydrate bound to apoB. For that reason in all subsequent calculations a molecular weight of 513,000 based on the amino acid sequence 10 11 is
used. The results of the chemical analysis are given in Tab. 1.
X- ray small-angle scattering
X-ray small-angle diagrams were recorded as described in detail in a previous publication 12• We used temperatures of 4°C and 37°C to record the scattering diagrams. These temperatures are below and above the phase transition temperature 13 of the cholesterol ester molecules inside the LDL particle. The actual phase transition temperatures Tm of our LDL preparations (LDL-1: 21.1 °C, LDL-3: 29.7°C, LDL-6: 29.9°C) were monitored by differential scanning calorimetry (DSC).

The method for evaluating the X-ray small-angle scattering diagrams was described previously4•8 7• 12• In brief, the particle structure is described by a set of parameters, which are adjusted by a non-linear least-square fit procedure to give an optimum fit to the experimentally determined X-ray scattering curve.
RESULTS AND DISCUSSION
Radial symmetry
To test the hypothesis of radial symmetry we tried to obtain fits of the scattering intensities by using the model "polydisperse ensemble of radially symmetric particles". No deviations from radial symmetry were allowed. It was possible to obtain satisfactory fits without any difficulty (Fig. 1a) in the case of scattering intensities recorded at 37°C. This holds for all types of LDL subtractions investigated in this study. Therefore there is no need to introduce symmetries other than radial to explain the observed scattering intensities of the LDL particles at 37°C.
Fits of the intensities recorded at 4°C were not as perfect as those of the high temperature form. In particular, the width of the scattering maximum at 1/3.7 nm'1 could not be reproduced completely satisfactorily by our model (Fig. 1b). A detailed analysis of this very small deviation turned out to be outside the precision of our scattering data. Although an asymmetry of the LDL particle at 4°C cannot be completely excluded on the basis of our data, there is no evidence to assume the existence of such deviations from radial symmetry. Other deviations from our model could exist and are even more probable. For example one could speculate that the ordered, liquid crystal-like core is of the same size in all particles within the polydisperse ensemble. In fact such a "monodisperse" core would produce a sharper maximum at 1/3.7 nm·1 than predicted by our model.
We conclude that with the assumption of a polydisperse ensemble of radially symmetric particles it was possible to obtain fits of the scattering curves that were within the precision of the experimental data, and therefore our data does not support a shape of the LDL particle with marked 'spikes' of protein as proposed by6•8• It should be noted that this was not the case with HDL particles12 where quadrupole-like deviations from radial symmetry had to be assumed to explain the measured scattering curves. The radial symmetry of the LDL particle together with the electron density profile implies a spread out conformation of the protein. Although apoB contains many hydrophobic domains 10 11, it must be localized predominantly inside the outer surface shell of high electron density, which has a width of about 2.2nm. This conformation is further supported by the fact that a large area of the particle surface has to be covered by protein since the surface of the LDL particle cannot be covered by phospholipid headgroups and free cholesterol alone2• 14• An area of at least 470 nm2 has to be covered by apoB, even if one assumes relatively


large and additive areas of 0.7nm2 per phospholipid and 0.41nm2 per cholesterol molecule, which are areas observed at the air-water interface for single compounds 16 Areas observed in mixed bilayers are usually smaller 16 and would suggest a larger apoB area covered by apoB. It is remarkable that the calculated area covered by apoB is nearly the same for all three LDL subtractions, which strongly supports our conclusion . The view that the apoB molecule covers a large amount of the particle surface is supported by many studies : it was shown by tryptic digestion 11 and by binding studies with monoclonal antibodies 17 (reviews: 18 18 that domain s inmany regions of apoB are located at the particle surface . Using nuclear magnetic resonance 20 •21 it could be demonstrated that about 20 % of the phospholipid headgroups are immobilized by interaction with apoB . Fast Fourier infrared spectroscopy 22 indicated that the a-helical, random coil and B-turn structures may be situated on or near the surface of the LDL particle, while the B-strands have no or only restricted contact with the external solution . It has been hypothesized that amphiphilic B-strands23 are the major lipid binding structure of apo810 •

High and low temperature form of the LDL particle
We now want to compare the determined electron density profiles of the low temperature form with the high temperature form of the LDL particle: As shown in Fig. 2 a common feature of all profiles measured at 4°C and at 37°C is the outer double shell consisting of a shell of high electron density (HEDS) at the particle surface, and a shell of low electron density (LEOS) just below this shell. Both, HEDS and LEOS are similar in all particles. Great differences exist inside the core region. For the high temperature form of the core only comparably small oscillations were found which did not cross the zero level. In contrast there exists a pronounced and reproducible shell structure inside the core of the LDL particle below the phase transition temperature. We find two peaks of high electron density at average radii of 6.37 ± 0.29 nm and 3.23 ± 0.21 nm (average of LDL-1, LDL-3, and LDL-6, at 4°C). In accordance with 24• 26 these two peaks in the electron density profile can well be explained by a localization of the steroid moiety of the cholesterol esters on two concentric shells (Fig. 3) at radii of 6.37 and 3.23 nm, respectively. Such a model results in a cross-sectional area of 0.33 to 0.38 nm2 per steroid system, a value close to that obtained for cholesterol esters in crystal packing, where values of 0.35 nm2 26 and 0.366 nm2 27 have been reported. These values are smaller than the one measured at the air-water interface (0.405 nm2) 16•
Details on the arrangement of the cholesterol ester acyl chains can be deduced from the electron density profile by a careful comparison of the measured dimensions with the volumes required to arrange the cholesterol esters in a certain way. The corresponding calculation shall be shown in detail for the case of an average LDL-3 particle which, in average, contains 1886 cholesterol ester molecules: We assume that the steroid shells are centered at radii of 3.2 and 6.4 nm, and that they have a width of 1.7 nm, corresponding to the length of a cholesterol molecule 27 •
According to the available surface in each shell 377 cholesterol ester molecules are located at the inner steroid shell and 1509 molecules at the outer steroid shell. If a volume of 0.46 nm3 per acyl chain is assumed 28, 118 chains can be packed inside the inner shell (below 3.2 - 1.7/2 = 2.35 nm). Consequently the remaining 259 acyl chains have to be localized between the two steroid shells. This shell (4.05 to 5.55 nm) has room for further 693 acyl chains. The remaining 816 acyl chains from the second steroid shell are localized at a radius of >7.25 nm, and are pointing towards the particle surface. The volumes required for the cholesterol moieties alone (238 and 951 nm3 correspond well with the volumes of the steroid shells given by the model, which are 224 nm3 (2.35 to 4.05 nm) and 880 nm3 (5.5 to 7.25 nm). Although the above calculations contain some simplifications, they undoubtedly show that some sort of alternating orientation of the acyl chains has to exist. One simple model is that about half of the acyl chains of each shell point radially towards the center of the particle, the other half pointing to the surface (Fig. 3). Such an arrangement is further supported by neutron small-angle scattering data since it perfectly reproduces the radii of gyration (R ) measured by Laggner et al.29 : Laggner published a mean radius of gyration of 6.0 ± 0.2 nm for the fully deuterated acyl chain, and a value of ± 0.3 nm for the deuterated C-25 isopropyl groups7 • From our model we calculate average values of 5.95 nm for the acyl chains and 7.03 nm for the C-25 isopropyl groups. Laggner's preferred model (all acyl chains pointing to the center of the particle) gives values of 5.0 and 6.9 nm, respectively.
In addition, our model facilitates an interdigitation of acyl chains of cholesterol esters and surface phospholipids. This interdigitation of acyl chains of core and surface lipids was proposed in the case of the particles3 12 30 , as well as protein free models of LDL31 , and seems to be an essential principle in lipoprotein structure.
At 37°C, above the phase transition, the arrangement of the cholesterol esters appears to be much less ordered. The oscillations of the electron density are of only half the amplitude compared to those at 4°C. Model calculations showed that they might originate from cut-off effects of the Fourier series used to represent Pm(r). Furthermore, it should be mentioned that the electron density near the very center of the particle is poorly defined, since the errors in determining the electron density profile are proportional to 1/r12 32 •
Comparing the size of LDL particles at 4 and 37°C, one finds slightly larger particle sizes for LDL below the phase transition point. This larger radius at 4°C is almost completely explained by an increase of the thickness of the outer surface shell (HEDSw,dth). Only in the case of the smallest LDL particles (LDL-6) a larger core is additionally measured. The small increase of HEDSw,dth• consistently found for all three subtractions, indicates that the phase transition of the core is accompanied by structural changes of the particle surface. Such changes are most probably related to a conformational change of the apoB molecule, as proposed by Laggner and Kostner 33, based on ESR spectroscopic data. Interestingly circular dichroism spectra of native LDL are identical at 4 and 50°C34 •
In conclusion we were able to demonstrate that our procedure of X-ray data evaluation is able to resolve differen es between human LDL subtractions, and the corresponding high and low temperature forms of the particle core. Besides new information on structural differences between LDL subtractions and conformation of apoB a novel interpretation of the arrangement of the cholesterol esters in the ordered state is proposed.
This work was supported by the Deutsche Forschungsgemeinschaft, SFB 60, Teilprojekt D8.
REFERENCES
1. D. Atkinson, and D. M. Small, 1986, Recombinant lipoproteins: implications for structure and assembly of native lipoproteins, Ann. Rev. Biophys. Chern., 15:403.
2. D. Atkinson, D. M. Small, and G. G. Shipley, 1980, X-ray and neutron scattering studies of plasma lipoproteins, in: "Lipoprotein structure, • A. M. Scanu, and F. R. Landsberger, eds., Annals of the New York Academy of Sciences, Vol. 348:284.
3. P. Laggner, and K. W. Muller, 1978, The structure of serum lipoproteins as analysed by X-ray small-angle scattering, 0. Rev. Bioohvs. 11:371.
4. M. W. Baumstark, W. Kreutz, A. Berg, I. Frey, and J. Keul, 1990, Structure of human low-density lipoprotein subtractions, determined by X-ray small-angle scattering, Biochim. Biophys. Acta 1037:48.
5. V. Luzzati, A. Tardieu, and L. P. Aggerbeck, 1979, Structure of serum low-density lipoprotein I. Solution X-ray scattering study of a hyperlipidemic monkey low-density lipoprotein, J. Mol. Bioi. 131:435.
6. M. W. Baumstark, W. Welte, and W. Kreutz, 1982, A theory for the evaluation of small-angle scattering diagrams of quasi radially symmetric particles considering polydispersity and deviations from radial symmery, Acta Cr'LSL A38:835.
7. M. W. Baumstark, and W. Kreutz, 1982, Iterative Deconvolution Method for Evaluating X-Ray Small Angle Scattering Diagrams., in: "Deconvolution Reconvolution, • M. Bouchy, ed., E.N.S.I.C. - I.N.P.L., Nancy.
8. T. G. Gulik-Krzywicki, M. Yates, and L. P. Aggerbeck, 1979, Structure of serum low-density lipoprotein. II. A freeze- etching electron microscopy study, J. Mol. Bioi. 131:475.
9. F. T. Lindgren, Preparative ultracentrifugal laboratory procedures and suggestions for lipoprotein analysis, 1975, ln.: •Analysis of lipids and lipoproteins, • E. G. Perkins, ed., American Oil Chemists' Society, Champaign, Ill.
10. T. J. Knott, R. J. Pease, L. M. Powell, S. C. Wallis, S. C. Rail jr, T. L. lnnerarity, B. Blackhart, W. H. Taylor, Y. Marcel, R. Milne, D. Johnson, M. Fuller, A. J. Losis, B. J. McCarthy, R. W. Mahley, B. Levy-Wilson, and J. Scott, 1986, Complete protein sequence and identification of structural domains of human apolipoprotein B, Nature 323:734.
11. C. Y. Yang, S. H. Chen, S. H. Gianturco, W. A. Bradley, J. T. Sparrow, M. Tanimura, W. H. Li, D. A. Sparrow, H. DeLoof, M. Rosseneu, F. S. Lee, Z. W. Gu, A. M. Gotto jr, and L. Chan, 1986, Sequence, structure, receptor-binding domains and internal repeats of human apolipoprotein B-100, Nature 323:738.
12. M. W. Baumstark, W. Welte, and W. Kreutz, 1983, Electron-density determination of three high-density lipoprotein subtractions, considering polydispersity and deviations from radial symmetry, Biochim. Bioohvs. Acta 751:108.
13. R: J. Deckelbaum, G. G. Shipley, and D. M. Small, 1977, Structure and interactions of lipids in human plasma low density lipoproteins, J. Bioi. Chern. 252:744.
14. P. Laggner, G. M. Kestner, U. Rakusch, and D. Worcester, 1981, Neutron small angle scattering on selectively deuterated human plasma low density lipoproteins, J. Bioi. Chern. 256:11832.
15. G. L. Gaines jr, 1966, "Insoluble monolayers at lipid-gas interface, • lnterscience, New York.
16. H. Lecuyer, D. G. Dervichian, 1969 , J. Mol. Bioi. 45:39.
17. Y. L. Marcel, T. L. lnnerarity, C. Spilman, R. W. Matiley, A. A. Protter, and R. W. Milne, 1987, Mapping of human apolipoprotein B antigenic determinants, Arteriosclerosis 7:166.
18. W.- H. Li, M. Tanimura, C.- C. Luo, S. Datta, and L. Chan, 1988, The apolipoprotein multigene family: biosynthesis, structure, structure-function relationships, and evolution, ,!, Lipid Res. 29:245.
19. G. Schonfeld, and E. S. Krul, 1986, Immunologic approaches to lipoprotein structure, J. Lipid Res. 27:583.
20. E. G. Finer, R. Henry, R. B. Leslie, and R.N. Robertson, 1975, NMR studies of pig low- and high-density serum lipoproteins. Molecular motions and morphology, Biochim. Biophys. Acta 380:320.
21. P. L. Yeagle, R. G. Langdon, and R. B. Martin, 1977, Phospholipid-protein interactions in human low density lipoprotein detected by 31P nuclear magnetic resonance: Biochemistry 16:3487.
22. E. Herzyk, D. C. Lee, R. C. Dunn, K. R. Bruckdorfer, and D. Chapman, 1987, Changes in the secondary structure of apolipoprotein B-100 after Cu2 + -catalysed oxidation of human low-density lipoproteins monitored by Fourier transform infrared spectroscopy, Biochim. Biophys. Acta 922:145.
23. D. Osterman, R. Mora, F. J. Kezdy, E. T. Kaiser, and S. C. Meredith, 1984, A synthetic amphiphilic B-strand tridecapeptide: a model for apolipoprotein B, J. Am. Chern. Soc. 106:6845.
24. D. Atkinson, R. J. Deckelbaum, D. M. Small, and G. G. Shipley, 1977, Structure of human plasma low-density lipoproteins: Molecular organisation of the central core, Proc. Natl. Acad. Sci. USA 74:1042.
25. P. Laggner, G. Degovics, K. W. Muller, 0. Glatter, 0. Kratky, G. Kestner, and A. Holasek, 1977, Molecular packing and fluidity of lipids in human serum low densiy lipoproteins, Hoppe Seyler's Z. Physiol. Chern. 358:771.
26. R. P. Rand, and V. Luzzati, 1968, X-ray diffraction study in water of lipids extracted from human erythrocytes, Biophys. J. 8:125.
27. B. M. Craven, and G. T. De Titta, 1976, Cholesteryl myristate: structure of the crystalline and mesophases, J. Chern. Soc .. Perkin Trans. 27:814.
28. C. Tanford, 1980, "The hydrophobic effect: Formation of micelles & biological membranes, •
2nd edition, John Wiley & Sons Inc., New York.
29. P. Laggner, G. M. Kestner, G. Degovics, and D. L. Worcester, 1984, Structure of the cholesteryl ester core of human plasma low density lipoproteins: Selective deuteration and neutron small-angle scattering, Proc. Natl. Acad. Sci. USA 81:4389.
30. W. Stoffel, 0. Zierenberg, B. Tunggal, and E. Schreiber, 13C Nuclear magnetic resonance spectroscopic evidence for hydrophobic lipid-protein interactions in human high density lipoproteins, Proc. Nat. Acad. Sci. USA 71:3696.
31. G. S. Ginsburg, D. M. Small, and D. Atkinson, 1982, Microemulsions of phospholipids and cholesterol esters. Protein-free models of low density lipoprotein, J. Bioi. Chern. 257:8216.
32. A. Tardieu, L. Mateu, C. Sardet, B. Weiss, V. Luzzati, L. Aggerbeck, and A. M. Scanu, 1976, Structure of human serum lipoproteins in solution. II. Small-angle X-ray scattering study of HDL3 and LDL, J. Mol. Bioi. 101:129.
33. P. Laggner, and G. M. Kestner, 1978, Thermotropic changes in the surface structure of lipoprotein B from human-plasma low-density lipoproteins, Eur. J. Biochem. 84:227.
34. G. S. Ginsburg, M. T. Walsh, D. M. Small, and D. Atkinson, 1984, Reassembled plasma low density lipoproteins. Phospholipid-cholesterol ester-apoprotein B complexes, J. Bioi. Chern. 259:6667.