Volumetric determination of apolipoprotein stoichiometry of circulating HDL subspecies.

Although HDL is inversely correlated with coronary heart disease, elevated HDL-cholesterol is not always protective. Additionally, HDL has biological functions that transcend any antiatherogenic role: shotgun proteomics show that HDL particles contain 84 proteins (latest count), many correlating with antioxidant and anti-inflammatory properties of HDL. ApoA-I has been suggested to serve as a platform for the assembly of these protein components on HDL with specific functions - the HDL proteome. However, the stoichiometry of apoA-I in HDL subspecies is poorly understood. Here we use a combination of immunoaffinity chromatography data and volumetric analysis to evaluate the size and stoichiometry of LpA-I and LpA-I,A-II particles. We conclude that there are three major LpA-I subspecies: two major particles, HDL[4] in the HDL3 size range (d = 85.0 ± 1.2 Å) and HDL[7] in the HDL2 size range (d = 108.5 ± 3.8 Å) with apoA-I stoichiometries of 3 and 4, respectively, and a small minor particle, HDL[1] (d = 73.8 ± 2.1Å) with an apoA-I stoichiometry of 2. Additionally, we conclude that the molar ratio of apolipoprotein to surface lipid is significantly higher in circulating HDL subspecies than in reconstituted spherical HDL particles, presumably reflecting a lack of phospholipid transfer protein in reconstitution protocols.


Calculations of the stoichiometry and dimensions of reconstituted HDL particles or isolated HDL fractions
These calculations require weight percentage measurements for the protein and lipid components of reconstituted HDL particles ( 22 ) or isolated whole-plasma fractions ( 23,24 ). Using the molecular weight and volume of each molecule of apoA-I, apoA-II, phospholipid (PL), CE, unesterifi ed cholesterol (UC), and TG, sequential permutations of protein stoichiometry per particle (e.g., two apoA-I, two apoA-I, and one apoA-II) allows calculation for that particular apolipoprotein stoichiometry of the total volume of the lipid core (CE and TG) and, by addition of the polar monolayer (apolipoprotein, PL and UC), the volume of the total HDL particle.
Assuming spherical symmetry (given the soft nature of HDL, a sphere is a reasonable approximation of the average shape of an HDL particle) the diameter of the core and total HDL particle can be calculated for each protein permutation. By difference, the thickness of the polar monolayer can also be calculated. As an example, for a given reconstituted HDL particle or isolated HDL fraction, as the total volume of the protein component increases, the number of each lipid moiety increases, and consequentially, the particle size increases; mathematical formulae can be derived that link protein stoichiometry to stoichiometry of each lipid class and HDL particle dimension. For each protein stoichiometry applied to a given particle or fraction, the calculated diameter is plotted and examined for best fi ts to diameters determined by NDGGE for HDL isolated by immunoaffi nity chromatography ( 16 ).
Other apolipoproteins, such as the apoCs or apoE, because of their minor concentration compared with apoA-I and apoA-II, have been omitted from all but one of the calculations. Individual NDGGE subspecies bands, particularly those containing apoA-I but no apoA-II, are generally broad, suggesting a mixture of minor protein components. We included the effects of one molecule of apoC-III, the longest and most abundant of the apoCs, on calculated diameter of the 4:0 stoichiometry for the double-shell model; the resulting value stays well within the broad size distribution of HDL [7]. We also included the effects of one molecule of apoE on the calculated diameter of the 4:0 stoichiometry for the double-shell model; the resulting value falls just outside the broad size distribution of HDL [7].

Correspondence of HDL subspecies defi ned by immunoaffi nity chromatography with subspecies defi ned by NDGGE
Immunoaffi nity chromatography. Fig. 1 summarizes the essential features of our previous characterization of nine LpA-I and LpA-I,A-II subspecies of HDL particles ( 15,16 ). Fig. 1A represents NDGGE analysis of total HDL (T-HDL), LpA-I, and LpA-I,A-II, three HDL fractions isolated from a subject by immunoaffi nity chromatography: i ) T-HDL represents whole-plasma particles retained by and then eluted from an anti-apoA-I immunoaffi nity column; ii ) LpA-I,A-II represents plasma particles retained by and then eluted from the anti-apoA-II immunoaffi nity column; and iii ) LpA-I represents plasma particles not retained by an anti-apoA-II immunoaffi nity column but retained by and eluted from an anti-apoA-I immunoaffi nity column. Nine apoA-Icontaining particles, designated HDL[1]-HDL [9], with mean diameter ranging from 76.4 to 131.8 Å ( Table 1 ) were identifi ed.
(d 1.125 to 1.21 g/ml ( 13 ). The HDL subspecies HDL 2 and HDL 3 have also been shown to be heterogeneous. Five subspecies were identifi ed by Blanche et al. ( 14 ) using nondenaturing gradient gel electrophoresis (NDGGE) analysis of HDL in the ultracentrifugal d < 1.20 g/ml fraction of human plasma and in HDL 2b , HDL 2a and HDL 3 prepared by density gradient ultracentrifugation. The mean hydrated density and particle size of the fi ve subspecies, from largest to smallest, were 1.085 g/ml and 10.57 nm in (HDL 2b ) gge ; 1.115 g/ml and 9.16 nm in (HDL 2a ) gge ; 1.136 g/ml and 8.44 nm in (HDL 3a ) gge ; 1.154 g/ml and 7.97 nm in (HDL 3b ) gge ; and 1.171 g/ml and 7.62 nm in (HDL 3c ) gge. This terminology represents a somewhat cumbersome choice of nomenclature.
Using immunoaffi nity chromatography, two subsets of plasma sHDL particles were isolated. One subset contains both apoA-I and apoA-II (LpA-I,A-II). The other subset contains apoA-I but not apoA-II (LpA-I) ( 15,16 ). Both LpA-I and LpA-I,A-II are heterogeneous in particle size. Attempts were made to assign the two major subspecies of LpA-I and the three major subspecies of LpA-I,A-II to the fi ve NDGGE HDL subspecies, and the stoichiometry of apoA-I and apoA-II in these subspecies was determined using chemical crosslinking ( 17 ). Here, we apply volumetric analysis to further analyze the size and stoichiometry of LpA-I and LpA-I,A-II subspecies using recently reported lipid and protein compositions of these particles, and we defi ne their upper and lower boundaries using an analytical method for volumetric limits.

Immunoaffi nity chromatography
In a previous study ( 16 ) we reported the characterization of HDL subspecies using a combination of apoA-I and A-II immunoaffi nity chromatography ( 15 ) with single vertical spin (SVS) ultracentrifugation (18)(19)(20) and negative stain electron microscopy. The chief artifact of the immunoaffi nity method used is elution with 0.1 M acetic acid, 1 mM EDTA, pH 3.0. The procedure appears to be minimally disruptive, since at least 98% of the total apoA-I is associated with HDL[1]-HDL [9] ( 15 ), in which the bands of free apolipoproteins are extremely minor compared with the total staining for HDL subspecies.
Ultracentrifugation by the SVS procedure has the advantage of short spin times (90-150 min), and thus less particle degradation than sequential fl otation. Very little free apoA-I is produced by this procedure. Shorter ultracentrifugation spin times, such as with SVS or other approaches, appear to be minimally disruptive. After a 24 h single spin at 40,000 rpm to isolate HDL subspecies, Davidson and colleagues saw a small amount of what appears to be free apoA-I. But this may be an artifact of the NDGGE gels because if the same ultracentrifugation fractions are passed over gel fi ltration columns, no free apoA-I is seen (Davidson, personal communication).
Using this combination of techniques, we identifi ed in this study a minimum of nine distinct subspecies of HDL. The vertical rotor procedure (SVS and vertical autoprofi le, VAP) used for the analysis of HDL subspecies is a modifi cation of one described earlier for single spin separation and analysis of the major classes of lipoproteins ( 21 ). of LpA-I and LpA-I,A-II to the subspecies of HDL prepared by ultracentrifugation ( 17 ), we found that the two distinct subspecies of LpA-I corresponding to HDL [4] and HDL [7] in Fig. 1A , fall into the (HDL 3a ) gge and (HDL 2b ) gge size intervals, respectively (align Fig. 2B with Fig. 2A ). In LpA-I,A-II, the subspecies corresponding to HDL [3] and HDL [5] appear to be a mixture of (HDL 3a and HDL 3b ) gge , and a mixture of (HDL 3a and HDL 2a ) gge , respectively, while LpA-I,A-II subspecies HDL [6] falls mostly in the (HDL 2a ) gge size interval (align Fig. 2C with Fig. 2A ). Thus, density cuts or size exclusion chromatography to isolate the HDL particles in the size interval of (HDL 3a ) gge will not be able to resolve HDL [3], HDL [4], and HDL [5] and will contain a mixture of LpA-I and LpA-I,A-II. This conclusion is confi rmed by Fig. 2D , an overlay of densitometry scans of the three immunoaffi nity isolated fractions, T-HDL, LpA-I,A-II and LpA-I, subjected to NDGGE in Fig. 1A .

Volumetric analyses of the stoichiometry of HDL subspecies
Stoichiometry of reconstituted particles with well-defi ned protein and lipid compositions. We developed a volumetric assay Matching of immunoaffi nity-isolated LpA-I and LpA-I,A-IIcontaining particles to HDL isolated by ultracentrifugation and NDGGE. In a study carried out to match the subspecies  of apoA-I and apoA-II per particle and using the weight percentage for each lipid component, a sequence of particle diameters can be calculated for each sHDL particle. Plugging the known apoA-I stoichiometries and lipid weight percentage into Table 2 , particle diameters of 74.2 and 80.7 Å are calculated for S80 and S93; the Stokes diameters reported for S80 and S93 are 80 Å and 93 Å, respectively ( 22 ), larger by 6-12 Å than diameters calculated by the volumetric method. It is known that hydrated protein ( 26,29,30 ) and lipid ( 31,32 ) are surrounded by one to three hydration shells of approximately 3 Å/shell. A publication by Atmeh and Elrazeq ( 28 ) shows that the Stokes diameters of sHDL determined by NDGGE are larger than expected, on the basis of which they suggest that sHDL particles are surrounded by approximately two hydration layers that affect electrophoretic mobility on NDGGE. However, the precise number of hydration shells for any molecule is not at all clear. Certain ions have one or even one-and-one-half hydration shells ( 33 ). Protein ( 29 ) likely is less hydrated that lipid ( 32 ), and its hydration is affected by the presence of associated lipid ( 32 ). Finally, the presence of ions affects the hydration shells of lipoproteins ( 34 ), and the unusually high fraction of charged for varying the apolipoprotein and lipid stoichiometries of native HDL subspecies to determine best fi ts to known particle diameters. Sequential permutations of protein stoichiometry (e.g., two apoA-I, two apoA-I, and one apoA-II) were used to convert the weight percentage of each lipid component (PL, UC, CE, and TG) to molecules per particle (see Table 2 footnotes for details). Using known volumes for each molecular component, we plotted and examined the results for best fi ts to diameters determined by NDGGE for HDL isolated by immunoaffi nity chromatography ( 16 ). Table 2 represents an example of the application of this volumetric method to the well-characterized S80 and S93 sHDL particles reconstituted in synthetico by Silva et al. ( 22 ). S80 and S93 were shown to contain two and three apoA-I, respectively, and the weight percentage for each lipid component was determined for each particle ( 22 ).
In developing this assay, we assumed that the protein components were unhydrated and their volume could be calculated by multiplying their molecular weights by a factor of 1.21 Å 3 /Da ( 26 ). Volumes for the lipid components were derived from McNamara et al. ( 27 ). Assuming a regular spherical shape ( 28 ), by sequentially varying the number  [1][2][3][4][5][6][7] subspecies are indicated by dotted vertical arrows: HDL [5], blue; HDL [4], red; HDL [3], green. Modifi ed from Cheung, et al. ( 17 ). D. Densitometry scans of the three lanes in Fig. 1A . T-HDL is black; LpA-I,A-II is blue; and LpA-I is red. The positions of the nine HDL subspecies are indicated with vertical dotted arrows.
Given the prominence of these two subspecies, we plugged the compositional data in supplementary Table  I into our volumetric method for determining the best fi t of the LpA-I subspecies HDL [4] and HDL [7] ( 16 ). The volumetric plots are shown in Fig. 4A , B . Since Fig. 2 shows that HDL [4] lies halfway between the (HDL 3a ) gge and (HDL 3b ) gge subspecies, in our volumetric analysis we entered compositional data that represented the average of HDL 3a and HDL 3b (supplementary Table I). From Fig.  4A , assuming a regular spherical shape ( 28 ), by sequentially varying the number of apoA-I and apoA-II per particle and using the weight percentage for each lipid component (PL, CE, UC, and TG) determined for the fi ve different HDL subspecies (supplementary Table I), a range residues in apoA-I ( ‫ف‬ 30%) compared with typical globular proteins ( ‫ف‬ 15%) may contribute to stronger hydration. Thus, while HDL is certainly hydrated, the precise number of hydration shells is not clear. Here, we assume that the number of hydration shells for HDL ranges between one and two.
Using the diameter of a single water molecule, 2.8 Å, for the thickness of a single hydration layer, a range of diameters assuming one or two hydration shells was calculated for S80 and S93 ( Table 2 ). One and two hydration layers give particle diameters of 79.8 and 85.4 Å for S80 and 86.3 and 92.7 Å for S93. This volumetric method can also be used to calculate the monolayer thickness (Tm) of surface components (apolipoprotein + PL + UC). Using the formula, Tm = (particle diameter Ϫ core diameter) / 2 , Tm is calculated to be 17.8 Å for both S80 and S93 ( Table 2 ).
Stoichiometry of circulating HDL subspecies. Huang et al. ( 24 ) reported the weight percentage for the protein and lipid of fi ve HDL fractions HDL( 2a-3c ) isolated by a onestep gradient ultracentrifugation method (supplementary Table I). The mean densities of their fi ve HDL subfractions are comparable to the corresponding fi ve gradient gel size subfractions of Blanche et al. ( 14 ). In a somewhat unusual twist, the HDL was fi rst partially depleted of apoA-II using sulfhydryl covalent chromatography to produce an HDL containing only about 20-30% of its original apoA-II content. Figure 3 represents NDGGE analyses of the fi ve resulting density cut fractions. It is of interest that there are essentially two major protein bands in each of the fi ve fractions ( Fig. 3 ) that correspond in diameter to the two major LpA-I subspecies, HDL [4] and HDL [7].   c Calculation of core and HDL diameters = 2r; r = (3V/(4 )) 1/3 assuming a sphere.
virtually identical to the measured diameter of 85.0 ± 1.2 Å ( Table 1 ). Since Fig. 3 shows that HDL [7] falls precisely in the HDL 2b subspecies density cut, in our volumetric analysis we entered the compositional data for (HDL 2b ) gge (supplementary Table I). From Fig. 4B , knowing that HDL [7] contains no apoA-II, three apoA-I (3:0) predicts a diameter of 95-100 Å, smaller by about 8-13 Å than the 108.5 Å of particle diameters can be calculated. Knowing that HDL [4] contains no apoA-II, two apoA-I alone predicts a diameter of 72-78 Å and four apoA-I alone predicts a diameter of 90-95 Å, both off by 5-10 Å from the measured diameter of 85.0 Å ( Table 1 ). The best fi t is to a protein stoichiometry of three apoA-I (and no apoA-II) and two layers of hydration, resulting in a calculated diameter of 85.2 Å ( Fig. 4A , black circle above 3:0 ) , Fig. 4. Best-fi t volumetric analyses of apoA-I-alone circulating HDL subspecies HDL [4] and HDL [7] quantifi ed by density cut ultracentrifugation. The apoA-I:A-II stoichiometries for each calculation are denoted on the x axis, and the diameters calculated at each stoichiometry for the particle containing one (lower gray point) and two (upper black point) hydration shells are plotted. The mean and standard deviation measured by NDGGE for each subspecies are denoted by narrow and shaded horizontal bands, respectively. A, B. Best-fi t volumetric analyses for the 85 Å diameter LpA-I HDL [4] and the 108.5 Å diameter LpA-I HDL [7] particles, respectively, using compositional data from Huang, et al. ( 24 ). Points for particles containing the same number of apoA-I and hydration shells are linked by thin lines. The best-fi t points for HDL [4] and HDL [7] -both with two hydration shells -are denoted by open arrowheads on the x axis above their apoA-I:A-II stoichiometries. The increase in the diameter of the 4:0 particle with two hydration shells by addition of one molecule of apoC-III is denoted by a black point with C inside, and the increase by addition of one molecule of apoE is denoted by a black point with E inside. C, D. Best-fi t volumetric analyses for the 85 Å diameter apoA-I-alone HDL [4] and the 108.5 Å diameter apoA-I-alone HDL [7] particles, respectively, using compositional data from Kontush, et al. ( 35 ). Error bars show variation in the data. There are two alternatives for the 3:0 particle: 3:0a is derived from the HDL 3c fraction and 3:0b is derived from the HDL 3b fraction. The best-fi t points for HDL [4] and HDL [7] -both with single hydration shells -are denoted by open arrowheads on the x axis above their apoA-I:A-II stoichiometries. the monolayer → planarity). The magnitude of this intercept, 21.3 Å, is signifi cant because the monolayer thickness of all-atom and coarse-grained planar POPC bilayers using the MARTINI force fi eld for coarse-grained lipid ( 36 ) are 20.9 Å and 21.1 Å, respectively.
All evidence suggests that the monolayer thickness in HDL subspecies is related to two factors: i ) the acyl chain tilt with decreasing radius and predominantly, ii ) the wellknown wedge effect of amphipathic helixes on monolayers to produce increased bilayer curvature ( 37 ) and thinning ( 38 ). Monolayer packing in small, protein-rich HDL appears to exist but is reduced to only two or three phospholipids between adjacent helixes ( 39 ).
Clearly, analysis of the fi ve more complicated particles is less robust than for HDL [4] and HDL [7] because i ) the HDL [4] and HDL [7] unequivocally do not include apoA-II and ii ) the HDL fractions isolated by Huang et al. ( 24 ) have been partially depleted of apoA-II. Nonetheless, our general compositional models for HDL subspecies ( Table 3 ) showing sequential changes in the stoichiometry of apoA-I and apoA-II fi t the general features of the models (dimer, trimer, tetramer) we previously proposed based on chemical crosslinking studies ( 17 ), and they are consistent with the results of a recent study by Gauthamadasa et al. ( 7 ) using a combination of chemical crosslinking and MALDI-MS analysis.
Although complicated by effects of hydration shells, size determination of HDL subspecies is less of an issue than stoichiometry. Although the immunoaffi nity method we used to isolate LpA-I and LpA-I,A-II from plasma does not isolate individually sized subspecies ( 15,16 ), NDGGE, when performed under conditions that allow all particles to reach their equilibrium positions, provides reasonably accurate estimate of particle sizes (most measured in quadruplet, Table 1 ).

DISCUSSION
The results described here have similarities to a recent publication by Gauthamadasa et al. ( 7 ) in suggesting that in the LpA-I subspecies the number of apoA-I molecules increased from two to three to four with an increase in the LpA-I particle size. Gauthamadasa et al. ( 7 ) results differ from ours in that they suggest that the entire population of LpA-I,A-II demonstrated the presence of only two proximal apoA-I molecules per particle, and we suggest two or three. In only slight disagreement, they suggest that the number of apoA-II molecules in the LpA-I,A-II particles vary from one dimeric apoA-II to three, whereas we suggest that the upper limit is two apoA-II. However, due to the uncertainties alluded regarding our analyses of LpA-I,A-II particles, three apoA-II is possible.
A publication of 1977 by Shen et al. ( 40 ) used many of the approaches and assumptions we used here. They used compositional analyses and geometric molecular arguments to infer the structure of HDL (and, in fact, all lipoprotein classes). Many of their conclusions and approaches were unique for the time. In particular, although proposed less measured by NDGGE. Five apoA-I (5:0) predicts a diameter of 112-117 Å, values that partially fall within the rather broad NDGGE band for HDL [7] ( Fig. 4B ). The best fi t is to a protein stoichiometry of four apoA-I (4:0); the double-shell model gives a diameter of 109.6 Å ( Fig. 4B , black circle above 4:0), close to 108.5 Å measured by NDGGE ( 16 ), while the single-shell model gives a diameter of 104.0 Å (gray circle above 4:0), at the lower edge of the HDL [7] band. Given the overlap of 5:0 with the HDL [7] band, it is possible that HDL [7] is a mixture of both 4:0 and 5:0.
Addition of one apoC-III molecule to the double-shell 4:0 model results in an HDL particle with a diameter of 111.5 Å, well within the HDL [7] band ( Fig. 4B , black circle with C). Addition of one apoE molecule to the doubleshell 4:0 model produces an HDL particle with a diameter of 116.4 Å, slightly outside the HDL [7] band ( Fig. 4B , black circle with E) but within the HDL [7] band if added to the single-shell model.
We also tested the compositional data of Kontush et al. ( 35 ) using our volumetric method. These investigators also calculated the weight percentage for the protein and lipid of the fi ve HDL fractions, HDL( 2a-3c ), isolated by the same density cuts used by Huang et al. ( 24 ) but without removal of apoA-II (supplementary Table II). These data, unlike the Huang et al. ( 24 ) data, provides error bars that have been incorporated into the analyses. Fig. 4C, D show the resulting volumetric plots for HDL [4] and HDL [7] using their data with error bars. In spite of the fact that the Kontush fractions ( 35 ) were not enriched in apoA-I versus apoA-II like the data of Huang et al. ( 24 ), the best fi ts for HDL [4] and HDL [7] are also to apoA-I-alone particles 3:0 and 4:0, respectively. However, error bars for the adjacent stoichiometries of LpA-I particles overlap the size range for HDL [4] (2:0) and HLD [7] (both 3:0 and 5:0).
Outer monolayer thickness of circulating HDL subspecies. We calculated the thickness of the surface lipid monolayer for all seven HDL subspecies in Table 3 . In Fig. 6 , we plot HDL subspecies monolayer thicknesses versus surface-tovolume ratios (S/V = 3/radius) for six native sHDL particles: HDL [2], HDL [3], HDL [4], HDL [5], HDL [6], and HDL [7] ( 16 ). These six sHDL particles fi t a straight line, y = Ϫ 0.01x + 0.2128, with a correlation coeffi cient of R 2 = 0.8545. The x intercept represents the limiting monolayer thickness of an infi nitely large sHDL, a planar monolayer, as the apoA-I/polar lipid ratio approaches zero. Mathematically, the larger the radius (r), the less curved the surface monolayer. Since S/V = 3/r, as r → ∞ , S/V → 0 (i.e., Volumetric analyses for the HDL [1], HDL [2], and HDL [3] subspecies, respectively, using compositional data from Huang, et al. ( 24 ). The best-fi t points for the three particles are denoted by three open arrowheads on the x axis above their apoA-I:A-II stoichiometries. B. Volumetric analyses for the HDL [5] and HDL [6] subspecies, respectively, using compositional data from Huang, et al. ( 24 ). The best-fi t points for the two particles are denoted by two open arrowheads on the x axis above their apoA-I:A-II stoichiometries. C. Volumetric analyses for the HDL [1], HDL [2], and HDL [3] subspecies, respectively, using compositional data from Kontush, et al. ( 35 ). Error bars show variation in the data. There are two alternatives for the 2:2 particle: 2:2a is derived from the HDL 3c fraction and 2:2b is derived from the HDL 3b fraction. The best-fi t points for the three particles are denoted by three open arrowheads on the x axis above their apoA-I:A-II stoichiometries. D. Volumetric analyses for the HDL [5] and HDL [6] subspecies, respectively, using compositional data from Kontush, et al. ( 35 ). The best-fi t points for the two particles are denoted by two open arrowheads on the x axis above their apoA-I:A-II stoichiometries.
rigorously before by, among others, Verdery and Nichols ( 41 ), they suggested the presence of a hydrophobic core surrounded by an amphipathic monolayer composed of protein, PL, and UC. There were, however, several questionable assumptions on their part: i ) they proposed that only PL and UC covered the core, not protein, whereas our MD simulation shows that protein makes contact with core molecules ( 39 ); ii ) in spite of the knowledge of the amphipathic helix at the time ( 42 ), they proposed that the protein of HDL was largely unfolded; iii ) they postulated that the protein covers the polar OH groups of UC, whereas our MD simulation study shows that this is clearly not the case; and iv ) they posited a sharp boundary between the core and the PL surface. Although for our geometric calculations we also assumed a sharp boundary, on average, between core and surface, our MD simulations analyses. By omitting immunoaffi nity chromatography, four of the nine HDL subspecies considered in our paper, HDL [1], HDL [4], HDL [8], and HDL [9], are missed. The most import of these, the LpA-I particle HDL [4], is lumped in with HDL [5] (their medium HDL or HDL 3a ) and HDL [3] (their small HDL or HDL 3b ). The very small HDL [1] and the very large HDL [8] and HDL [9] are missed entirely.
It is also worth mentioning that the single spin density gradient ultracentrifugation method described involves a rather long spin time (40,000 rpm × 48 h.) and, on the basis of NDGGE of the fi ve isolated fractions, results in isolation of an HDL [2] particle (their very small HDL or HDL 3c ) that is 84.7 Å in diameter, a particle show that there is considerable interdigitation between core molecules and the surface PL and, to a lesser extent, UC ( 39 ).
A recent comprehensive review of HDL subspecies and their relationship to CHD ( 43 ) is relevant to this article and its conclusions. The review covers most of the various methods for isolation and analysis of HDL subspecies: fl otation ultracentrifugation, zonal ultracentrifugation, density gradient ultracentrifugation (including VAP), precipitation, ion mobility, NDGGE, and 2D gel electrophoresis.
Unfortunately, although mentioned in a table, immunoaffi nity chromatography is not discussed. This technique provides the core basis for our present HDL subspecies Fig. 6. Linear regression plots of monolayer thickness measured by volumetric analysis versus surface-tovolume ratios. The analyses assume spherical shapes for all six native subspecies. Filled circles, HDL [2], HDL [3], HDL [4], HDL [5], HDL [6], and HDL [7]. Open circles, HDL [4] and HDL [7] alone; Open circles upper (d = 131.8 Å, 3/ r = 6/131.8 = 0.0455) and lower ( r = 13.5 Å) limits (labeled MAX and MIN, respectively) of monolayer thickness plotted along the linear regression line (solid diagonal). The surface-to-volume ratio (S/V = (4 r 2 )/(4/3 r 3 ) = 3/radius) varies inversely with particle diameter and is a measure of the ratio of surface moieties (protein and polar lipid) to core lipid. The x intercept of the linear regression line (equation and R 2 shown in black in the lower left-hand corner) to the six native HDL subspecies are indicated. The dotted diagonal line is the regression line to HDL [4] and HDL [7] alone whose equation and intercept are shown in open (white) fi gures.  [3], HDL [5], and HDL [6]) are less certain both because of their increased complexity and because of uncertainty about their lipid compositions ( Fig. 5 ).
Understanding the biological role of the various HDL subspecies is currently in its infancy. The two major LpA-I particles, HDL [7] and HDL [4], particularly HDL [7], have been suggested to be atheroprotective. Because the existence of HDL [4] is generally not recognized, its role remains unclear. Cheung and Albers in their original description of immunoaffi nity-isolated particles ( 15 ) showed isoelectric-focusing gels that seemed to imply that the majority of the members of the HDL proteome might be associated with the LpA-I particles, suggesting that apoA-II might regulate the binding of certain members of the HDL proteome. One step to further the understanding of the role of the diverse HDL subspecies will be to noninvasively isolate and determine the proteome content of individual HDL subspecies. Functional assays of individual HDL subspecies would also be helpful.
An additional conclusion from this article is that the thickness of the polar monolayer -a composite of apolipoproteins, PL, and UC -is directly proportional to the particle diameter. This raises the question of the biological signifi cance of this direct correlation of monolayer thickness with particle size. There as several possibilities: i ) the very small particles possess very little contiguous polar lipid surface area and this could affect the binding of remodeling proteins, such as LCAT, CEPT, or phospholipid transfer protein (PLTP) or many members of the more diverse HDL proteome; ii ) even those members of the HDL proteome that have binding sites on apoA-I, such as LCAT, may be affected because of conformational changes induced in apoA-I by a thinned polar lipid monolayer; and iii ) the thinning polar lipid monolayer much too large to be HDL [2]. This size suggests that either the particle is damaged or contaminated with larger HDL sub species. Therefore, conclusions about the large proteome associated with this subspecies must be suspect. Figure 6 provides support for the calculated stoichiometries of the six circulating HDL subspecies, HDL[2]-HDL [7], shown in Table 3 . When monolayer thickness is plotted against S/V ratio, the resulting points fi t a linear regression line with a high correlation coeffi cient. The x intercept of the regression line, representing the limiting monolayer thickness as the S/V ratio approaches zero (i.e., a planar lipid bilayer) is equivalent to the thickness of a planar lipid monolayer. Since the HDL [4] and HDL [7] subspecies are based upon the most solid numbers -the monolayer thickness for the remaining four HDL subspecies containing apoA-II might be biased by removal of most of the apoA-II ( 14 ) -we plotted a regression line for HDL [4] and HDL [7] alone. This regression line (dotted line in Fig. 6 ) is virtually identical to the regression line for all six subspecies; the x intercept is 20.4 Å. All HDL subspecies fall between the minimal monolayer thickness (13.5 Å) and the S/V ratio of the largest subspecies, HDL [9], whose diameter is 131.8 Å ( 16 ), limits that are plotted as large open circles and labeled MIN and MAX in Fig. 6 . Figure 7 is a schematic diagram that summarizes the basic conclusions of this article regarding size; apoA-I, apoA-II, and lipid stoichiometries; and relative abundance (major or minor) of the seven HDL subspecies HDL[1]-HDL [7]. The other two subspecies discussed earlier, HDL [8] and HDL [9], because of uncertainties in stoichiometries and because they represent minor particles, are not included in the diagram. Apolipoprotein stoichiometries for the LpA-I particles (HDL [4] and HDL [7] and, to a lesser degree, HDL [1]) are the most Fig. 7. Schematic illustration of the best-fi t apoA-I:apoA-II stoichiometries for each of the HDL[1]-HDL [7] subspecies of plasma LpA-I and LpA-I,A-II isolated by immunoaffi nity chromatography and analyzed by NDGGE. Relative diameters in the diagram are proportional to the measured diameter of each subspecies. The three distinct LpA-I subspecies are in dark gray, and the four LpA-I,A-II subspecies are in light gray. All are considered major bands except HDL [1], which is usually found in small quantities in normolipidemic plasma but whose level is increased in hyperlipidemic plasma and the plasma of individuals with coronary disease ( 45 ). The subspecies with the least certain apolipoprotein stoichiometries are indicated by question marks. Diameters of each particle and lipid composition by volumetric analysis are also shown. might be involved in increasing, decreasing, or keeping constant the lipid surface pressure between HDL subspecies. As we demonstrated previously, LDL has mechanisms built into apoB to dampen changes in surface pressure between different-sized subspecies ( 44 ).
A corollary of this conclusion is that the apolipoproteinto-lipid molar ratio is signifi cantly higher for circulating HDL subspecies compared with reconstituted sHDL particles S80 and S93 ( 22 ). This issue is considered in more detail in a publication ( 39 ) in which molecular dynamics simulations are used to examine reconstituted and circulating sHDL particles at the molecular level.