Ligand Size as a Determinant for Catabolism by the Low Density Lipoprotein (LDL) Receptor Pathway A LATTICE MODEL FOR LDL BINDING*

Low density lipoproteins (LDL) are large (Mr = 2.5 X 10’) in comparison to LDL receptors (Mr = 115,000). Since most LDL receptors are clustered in coated pits, we tested the hypothesis that crowding of receptor- bound LDL particles would cause steric effects. The apparent affinity of LDL for receptors on cultured fibroblasts decreased near saturation causing concave- upward Scatchard plots. Both the higher and lower affinity components of binding were up-regulated by the cholesterol synthesis inhibitor, lovastatin, indicating that the entire binding curve was sterol-respon- sive. In contrast, neither component of LDL binding was present on lovastatin-treated or untreated null fibroblasts which are incapable of expressing LDL receptors. Therefore, the concave-upward Scatchard plots were entirely due to binding to LDL receptors. These results are consistent with a lattice model in which receptor-bound LDL are large enough to decrease binding to adjacent receptors. A lattice model implies that large LDL should produce steric effects at a lower receptor occupancy than should small LDL. This was tested using seven LDL fractions that differed in diameter from 20 to 27 nm. Fewer large than small LDL were bound to the cell surface at 4 “C and 37 “C, and fewer were internalized and degraded at 37 “C.

Since most LDL receptors are clustered in coated pits, we tested the hypothesis that crowding of receptorbound LDL particles would cause steric effects. The apparent affinity of LDL for receptors on cultured fibroblasts decreased near saturation causing concaveupward Scatchard plots. Both the higher and lower affinity components of binding were up-regulated by the cholesterol synthesis inhibitor, lovastatin, indicating that the entire binding curve was sterol-responsive. In contrast, neither component of LDL binding was present on lovastatin-treated or untreated null fibroblasts which are incapable of expressing LDL receptors. Therefore, the concave-upward Scatchard plots were entirely due to binding to LDL receptors. These results are consistent with a lattice model in which receptor-bound LDL are large enough to decrease binding to adjacent receptors. A lattice model implies that large LDL should produce steric effects at a lower receptor occupancy than should small LDL.
This was tested using seven LDL fractions that differed in diameter from 20 to 2 7 nm. Fewer large than small LDL were bound to the cell surface at 4 "C and 37 "C, and fewer were internalized and degraded at 3 7 "C. Since large LDL bound via both apolipoprotein (apo) E and apoB100, receptor cross-linking could have caused fewer large LDL to be bound at saturation. However, when the potential for cross-linking was prevented by an apo-E-specific monoclonal antibody (1D7), the difference in binding by large uersus small LDL was not eliminated; instead, it was exaggerated. Taken together, these results support a lattice model for LDL binding and indicate that steric hindrance associated with crowding of LDL particles on receptor lattices is a major determinant for catabolism by the LDL receptor pathway in vitro.
The low density lipoprotein (LDL)' receptor pathway is the major route for high affinity uptake of cholesterol into mam-*This work was supported by Research Grants HL02024 and HL14230 from the National Institutes of Health and by the Department of Veterans Affairs Research Fund. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 4 To whom correspondence and reprint requests should be addressed.
' The abbreviations used are: LDL, low density lipoproteins; HDL, high density lipoproteins; apo, apolipoprotein; LRP, LDL receptorrelated protein; SDS-PAGE, sodium dodecyl sulfate-polyacrylamide gel electrophoresis. malian cells (for review, see Ref. 1). Binding of LDL to LDL receptors poses special problems due to the large differences in size between the ligands and receptors. A single LDL particle (Mr = 2.5 X lo6) is more than 20 times larger than an LDL receptor (Mr = 115,000) (1,2). Ligand size might not be important if the receptors were widely separated on the cell surface, but they are not. Seventy to eighty percent of the receptors are clustered in clathrin-coated pits which comprise less than 2% of the cell-surface area (3). By electron microscopy, using ferritin-conjugated LDL as a probe, many LDL particles may be seen within a single coated pit (3). This suggests that binding of additional LDL particles near saturation might be sterically hindered. However, according to current biochemical evidence, ligand binding to LDL receptors occurs by independent interactions between single particles and single receptors as indicated by linear Scatchard plots and first order kinetics (1,4,5).
We hypothesized that receptor-bound LDL are large enough to sterically hinder binding to nearby receptors. Consequently, binding should conform to a lattice model. Lattice models are applicable to many macromolecular interactions (6-11). A feature common to receptor lattices is that the binding of large ligands decreases or excludes binding to nearby receptors. On a lattice of LDL receptors, large LDL might hinder binding to more adjacent receptors than would small LDL. Therefore, fewer large than small LDL would be bound, internalized, and degraded by cells. This was tested in cultured fibroblasts by studying the surface binding and receptor-mediated catabolism of LDL and seven ultracentrifugal LDL fractions that differed in size.

EXPERIMENTAL PROCEDURES
Human Subjects-Lipoproteins from nine normolipidemic human subjects were studied. Their ages ranged from 26 to 51 years; six were female; three were male. Since apoE was involved in binding of large LDL to receptors, we determined apoE phenotypes. All subjects had the most common phenotype (E3/3) except one whose phenotype was E4/2. All subjects gave written informed consent for the study which was approved by the Human Research Committee at The University of Iowa.
Lipoprotein Prepuration-Subjects fasted for 14 h before blood sampling. Samples were adjusted to contain 1 mg of EDTA (sodium salt)/ml and were immediately placed on ice. The plasma was separated from the cells by centrifugation at 2,000 rpm for 15 min at 4 "C. To prevent proteolytic degradation, plasma was adjusted to contain 10,000 units of aprotinin/liter (Mobay Chemical Corp., New York), 1 mM benzamidine, 1 mM phenylmethylsulfonyl fluoride, and 80 mg of gentamicin/liter (Sigma) (12).
Plasma LDL (d = 1.02 to 1.05 g/ml) were isolated by ultracentrifugation (13). The LDL were fractionated by overlayering 2 ml of the d = 1.006 to 1.05 g/ml lipoproteins on a NaCl density gradient from 1.012 to 1.065 g/ml followed by centrifugation in an SW41 rotor (Beckman Instruments) at 39,000 rpm, 18 "C for 48 h. Fractions (1 ml each) were removed from the top of the centrifuge tube by pipetting and then dialyzed against a buffer containing 0.15 M NaCl and 1 mM EDTA, pH 7.4, at 4 "C. Lipoproteins were iodinated (specific activity 300-600 cpm/ng) by the iodomonochloride method (14).
Lipoprotein and Apolipoprotein Characterization-Protein, cholesterol, triglyceride, and phospholipid concentrations were measured in duplicate or triplicate (15)(16)(17). The relative apolipoprotein content of lipoproteins was determined using electrophoresis on 5-20% sodium dodecyl sulfate-polyacrylamide (SDS-PAGE) gradient gels stained with Coomassie Blue R-250 or silver (15,18,19). Coomassie Bluestained gels were scanned at 600 nm on a CS-930 scanner (Shimadzu, Kyoto, Japan) (15). ApoE phenotypes were determined by isoelectric focusing (20). Average molecular diameters of the LDL particles were estimated by electron microscopy (21). Electrophoretic mobility of each fraction was determined by 1% agarose electrophoresis (Corning, Palo Alto, CA) (15). The density of each LDL fraction was estimated by measuring the refractive index of a corresponding fraction containing no lipoproteins.
Fibroblast Binding Assays-Human foreskin fibroblasts were cultured from four normal infants. Mutant fibroblasts (null cells) that are incapable of expressing LDL receptors due to homozygosity for null alleles (22) were purchased from the NIGMS Human Genetic Mutant Cell Repository (GM00486A), Camden, NJ. Fibroblasts were grown to confluency in 35-mm plastic wells as previously described, and LDL receptors were up-regulated by incubation with cholesteroldepleted media (containing 10% lipoprotein-deficient serum) for 48 h prior to the binding assays (23). To further up-regulate LDL receptors, in some cases, lovastatin (provided by Merck) was added to the media (final concentration 1 pg/ml) for 24 h prior to the binding assay (24).
The surface binding of lZ5I-LDL to metabolically inactive (4 "C) or active (37 "C) fibroblasts was determined in duplicate (23). Nonspecific binding of "'1-LDL was not significantly different whether it was defined as the amount bound in the presence of either a 50-fold excess of unlabeled LDL at each concentration tested, or 5,000 pg/ ml unlabeled LDL at all ligand concentrations (data not shown). Therefore, we defined nonspecific binding as that bound in the presence of a 50-fold excess of unlabeled LDL. At 37 "C, surfacebound lZ5I-LDL was determined by heparin release. Internalization and degradation of lZ5I-LDL were determined by resistance to heparin displacement from the cell surface and by appearance of trichloroacetic acid-soluble radioactivity in the medium, respectively (23). To ensure that equivalent cell numbers were present in all wells, total cellular protein was measured in every sixth well; cellular protein varied by less than 10% within each assay.
Binding data were analyzed by a nonlinear, least squares curvefitting program (LIGAND) (25) using one or two saturable site models; a nonsaturable site was included in some models to represent nonspecific binding. Maximum bound (Emax), equilibrium dissociation constant ( K D ) , and, in some cases, nxspecific binding were fitted parameters. Average KO were calculated as the geometric mean (26).
The contribution of apoBlOO or apoE to the binding was determined using monoclonal antibodies that specifically inhibit one or the other apoprotein binding (15). Antibodies 1D7 and 4G3, which inhibit apoE or apoBlOO binding, respectively, were generously pro-

Binding of lZ5I-LDL to Metabolically Inactive Celk at 4 . T -
We began our studies using unfractionated LDL ( d = 1.02 to 1.05 g/ml) with the hypothesis that, near saturation, their apparent affinity should decrease due to crowding of LDL particles as they bound to clustered receptors. Fig. 1 shows that the apparent affinity of lZ5I-LDL for LDL receptors decreased near saturation causing a curvilinear, concave-upward Scatchard plot. A model with two saturable sites (solid line) described the data better than did a model with one saturable site (dotted line). Above a concentration of approximately 30 pg of protein/ml, the Scatchard plot became horizontal, indicating nonsaturable binding. Previous Scatchard plots of LDL binding appeared linear (1,4,5). However, we used more than a thousandfold range of lZ5I-LDL concentrations (0.04 to 100 pg of protein/ml). If we were to truncate Cells were grown to confluency in 35-mm plastic wells and incubated with cholesterol-depleted medium for 48 h to upregulate LDL receptors prior to the assay. Media containing a 2,500fold range (0.04-100 pg of protein/ml) of '"1-LDL (d = 1.02-1.05 g/ ml) were incubated with cells in duplicate wells for 3 h at 4 "C. Nonspecific binding was determined by incubation with a 50-fold excess of unlabeled LDL and was subtracted from the total lZ5I-LDL binding to give the data shown. Following washing to remove unbound ligands, the cells were solubilized, and total or nonspecific binding of "T-LDL was determined by measurement of the radioactivity present per well. The solid line was calculated using a nonlinear, least squares curve-fitting program (LIGAND) (24) and is the best fit for a model that includes two saturable binding sites. The dashed line represents the curve predicted by a model including one saturable and one nonsaturable site. The flat portion of the dashed line represents the nonsaturable site. The two saturable site model described the data better than did the one saturable site model ( p < 0.01).
our data to a 50-fold range of LDL concentrations (for example, 0.25 to 12.5 pg of protein/ml), as is commonly done (23), the curvilinearity would not be so apparent. The shape of the Scatchard plot in Fig. 1 suggested several alternative models for binding including a lattice model, negative cooperativity, cross-linking of receptors by multivalent ligands, or the existence of two or more classes of receptors. However, both equilibrium binding (below) and kinetic studies (described in detail elsewhere)' were most consistent with a lattice model.
To determine if more than one receptor type was involved, we tested the sterol sensitivity of LDL binding using lovastatin, a cholesterol synthesis inhibitor (24). As shown in Fig.  2, lZ5I-LDL binding to fibroblasts was up-regulated by lovastatin treatment when compared to untreated cells and yielded a Scatchard plot which was curvilinear to a similar degree. Since LDL receptors are the only known sterol-responsive receptors for LDL, the curvilinearity could not easily be explained by binding to both LDL receptors and other sites such as the LDL receptor-related protein (LRP) (30,31).
No high affinity lZ5I-LDL binding to lovastatin-treated or untreated null fibroblasts was detected (Fig. 3). Null fibroblasts are incapable of expressing LDL receptors, but they express LRP normally (31). At all ligand concentrations tested, the ratio of bound to free ligand was less than 0.0005 (Fig. 3B). This extremely low level of binding was nonsaturable and could not contribute significantly to binding by similarly treated normal cells ( Figs. 1 and 2). Thus, the capacity of LRP or other potential LDL binding sites to bind LDL at the cell surface of fibroblasts was too low to be measured easily and, with respect to our studies, was not an important factor.
Concave-upward Scatchard plots may be due t o low affinity, nonspecific binding. However, the total binding was similar to the specific binding (Fig. 2). Nonspecific binding contributed little to the shape of these curves whether it was measured using a 50-fold excess of unlabeled LDL or resistance to heparin release (not shown). Also, the ratio of specific to nonspecific binding was higher in lovastatin-treated normal cells, as expected, because nonspecific binding should not be up-regulated by lovastatin.
Binding of lZ5I-LDL Fractions to Cells at 4 "C-We hypothesized that the curvilinearity in Scatchard plots was due to crowding of LDL particles on a lattice of receptors near saturation. In a lattice model, binding of LDL to a nearly empty lattice could proceed with relatively high affinity, but the apparent affinity should decrease near saturation due to difficulty "parking" many particles on a crowded lattice (6,8,9). Also, large LDL should cause steric effects at lower receptor occupancy than small LDL. To further test these ideas, we studied the binding of lZ5I-LDL fractions that differed in size.
Seven LDL fractions (d = 1.006 to 1.05 g/ml) were isolated by ultracentrifugation and characterized by size (electron microscopy), chemical composition, and apolipoprotein con-   Table I, their particle diameters ranged from 27 (fraction 1) to 20 nm (fraction 7). A 27 nm particle has nearly twice the cross-sectional area of a 20 nm particle. For example, assuming that the LDL receptor (Mr = 115,000) is globular, a 27 nm particle could cover the cross-sectional area equivalent to the area covered by 18 receptors, whereas a 20 nm particle could cover 9.6. The fractions also differed in their cholesteroktriglyceride ratios and their flotation densities ( Table I). By scanning densitometry of 5-20% SDS-PAGE, the relative apoBlOO content increased from 89% in fraction 1 to 98% in fraction 7, whereas the apoE content decreased from 10% in fraction 1 to undetectable in fraction 7 (Fig. 4). Approximately 80% of the total protein in the d = 1.006 to 1.05 g/ml fraction was in fractions 5-7 (Table I). Thus, unfractionated LDL ( d = 1.02 to 1.05 g/ ml) contained predominantly small LDL and very few particles that were similar to those in fractions 1-3.
The binding of each lZ5I-LDL fractions to fibroblasts at 4 "C caused concave-upward Scatchard plots with apparent decreases in affinity near saturation (Fig. 5). Maximum binding (BmJ by the high affinity sites varied with particle size and increased by 3-to 4-fold when small (fraction 7) were compared to large LDL (fraction 1). This pattern of binding was observed whether or not fibroblasts were treated with lovastatin and therefore, did not depend on the level of LDL receptor expression (Fig. 6). Based on the initial slopes of the Scatchard plots, the affinity of large LDL (fraction 1) was higher than that of small LDL (fraction 7). Because the curves appeared to approach the x-axis asymptotically, neither affinity nor receptor number could be accurately measured near saturation. Binding data from a series of experiments are summarized in Table 11. Using monoclonal antibodies that inhibited either apo-B100-(4G3 or MB47) or apoE-mediated binding (1D7), we found that large LDL bound via both apoBlOO and apoE, whereas small LDL bound only via apoBlOO (Table 11). This raised the possibility that large LDL might cross-link two receptors by simultaneously binding via both apoE and apoB100. Therefore, a comparison of binding by lZ5I-LDL fractions was performed in which apoE-mediated binding either was or was not inhibited by an excess of the monoclonal antibody, 1D7. When apoE-mediated binding was blocked by 1D7, the Scatchard plot of the binding of fraction 1 was shifted to the left, indicating less binding, whereas the plot of fraction 6 binding was not affected much (Fig. 7). The effect of 1D7 on the binding of 1251-fraction 3 was intermediate between its effects on fractions 1 and 6 (not shown). Similar results were obtained whether an excess of unlabeled LDL or heparin release was used to measure nonspecific binding (not shown). Receptor cross-linking by apoBlOO alone is unlikely sence of lovastatin as described in the legend for Fig. 2. Only specifically bound "'I-LDL is shown. Total binding was less than 2 ng of protein at all concen-   because apoBlOO appears to be univalent and exists a t a molar ratio of one molecule/particle (27-29, 32). Monoclonal antibodies 4G3 or MB47 almost completely inhibited binding by fractions 5-7 (Table 11) or unfractionated LDL (not shown).
Binding of '2"I-LDL Fractions to Cells at 37 "C-The experiments discussed above were performed on metabolically inactive cells. To test the lattice model on metabolically active cells, we performed studies a t 37 "C. As predicted from the binding at 4 "C, fewer large than small LDL were bound to the surface of fibroblasts a t 37 "C (Fig. 8A). This was determined by heparin release of surface-bound 12"I-LDL after 5 h. Because fewer large than small LDL were bound to the surface, fewer were internalized and degraded. Since large LDL contain more protein per particle than small LDL, the differences between their catabolism are underestimated in FIG. 6. Effect of lovastatin t r e a t m e n t on Scatchard plots of binding of '"I-LDL fractions to normal human fibroblasts at 4 "C. Assay conditions were as described in the Fig. 2 legend. Specific binding of "'I-LDL fractions 2, 4, or 6, as indicated, is shown. Fig. 8 and would be slightly greater if expressed on a molar basis. The pattern of internalization and degradation was similar when LDL receptor expression was up-regulated by lovastatin (Fig. 9) or down-regulated by growth of cells in cholesterol-containing medium (not shown).

DISCUSSION
We considered several alternative models for LDL binding before concluding that a lattice model provides the best description. The current model, in which each LDL binding Model for LDL Binding  on Scatchard plots of la61-LDL fractions binding to normal human fibroblasts at 4 "C. Cells were prepared as described in the Fig. 1 legend. Concentrations of '"1-LDL fractions ranging from 0.06 to 20 pg of protein/ml were incubated for 1 h at 4 "C in the presence or absence of a 10-fold excess (by protein mass) of a monoclonal antibody (1D7) which specifically inhibits apoE-mediated binding (27,28). Specific binding, determined by subtracting from total binding the amount bound in the presence of a 50-fold excess of unlabeled LDL, is shown. event is independent of all others, does not predict a concaveupward Scatchard plot. Scatchard plots of LDL binding appear linear (1,4,5), with rare exceptions (33), when restricted to a 50-fold range of ligand concentrations. However, binding to receptor lattices may yield nearly linear Scatchard plots until steric effects become important near saturation (6,8,9). Similarly, the presence of two classes of receptors, negative cooperativity or receptor cross-linking may not be apparent if a broad range of ligand concentrations is not tested.
Multiple ligands that differ in affinity could have been present due to heterogeneity of LDL, but this would cause concave-downward, not concave-upward Scatchard plots (34, 35). The presence of two classes of receptors is unlikely because neither the high nor low affinity components of lz5I-LDL binding were present in null cells which could not express LDL receptors (Fig. 3). Both binding components were up-regulated by lovastatin, a cholesterol synthesis inhib-itor (Fig. 2). Since LDL receptors are the only known sterolsensitive binding sites for LDL (1,30,31), these results indicate that binding to LDL receptors alone causes concaveupward Scatchard plots.
Since large LDL bind via both apoE and apoB100, we considered a model in which two receptors were cross-linked by a single particle containing these apoproteins. Because univalent binding, which has lower affinity, becomes more predominant as receptor saturation is approached, cross-linking of receptors by multivalent ligands causes concave-upward Scatchard plots (36, 37). Despite reporting linear Scatchard plots, a cross-linking model has been proposed to explain the binding of apoE-HDL,, a multivalent ligand that contains 16 apoE molecules/particle (4, 5). By radiation inactivation of LDL receptors, as assessed by apoE-HDL, or LDL binding, the receptor binds as a protein with M , = 106,000, which is very close to the LDL receptor monomer (Mr = 115,000) (38).
These results exclude the possibility that a receptor dimer is involved in ligand binding, but do not preclude cross-linking of two monomers by a multivalent ligand. Although the LDL receptor has seven potential ligand binding sites (39), the combined size of these sites (Mr = 30,000-35,000) is smaller than LDL by a factor of 70 or more. Therefore, it is unlikely that a single receptor could simultaneously bind multiple LDL particles. Also, by a solid phase assay, the stoichiometry for LDL binding was found to be 1:l (40).
A lattice model for LDL binding could include receptor cross-linking by multivalent ligands. Ligand size would still determine the area of the lattice that was sterically hindered from binding (6,8,9). ApoE-HDL, have an average diameter of 24 nm (41) and could cover nearly 50% more area on a lattice than could an LDL particle (20 nm). It is possible that the effective volume excluded by multivalent ligands such as apoE-HDL, or fraction 1 particles is greater than expected based on their size alone, but this has not been tested directly. The effect of volume exclusion might not be related in a simple linear fashion to the cross-sectional area of the particle. For example, the shape of ligands is important. Rodshaped ligands cause greater excluded volume effects than do spherical ligands of the same size (9). Although lipoproteins appear spherical, the arrangement of receptor-recognition sites on apoE-HDL, or fraction 1 particles is probably not spherical. Theoretically, this could be important if receptor cross-linking occurred. However, several experimental observations weigh against receptor cross-linking alone as a mechanism to explain binding by human LDL fractions.
First, when the potential for cross-linking was eliminated by performing binding assays in the presence of an apoEspecific monoclonal antibody (1D7), the binding of large LDL was inhibited, and the number of high affinity sites decreased (Fig. 7). If cross-linking of receptors by large LDL caused the apparent number of sites to decrease, preventing cross-linking should have had the opposite effect. Second, even in the absence of 1D7, the binding of fractions 4 through 7 was primarily apoB100-mediated, but caused concave-upward Scatchard plots and differences in the receptor number estimates ( Fig. 5 and Table 11). Because apoBlOO appears to be univalent (27)(28)(29)32), a receptor-cross-linking mechanism is unlikely. Third, the dissociation rate of LDL and LDL fractions was not dependent on the degree of receptor occupancy. As explained in more detail elsewhere: a cross-linking model predicts that univalent binding should be more predominant than multivalent binding at high degrees of occupancy and is manifest by a more rapid dissociation rate (37).
The increased affinity of large uersus small LDL does not require that receptor cross-linking occur. The presence of Model for LDL Binding Surface binding, internalization, and degradation of "'1-LDL fractions 1, 3, 5 , and 7 by normal human fibroblasts at 37 OC. Fibroblasts were prepared as described in the Fig. 1 legend. After incubation for 5 h at 37 "C, surface-bound (panel A ) and internalized (panel B ) lz5I-LDL were measured as heparin-releasable or heparin-resistant radioactivity, respectively. Degraded Iz5I-LDL was measured as trichloroacetic acid-soluble radioactivity ( p a n e l C). Nonspecifically bound, internalized, and degraded "'I-LDL were determined by incubation in the presence of a 50-fold excess of unlabeled LDL for each concentration tested. Nonspecific binding was 10-15% of the total binding (not shown) and was subtracted to give the data shown. Effect of lovastatin on surface binding, internalization, and degradation of "'I-LDL fractions 1, 3, 5 , and 7 by normal human fibroblasts at 37 "C. The data shown were obtained by duplicating the experiment shown in Fig. 8 except that the cells were treated with lovastatin as described in the Fig. 2 legend. The data shown in Fig. 8 and this figure were obtained in the same assay. both apoE and apoBlOO may permit more acceptable orientations for binding than exist when only apoBlOO is present (36, 42). Also, apoE may bind with higher affinity than does apoB100. Similarly, apoE-HDL,, which has 16 apoE molecules/particle, presumably has many more acceptable orientations for binding than does LDL (4,5).
Negative cooperativity may cause curvilinear Scatchard plots (43). In lattice models, negative cooperativity may exist independently of steric effects which decrease the accessibility of receptor sites (6). If ligand binding induces a conformational change in neighboring receptors, the dissociation rate may increase with receptor occupancy. In this respect, negative cooperativity may be indistinguishable from a crosslinking model. However, as described elsewhere,* the dissociation rate of LDL was not dependent on the degree of receptor occupancy.
We propose a lattice model as a unifying hypothesis to explain well established characteristics of binding to LDL receptors. Namely, the receptors are relatively small and closely spaced and must interact with much larger lipoproteins (1). Recently,Robenek et al. (44) used electron microscopy to show that receptor-bound LDL particles on the cell surface are in direct contact with each other. It is difficult to envisage how these particles achieved such close contact without encountering steric hindrance. In a lattice model, unlike models involving negative cooperativity or receptor cross-linking, steric hindrance is an essential feature. Binding of large ligands to other clustered receptors, such as LRP, scavenger, or asialoglycoprotein receptors (lo), might also conform to a lattice model. Lattices occur whenever ligands are large enough to cover adjacent sites and exclude them from binding. Mathematical equations have been developed that describe the binding of some proteins and drugs to DNA, a one-dimensional lattice (6, 11). Equations have also been developed that describe tropomyosin-troponin binding to actin, polyclonal antibodies binding to antigens, and adsorption of polymers to membranes (7-9,45). The latter are examples of two-dimensional lattices. Since the Scatchard plots of LDL binding approached the xaxis asymptotically, the number of LDL receptors could not be measured accurately, and the stoichiometry of LDL binding could not be determined. More information is needed about the size and spacing of LDL receptor aggregates on cell surfaces before equations can be written specifically to describe an LDL receptor lattice.
Most of the LDL receptors on the surfaces of intact cells are associated with clathrin in coated pits (1, 3). Clathrin forms predominantly hexagonal arrays underneath the cell surface (46). Clathrin hexagons are large, 30 nm in diameter (46), in comparison to the ligand sizes which appeared to cause steric effects, 20 to 27 nm particles. Thus, it seems likely that more than one LDL receptor was present per hexagon. In agreement with this possibility, van Driel et al.
(47) showed that up to 20% of the LDL receptors on the cell surface could be cross-linked by a cross-linking reagent and concluded that many LDL receptors existed as noncovalently attached dimers or higher order aggregates. Of interest, LDL receptors self-associate in the absence of clathrin (47). Therefore, with respect to a lattice model, the role of clathrin remains to be determined.
Fewer large than small LDL were internalized and degraded by fibroblasts at 37 "C (Fig. 8 ). This observation was not predicted by previous studies of LDL catabolism (1) and, at first glance, was surprising because large LDL bound with higher affinity than did small LDL (Table 11). However, in the context of a lattice model, the importance of ligand size is obvious. Due to steric hindrance, fewer large than small LDL were bound to the cell surface, which caused fewer to be internalized and degraded.
A lattice model has important implications for receptormediated catabolism of lipoproteins in vivo. Receptor lattices sterically resist saturation and are sensitive to a broader range of ligand concentrations than expected for a single site model. This may be significant because the concentration of LDL in normolipidemic plasma, 800 to 900 pg of protein/ml (48), should completely saturate the high affinity component of LDL binding.
In addition, our data suggest that the receptor-mediated catabolism of small LDL in vivo may be more rapid than that of large LDL, and, in some humans and pigs, this has been shown (49, 50). Since receptor-mediated clearance and lipolysis of lipoproteins occurs simultaneously in vivo, the situation is more complicated than our in vitro model. Large LDL are more triglyceride-rich than small LDL, and their affinity for LDL receptors may increase during active lipolysis (51). Also, because LDL receptors may be down-regulated in vivo, the degree of receptor clustering may be less. More studies are needed to determine the applicability of a lattice model to lipoprotein catabolism in vivo.
In summary, we found that ligand size is a major determinant for catabolism of LDL by the LDL receptor pathway in vitro. To explain our data, we propose a lattice model in which receptor-bound LDL are large enough to decrease or exclude binding to adjacent receptors.