The effect of receptor clustering on diffusion-limited forward rate constants.

The effect of receptor clustering on the diffusion-limited forward rate constant (k+) is studied theoretically by modeling cell surface receptors by hemispheres distributed on a plane. We give both exact results and bounds. The exact results are obtained using an electrostatic analogue and applying the method of the images. Accurate upper bounds on k+ are found from a variational principle.     

Influence of cell density and receptor number on the binding and distribution of cell surface epidermal growth factor receptors

Summary Previous studies have shown that cell density influences the expression of receptors for at least four growth factors. The data presented in this report demonstrate that epidermal growth factor receptors are regulated differently on cells expressing over a million receptors as opposed to cells expressing approximately fivefold fewer receptors. Specifically, we show that BT-20, MDA-468, and A-431-R1 cells, which exhibit a large number of epidermal growth factor receptors, preferentially down-regulate the high affinity class of these receptors as cell density increases. In addition, we show that these cells express cell surface epidermal growth factor receptors that are localized predominately to the periphery of the cells. In contrast, A-549 and BSC-1 cells, which exhibit fewer cell surface epidermal growth factor receptors and which reduce all affinity classes of epidermal growth factor receptors as cell density increases, exhibit a diffuse cell surface distribution of these receptors at both low and high densities.     

Analysis of competition binding between soluble and membrane-bound ligands for cell surface receptors

Binding of the Fc portion of IgG coated on targets to Fcgamma receptors (e.g., CD16) expressed on leukocytes (i.e., 2D binding) is an initiating step for immune responses such as phagocytosis or antibody-dependent cellular cytotoxicity. In vivo, circulating leukocytes are exposed to plasma IgG. The competition from soluble IgG (i.e., 3D binding) may affect the 2D binding. Many cell surface receptors, CD16 included, have soluble counterparts. While their physiological significance is not clear, receptor-based competitive inhibition therapy, in which soluble receptors, ligands, and their analogs are employed to compete with surface-bound receptors and ligands to prevent unwanted adhesion, is widely used to treat various diseases. To provide a quantitative basis for design of these therapeutic approaches, we developed a mathematical model for 2D and 3D competition binding. The model relates cell-surface adhesion (in the presence and absence of dislodging forces) to the concentration of the soluble competitor, the densities of the surface-bound receptors and ligands, as well as the binding affinities of the 2D and 3D interactions. Binding of CD16-expressing cells to an IgG-coated surface in the presence of a soluble competitor (IgG or anti-CD16 antibody) was quantified by a centrifugation assay. The agreement between experiment and theory supports the validity of the model, which could be useful in predicting the efficacy of the competitor.     

Diffusion-limited forward rate constants in two dimensions. Application to the trapping of cell surface receptors by coated pits.

A variety of receptors are known to aggregate in specialized cell surface structures called coated pits, prior to being internalized when the coated pits close off. At 37 degrees C on human fibroblasts, as well as on other cell types, a recycling process maintains a constant number of coated pits on the cell surface. In this paper, we explore implications for receptor aggregation and internalization of the two types of recycling models that have been proposed for the maintenance of the coated pit concentration. In one model, coated pits alternate between accessible and inaccessible states at fixed locations on the cell surface, while in the other model, coated pits recycle to random locations on the cell surface. We consider receptors that are randomly inserted in the membrane, move by pure diffusion with diffusion coefficient D, and are instantly and irreversibly trapped when they reach a coated pit boundary (the diffusion limit). For such receptors, we calculate for each of the two models: the mean time tau to reach a coated pit, the forward rate constant k+ for the interaction of a receptor with a coated pit, and the fraction phi of receptors aggregated in coated pits. We show that for the parameters that characterize coated pits on human fibroblasts, the way in which coated pits return to the surface has a negligible effect on the values of tau, k+, and phi for mobile receptors, D greater than or equal to 1.0 X 10(-11) cm2/s, but has a substantial effect for "immobile" receptors, D much less than 1 X 10(-11) cm2/s. We present numerical examples to show that it may be possible to distinguish between these models if one can monitor slowly diffusing receptors (D less than 1 X 10(-11) cm2/s) on cells whose coated pits have relatively short lifetimes (less than or equal to 1 min). Finally, we show that for the low-density lipoprotein (LDL) receptor on human fibroblasts (D = 4.5 X 10(-11) cm2/s), the predicted and observed values of K+ and phi are in close agreement. Therefore, even for slowly diffusing LDL receptor, unaided diffusion as the transport mechanism of receptors to coated pits is consistent with measured rates of LDL internalization.     

Spurious cell surface receptors: inadequate correction for saturable, nonspecific binding mimics receptor binding

Methods commonly used for the characterization of receptors on cell surfaces may be subject to adsorption artifacts that mimic the action of receptors even when no receptors are present. Traditional techniques such as incubation in the presence of an unrelated protein to minimize adsorption or extensive washing to eliminate nonspecific binding may be inadequate to ensure that the observed binding is due to a cell membrane--ligand interaction. In this paper three serum proteins, albumin, transferrin, and immunoglobulin G, are shown to exhibit behavior suggestive of receptor-mediated binding even in the absence of cells. Two types of control studies are suggested to establish that observed binding is attributable to interaction with cells.     

Time dependent rate of diffusion-influenced ligand binding to receptors on cell surfaces.

The theory of the kinetics of binding of ligands to a sphere partially covered by receptors is extended to provide the full time dependence of the reactive flux. The ligands diffuse to the receptors; the receptors are either fully or partially absorbing. The total flux into the sphere with many receptors is expressed analytically in terms of the flux into a single isolated receptor on the sphere. At steady state, the Berg-Purcell formula is generalized to the case where the binding to a single receptor is only partially diffusion controlled. At short times, the receptors behave independently and the total flux is the sum of the fluxes to the isolated receptors.     

Aggregation of cell surface receptors by multivalent ligands

Using a combination of branching processes and kinetic equations a solution is provided to the problem of describing the size of aggregates formed on cell surfaces when multivalent ligands bind and cross-link multivalent receptors. A criterion is given for the onset of gelation in infinite 2-dimensional systems, which may be relevant to the phenomenon of ligand-induced receptor patching.     

A new method for measuring binding of labeled ligands to membrane receptors.

Two different automated procedures for protein microdetermination by the Lowry method have been devised to analyze samples with high and low concentrations of nonionic detergents. Autoanalytical monitoring of the protein concentration of column effluents has been achieved by substituting 50 mm Tricine for 50 mm Tris in an eluting buffer containing 0.05% Poly-Tergent.     

A statistical theory for flow cytometry profiles in terms of the binding of ligands to cell surface receptors and changes in gene expression

Flow cytometry analysis is a technique used for obtaining light scattering and fluorescence intensity data in order to characterise a chosen cell line. From a sample of the data obtained, it is desired to infer the distribution of cell size, cell granularity and occupancy of cell surface receptors, by constructing histograms for the variables of interest. Often an attempt is made, for instance, to account for the changes in shape of these histograms in terms of alterations in gene expression, etc. In this paper we analyse the way that changes in the sample histograms can be interpreted in three frequently encountered situations, namely (a) when there is one cell line exposed to alterations in chemical potential of ligand, (b) when there are two cell lines exposed separately to saturating concentrations of the same ligand, and (c) when two ligands are added in saturating amounts, first separately, then together, to the same cell line. We demonstrate that, under a wide range of assumptions, the change in histogram shape can be accounted for in terms of a proportionate and absolute component and examples are given to illustrate this. Finally, a computer program to analyse experimental data in terms of estimated shift and stretch parameters is described.     

Equilibrium theory for the clustering of bivalent cell surface receptors by trivalent ligands. Application to histamine release from basophils.

For certain cell types, the cross-linking of bivalent cell surface receptors by multivalent ligands is an important biochemical step in the transmission of information across the cell's membrane to its interior. The formation of cell surface receptor-ligand aggregates has been shown to "turn on" and "turn off" particular cell responses. It has been hypothesized that very large aggregates generate signals that small aggregates cannot. This hypothesis has not been rigorously tested as yet, in part because of a lack of quantitative information about aggregate sizes. Here we develop a general equilibrium theory for the clustering of bivalent receptors by trivalent ligands. In addition to predicting the concentrations of receptor-ligand aggregates of all possible sizes, we show that a range of ligand concentrations exists at which extremely large aggregates, i.e., superaggregates, form on the cell surface. The formation of a superaggregate corresponds to a sol-gel phase transition, and we study this transition in some detail. For the biologically interesting case of histamine release by basophils, we show, using realistic parameter values, that such transitions should occur when the cells are from highly allergic individuals. We prescribe in detail experimental conditions under which such transitions should occur. These conditions can be used as a guide to test whether or not large aggregates provide signals to cells that small aggregates do not.     

The effect of diffusion on the binding of membrane-bound receptors to coated pits.

We have formulated a kinetic model for the primary steps that occur at the cell membrane during receptor-mediated endocytosis. This model includes the diffusion of receptor molecules, the binding of receptors to coated pits, the loss of coated pits by invagination, and random reinsertion of receptors and coated pits. Using the mechanistic statistical theory of nonequilibrium thermodynamics, we employ this mechanism to calculate the two-dimensional radial distribution of receptors around coated pits at steady state. From this we obtain an equation that describes the effect of receptor diffusion on the rate of binding to coated pits. Our equation does not assume that ligand binding is instantaneous and can be used to assess the effect of diffusion on the binding rate. Using experimental data for low density lipoprotein receptors on fibroblast cells, we conclude that the effect of diffusion on the binding of these receptors to coated pits is no more than 84% diffusion controlled. This corresponds to a dissociation rate constant for receptors on coated pits (k-) that is much less than the rate constant for invagination of the pits (lambda = 3.3 X 10(-3)/s) and a correlation length for the radial distribution function of six times the radius of a coated pit. Although the existing experimental data are compatible with any value of k-, we obtain a lower bound for the value of the binding constant (k+) of 2.3 X 10(-2)(micron)2/s. Comparison of the predicted radial distributions with experiment should provide a clear indication of the effect of diffusion on k+.     

Heterogeneities in EGF receptor density at the cell surface can lead to concave up scatchard plot of EGF binding

The mechanism responsible for the concave up nature of the Scatchard plot of epidermal growth factor (EGF) binding on EGF receptor (EGFR) has been a controversial issue for more than a decade. Past efforts to mechanistically simulate the concave up nature of the Scatchard plot of EGF binding have shown that negative cooperativity in EGF binding on an EGFR dimer or inclusion of some external site or binding event can describe this behavior. However, herein we show that heterogeneity in the density of EGFR due to localization in certain regions of the plasma membrane, which has been experimentally reported, can also lead to concave up shape of the Scatchard plot of the EGF binding on EGFR.     

The amino-terminal region of toll-like receptor 4 is essential for binding to MD-2 and receptor translocation to the cell surface

Toll-like receptor 4 (TLR4) and MD-2 are pivotal components that elicit inflammatory responses to lipopolysaccharide (LPS). They have been shown to form a physical complex on the cell surface that responds directly to LPS. However, the functional region of TLR4 required for association with MD-2 and LPS responsiveness is poorly understood. To identify the region of TLR4, we created a series of mutants with deletions in the extracellular domain and examined their activities in human embryonic kidney 293 cells. A mutant with a 317-amino acid deletion from the membrane proximal region of TLR4 was capable of associating with MD-2, while only a 9-amino acid truncation of the N terminus severely impaired the interaction. The association between the two molecules was well correlated with TLR4 maturation into an endoglycosidase H-resistant form and the cell surface expression. Mouse MD-2 bound to human TLR4, but its activity to facilitate the cell surface expression of TLR4 and confer LPS responsiveness was much weaker than that of human MD-2, indicating species specificity. A chimeric receptor composed of the N-terminal region of human TLR4 and the adjacent region of mouse TLR4 showed preference for human MD-2 in its transport to the cell surface and responsiveness to LPS. Taken together, the N-terminal region of TLR4 is essential for association with MD-2, which is required for the cell surface expression and hence the responsiveness to LPS.     

Determination of an antibody-antigen binding constant by enzyme immunoassay and a theory for analysis of competitive binding of two ligands to heterogeneous receptor

A method for determining antigen-antibody binding constants by using enzyme-labeled antigens has been developed. In the measurement, enzyme-labeled and unlabeled antigens (Ag* and Ag) were allowed to compete in binding to the antibody (Ab) under conditions where Ag* much less than Ab much less than Ag. The data were analyzed according to a new theory developed for the analysis of competitive binding of two ligands to a heterogeneous receptor. The theory indicates that the binding degree of a labeled ligand measured at various concentrations of the receptor can be used to prepare a standard curve relating the binding degree of the labeled ligand and the average of the concentrations of the free receptor components which are in binding equilibrium with another unlabeled ligand. For homogeneous receptors, the method gives usual binding constants for the unlabeled ligand, but for heterogeneous receptors, it gives a new type of average binding constant for the unlabeled ligand in which the contribution of each receptor component is amplified in proportion to its affinity against the labeled ligand. This average binding constant was named the "affinity-average binding constant." A rabbit anti-blasticidin S (BLS) antiserum analyzed by the present method using beta-galactosidase-labeled BLS as the labeled ligand was found to be fairly homogeneous with respect to the affinity and to have a binding constant of 1.48 +/- 0.24 (S.D.) X 10(8) M-1 for unlabeled BLS.     

A filter assay for binding of labeled ligands to membrane-bound receptors

A filter assay was developed for the specific binding of labeled ligands to the acetylcholine receptor in an unpurified suspension of membrane fragments from Torpedo californica. Binding to the filter membrane and the standard deviation of replicates were studied, and it was possible to reduce relative standard deviation to about 3% by accounting for the variable weight of the particles dispensed, stopping the loss of particles to the filter apparatus, regulating the transmembrane pressure during filtration, controlling the time the filter remains subject to suction after all the liquid has passed through the filter, and correcting for variable counting efficiency. A method for dispensing equal aliquots of suspended particulates is also described.     

Cell density regulates the number of cell surface receptors for fibroblast growth factor

Previous studies have shown that the binding of fibroblast growth factor to several different non-transformed cell lines decreases as cell density increases. However, it was not determined whether this is due to a reduction in receptor number or to a decrease in receptor affinity. In this study, we demonstrate that the reduction in fibroblast growth factor binding is due to a reduction in receptor number. In addition, flow cytometric analysis indicated little or no difference in the cell cycle distribution of the cells at low and high cell densities, yet the binding of fibroblast growth factor was reduced substantially at high cell densities. Thus, the reduction in growth factor binding observed in this study does not appear to result from cell cycle-dependent regulation of growth factor receptors.     

Interaction of high density lipoprotein with its receptor on cultured fibroblasts and macrophages. Evidence for reversible binding at the cell surface without internalization

Cultured extrahepatic cells possess a specific high affinity receptor for high density lipoprotein (HDL) that is induced by cholesterol delivery to cells. Current results suggest that HDL receptors on cultured human fibroblasts and mouse peritoneal macrophages promote reversible binding of HDL to the cell surface without internalization of lipoprotein particles. When 125I-HDL3 was bound to cultured cells at 0 degrees C and then warmed to 37 degrees C after removal of unbound lipoprotein, most of the cell surface-bound HDL was released rapidly (t1/2 = 3 min) into the medium without entering a cellular pool that was inaccessible to digestion by trypsin at 0 degrees C. This lack of internalization of HDL was evident under conditions where internalization of 125I-low density lipoprotein and 125I-transferrin were readily detected. When cells were exposed to 125I-HDL3 at 37 degrees C, only a trace amount of iodinated apoprotein remained associated with cells after treatment of cells with trypsin. Fibroblasts treated with medium containing increasing concentrations of cholesterol exhibited a dose-dependent increase in reversible, trypsin-sensitive binding of 125I-HDL3 at 37 degrees C without an attendant increase in trypsin-resistant binding. These results suggest that reversible binding of HDL to its cell-surface receptor without subsequent endocytosis of receptor-HDL complexes is the mechanism by which HDL receptors facilitate cholesterol transport from cells.