Bivalency in the Immune System

IgG and IgE antibodies, prime components of the immune system, are bivalent proteins containing two identical receptors (Fab sites; Fig. 2.12) [21]. When binding bivalently to a surface (Fig. 2.12a) or to a soluble bivalent ligand (Fig. 2.12b), we postulate that the enhancement (P) for a given antibody is inversely proportional to the monovalent dissociation constant (K|fflnlty) and directly proportional to the effective concentration (Ceff) of ligand near an available receptor (Fig. 2.12). If we assume Ceff to be constant for all antibodies (that is, that they have the same average distance between Fab sites), then greater enhancements will result from higher affinity (lower K|fEnity) ligands. At cell surfaces, the enhancement for the binding of a polyclonal mixture of IgG with high monovalent affinity (average K|ffinity ~ 1 nM) to the surface of Bacillus sp. was ~100 [143]. Cremer and co-workers examined the binding of a polyclonal mixture of IgG to phospholipid mem-

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Binding of bivalent antibodies (IgG or IgE) to bivalent ligands and surfaces. (a) The stepwise equilibria characterizing binding of an antibody bivalently to a surface displaying li-gands are shown. The dissociation constant for the second step (Kdintra) is taken to be the theoretical value assuming no cooperativity between Fab sites (Fig. 2.6). (b) Two different pathways are available to antibodies binding to bivalent ligands in solution depending on the length of the linker in the bivalent ligand [100, 145]. The dissociation constants for the top pathway (intramolecular ring closure) are analogous to those in (a). The enhancement

Binding of bivalent antibodies (IgG or IgE) to bivalent ligands and surfaces. (a) The stepwise equilibria characterizing binding of an antibody bivalently to a surface displaying li-gands are shown. The dissociation constant for the second step (Kdintra) is taken to be the theoretical value assuming no cooperativity between Fab sites (Fig. 2.6). (b) Two different pathways are available to antibodies binding to bivalent ligands in solution depending on the length of the linker in the bivalent ligand [100, 145]. The dissociation constants for the top pathway (intramolecular ring closure) are analogous to those in (a). The enhancement

(p) applies to both (a) and the top pathway in (b). (c) IgE bound to mast cells by their Fc regions can bind to bivalent ligands in two different pathways analogous to those in (b), again depending on the length of the linker in the bivalent ligand [102, 146]. These two pathways have different effects on degranulation of the mast cells: bivalent ligands with long linkers form "cyclic monomers" and inhibit degranulation, while bivalent ligands with short linkers cross-link the surface-bound IgEs and induce degranulation. The two IgEs are shaded differently to aid visualization of the aggregate.

branes containing ligand lipids; an enhancement of ~40 was observed for the weak-affinity system studied (KdiEnity~ 50 p.M) [144].

Pecht, Licht, and co-workers used bivalent ligands with long, rigid poly(proline) linkers to examine the formation of soluble IgE "closed monomers": both receptor sites of the antibody were bound to the same bivalent ligand (Fig. 2.12b, top pathway) [100]. They measured enhancements of roughly the same order of magnitude (ß ~20) for medium-affinity ligands (K|fEnity ~ 0.1 p.M) containing sufficiently long linkers to bridge both Fab sites as for the cell-surface results. The relatively low enhancements observed in these studies indicate low values of Ceff of a ligand in proximity to an available (unbound) Fab site of the antibody. Consistent with this low value of Ceff, crystal structures revealed that the two receptors on an antibody are ~8 nm apart and are flexibly coupled to one another [147-149]. We expect this large distance and flexible coupling to increase the entropic cost of association (Section 2.4.5).

A number of investigators showed that bivalent ligands too short to form "closed monomers" can form discrete cyclic antibody aggregates (e.g., cyclic dimers where two antibodies are bridged by two bivalent ligands; Fig. 2.12b, bottom pathway) [104, 150-156]. In solution, these aggregates were shown to be stable on relatively long time-scales (for analysis by HPLC and ultracentrifuga-tion) [104, 155-157].

Holowka and Baird discussed the importance of aggregation of IgE (that are bound to mast cells by their Fc region) on the release of histamine, a process referred to as degranulation (Fig. 2.12 c) [158]. Degranulation of mast cells can be either inhibited or promoted by the binding of oligovalent ligands to IgE bound to mast cells: long oligovalent ligands that can form "closed monomers" (i.e., span both Fab sites of an IgE; bind intramolecularly to one IgE) can inhibit degranulation (Figure 2.12c, top pathway), while short oligovalent ligands that aggregate IgEs intermolecularly result in degranulation (Fig. 2.12 c, bottom pathway). Baird and co-workers reported the inhibition of degranulation of mast cells by bivalent ligands containing long oligo(ethylene glycol) linkers (> 9 units) [146] and long DNA linkers (30-mer; bivalent ligands with shorter DNA linkers promoted degranulation) [102], and by large ligand-displaying dendrimers (smaller dendrimers promoted degranulation) [146]. They observed enhancements (ß) of up to 100. Ligands that inhibit the degranulation of mast cells could be useful in the treatment ofallergies.

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