Harnessing Avidity: Quantifying Entropic and Energetic Effects of Linker Length and Rigidity Required for Multivalent Binding of Antibodies to HIV-1 Spikes

Abstract

Due to the low density of envelope (Env) spikes on the surface of HIV-1, neutralizing IgG antibodies rarely bind bivalently using both antigen-binding arms (Fabs) to crosslink between spikes (inter-spike crosslinking), instead resorting to weaker monovalent binding that is more sensitive to Env mutations. Synthetic antibodies designed to bivalently bind a single Env trimer (intra-spike crosslinking) were previously shown to exhibit increased neutralization potencies. In initial work, diFabs joined by varying lengths of rigid double-stranded DNA (dsDNA) were considered. Anticipating future experiments to improve synthetic antibodies, we investigate whether linkers with different rigidities could enhance diFab potency by modeling DNA-Fabs containing different combinations of rigid dsDNA and flexible single-stranded DNA (ssDNA) and characterizing their neutralization potential. Model predictions suggest that while a long flexible polymer may be capable of bivalent binding, it exhibits weak neutralization due to the large loss in entropic degrees of freedom when both Fabs are bound. In contrast, the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer, and avidity can be further boosted by incorporating more Fabs into these constructs. These results inform the design of multivalent anti-HIV-1 therapeutics that utilize avidity effects to remain potent against HIV-1 in the face of the rapid mutation of Env spikes. SignificanceIgG antibodies utilize avidity to increase their apparent affinities through simultaneous binding of two antigen-binding Fabsif one Fab dissociates from an antigen, the other Fab can remain attached, allowing rebinding. HIV-1 foils this strategy by having few, and highly-separated, Envelope spike targets for antibodies, forcing most IgGs to bind monovalently. Here we develop a statistical mechanics model of synthetic diFabs joined by DNA linkers of different lengths and flexibilities. This framework enables us to translate the energetic and entropic effects of the linker into the neutralization potency of a diFab. We demonstrate that the avidity of multivalent binding is enhanced by using rigid linkers or including additional Fabs capable of simultaneous binding, providing the means to quantitatively predict the potencies of other antibody designs.

When two are better than one: Modeling the mechanisms of antibody mixtures

“…comparing the IC 50 s of the A/Wisconsin/67/05 and B/Harbin/7/94 strains of the 4-fused domains on an IgG backbone in Fig 5D to the corresponding IC 50 s for the individual antibody domains in Panels A and B). For such constructs, the composition of the linker can heavily influence the ability to multivalently bind and neutralize a virus [11,14], although Laursen et al surprisingly found little variation when they modified the length of their amino acid linker (see Table S11 in Ref [7]). Another curious feature of their system was that placing their linear 4-domain antibody (Fig 5C) on an IgG backbone (Fig 5D ) only resulted in a 2x decrease in IC 50 , suggesting that the two "arms" of the IgG could not simultaneously bind.…”

“…Relative to the unbound HA state, the Ab A1 or Ab A2 portions of the antibody will neutralize the virus with relative probability c IC50,A1 or c IC50,A2 , respectively. Although neutralization is mediated by antibody binding, the two quantities may or may not be proportional [9][10][11], and hence we replace dissociation constants with IC 50 s in our model (see S1 Text Section C).…”

“…another that binds influenza A group 2 strains (Ab A2 ), and two antibodies that bind to 223 influenza B strains (Ab quantities may or may not be proportional [9][10][11], and hence we replace dissociation 240 constants with IC 50 s in our model (see S1 Text Section C). (5)).…”

“…This IC 50 s for the individual antibody domains in Panels A and B). For such constructs, the 358 composition of the linker can heavily influence the ability to multivalently bind and 359 neutralize a virus [11,14], although Laursen et al surprisingly found little variation 360 when they modified the length of their amino acid linker (see Table S11 in Ref [7]).…”