Self-Assembly of Hexameric IgG Immune Complexes

Abstract

Antibody-mediated activation of the complement system depends on the assembly of six immunoglobulin G molecules into a surface-bound hexamer that can ligate the six globular heads of C1q for downstream target cell killing. Experimental studies have shown that antibody valency, target cell surface antigen density, antibody affinity, and hexamer formation strength can all impact hexamer formation. However, a comprehensive picture of the IgG hexamerization regimes is still lacking, as most experiments perturb only one variable at a time. Here, we present a minimal statistical physics model of thermodynamic equilibrium, in which monovalent and bivalent IgG Ab-Ag complexes form on the cell surface and nucleate into hexamers through separate pathways. We probe antibody valency, antibody affinity, antigen density, and hexamer formation strength simultaneously in our model to investigate distinct regimes of hexamer formation. The analytical limits of conserved sum rules and numerical phase diagrams of our model suggest that at moderate antibody affinities, hexamers form at low surface antigen densities through "precursor sampling," where the dominance of free monovalent vs. bivalent complexes is observed. At intermediate density, aggregation kinetics favor bivalent hexamers; however, at saturating density, a "geometric packing limit" may impose a strict ceiling, where monovalent hexamers dominate. Meanwhile, increasing the strength of hexamer formation shifts these transitions to lower antigen densities but does not eliminate the preference for monovalent hexamer formation at high surface antigen densities. The resulting phase diagrams help to reconcile experimental studies on monovalent vs. bivalent hexamer formation and suggest potential design rules to consider for antibody therapeutics that activate complement.