Mathematical analysis of emicizumab: affinity-driven complex formation and lipid-surface reactions

Background: Emicizumab is a bispecific antibody that binds activated factor (F)IXa with 1-arm and FX with the other. Binding bridges FIXa and FX, replacing the function of FVIII in hemophilia A. Unlike FVIII, emicizumab does not bind directly to lipid surfaces. Objectives: This study aimed to investigate emicizumab’s lipid-surface dependent mechanisms through mathematical modeling and biochemical assays. Methods: We expanded our mathematical model of tissue factor (TF):VIIa activation of FX to incorporate emicizumab and FIXa interactions. We calibrated our model using experimental data. Results: High concentrations of emicizumab inhibit FX activation by TF:VIIa. Our mathematical model explains these observations only when FX bound to emicizumab is partially restricted from binding to lipid surfaces and to TF:VIIa. Lipid enhances FX activation of FIXa in the presence of emicizumab. In our 2-arm interaction model, we estimated kinetic rates for emicizumab-dependent activation of FX on the lipid surface. The model successfully predicted FIXa activation of FX with and without emicizumab across many experimental conditions. Ternary complexes (FIXa, FX, and emicizumab) in solution decreased when lipid increased while ternary complexes on lipid increased. Sensitivity analysis, which varied lipid, dissociation constants, and catalytic rates, highlighted the impact of binding-arm affinity on reaction velocities. Conclusion: High concentrations of emicizumab decrease TF:VIIa activation of FX by reducing FX binding to both the lipid surface and TF:VIIa. Emicizumab enhances FIXa activation of FX on the lipid surface by preferentially binding to lipid-bound FX and subsequently to lipid-bound FIXa with an enhanced association rate due to colocalization on the lipid surface.