A Generalization of the Ternary Binding Model to Membrane-Confined Systems with Finite Copy Number
Bispecific T cell engagers and related immunotherapies are dosed using equilibrium binding models derived for well-mixed solution, yet therapeutic activity occurs at nanoscale membrane synapses with finite receptor copy numbers. Here we show that membrane confinement introduces geometry-dependent corrections to the landmark Douglass [6] ternary binding model, shifting formation half-points (TF50) by 2-10-fold at clinically relevant antigen densities. We present two complementary formulations--effective concentration and surface density--that preserve the Douglass framework while explicitly accounting for synapse geometry, surface topology, and the accessibility factor () of surface receptors. We further derive stochastic descriptions of trimer formation via the chemical master equation, demonstrating the recovery of the classical Ternary Binding Model equilibrium in appropriate limits. We illustrate the framework using the CD19-targeting BiTE blinatumomab as a case study. Accounting for microvillus-driven patchy close contact during immune surveillance yields a mechanistic explanation for why higher target antigen density can increase the dose required to achieve a fixed level of ternary formation: in the membrane-confined regime, excess target acts as a local antigen sink that sequesters drug and reduces the free fraction available for productive bridging. Rather than fitting to a single shift value, we emphasize the robust scaling and regime structure predicted by the theory (density-proportional behavior in the sink-dominated limit, and collapse toward affinity-limited behavior outside that limit). The generalized framework provides ready-to-use correction formulas and parameter-estimation guidance, establishing a rigorous foundation for antigen-density-aware dosing strategies in T cell engager pharmacology. Statement of SignificanceBispecific T cell engagers are currently interpreted largely through bulk-solution binding models, but at nanometer-scale immune synapses those models can miss a distinct, decision-relevant regime. We generalize the standard ternary binding model to membrane-confined synapses and relate whole-cell receptor counts to effective concentrations in the contact zone. In a blinatumomab case study, the framework explains a paradoxical observation: increasing target density can shift half-maximal ternary-complex formation to higher doses because abundant antigen acts as a local sink that sequesters drug. These results show when bulk affinity alone is insufficient for potency interpretation and support antigen-density-aware dosing and experiments that distinguish geometric from chemical control.