A Generalization of the Ternary Binding Model to Membrane‐Confined Systems With Finite Copy Number

Abstract

ABSTRACT The standard Douglass ternary binding model (TBM) for three‐body equilibria assumes a well‐mixed, three‐dimensional solution. When applied to bispecific T‐cell engagers (BiTEs), however, the productive trimeric complex forms not in bulk solution but within a nanoscale membrane synapse with finite receptor copy numbers. We present a generalization of the TBM to membrane‐confined systems that replaces the macroscopic bulk volume with a coarse‐grained reactive contact volume defined by synapse geometry and microvillus topology, and extends the deterministic equilibrium to a stochastic description via the chemical master equation. The framework preserves the original algebra while restoring its representational capacity for the regime in which therapeutic activity occurs. A key finding is that conventional bulk mapping places the system in the affinity‐limited regime, where antigen density is mathematically inert and the TBM predicts identical dose–response regardless of target expression. Membrane confinement shifts effective antigen concentration by six orders of magnitude—from nM to nM—restoring antigen density as a governing variable for trimer formation. Using blinatumomab (anti‐CD19 BiTE) as a case study, we introduce the absolute formation dose : the drug concentration required to produce a fixed number of ternary complexes sufficient for T‐cell activation. This metric replaces the conventional , which normalizes each cell line to its own maximum, erasing the density dependence that confinement rescues. For NALM‐6 and HAL‐01 cell lines (CD19 density ratio ), the framework predicts a corresponding ‐fold difference in required dose—a prediction structurally invisible to the bulk formulation.