Douglass, E. F.; Bastian, W.; Mochel, J. P.

Multivalent ligand-receptor interactions underlie most forms of cell-cell communication, yet a general quantitative framework for "avidity" has remained elusive for over a century. Here, we derive closed-form expressions for signaling potency (EC50) in multivalent systems directly from first principles, extending exact analytical models of ternary complex equilibria to account for receptor confinement at cell surfaces. These equations unify antibody-antigen and cytokine-receptor interactions under a common mathematical framework in which potency emerges as a function of binding constants and receptor density. In contrast to monovalent models, EC50 is no longer equal to the dissociation constant (Kd), but instead reflects receptor-dependent avidity effects that vary across cellular contexts. We validate these predictions across biophysical measurements, in vitro binding and signaling assays, in vivo murine cytokine perturbation data, and human spatial transcriptomic datasets. The framework explains longstanding empirical observations, including enhanced antibody potency through avidity and asymmetric control of cytokine signaling by receptor subunits. By embedding these equations within a regression-compatible formulation, we enable inference of signaling drivers from single-cell and spatial transcriptomic data. This work establishes a mechanistic bridge between molecular binding, receptor context, and tissue-level signaling, providing a quantitative foundation for interpreting and modeling intercellular communication in health and disease.