RAPID: a boundary-aware closed-form model for bead-based immunoassays

Bead-based immunoassays are widely used for quantitative sensing, yet classical kinetic models often diverge from experimental behaviors because boundary conditions and practical constraints during assay setup are not explicitly encoded. Here we present RAPID (Reaction-calibrated and Adapted Predictive Immunoassay Dynamics), a boundary-aware and closed-form predictive model that introduces three empirical scaling factors (α, β, and γ) to reconcile theory with experiment by adjusting the effective antibody–antigen ratio (α), bead geometry and transport scaling (β), and mass-transport-limited kinetic time (γ). Using human IgG (hIgG) as a model antigen, RAPID improved the fit accuracy ( = 0.8572 to $$\:{R}^{2}$$ = 0.9741) while preserving an analytical structure suitable for design-stage prediction without numerical solvers. External validity was examined with independent antigen–antibody systems (cardiac troponin I and myoglobin), where RAPID consistently reduced error and retained the characteristic dose-response shape across concentration ranges. The scaling factors were experimentally calibrated by matching model predictions to measured binding responses across systematically varied assay conditions, yielding physically interpretable constants (α = 3.695, β = 0.945, and γ = 0.052) under the hIgG condition. By compactly representing steric accessibility (α), geometric and transport effects (β), and diffusion-to-capture kinetics (γ), RAPID provides a platform-specific yet antigen-independent analytical framework that bridges mechanistic theory and experimental optimization. We anticipate that this framework will facilitate rapid in silico screening of assay parameters (e.g., antibody loading, bead size, incubation time) and accelerate the rational design of bead-based immunoassays in both research and point-of-care contexts.