ART: A Compositional Physical Theory for the End-to-End Design of Solid-Phase Immunosensors

Abstract

Predicting complete solid phase immunoassay performance remains challenging because antibody recognition, reactor transport, molecular transduction and physical observation are coupled rather than independent. Here, we formulate ART as a compositional physical theory expressed as Y = Ts[Tm[AR(X)]]. Recognition A and reactor transport R jointly determine the retained molecular state, while molecular transduction Tm and physical observation Ts operate through replaceable interfaces. Finite-time kinetic and reaction diffusion calculations across plate, tubular and bead formats show that antibodies with identical dissociation constants can produce different capture responses because of distinct association and dissociation rates. In fixed-length tubular reactors, mass-conserving transport distinguishes surface capture density from fractional recovery, revising a first-passage-based local density optimum while preserving a multicriterion design window. An AR-only concentration-threshold map identifies when recognition kinetics or reactor redesign offers greater local leverage. The benefits of improved affinity also depend on the kinetic pathway and reactor regime. For enzymatic transduction, we propose a four-parameter, substrate-conserving model in which the saturation-shape parameter is hm = KM/S0 under a one effective substrate approximation. Accumulated TMB color and time-dependent luminol emission represent distinct consequences of reaction progress, while Ts describes measurement limits through a simplified floor slope roof model. ELISA with OD450 readout and tubular chemiluminescence with camera detection illustrate the end-to-end framework. These examples remain conditional model demonstrations, and existing complete chain curves have not yet been recalibrated using the new enzyme model. ART provides a modular quantitative framework for assay design based on explicit physical interfaces and coupled processes.