Analytical physics framework for competitive binding and transport in lateral flow assays: Application to fentanyl detection

Competitive lateral flow assays (cLFAs) have been widely used for decades, yet improvements in sensitivity remain largely empirical. A general physics-based model that predicts assay performance has been missing. We address this gap by developing an analytical framework derived from first principles of transport, competitive binding, and electrostatic interactions. The model provides closed-form expressions for the limit of detection (LOD), identifies the physical parameters that constrain sensitivity, and quantitatively links nanoparticle concentration, antibody loading, and electrostatic exclusion to the measured signal. To demonstrate generality and practical utility, we apply the model to fentanyl detection using gold nanoparticle reporters. Guided by the framework, we reduced antibody loading and minimized non-participating analyte effects, achieving a ∼100-fold improvement in sensitivity over commercial fentanyl tests (LOD ≈ 7 pg ml−1). This analytically tractable formulation offers a basis for predictive performance benchmarking and rational optimization of competitive LFAs and related point-of-care assays.