Single molecule enzyme-linked immunosorbent assays: theoretical considerations.

We have developed a highly sensitive immunoassay-called digital ELISA-that is based on the detection of single enzyme-linked immunocomplexes on beads that are sealed in arrays of femtoliter wells. Digital ELISA was designed to be highly efficient in the capturing of target proteins, labeling of these proteins, and their detection in single molecule arrays (SiMoA); in essence, the goal of the assay is to "capture every molecule, detect every molecule". Here we provide the theoretical basis for the design of this assay derived from simple equations based on bimolecular interactions. Using these equations and knowledge of the concentrations of reagents, the times of interactions, and the on- and off-rates of the molecular interactions for each step of the assay, it is possible to predict the number of immunocomplexes that are formed and detected by SiMoA. The unique ability of SiMoA to count single immunocomplexes and determine an average number of enzymes per bead (AEB), makes it possible to directly compare the number of molecules detected experimentally to those predicted by theory. These predictions compare favorably to experimental data generated for a digital ELISA for prostate specific antigen (PSA). The digital ELISA process is efficient across a range of antibody affinities (K(D)~10(-11) -10(-9) M), and antibodies with high on-rates (k(on)>10(5) M(-1) s(-1)) are predicted to perform best. The high efficiency of digital ELISA and sensitivity of SiMoA to enzyme label also makes it possible to reduce the concentration of labeling reagent, reduce backgrounds, and increasing the specificity of the approach. Strategies for dealing with the dissociation of antibody complexes over time that can affect the signals in an assay are also described.