Finite element analysis of biomolecular interactions in the 2-step PEdELISA process. (A) Schematic of the theoretical sphere, namely the “reaction volume,” used for modeling work, whose quantity is equal to the total sample volume divided by the number of beads, assuming that the beads are evenly distributed in the buffer/sample solution. Reagent mass transport and binding kinetics are considered at the surface of a single magnetic bead placed in its center for one-half of the geometry due to symmetry. (B) Step 1: immune-complex formation process involving the conjugation between target antigen molecules, capture antibodies immobilized on the bead surface, and detection antibodies freely floating in the reaction volume. (C) Step 2: avidin-HRP labeling process involving the conjugation of avidin-HRP with the biotinylated detection antibodies. The average number of targets (ie, capture antibody-antigen-detection antibody immune-complexes) formed per bead, λ, is calculated as a function of the step 1 incubation time and the analyte concentration at K_d = 10⁻¹⁰ M (D) and K_d = 10⁻⁹ M (E). The model predicts that the PEdELISA readout linearly increases with the analyte concentration when λ is small (<0.1). By accounting for the experimentally obtained noise floor, the LOD value can be theoretically determined for a given value of the step 1 incubation time. (F) Predicted kinetics of the second step of the PEdELISA process. The fraction of the formation of HRP enzyme-labeled antibody-antigen-antibody immune-complexes is presented for 3 representative HRP concentrations (1 pM, 10 pM, and 100 pM).