Mathematical Analysis of Kinetics of Radioligand Assays: Improved Sensitivity Obtained by Delayed Addition of Labeled Ligand

ABSTRACT A theoretical analysis of the transient state (kinetics) of radioligand assay systems leads to a system of 5 first order, nonlinear differential equations and 3 equations for conservation of mass. Numerical solution to these equations makes it possible to predict the position of the standard curve for radioimmunoassays (RIA) and radioligand assays (RLA) as a function of time under a variety of boundary conditions. Three special cases have been considered: A) Labeled antigen, unlabeled antigen, and antibody or binding protein are added simultaneously; B) unlabeled antigen and antibody react to equilibrium in a preincubation, and then labeled antigen is added; and C) labeled antigen and antibody react until equilibrium is reached and then unlabeled antigen is added. This kinetic analysis, aided by computer simulation studies, demonstrates that improved sensitivity can be achieved by delayed addition of labeled antigen (Case B, above), providing a theoretical basis for the improved sensitivity of “n...