Theoretical Analysis of the Parr Antibody Assay with a Computer Model: Importance of Antigen Concentration and Antibody Affinity

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Abstract
The Farr assay for antibody was analyzed theoretically in order to determine the maximum sensitivity of the assay, the quantitative relationship between actual antibody concentration and antibody estimates by the Farr technique, and the relationship between antibody affinity and the Farr avidity index. Analysis shows that sensitivity is limited by the antigen concentration when large amounts of antigen are used in the assay. Sensitivity at low antigen concentrations is maximal and varies with the affinity of the antibody studied. Antibody titers obtained by the Farr technique using low antigen concentrations vary with antibody affinity as well as antibody concentration. Titers measured at high antigen concentration are less affected by affinity and correlate better with antibody concentration. Antibody measurements expressed as Antigen Binding Capacity reflect antibody concentration only when the antigen concentration used in the assay exceeds a value equal to ten times the reciprocal of the antibody affinity constant. The Farr avidity index correlates with antibody affinity over a narrow affinity range. Different ranges of affinity can be examined by changing the antigen concentrations.