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A Mathematical Model Relating Circulating Antibody and Antibody Forming Cells¹

From the Biological and Medical Sciences Division, United States Naval Radiological Defense Laboratory, San Francisco, California

Abstract

A mathematical model is developed which equates numbers of antibody-forming cells to the corresponding circulating antibody. Using data for numbers of Jerne antibody plaque-forming cells in the mouse spleen following sheep erythrocyte sensitization, the model is applied to predict the time course of the circulating immune hemolysin. The calculated antibody concentrations are compared with experimentally determined values. Since no information is available describing average cellular rate of antibody synthesis during the course of an immune response, mathematical expressions for this quantity are selected arbitrarily for use in the model. Closest agreement between model and experiment obtains when cellular synthesis rate increases rapidly during the early phase of the response, but is constant later. Some of the assumptions underlying the model are probably valid only for 19S antibody synthesized in the spleen.

Footnotes

¹ These studies have been supported by funds from the Bureau of Medicine and Surgery, United States Navy Department. The opinions and assertions herein are not to be construed as official or as reflecting the views of the Navy Department.

² Lieutenant, Medical Corps, United States Naval Reserve.