A mathematical approach to the analysis of diversity in antibody gene families

In this article, we develop a mathematical approach for the analysis of diversity in antibody gene families. This approach is arrived at by examing two general questions about protein populations: (1) What is a relative measure of the diversity exhibited by one protein family when compared with a second? (2) What is the probability that two protein populations were derived from a single common population? These quantitative approaches permit a variety of precise evolutionary, genetic, and developmental questions to be asked of antibody gene families. Using this methodology, we demonstrate that the diversity in mouse K-immunoglobulin chains is considerably greater than in their human K counterparts. We also show that the variable (Vl) regions of light chains associated with IgG and IgA immunoglobulins in the mouse appear to have been derived from a common population of Vl genes. This approach also can be used to analyse sequence data from other informational multigene families.