A mathematical description of nonself for biallelic genetic systems in pregnancy, transfusion, and transplantation

A central issue in immunology is the immunological response against nonself. The prerequisite for a specific immunological response is the exposure to the immune system of a nonself antigen. Mathematical equations are presented, which define the fraction of all outcomes with a nonself allele in biallelic systems at the population level in pregnancy and transfusion/transplantation medicine. When designing assays, the mathematical descriptions can be used for estimating the number of genetic markers necessary to obtain a predetermined probability level in detecting nonself alleles of a given frequency. For instance, the equations can be helpful in the design of assays, where the nonself allele can be detected by analysis of cfDNA in plasma from pregnant women, to estimate fetal fraction or to monitor changes in cfDNA in plasma of transplantation patients. The equations give exact, quantitative descriptions of all nonself situations in pregnancy and transfusion/transplantation.