A mathematical description of non-self for biallelic genetic systems in pregnancy, transfusion, and transplantation

Abstract

A central issue in immunology is the immunological reaction against non-self. The prerequisite for a specific immunological reaction is the exposure to the immune system of a non-self-antigen. A simple mathematical description of the fraction of a non-self-allele in biallelic systems at the population level in transfusion/transplantation medicine and in pregnancy is presented. Furthermore, when designing assays, the mathematical descriptions may help estimate the number of genetic markers necessary to obtain a predetermined probability level in detecting non-self-alleles of a given frequency. For instance, the described equations can be helpful, in the design of assays where the non-self-allele can be detected by analysis of cfDNA in plasma from pregnant women to estimate fetal fraction or cfDNA and to monitor changes in cfDNA in plasma of transplantation patients. Besides the equations that describe all non-self-situations in pregnancy and transfusion/transplantation, a novel way of estimating immunogenicity related to allele frequency is proposed.