Serological interpretation--theoretical limits to information from blocking

Contemporary immunogenetics uses a symbolism that tacitly assumes a one-to-one correspondence between genes, antigens, and antibody reagents that identify these. Thus a particular gene will be symbolized by an identifier, say X, and the reagent that supposedly uniquely identifies X is called anti-X. Ultimately, the precise relation between genes and antibody reagents will be determined by molecular techniques. Previous mathematical work has shown that by allowing a general relation (not constrained by symbolic conventions), alternative genetic descriptions can be found for some systems. This work predicts that when the relation is identified for these systems by molecular means, there will be an unresolved cross-reactivity, that is, there will not be a simple one-to-one correspondence between genes and the reagents used to identify them. This will contradict the notation in which the immunogenetic systems are described. Serology will have to be reinterpreted in terms of a more general notation that will allow for cross-reactivity. The focus of a mathematical model will switch from making inferences about genes, antigens, and antibodies in some system to analyzing genetics and serology as described by the notation. This paper investigates the information theoretically available from the serological operations of blocking, absorption, and elution. We show that, except for antigens (called undetectable) that mimic combinations of other antigens (in all cells in the system), blocking can theoretically reveal the relationship between antigens and antibodies in a system.