Theoretical studies of clonal selection: minimal antibody repertoire size and reliability of self-non-self discrimination.

Viewing the immune system as a molecular recognition device designed to identify “foreign shapes”, we estimate the probability that an immune system with N_Ab monospecific antibodies in its repertoire can recognize a random foreign antigen. Furthermore, we estimate the improvement in recognition if antibodies are multispecific rather than monospecific. From our probabilistic model we conclude: (1) clonal selection is feasible, i.e. with a finite number of antibodies an animal can recognize an effectively infinite number of antigens; (2) there should not be great differences in the specificities of antibody molecules among different species; (3) the region of a foreign molecule recognized by an antibody must be severely limited in extent; (4) the probability of recognizing a foreign molecule, P, increases with the antibody repertoire size N_Ab; however, below a certain value of N_Ab the immune system would be very ineffectual, while beyond some high value of N_Ab further increases in N_Ab yield diminishing small increases in P; (5) multispecificity is equivalent to a modest increase (probably less than 10) in the antibody repertoire size N_Ab, but this increase can substantially improve the probability of an immune system recognizing a foreign molecule.Besides recognizing foreign molecules, the immune system must distinguish them from self molecules. Using the mathematical theory of reliability we argue that multisite recognition is a more reliable method of distinguishing between molecules than single site recognition. This may have been an important evolutionary consideration in the selection of weak non-covalent interactions as the basis of antigen-antibody bonds.