Because rearrangements are made on a combinatorial basis, one may give an estimate of a minimum number of discrete Igs and TCRs that can be generated from this mechanisms. What is the situation on the immune system side? Both Igs and TCRs are generated from mosaic genes that must rearrange before becoming functional. Again, the number would be within somewhat similar ranges, perhaps slightly lower. Because T-cell epitopes are linear peptides, with a variable length, a calculation may also be made of the potential number of different peptides that might be generated. Both values are simply enormous, so the repertoire problem is a major issue. This order of magnitude is reasonably consistent with the 1017 previously given, because we excluded a large part of the living world in the later estimate. One now has to take into account the allelic variants and the number of individual epitopes that can be defined at any protein surface. Taking an average number of 105 genes/species leads to 1011 different protein molecules. The evaluation of the number of such species is somewhat greater than 106. To stick to a minimal value, one may limit oneself to animal species (which already excludes viruses, bacteria, and plants!). Another possible approach would be to start from an estimate of the number of gene products that can be generated by the living world. Calculations have been made, and the number is astronomic, about 10 different structures.
Given this size, one may question how many different chemical organic structures could theoretically fill one antibody combining site. One is based on the average size of the antibody combining site, which may be taken as 600 A2, although large variations do exist from one antibody to another (see Immunoglobulin Structure). Is it possible to give an estimate of the number of potential epitopes that may eventually be encountered by an individual? Several theoretical approaches have been proposed. This is what immunologists call the repertoire problem. Because the immune response is specific, a basic question is to understand what are the structural and genetic bases that allow the immune system to make the necessary huge number of different recognition molecules-that is, immunoglobulins (Igs) and T-cell receptors (TCRs) that are required to interact specifically with all the potential antigens of the living world.