An Overview of Computational and Theoretical Immunology

Abstract

In this talk, I will give an overview of the operating principles of the immune system emphasizing its role as a pattern recognizer. The fundamental algorithm that the immune system uses to recognize foreign cells and molecules is called clonal selection. The basic idea is to generate cells each of which has many copies of a unique receptor on its surface. In the case of B lymphocytes, which are the cells in the immune system that secrete antibody, the receptor is a membrane associated form of antibody called surface immunoglobulin (sIg). Each lymphocyte during its development expresses a pseudo random set of genes, which code for its surface Ig. The diversity of Ig genes is such that potentially about 10¹⁰ different sIg molecules could be made. A mouse, for example, only has 10⁸ lymphocytes so that at any given time only a small fraction of its potential repertoire of receptor types can be found in the animal. This is called the expressed repertoire. When a foreign molecule (antigen) is encountered, one hopes the diversity of receptor types is sufficiently large that one or more lymphocytes will recognize the antigen. If this occurs, the lymphocyte will be triggered to proliferate and make copies of itself, as well as to differentiate into cells that secrete high levels of antibody. The antibody they secrete is a soluble form of their sIg. Thus, in essence antigen selects the lymphocytes that can recognize it and causes those cells to expand into a clone, hence the name clonal selection. Given this scenario and assuming a random repertoire of size N such that each receptor has a probability p of recognizing a random antigen, one can easily see that the probability of an antigen not being recognized by any receptor is $(1-p)^N = \exp[N \ln(1-p)]$, which for p≪ 1 is approximately e^{− − pN}, and the probability of recognizing an antigen is 1–e^{− − pN}. Note that if p=1, the immune system would only need one receptor, but since this receptor would also recognize self molecules it would not be useful. Consequently, one must also require that the immune discriminate between self and non-self.