## Abstract

Lymphocyte receptor response to antigen is degenerate. Each receptor can have a high affinity to more than one antigen. The optimal level of degeneracy was previously modeled using different methods; all showing that the degeneracy level should be inversely proportional to the probability that an antigen belongs to the self repertoire. Here we develop a new formalism, reproducing the results of previous models, which enables us to study the relation between receptor degeneracy and the pathogen-immune cell interaction dynamics, in primary and secondary response. We begin by developing a general formalism and reproducing the results obtained by Nemazee: (1) that an optimal immune system will have a capacity which is inversely proportional to the fraction of self-antigens and (2) that the number of self-reactive cells that the body destroys is tuned by this capacity optimization to be 63%. We then use our extended framework to relate the minimal number of B cell precursor required to mount an immune response to the naive B cell production rate. Finally, we analyze the dynamics of the interaction between the immune system and a pathogen and show that memory cells may be used as the first line of defense, while newly created cells are used later to refine the immune response.

Original language | English |
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Pages (from-to) | 535-545 |

Number of pages | 11 |

Journal | Bulletin of Mathematical Biology |

Volume | 65 |

Issue number | 3 |

DOIs | |

State | Published - May 2003 |

### Bibliographical note

Funding Information:The work of YL was partially covered by a grant from the PMMB Burrough Welcome Foundation.

### Funding

The work of YL was partially covered by a grant from the PMMB Burrough Welcome Foundation.

Funders | Funder number |
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PMMB Burrough Welcome Foundation |