## Abstract

We use statistical mechanical techniques to model the adaptive immune system, represented by lymphocyte networks in which B cells interact with T cells and antigen. We assume that B- and T-clones evolve in different thermal noise environments and on different timescales, and derive stationary distributions and study expansion of B clones for the case where these timescales are adiabatically separated. We compute characteristics of B-clone sizes, such as average concentrations, in parameter regimes where T-clone sizes are modelled as binary variables. This analysis is independent of the network topology, and its results are qualitatively consistent with experimental observations. To obtain the full distributions of B-clone sizes we assume further that the network topologies are random and locally equivalent to trees. This allows us to compete these distributions via the Bethe-Peierls approach. As an example we calculate B-clone distributions for immune models defined on random regular networks.

Original language | English |
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Article number | 035602 |

Journal | Journal Of Physics A-Mathematical And Theoretical |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 21 Dec 2016 |

## Keywords

- adaptive immune system
- lymphocyte network
- statistical physics