Dynamical analysis of a degenerate primary and secondary humoral immune response

Yoram Louzoun, Martin Weigert, Gyan Bhanot

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)535-545
Number of pages11
JournalBulletin of Mathematical Biology
Issue number3
StatePublished - May 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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