Mimicking the Strategy of the Immune System: Insight Gained from Mathematics

  • Z. Agur
  • G. Mazor
  • I. Meilijson
Conference paper
Part of the NATO ASI Series book series (volume 66)


The humoral immune response to antigenic challenge involves a Darwinian process of somatic mutations and selection for B-cells carrying higher affinity antibodies. Insufficient knowledge about this process may hamper the use genetically engineered antibodies for vaccination. The aim of the present work is to circumvent some of the experimental difficulties in the study of affinity maturation by investigating this system mathematically. Using dynamic programming methods we look for mutation rate as a function of clone size, which maximizes the probability that the required antibody structure is generated before the pathogen kills the host. We show analytically that the globally optimal strategy for a fast production of high affinity antibodies is to utilize a step-function mutation rate, i.e., a minimal mutation rate in early stages of the immune response, followed by the maximal possible rate when the proliferating B-cells population size exceeds a given threshold. Based on the methodology we have followed it may be concluded that the good performance of this simple, thrifty, two-stage strategy cannot be improved by evolutionary development of a more complex control of the response. Laboratory experiments are suggested for testing the validity of our theoretical results.


Mutation Rate Antigenic Challenge Affinity Maturation Dynamic Programming Method Clone Size 
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  1. 1.
    Agur Z, Mazor G, Meilijson I (1991) Maturation of the humoral immune response as an optimization problem. Proc R Soc London B 245: 147–150CrossRefGoogle Scholar
  2. 2.
    Berek C, Milstein C (1987) Activation of memory and virgin B cell clones in hyperimmune animals. Immunol Rev 96: 23–41PubMedCrossRefGoogle Scholar
  3. 3.
    Berek C, Griffiths GM, Milstein C (1985) Molecular events during maturation of the immune response to oxazolone. Nature 316: 412–418PubMedCrossRefGoogle Scholar
  4. 4.
    Blackwell D (1965) Discounted dynamic programming. Annals of Math Statistics 36: 226–235CrossRefGoogle Scholar
  5. 5.
    French DL, Laskov R, ScharfF MD (1989) The role of somatic hypermutation in the generation of antibody diversity. Science 244: 1152–1157PubMedCrossRefGoogle Scholar
  6. 6.
    Griffiths GM, Berek C, Kaartinen M, Milstein C (1984) Somatic mutation and the maturation of the immune response to 2-phenyl-oxazolone. Nature 312: 271–275PubMedCrossRefGoogle Scholar
  7. 7.
    Maclennan ICM, Gray D (1986) Antigen driven selection of virgin and memory B-cells. Immunol Rev 91: 271–275 (1986)Google Scholar
  8. 8.
    Manser T (1990) The efficiency of antibody affinity maturation: can the rate of B-cell division be limiting? Immunol Today 11: 305–307PubMedCrossRefGoogle Scholar
  9. 9.
    Manser T (1991) Reply. Immunol Today 12: 93–94CrossRefGoogle Scholar
  10. 10.
    Milstein C (1991) Affinity maturation of antibodies. Immunol Today 12: 93PubMedCrossRefGoogle Scholar
  11. 11.
    Rajewsky K, Forster I, Cumano A (1987) Evolutionary and somatic selection of the antibody repertoire in the mouse. Science 238: 1088–1094PubMedCrossRefGoogle Scholar
  12. 12.
    Winter G, Milstein C (1991) Man-made antibodies. Nature 349: 293–299PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Z. Agur
    • 1
  • G. Mazor
    • 1
    • 2
  • I. Meilijson
    • 1
    • 2
  1. 1.Department of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityIsrael

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