1. Immunology and Inflammation
  2. Physics of Living Systems

Quantitative modeling of the effect of antigen dosage on B-cell affinity distributions in maturating germinal centers

  1. Marco Molari
  2. Klaus Eyer
  3. Jean Baudry
  4. Simona Cocco
  5. Rémi Monasson  Is a corresponding author
  1. PSL Research and CNRS, France
  2. ETH, Switzerland
  3. ESPCI, PSL Research and CNRS, France
  4. École Normale Supérieure, France
https://doi.org/10.7554/eLife.55678
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  1. Marco Molari
  2. Klaus Eyer
  3. Jean Baudry
  4. Simona Cocco
  5. Rémi Monasson
(2020)
Quantitative modeling of the effect of antigen dosage on B-cell affinity distributions in maturating germinal centers
eLife 9:e55678.
https://doi.org/10.7554/eLife.55678
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Abstract

Affinity maturation is a complex dynamical process allowing the immune system to generate antibodies capable of recognizing antigens. We introduce a model for the evolution of the distribution of affinities across the antibody population in germinal centers. The model is amenable to detailed mathematical analysis, and gives insight on the mechanisms through which antigen availability controls the rate of maturation and the expansion of the antibody population. It is also capable, upon maximum-likelihood inference of the parameters, to reproduce accurately the distributions of affinities of IgG-secreting cells we measure in mice immunized against Tetanus Toxoid under largely varying conditions (antigen dosage, delay between injections). Both model and experiments show that the average population affinity depends non-monotonically on the antigen dosage. We show that combining quantitative modelling and statistical inference is a concrete way to investigate biological processes underlying affinity maturation (such as selection permissiveness), hardly accessible through measurements.

Data availability

All the data analysed in this work are reported in the supporting excel file attached to the submission. These data come from (1) new experiments reported in the present work, and (2) previously published experiments, see Eyer et al., 2017 (referenced in manuscript). The code containing the implementation of our stochastic and deterministic model is made publicly available in the following repository: https://github.com/mmolari/affinity_maturation. The repository also includes the experimental dataset, the code to run the inference procedure and the code to reproduce the figures of the main paper (Fig. 2 to 6). Please refer to README.md file for further details.

Article and author information

Author details

  1. Marco Molari

    Laboratoire de Physique de l'École Normale Supérieure, PSL Research and CNRS, Paris, France
    Competing interests
    The authors declare that no competing interests exist.

  2. Klaus Eyer

    Laboratory for Functional Immune Repertoire Analysis, Institute of Pharmaceutical Sciences, ETH, Zurich, Switzerland
    Competing interests
    The authors declare that no competing interests exist.

  3. Jean Baudry

    Laboratoire Colloides et Materiaux Divises (LCMD), Chemistry, Biology and Innovation (CBI), ESPCI, PSL Research and CNRS, Paris, France
    Competing interests
    The authors declare that no competing interests exist.

  4. Simona Cocco

    Laboratoire de Physique Statistique, École Normale Supérieure, Paris, France
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1852-7789

  5. Rémi Monasson

    Laboratoire de Physique de l'École Normale Supérieure, PSL Research and CNRS, Paris, France
    For correspondence
    monasson@lpt.ens.fr
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-4459-0204

Funding

H2020 European Research Council (80336)

  • Klaus Eyer

Agence Nationale de la Recherche (CE30-0021-01 RBMPro)

  • Rémi Monasson

Agence Nationale de la Recherche (ANR-10-LABX-31)

  • Jean Baudry

Agence Nationale de la Recherche (ANR- 10-EQPX-34)

  • Jean Baudry

Agence Nationale de la Recherche (ANR-10-IDEX-0001-02 PSL)

  • Jean Baudry
  • Simona Cocco
  • Rémi Monasson

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Ethics

Animal experimentation: Experiments using mice were validated by the CETEA ethics committee number 89 (Institut Pasteur, Paris, France) under #2013-0103, and by the French Ministry of Research under agreement #00513.02.

Copyright

© 2020, Molari et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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