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Multi-type Galton-Watson Processes with Affinity-Dependent Selection Applied to Antibody Affinity Maturation.

Irene Balelli1,2, Vuk Milišić3, Gilles Wainrib4,5

  • 1Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), laboratoire d'excellence Inflamex, Université Paris 13, 93430, Villetaneuse, France. balelli@math.univ-paris13.fr.

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Summary

This study models evolutionary dynamics, finding an optimal selection rate to maximize B-cell production during immune responses. Understanding these parameters is key for adaptive immunity research.

Keywords:
Affinity-dependent selectionEvolutionary landscapesGerminal center reactionMulti-type Galton–Watson process

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Area of Science:

  • Evolutionary biology
  • Immunology
  • Mathematical modeling

Background:

  • Antibody affinity maturation is crucial for adaptive immunity.
  • B-cells in germinal centers undergo selection, mutation, and division.
  • Understanding these processes informs immune response modeling.

Purpose of the Study:

  • To analyze interactions between division, mutation, and selection in a simplified evolutionary model.
  • To model antibody affinity maturation of B-cells.
  • To determine how biological parameters influence system functionality.

Main Methods:

  • Developed a mathematical framework for evolutionary dynamics.
  • Classified populations into distinct fitness levels.
  • Simulated interactions of division, mutation, and selection.

Main Results:

  • Identified an optimal selection rate value.
  • This optimal rate maximizes selected B-cells per generation.
  • Demonstrated parameter-dependent system functionality.

Conclusions:

  • The selection rate critically impacts B-cell population dynamics.
  • Optimal parameter tuning can enhance antibody maturation efficiency.
  • The model provides insights into adaptive immunity mechanisms.