Bulletin of Mathematical Biology

, Volume 81, Issue 3, pp 830–868 | Cite as

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

  • Irene BalelliEmail author
  • Vuk Milišić
  • Gilles Wainrib


We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in germinal centers during an immune response. This is a key process in adaptive immunity leading to the production of high-affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system’s functionality. We identify the existence of an optimal value of the selection rate, able to maximize the number of selected B-cells for a given generation.


Multi-type Galton–Watson process Germinal center reaction Affinity-dependent selection Evolutionary landscapes 

Mathematics Subject Classification

60J85 60J80 92B99 92D15 



This work was supported by the Labex inflamex, ANR Project 10-LABX-0017.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), laboratoire d’excellence InflamexUniversité Paris 13VilletaneuseFrance
  2. 2.Centre INSERM U1219, and INRIA - Statistics in System Biology and Translational Medicine TeamBordeaux UniversityBordeauxFrance
  3. 3.Département d’InformatiqueEcole Normale SupérieureParisFrance
  4. 4.Owkin, Inc.New YorkUSA

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