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Mathematical foundations of antibody affinity maturation

Abstract : The adaptive immune system is able to produce a specific response against almost any pathogen that could penetrate our organism and inflict diseases. This task is assured by the production of antigen-specific antibodies secreted by B-cells. The agents which causes this reaction are called antigens: during an immune response B-cells are submitted to a learning process in order to improve their ability to recognize the immunizing antigen. This process is called antibody affinity maturation. We set a highly flexible mathematical environment in which we define and study simplified mathematical evolutionary models inspired by antibody affinity maturation. We identify the fundamental building blocks of this extremely efficient and rapid evolutionary mechanism: mutation, division and selection. Starting by a rigorous analysis of the mutational mechanism in Chapter 2, we proceed by successively enriching the model by adding and analyzing the division process in Chapter 3 and affinity-dependent selection pressures in Chapter 4. Our aim is not to build a very detailed and comprehensive mathematical model of antibody affinity maturation, but rather to investigate interactions between mutation, division and selection in a simplified theoretical context. We want to understand how the different biological parameters affect the system’s functionality, as well as estimate the typical time-scales of the exploration of the state-space of B-cell traits. Beyond the biological motivations of antibody affinity maturation modeling, the analysis of this learning process leads us to build a mathematical model which could be relevant to model other evolutionary systems, but also gossip or virus propagation. Our method is based on the complementarity between probabilistic tools and numerical simulations.
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Submitted on : Thursday, June 27, 2019 - 1:59:14 PM
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  • HAL Id : tel-02167077, version 1


Irène Balelli. Mathematical foundations of antibody affinity maturation. General Mathematics [math.GM]. Université Sorbonne Paris Cité, 2016. English. ⟨NNT : 2016USPCD091⟩. ⟨tel-02167077⟩



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