Mathematical foundations of antibody affinity maturation

PhD Thesis manuscript. Supervisors: Milišić, V., Wainrib, G., Zaag, H. Antibody affinity maturation is a key process in adaptive immunity : it is a mechanism which allows B-cells to produce high affinity antibodies against a specific antigen. We developed and studied a mathematical framework which allows to pattern the learning process to whom B-lymphocytes are submitted during an immune response. In particular, we model antibody traits as N-length binary strings. Antibody-antigen affinity is naturally characterized using the Hamming distance: therefore the N-dimensional hypercube vertex set defines the affinity landscape of B-cell traits. Our aim is to propose and analyze a mathematical model of the division-mutation-selection process of B-cells during an immune response. Besides the biological motivations, the analysis of this learning process brought 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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Recommended citation: Balelli, I. (2016). Mathematical foundations of antibody affinity maturation (Doctoral dissertation, Université Sorbonne Paris Cité).