title: Mathematical modeling of lymphocytes selection in the germinal center.
abstract: Lymphocyte selection is a fundamental process of adaptive immunity. In order to produce B-lymphocytes with a target antigenic profile, mutation selection and division occur in the germinal center, a specific part of lymph nodes. We introduce in this article a simplified mathematical model of this phenomenon, taking into account the main mechanisms. This model is written as a non-linear, non-local, inhomogeneous second order partial differential equation, for which we develop a mathematical analysis. We assess, mathematically and numerically, in the case of piecewise-constant coefficients, the performance of the biological function by evaluating the duration of this production process as a function of several parameters such as the mutation rate or the selection profile, in various asymptotic regimes.
authors: Laboratoire Analyse, Géométrie et Applications CNRS UMR 7539, Université Paris 13, 99 av. Jean-Baptiste Clément, 93430, Villetaneuse, France.
authors: Vuk
authors: V
authors: Milisic
authors: Département d'Informatique (DATA), Ecole Normale Supérieure, 45 rue d'Ulm, 75005, Paris, France. gilles.wainrib@ens.fr.
authors: Gilles
authors: G
authors: Wainrib
mesh_terms: D056704:Adaptive Immunity / Q000235:genetics* / Q000276:immunology*; D000818:Animals; D001402:B-Lymphocytes / Q000166:cytology* / Q000276:immunology; D018858:Germinal Center / Q000166:cytology* / Q000276:immunology*; D006801:Humans; D018448:Models, Immunological; D009154:Mutation
keywords: Adaptive immunity; Affinity maturation; Division-mutation-selection; Germinal center; Parabolic partial differential equation; Population dynamics; Somatic hypermutation