Mathematical modeling of lymphocytes selection in the germinal center
Abstract
Lymphocyte selection is a fundamental operation of adaptive immunity. In order to produce B-lymphocytes with a desired antigenic profile, a process of mutation-selection occurs in the germinal center, which is part of the lymph nodes. We introduce in this article a simplified mathematical model of this process, taking into account the main mechanisms of division, mutation and selection. This model is written as a non-linear, non-local, inhomogeneous second order partial differential equation, for which we develop a mathematical analysis in the case of piecewise-constant coefficients. We assess, mathematically and numerically, 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.
Keywords
Cite
@article{arxiv.1501.06725,
title = {Mathematical modeling of lymphocytes selection in the germinal center},
author = {Vuk Milisic and Gilles Wainrib},
journal= {arXiv preprint arXiv:1501.06725},
year = {2015}
}