Mathematical modeling of lymphocytes selection in the germinal center
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- 作者：Vuk Milisic ; Gilles Wainrib
- 关键词：Division ; mutation ; selection ; Germinal center ; Somatic hypermutation ; Affinity maturation ; Adaptive immunity ; Parabolic partial differential equation ; Population dynamics
- 刊名：Journal of Mathematical Biology
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：74
- 期：4
- 页码：933-979
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematical and Computational Biology; Applications of Mathematics;
- 出版者：Springer Berlin Heidelberg
- ISSN：1432-1416
- 卷排序：74
文摘
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.