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.
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Milisic, V., Wainrib, G. Mathematical modeling of lymphocytes selection in the germinal center. J. Math. Biol. 74, 933–979 (2017). https://doi.org/10.1007/s00285-016-1038-9
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DOI: https://doi.org/10.1007/s00285-016-1038-9
Keywords
- Division-mutation-selection
- Germinal center
- Somatic hypermutation
- Affinity maturation
- Adaptive immunity
- Parabolic partial differential equation
- Population dynamics