Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017 Mar;74(4):933-979.
doi: 10.1007/s00285-016-1038-9. Epub 2016 Aug 11.

Mathematical modeling of lymphocytes selection in the germinal center

Vuk Milisic  1 , Gilles Wainrib  2
Affiliations

Mathematical modeling of lymphocytes selection in the germinal center

Vuk Milisic et al. J Math Biol. 2017 Mar.

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.

Keywords: Adaptive immunity; Affinity maturation; Division-mutation-selection; Germinal center; Parabolic partial differential equation; Population dynamics; Somatic hypermutation.

PubMed Disclaimer

Similar articles

See all similar articles

References

    1. BMC Bioinformatics. 2013;14 Suppl 6:S8 - PubMed
    1. J Theor Biol. 2001 Jun 7;210(3):265-85 - PubMed
    1. Cell. 2014 Oct 23;159(3):700-700.e1 - PubMed
    1. Immunol Rev. 1998 Apr;162:107-16 - PubMed
    1. Curr Opin Immunol. 2002 Apr;14(2):235-40 - PubMed

LinkOut - more resources