Mathematical modeling of lymphocytes selection in the germinal center

TL;DR

This paper presents a simplified mathematical model of lymphocyte selection in germinal centers, analyzing how mutation and selection influence B-cell production using PDEs, with insights into process duration under different parameters.

Contribution

It introduces a novel PDE-based model capturing key mechanisms of lymphocyte mutation and selection in germinal centers, with mathematical and numerical analysis.

Findings

Model effectively describes lymphocyte selection dynamics.

Process duration depends on mutation rate and selection profile.

Mathematical analysis provides insights into biological process efficiency.

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.