Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation

TL;DR

This paper models antibody affinity maturation using a multi-type Galton-Watson process, revealing how biological parameters influence immune response efficiency and identifying an optimal selection rate for B-cell proliferation.

Contribution

It introduces a novel mathematical framework for modeling affinity-dependent selection in antibody maturation, linking stochastic processes with immune system dynamics.

Findings

Existence of an optimal selection rate maximizing B-cell count.

Mathematical characterization of division, mutation, and selection interactions.

Insights into parameters affecting immune response effectiveness.

Abstract

We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in Germinal Centers during an immune response. This is a key process in adaptive immunity leading to the production of high affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system's functionality. We identify the existence of an optimal value of the selection rate, able to maximize the number of selected B-cells for a given generation.