Survival probability and size of lineages in antibody affinity maturation

TL;DR

This paper models the survival and size of B-cell lineages during antibody affinity maturation, revealing how progenitor affinity and antigen availability influence population survival and extinction dynamics, with implications for vaccine design.

Contribution

It provides a mathematical framework to predict lineage survival probabilities and extinction times in affinity maturation, incorporating competition and population dynamics.

Findings

Higher progenitor affinity increases survival probability.

Antigen concentration critically affects population bottleneck outcomes.

Mathematical expressions for extinction time and progeny size are derived.

Abstract

Affinity Maturation (AM) is the process through which the immune system is able to develop potent antibodies against new pathogens it encounters, and is at the base of the efficacy of vaccines. At its core AM is analogous to a Darwinian evolutionary process, where B-cells mutate and are selected on the base of their affinity for an Antigen (Ag), and Ag availability tunes the selective pressure. In cases when this selective pressure is high the number of B-cells might quickly decrease and the population might risk extinction in what is known as a population bottleneck. Here we study the probability for a B-cell lineage to survive this bottleneck scenario as a function of the progenitor affinity for the Ag. Using recursive relations and probability generating functions we derive expressions for the average extinction time and progeny size for lineages that go extinct. We then extend our results to the full population, both in the absence and presence of competition for T-cell help, and quantify the population survival probability as a function of Ag concentration and initial population size. Our study suggests the population bottleneck phenomenology might represent a limit case in the space of biologically plausible maturation scenarios, whose characterization could help guide the process of vaccine development.