Survival probability and size of lineages in antibody affinity maturation

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.

A Multiscale Spatial Modeling Framework for the Germinal Center Response

“…Molari et al developed stochastic and deterministic models to show that the average GC B cell affinity is determined non-monotonically by the antigen dosage, and clonal dominance and limited diversity can be achieved over time (Molari et al 2020). Using stochastic models and analytical solutions Molari et al studied the probability for a B cell lineage to surpass the population bottleneck as a function of the antigen concentration and initial B cell population size (Molari et al 2021). More recently Yan et al developed a spatiotemporal stochastic model to understand the determinants of GC size and found there is a critical GC volume to achieve best performance (Yan et al 2022).…”