Quantitative modeling of the effect of antigen dosage on B-cell affinity distributions in maturating germinal centers

Abstract

Affinity maturation is a complex dynamical process allowing the immune system to generate antibodies capable of recognizing antigens. We introduce a model for the evolution of the distribution of affinities across the antibody population in germinal centers. The model is amenable to detailed mathematical analysis and gives insight on the mechanisms through which antigen availability controls the rate of maturation and the expansion of the antibody population. It is also capable, upon maximum-likelihood inference of the parameters, to reproduce accurately the distributions of affinities of IgG-secreting cells we measure in mice immunized against Tetanus Toxoid under largely varying conditions (antigen dosage, delay between injections). Both model and experiments show that the average population affinity depends non-monotonically on the antigen dosage. We show that combining quantitative modeling and statistical inference is a concrete way to investigate biological processes underlying affinity maturation (such as selection permissiveness), hardly accessible through measurements.

The Quantitative Assessment of the Secreted IgG Repertoire after Recall to Evaluate the Quality of Immunizations

“…In this study, an analytical pathway as the one presented might help to shed light into the underlying mechanisms. This quantitative data will also serve as a great basis for the modeling of the immune reaction and the resulting secreted IgG repertoire (46).…”

Survival probability and size of lineages in antibody affinity maturation

“…If this selection pressure is not too strong then the population will later expand and mature. Through a mechanism analogous to the one studied in [13] Ag concentration then controls the maturation speed, as can be seen by comparing the speed of decrease in average binding energy of the population after the bottleneck in the cases C = 10 and C = 3.5 in fig. 3B.…”

“…In spite of the many recent experimental advancements in the study of AM, several open questions still remain to be answered, which have important implications in vaccine design. For example understanding the role of Ag availability in controlling maturation might lead to optimization of Ag dosage in vaccines [12][13][14], or understanding the effect of B-cell precursor frequency and affinity might help improving immunogen design [15,16]. Given the complexity of this process, computational models represent an invaluable tool to guide our understanding of AM [17,18].…”

“…Experimental analysis of vaccine-responsive lineages shows signatures of selection in their reconstructed phylogenies [19]. This selection pressure, which is partially controlled by Ag availability [13], is important to push lineages towards maturation, but at the same time an excessive pressure might be deleterious. Indeed, several maturation models present a phenomenology termed population bottleneck [20][21][22], in which strong selection pressure causes a decrease in GC population size, potentially leading to extinction.…”

“…Failure to do so results in cell death, and only cells that are able to bind the Ag with sufficient affinity survive this step of selection. Similarly to [13,21] we consider the survival probability for a cell with binding energy to be given by the following Langmuir isotherm:…”