Calculating germinal centre reactions

A branching stochastic evolutionary model of the B-cell repertoire

We propose a stochastic framework to describe the evolution of the B-cell repertoire during germinal center (GC) reactions. Our model is formulated as a multitype age-dependent branching process with time-varying immigration. The immigration process captures the mechanism by which founder B cells initiate clones by gradually seeding GC over time, while the branching process describes the temporal evolution of the composition of these clones. The model assigns a type to each cell to represent attributes of interest. Examples of attributes include the binding affinity class of the B cells, their clonal family, or the nucleotide sequence of the heavy and light chains of their receptors. The process is generally non-Markovian. We present its properties, including as t → ∞ when the process is supercritical, the most relevant case to study expansion of GC B cells. We introduce temporal alpha and beta diversity indices for multitype branching processes. We focus on the dynamics of clonal dominance, highlighting its non-stationarity, and the accumulation of somatic hypermutations in the context of sequential immunization. We evaluate the impact of the ongoing seeding of GC by founder B cells on the dynamics of the B-cell repertoire, and quantify the effect of precursor frequency and antigen availability on the timing of GC entry. An application of the model illustrates how it may help with interpretation of BCR sequencing data.

Germinal centers are permissive to subdominant antibody responses

Introduction

A protective humoral response to pathogens requires the development of high affinity antibodies in germinal centers (GC). The combination of antigens available during immunization has a strong impact on the strength and breadth of the antibody response. Antigens can display various levels of immunogenicity, and a hierarchy of immunodominance arises when the GC response to an antigen dampens the response to other antigens. Immunodominance is a challenge for the development of vaccines to mutating viruses, and for the development of broadly neutralizing antibodies. The extent by which antigens with different levels of immunogenicity compete for the induction of high affinity antibodies and therefore contribute to immunodominance is not known.

Methods

Here, we perform in silico simulations of the GC response, using a structural representation of antigens with complex surface amino acid composition and topology. We generate antigens with complex domains of different levels of immunogenicity and perform simulations with combinations of these domains.

Results

We found that GC dynamics were driven by the most immunogenic domain and immunodominance arose as affinity maturation to less immunogenic domain was inhibited. However, this inhibition was moderate since the less immunogenic domain exhibited a weak GC response in the absence of the most immunogenic domain. Less immunogenic domains reduced the dominance of GC responses to more immunogenic domains, albeit at a later time point.

Discussion

The simulations suggest that increased vaccine valency may decrease immunodominance of the GC response to strongly immunogenic domains and therefore, act as a potential strategy for the natural induction of broadly neutralizing antibodies in GC reactions.

The role of geometric features in a germinal center

The germinal center (GC) is a self-organizing structure produced in the lymphoid follicle during the T-dependent immune response and is an important component of the humoral immune system. However, the impact of the special structure of GC on antibody production is not clear. According to the latest biological experiments, we establish a spatiotemporal stochastic model to simulate the whole self-organization process of the GC including the appearance of two specific zones: the dark zone (DZ) and the light zone (LZ), the development of which serves to maintain an effective competition among different cells and promote affinity maturation. A phase transition is discovered in this process, which determines the critical GC volume for a successful growth in both the stochastic and the deterministic model. Further increase of the volume does not make much improvement on the performance. It is found that the critical volume is determined by the distance between the activated B cell receptor (BCR) and the target epitope of the antigen in the shape space. The observation is confirmed in both 2D and 3D simulations and explains partly the variability of the observed GC size.

Heterogeneity of germinal center B cells: New insights from single-cell studies

Upon antigen exposure, activated B cells in antigen-draining lymphoid organs form microanatomical structures, called germinal centers (GCs), where affinity maturation occurs. Within the GC microenvironment, GC B cells undergo proliferation and B cell receptor (BCR) genes somatic hypermutation in the dark zone (DZ), and affinity-based selection in the light zone (LZ). In the current paradigm of GC dynamics, high-affinity LZ B cells may be selected by cognate T- follicular helper cells to either differentiate into plasma cells or memory B cells, or re-enter the DZ and initiate a new round of proliferation and BCR diversification, before migrating back to the LZ. Given the diversity of cell states and potential cell fates that GC B cells may adopt, the two-state DZ-LZ paradigm has been challenged by studies that explored GC B-cell heterogeneity with a variety of single-cell technologies. Here, we review studies and single-cell technologies which have allowed to refine the working model of GC B-cell cellular and molecular heterogeneity during affinity maturation. This review also covers the use of single-cell quantitative data for mathematical modeling of GC reactions, and the application of single-cell genomics to the study of GC-derived malignancies.

In Silico Analysis of the Longevity and Timeline of Individual Germinal Center Reactions in a Primary Immune Response

Germinal centers (GCs) are transient structures in the secondary lymphoid organs, where B cells undergo affinity maturation to produce high affinity memory and plasma cells. The lifetime of GC responses is a critical factor limiting the extent of affinity maturation and efficiency of antibody responses. While the average lifetime of overall GC reactions in a lymphoid organ is determined experimentally, the lifetime of individual GCs has not been monitored due to technical difficulties in longitudinal analysis. In silico analysis of the contraction phase of GC responses towards primary immunization with sheep red blood cells suggested that if individual GCs had similar lifetimes, the data would be consistent only when new GCs were formed until a very late phase after immunization. Alternatively, there could be a large variation in the lifetime of individual GCs suggesting that both long and short-lived GCs might exist in the same lymphoid organ. Simulations predicted that such differences in the lifetime of GCs could arise due to variations in antigen availability and founder cell composition. These findings identify the potential factors limiting GC lifetime and contribute to an understanding of overall GC responses from the perspective of individual GCs in a primary immune response.

Survival probability and size of lineages in antibody affinity maturation

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.

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

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.

Computational Model Reveals a Stochastic Mechanism behind Germinal Center Clonal Bursts

Germinal centers (GCs) are specialized compartments within the secondary lymphoid organs where B cells proliferate, differentiate, and mutate their antibody genes in response to the presence of foreign antigens. Through the GC lifespan, interclonal competition between B cells leads to increased affinity of the B cell receptors for antigens accompanied by a loss of clonal diversity, although the mechanisms underlying clonal dynamics are not completely understood. We present here a multi-scale quantitative model of the GC reaction that integrates an intracellular component, accounting for the genetic events that shape B cell differentiation, and an extracellular stochastic component, which accounts for the random cellular interactions within the GC. In addition, B cell receptors are represented as sequences of nucleotides that mature and diversify through somatic hypermutations. We exploit extensive experimental characterizations of the GC dynamics to parameterize our model, and visualize affinity maturation by means of evolutionary phylogenetic trees. Our explicit modeling of B cell maturation enables us to characterise the evolutionary processes and competition at the heart of the GC dynamics, and explains the emergence of clonal dominance as a result of initially small stochastic advantages in the affinity to antigen. Interestingly, a subset of the GC undergoes massive expansion of higher-affinity B cell variants (clonal bursts), leading to a loss of clonal diversity at a significantly faster rate than in GCs that do not exhibit clonal dominance. Our work contributes towards an in silico vaccine design, and has implications for the better understanding of the mechanisms underlying autoimmune disease and GC-derived lymphomas.