A Population Dynamics Model for Clonal Diversity in a Germinal Center

Abstract

Germinal centers (GCs) are micro-domains where B cells mature to develop high affinity antibodies. Inside a GC, B cells compete for antigen and T cell help, and the successful ones continue to evolve. New experimental results suggest that, under identical conditions, a wide spectrum of clonal diversity is observed in different GCs, and high affinity B cells are not always the ones selected. We use a birth, death and mutation model to study clonal competition in a GC over time. We find that, like all evolutionary processes, diversity loss is inherently stochastic. We study two selection mechanisms, birth-limited and death limited selection. While death limited selection maintains diversity and allows for slow clonal homogenization as affinity increases, birth limited selection results in more rapid takeover of successful clones. Finally, we qualitatively compare our model to experimental observations of clonal selection in mice.

Calculating germinal centre reactions

“…Several GCs in parallel [24,30,35] Several consecutive exposures [24,35] Spatially resolved GC [33,34,42] Shape space sequence [33,34,50] Co-evolving epitopes [49] Binary sequence [35,49] Sequence-free [40,41,48,52,54] Seeding by memory B cells [24,35] Stochastic differential equations [49] ODE-based simulation [41,48,54] Agent-based simulation [24,33,34,35,50,40] Class-switching [54] Molecular detail of T-B interaction [33,34] Full AA alphabet sequence [24,43] Role for plasma B cells [49,54,30] Treatment of Ab CDR and FWR regions [24,52] Rugged fitness landscape [30] Several epitopes simultaneously [30,35,48,50,53] Role for memory B cells [35,24] ...…”

“…By contrast, the contribution of selective expansion of rare high-quality precursors to overall improvement can be substantial if a large and diverse pool of GC founder cells is considered [24]. Correspondingly, the mean affinity of a GC B cell population correlates negatively with its clonal diversity in a setting with many different founder cells [40]. However, highly abundant subclones do not necessarily have highest affinity, as best variants can arise late during the reaction and thus have insufficient time for expansion [41].…”

The Bayesian optimist's guide to adaptive immune receptor repertoire analysis

“…Another vein of work uses agent-based and differential equation-based modeling to iteratively improve compartmental models of B-cell development. [182][183][184][185][186][187][188][189][190][191] For chronic infections such as HIV, antibody-pathogen coevolution certainly plays a role 192 although the dynamics between antibody emergence and viral escape are difficult to pin down. 193 Some researchers have found a "trunk-canopy" tree structure from mature sequence data, in which a long "trunk" branch from the root extends from the naive sequence, after which there is a "canopy" of diversification.…”

Benchmarking tree and ancestral sequence inference for B cell receptor sequences

“…Many interesting simulators have different goals. Detailed mechanistic models have been proposed to model all cells and all interactions in a GC using first principles from biophysics (41)(42)(43). Others have suggested probabilistic frameworks modeling summary statistics of SHM (44,45) and, as a middle ground between ultra fine grained models and plain summary statistics, models attempting to explain population level trends using systems of differential equations have been suggested (46).…”