Affinity maturation for an optimal balance between long-term immune coverage and short-term resource constraints

Abstract

In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. We assume that the immune system follows a strategy that maximizes the long-term immune coverage and minimizes the short-term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision process on a finite dimensional phenotypic space, where a pre-existing population of naive cells is sequentially challenged with a neutrally evolving strain. We unveil a trade-off between immune protection against future strains and the necessary reorganization of the repertoire. This plasticity of the repertoire drives the emergence of distinct regimes for the size and diversity of the memory pool, depending on the density of naive cells and on the mutation rate of the strain. The model predicts power-law distributions of clonotype sizes observed in data, and rationalizes antigenic imprinting as a strategy to minimize metabolic costs while keeping good immune protection against future strains.

Dynamics of immune memory and learning in bacterial communities

“…Quantitative frameworks to model immune diversity and clone abundance have revealed that simple low-level interactions can give rise to complex outcomes including broad distributions of clone abundance [1, 2, 3, 4, 5, 6], long-lived biologically realistic transient states [7, 5], and clonal restructuring following immune challenges [8, 9, 10, 11, 5]. Phenomenological models of pathogen co-evolution with the immune system have accelerated our understanding of how the fitness landscape generated by the immune system constrains pathogen evolution [12, 13, 7, 14, 15], how the adaptive immune system responds to rapid pathogen evolution [16, 17, 14, 15], and what drives pathogen extinction [7, 13] or the extinction of particular clonal cell lineages [17, 10]. These models have also explored trade-offs such as between immune receptor specificity and cross-reactivity [4, 18], between the specifity of host-pathogen discrimination and sensitivity to pathogens [8, 19, 20], between the speed of an immune response and the efficiency of that response [14], or between metabolic resource use and immune coverage [15].…”

“…Phenomenological models of pathogen co-evolution with the immune system have accelerated our understanding of how the fitness landscape generated by the immune system constrains pathogen evolution [12, 13, 7, 14, 15], how the adaptive immune system responds to rapid pathogen evolution [16, 17, 14, 15], and what drives pathogen extinction [7, 13] or the extinction of particular clonal cell lineages [17, 10]. These models have also explored trade-offs such as between immune receptor specificity and cross-reactivity [4, 18], between the specifity of host-pathogen discrimination and sensitivity to pathogens [8, 19, 20], between the speed of an immune response and the efficiency of that response [14], or between metabolic resource use and immune coverage [15]. All of these models have shown rich dynamics and qualitatively different states of diversity and evolution arising from simple rules.…”

Learning and Memory Strategies in Evolving Environments

“…Here the connection to our deliberation parameter (β) is even clearer as we chose our naïve cost to be a monotonic function of β. With this clear mapping to our model, it is no surprise that [101] finds the same three regimes described above, while their model relies on more assumptions of the actual biological process.…”

“…Thus, even though some states are suboptimal, the population will not die out because it does not have a fitting solution. This tradeoff between the possible gain in one environment and preparation for other environments illustrates a vital component of these models, namely, focusing on long-term growth, not short-term gains, similar to many other studies [96][97][98][99][100][101]. This concept is also the basis for the optimizations in this thesis.…”

“…While all these observations might appear to be intuitively clear, our work was the first to propose a utility of an immune memory response to evolved pathogens. Indeed, a recent (published after [1]) preprint suggests a different model for this problem [101]. While they use a different function to model the cross-reactive affinity function between receptors and antigens, their parameters to describe the immune system are simply different interpretations of our model.…”