Optimal Sequential Immunization Can Focus Antibody Responses against Diversity Loss and Distraction

A multiscale spatial modeling framework for the germinal center response

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymphoid organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events, including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanistic and applied research questions on the adaptive humoral immune response in the future.

A Multiscale Spatial Modeling Framework for the Germinal Center Response

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymph organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanic and applied research questions in future.

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.

Hierarchical sequence-affinity landscapes shape the evolution of breadth in an anti-influenza receptor binding site antibody

Broadly neutralizing antibodies (bnAbs) that neutralize diverse variants of a particular virus are of considerable therapeutic interest. Recent advances have enabled us to isolate and engineer these antibodies as therapeutics, but eliciting them through vaccination remains challenging, in part due to our limited understanding of how antibodies evolve breadth. Here, we analyze the landscape by which an anti-influenza receptor binding site (RBS) bnAb, CH65, evolved broad affinity to diverse H1 influenza strains. We do this by generating an antibody library of all possible evolutionary intermediates between the unmutated common ancestor (UCA) and the affinity-matured CH65 antibody and measure the affinity of each intermediate to three distinct H1 antigens. We find that affinity to each antigen requires a specific set of mutations - distributed across the variable light and heavy chains - that interact non-additively (i.e., epistatically). These sets of mutations form a hierarchical pattern across the antigens, with increasingly divergent antigens requiring additional epistatic mutations beyond those required to bind less divergent antigens. We investigate the underlying biochemical and structural basis for these hierarchical sets of epistatic mutations and find that epistasis between heavy chain mutations and a mutation in the light chain at the V_H-V_L interface is essential for binding a divergent H1. Collectively, this is the first work to comprehensively characterize epistasis between heavy and light chain mutations and shows that such interactions are both strong and widespread. Together with our previous study analyzing a different class of anti-influenza antibodies, our results implicate epistasis as a general feature of antibody sequence-affinity landscapes that can potentiate and constrain the evolution of breadth.

Moving the needle: Employing deep reinforcement learning to push the boundaries of coarse-grained vaccine models

Highly mutable infectious disease pathogens (hm-IDPs) such as HIV and influenza evolve faster than the human immune system can contain them, allowing them to circumvent traditional vaccination approaches and causing over one million deaths annually. Agent-based models can be used to simulate the complex interactions that occur between immune cells and hm-IDP-like proteins (antigens) during affinity maturation-the process by which antibodies evolve. Compared to existing experimental approaches, agent-based models offer a safe, low-cost, and rapid route to study the immune response to vaccines spanning a wide range of design variables. However, the highly stochastic nature of affinity maturation and vast sequence space of hm-IDPs render brute force searches intractable for exploring all pertinent vaccine design variables and the subset of immunization protocols encompassed therein. To address this challenge, we employed deep reinforcement learning to drive a recently developed agent-based model of affinity maturation to focus sampling on immunization protocols with greater potential to improve the chosen metrics of protection, namely the broadly neutralizing antibody (bnAb) titers or fraction of bnAbs produced. Using this approach, we were able to coarse-grain a wide range of vaccine design variables and explore the relevant design space. Our work offers new testable insights into how vaccines should be formulated to maximize protective immune responses to hm-IDPs and how they can be minimally tailored to account for major sources of heterogeneity in human immune responses and various socioeconomic factors. Our results indicate that the first 3 to 5 immunizations, depending on the metric of protection, should be specially tailored to achieve a robust protective immune response, but that beyond this point further immunizations require only subtle changes in formulation to sustain a durable bnAb response.

Multiscale affinity maturation simulations to elicit broadly neutralizing antibodies against HIV

The design of vaccines against highly mutable pathogens, such as HIV and influenza, requires a detailed understanding of how the adaptive immune system responds to encountering multiple variant antigens (Ags). Here, we describe a multiscale model of B cell receptor (BCR) affinity maturation that employs actual BCR nucleotide sequences and treats BCR/Ag interactions in atomistic detail. We apply the model to simulate the maturation of a broadly neutralizing Ab (bnAb) against HIV. Starting from a germline precursor sequence of the VRC01 anti-HIV Ab, we simulate BCR evolution in response to different vaccination protocols and different Ags, which were previously designed by us. The simulation results provide qualitative guidelines for future vaccine design and reveal unique insights into bnAb evolution against the CD4 binding site of HIV. Our model makes possible direct comparisons of simulated BCR populations with results of deep sequencing data, which will be explored in future applications.

Vaccination has saved more lives than any other medical procedure. But, we do not have robust ways to develop vaccines against highly mutable pathogens. For example, there is no effective vaccine against HIV, and a universal vaccine against diverse strains of influenza is also not available. The development of immunization strategies to elicit antibodies that can neutralize diverse strains of highly mutable pathogens (so-called ‘broadly neutralizing antibodies’, or bnAbs) would enable the design of universal vaccines against such pathogens, as well as other viruses that may emerge in the future. In this paper, we present an agent-based model of affinity maturation–the Darwinian process by which antibodies evolve against a pathogen–that, for the first time, enables the in silico investigation of real germline nucleotide sequences of antibodies known to evolve into potent bnAbs, evolving against real amino acid sequences of HIV-based vaccine-candidate proteins. Our results provide new insights into bnAb evolution against HIV, and can be used to qualitatively guide the future design of vaccines against highly mutable pathogens.

A Coarse-Grained Model of Affinity Maturation Indicates the Importance of B-Cell Receptor Avidity in Epitope Subdominance

The elicitation of broadly neutralizing antibodies (bnAbs) is a major goal in the design of vaccines against rapidly-mutating viruses. In the case of influenza, many bnAbs that target conserved epitopes on the stem of the hemagglutinin protein (HA) have been discovered. However, these antibodies are rare, are not boosted well upon reinfection, and often have low neutralization potency, compared to strain-specific antibodies directed to the HA head. Different hypotheses have been proposed to explain this phenomenon. We use a coarse-grained computational model of the germinal center reaction to investigate how B-cell receptor binding valency affects the growth and affinity maturation of competing B-cells. We find that receptors that are unable to bind antigen bivalently, and also those that do not bind antigen cooperatively, have significantly slower rates of growth, memory B-cell production, and, under certain conditions, rates of affinity maturation. The corresponding B-cells are predicted to be outcompeted by B-cells that bind bivalently and cooperatively. We use the model to explore strategies for a universal influenza vaccine, e.g., how to boost the concentrations of the slower growing cross-reactive antibodies directed to the stem. The results suggest that, upon natural reinfections subsequent to vaccination, the protectiveness of such vaccines would erode, possibly requiring regular boosts. Collectively, our results strongly support the importance of bivalent antibody binding in immunodominance, and suggest guidelines for developing a universal influenza vaccine.

Increased B Cell Selection Stringency In Germinal Centers Can Explain Improved COVID-19 Vaccine Efficacies With Low Dose Prime or Delayed Boost

The efficacy of COVID-19 vaccines appears to depend in complex ways on the vaccine dosage and the interval between the prime and boost doses. Unexpectedly, lower dose prime and longer prime-boost intervals have yielded higher efficacies in clinical trials. To elucidate the origins of these effects, we developed a stochastic simulation model of the germinal center (GC) reaction and predicted the antibody responses elicited by different vaccination protocols. The simulations predicted that a lower dose prime could increase the selection stringency in GCs due to reduced antigen availability, resulting in the selection of GC B cells with higher affinities for the target antigen. The boost could relax this selection stringency and allow the expansion of the higher affinity GC B cells selected, improving the overall response. With a longer dosing interval, the decay in the antigen with time following the prime could further increase the selection stringency, amplifying this effect. The effect remained in our simulations even when new GCs following the boost had to be seeded by memory B cells formed following the prime. These predictions offer a plausible explanation of the observed paradoxical effects of dosage and dosing interval on vaccine efficacy. Tuning the selection stringency in the GCs using prime-boost dosages and dosing intervals as handles may help improve vaccine efficacies.

Binding affinity landscapes constrain the evolution of broadly neutralizing anti-influenza antibodies

Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.

Coevolutionary transitions emerging from flexible molecular recognition and eco-evolutionary feedback

Highly mutable viruses evolve to evade host immunity that exerts selective pressure and adapts to viral dynamics. Here, we provide a framework for identifying key determinants of the mode and fate of viral-immune coevolution by linking molecular recognition and eco-evolutionary dynamics. We find that conservation level and initial diversity of antigen jointly determine the timing and efficacy of narrow and broad antibody responses, which in turn control the transition between viral persistence, clearance, and rebound. In particular, clearance of structurally complex antigens relies on antibody evolution in a larger antigenic space than where selection directly acts; viral rebound manifests binding-mediated feedback between ecology and rapid evolution. Finally, immune compartmentalization can slow viral escape but also delay clearance. This work suggests that flexible molecular binding allows a plastic phenotype that exploits potentiating neutral variations outside direct contact, opening new and shorter paths toward highly adaptable states.

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A scale-crossing framework identifies key determinants of viral-immune coevolution

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Fast specific response influences slow broad response by shaping antigen dynamics

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Antibody footprint shift enables breadth acquisition and viral clearance

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Model explains divergent kinetics and outcomes of HCV infection in humans

Administration of Multivalent Influenza Virus Recombinant Hemagglutinin Vaccine in Combination-Adjuvant Elicits Broad Reactivity Beyond the Vaccine Components

Combining variant antigens into a multivalent vaccine is a traditional approach used to provide broad coverage against antigenically variable pathogens, such as polio, human papilloma and influenza viruses. However, strategies for increasing the breadth of antibody coverage beyond the vaccine are not well understood, but may provide more anticipatory protection. Influenza virus hemagglutinin (HA) is a prototypic variant antigen. Vaccines that induce HA-specific neutralizing antibodies lose efficacy as amino acid substitutions accumulate in neutralizing epitopes during influenza virus evolution. Here we studied the effect of a potent combination adjuvant (CpG/MPLA/squalene-in-water emulsion) on the breadth and maturation of the antibody response to a representative variant of HA subtypes H1, H5 and H7. Using HA protein microarrays and antigen-specific B cell labelling, we show when administered individually, each HA elicits a cross-reactive antibody profile for multiple variants within the same subtype and other closely-related subtypes (homosubtypic and heterosubtypic cross-reactivity, respectively). Despite a capacity for each subtype to induce heterosubtypic cross-reactivity, broader coverage was elicited by simply combining the subtypes into a multivalent vaccine. Importantly, multiplexing did not compromise antibody avidity or affinity maturation to the individual HA constituents. The use of adjuvants to increase the breadth of antibody coverage beyond the vaccine antigens may help future-proof vaccines against newly-emerging variants.

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.

Shaping Polyclonal Responses via Antigen-Mediated Antibody Interference

Broadly neutralizing antibodies (bnAbs) recognize conserved features of rapidly mutating pathogens and confer universal protection, but they emerge rarely in natural infection. Increasing evidence indicates that seemingly passive antibodies may interfere with natural selection of B cells. Yet, how such interference modulates polyclonal responses is unknown. Here we provide a framework for understanding the role of antibody interference—mediated by multi-epitope antigens—in shaping B cell clonal makeup and the fate of bnAb lineages. We find that, under heterogeneous interference, clones with different intrinsic fitness can collectively persist. Furthermore, antagonism among fit clones (specific for variable epitopes) promotes expansion of unfit clones (targeting conserved epitopes), at the cost of repertoire potency. This trade-off, however, can be alleviated by synergy toward the unfit. Our results provide a physical basis for antigen-mediated clonal interactions, stress system-level impacts of molecular synergy and antagonism, and offer principles to amplify naturally rare clones.

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Multi-epitope antigens mediate antibody interference that couples B cell lineages

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Trade-off exists between repertoire potency and persistence of broad lineages

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Antigen-mediated synergy toward intrinsically unfit clones alleviates the trade-off

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Amplifying rare clones by leveraging molecular interference structure

Preferential Presentation of High-Affinity Immune Complexes in Germinal Centers Can Explain How Passive Immunization Improves the Humoral Response

Passive immunization (PI) with external antibodies has been used classically for rapid but temporary alleviation of disease. Transcending this role, recent studies have shown PI to induce lasting improvements in natural antibody production, suggesting that PI could become a powerful tool to engineer humoral responses. We propose a mechanism with which PI can alter the humoral response. Antigen-specific B cells evolve and get selected in germinal centers (GCs) on the basis of their ability to acquire antigen from antibody-antigen complexes presented in GCs. When external antibodies of high affinity for antigen are used, they form the majority of the complexes in GCs, letting only B cells with even higher affinities be selected. Using an in silico GC reaction model, we show that this mechanism explains the improved humoral responses following PI. The model also synthesizes several independent experimental observations, indicating the robustness of the mechanism, and proposes tunable handles to optimize PI.

Optimizing immunization protocols to elicit broadly neutralizing antibodies

Natural infections and vaccination with a pathogen typically stimulate the production of potent antibodies specific for the pathogen through a Darwinian evolutionary process known as affinity maturation. Such antibodies provide protection against reinfection by the same strain of a pathogen. A highly mutable virus, like HIV or influenza, evades recognition by these strain-specific antibodies via the emergence of new mutant strains. A vaccine that elicits antibodies that can bind to many diverse strains of the virus-known as broadly neutralizing antibodies (bnAbs)-could protect against highly mutable pathogens. Despite much work, the mechanisms by which bnAbs emerge remain uncertain. Using a computational model of affinity maturation, we studied a wide variety of vaccination strategies. Our results suggest that an effective strategy to maximize bnAb evolution is through a sequential immunization protocol, wherein each new immunization optimally increases the pressure on the immune system to target conserved antigenic sites, thus conferring breadth. We describe the mechanisms underlying why sequentially driving the immune system increasingly further from steady state, in an optimal fashion, is effective. The optimal protocol allows many evolving B cells to become bnAbs via diverse evolutionary paths.

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.

Tuning environmental timescales to evolve and maintain generalists

Natural environments can present diverse challenges, but some genotypes remain fit across many environments. Such "generalists" can be hard to evolve, outcompeted by specialists fitter in any particular environment. Here, inspired by the search for broadly neutralizing antibodies during B cell affinity maturation, we demonstrate that environmental changes on an intermediate timescale can reliably evolve generalists, even when faster or slower environmental changes are unable to do so. We find that changing environments on timescales comparable with evolutionary transients in a population enhance the rate of evolving generalists from specialists, without enhancing the reverse process. The yield of generalists is further increased in more complex dynamic environments, such as a "chirp" of increasing frequency. Our work offers design principles for how nonequilibrium fitness "seascapes" can dynamically funnel populations to genotypes unobtainable in static environments.

HIV-1 gp120-CD4-Induced Antibody Complex Elicits CD4 Binding Site-Specific Antibody Response in Mice

Elicitation of broadly neutralizing Ab (bNAb) responses toward the conserved HIV-1 envelope (Env) CD4 binding site (CD4bs) by vaccination is an important goal for vaccine development and yet to be achieved. The outcome of previous immunogenicity studies suggests that the limited accessibility of the CD4bs and the presence of predominant nonneutralizing determinants (nND) on Env may impede the elicitation of bNAbs and their precursors by vaccination. In this study, we designed a panel of novel immunogens that 1) preferentially expose the CD4bs by selective elimination of glycosylation sites flanking the CD4bs, and 2) minimize the nND immune response by engineering fusion proteins consisting of gp120 Core and one or two CD4-induced (CD4i) mAbs for masking nND epitopes, referred to as gp120-CD4i fusion proteins. As expected, the fusion proteins possess improved antigenicity with retained affinity for VRC01-class, CD4bs-directed bNAbs and dampened affinity for nonneutralizing Abs. We immunized C57BL/6 mice with these fusion proteins and found that overall the fusion proteins elicit more focused CD4bs Ab response than prototypical gp120 Core by serological analysis. Consistently, we found that mice immunized with selected gp120-CD4i fusion proteins have higher frequencies of germinal center-activated B cells and CD4bs-directed memory B cells than those inoculated with parental immunogens. We isolated three mAbs from mice immunized with selected gp120-CD4i fusion proteins and found that their footprints on Env are similar to VRC01-class bNAbs. Thus, using gp120-CD4i fusion proteins with selective glycan deletion as immunogens could focus Ab response toward CD4bs epitope.

Evolving generalists in switching rugged landscapes

Evolving systems, be it an antibody repertoire in the face of mutating pathogens or a microbial population exposed to varied antibiotics, constantly search for adaptive solutions in time-varying fitness landscapes. Generalists refer to genotypes that remain fit across diverse selective pressures; while multi-drug resistant microbes are undesired yet prevalent, broadly-neutralizing antibodies are much wanted but rare. However, little is known about under what conditions such generalists with a high capacity to adapt can be efficiently discovered by evolution. In addition, can epistasis-the source of landscape ruggedness and path constraints-play a different role, if the environment varies in a non-random way? We present a generative model to estimate the propensity of evolving generalists in rugged landscapes that are tunably related and alternating relatively slowly. We find that environmental cycling can substantially facilitate the search for fit generalists by dynamically enlarging their effective basins of attraction. Importantly, these high performers are most likely to emerge at intermediate levels of ruggedness and environmental relatedness. Our approach allows one to estimate correlations across environments from the topography of experimental fitness landscapes. Our work provides a conceptual framework to study evolution in time-correlated complex environments, and offers statistical understanding that suggests general strategies for eliciting broadly neutralizing antibodies or preventing microbes from evolving multi-drug resistance.

Steady-state reduction of generalized Lotka-Volterra systems in the microbiome

The generalized Lotka-Volterra (gLV) equations, a classic model from theoretical ecology, describe the population dynamics of a set of interacting species. As the number of species in these systems grow in number, their dynamics become increasingly complex and intractable. We introduce steady-state reduction (SSR), a method that reduces a gLV system of many ecological species into two-dimensional subsystems that each obey gLV dynamics and whose basis vectors are steady states of the high-dimensional model. We apply this method to an experimentally-derived model of the gut microbiome in order to observe the transition between "healthy" and "diseased" microbial states. Specifically, we use SSR to investigate how fecal microbiota transplantation, a promising clinical treatment for dysbiosis, can revert a diseased microbial state to health.

de la Fuente I. Weighted lambda superstrings applied to vaccine design

We generalize the notion of λ-superstrings, presented in a previous paper, to the notion of weighted λ-superstrings. This generalization entails an important improvement in the applications to vaccine designs, as it allows epitopes to be weighted by their immunogenicities. Motivated by these potential applications of constructing short weighted λ-superstrings to vaccine design, we approach this problem in two ways. First, we formalize the problem as a combinatorial optimization problem (in fact, as two polynomially equivalent problems) and develop an integer programming (IP) formulation for solving it optimally. Second, we describe a model that also takes into account good pairwise alignments of the obtained superstring with the input strings, and present a genetic algorithm that solves the problem approximately. We apply both algorithms to a set of 169 strings corresponding to the Nef protein taken from patiens infected with HIV-1. In the IP-based algorithm, we take the epitopes and the estimation of the immunogenicities from databases of experimental epitopes. In the genetic algorithm we take as candidate epitopes all 9-mers present in the 169 strings and estimate their immunogenicities using a public bioinformatics tool. Finally, we used several bioinformatic tools to evaluate the properties of the candidates generated by our method, which indicated that we can score high immunogenic λ-superstrings that at the same time present similar conformations to the Nef virus proteins.

HIV-1 immunogens and strategies to drive antibody responses towards neutralization breadth

Despite enormous efforts no HIV-1 vaccine has been developed that elicits broadly neutralizing antibodies (bNAbs) to protect against infection to date. The high antigenic diversity and dense N-linked glycan armor, which covers nearly the entire HIV-1 envelope protein (Env), are major roadblocks for the development of bNAbs by vaccination. In addition, the naive human antibody repertoire features a low frequency of exceptionally long heavy chain complementary determining regions (CDRH3s), which is a typical characteristic that many HIV-1 bNAbs use to penetrate the glycan armor. Native-like Env trimer immunogens can induce potent but strain-specific neutralizing antibody responses in animal models but how to overcome the many obstacles towards the development of bNAbs remains a challenge. Here, we review recent HIV-1 Env immunization studies and discuss strategies to guide strain-specific antibody responses towards neutralization breadth.

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

Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given datasets. This procedure is well developed in the Bayesian perspective, in which one infers probability distributions describing to what extent various possible parameters agree with the data. In this paper, we motivate and review probabilistic modeling for adaptive immune receptor repertoire data then describe progress and prospects for future work, from germline haplotyping to adaptive immune system deployment across tissues. The relevant quantities in immune sequence analysis include not only continuous parameters such as gene use frequency but also discrete objects such as B-cell clusters and lineages. Throughout this review, we unravel the many opportunities for probabilistic modeling in adaptive immune receptor analysis, including settings for which the Bayesian approach holds substantial promise (especially if one is optimistic about new computational methods). From our perspective, the greatest prospects for progress in probabilistic modeling for repertoires concern ancestral sequence estimation for B-cell receptor lineages, including uncertainty from germline genotype, rearrangement, and lineage development.

How Germinal Centers Evolve Broadly Neutralizing Antibodies: the Breadth of the Follicular Helper T Cell Response

Many HIV-1-infected patients evolve broadly neutralizing antibodies (bnAbs). This evolutionary process typically takes several years and is poorly understood as selection taking place in germinal centers occurs on the basis of antibody affinity. B cells with the highest-affinity receptors tend to acquire the most antigen from the follicular dendritic cell (FDC) network and present the highest density of cognate peptides to follicular helper T (Tfh) cells, which provide survival signals to the B cell. bnAbs are therefore expected to evolve only when the B cell lineage evolving breadth is consistently capturing and presenting more peptides to Tfh cells than other lineages of more specific B cells. Here we develop mathematical models of Tfh cells in germinal centers to explicitly define the mechanisms of selection in this complex evolutionary process. Our results suggest that broadly reactive B cells presenting a high density of peptides bound to major histocompatibility complex class II molecules (pMHC) are readily outcompeted by B cells responding to lineages of HIV-1 that transiently dominate the within host viral population. Conversely, if broadly reactive B cells acquire a large variety of several HIV-1 proteins from the FDC network and present a high diversity of several pMHC, they can be rescued by a large fraction of the Tfh cell repertoire in the germinal center. Under such circumstances the evolution of bnAbs is much more consistent. Increasing either the magnitude of the Tfh cell response or the breadth of the Tfh cell repertoire markedly facilitates the evolution of bnAbs. Because both the magnitude and breadth can be increased by vaccination with several HIV-1 proteins, this calls for experimental testing.IMPORTANCE Many HIV-infected patients slowly evolve antibodies that can neutralize a large variety of viruses. Such broadly neutralizing antibodies (bnAbs) could in the future become therapeutic agents. bnAbs appear very late, and patients are typically not protected by them. At the moment, we fail to understand why this takes so long and how the immune system selects for broadly neutralizing capacity. Typically, antibodies are selected based on affinity and not on breadth. We developed mathematical models to study two different mechanisms by which the immune system can select for broadly neutralizing capacity. One of these is based upon the repertoire of different follicular helper T (Tfh) cells in germinal centers. We suggest that broadly reactive B cells may interact with a larger fraction of this repertoire and demonstrate that this would select for bnAbs. Intriguingly, this suggests that broadening the Tfh cell repertoire by vaccination may speed up the evolution of bnAbs.