Predicted and inferred waiting times for key mutations in the germinal centre reaction: evidence for stochasticity in selection

Repeated vaccination with homologous influenza hemagglutinin broadens human antibody responses to unmatched flu viruses

The on-going diversification of influenza virus necessicates annual vaccine updating. The vaccine antigen, the viral spike protein hemagglutinin (HA), tends to elicit strain-specific neutralizing activity, predicting that sequential immunization with the same HA strain will boost antibodies with narrow coverage. However, repeated vaccination with homologous SARS-CoV-2 vaccine eventually elicits neutralizing activity against highly unmatched variants, questioning this immunological premise. We evaluated a longitudinal influenza vaccine cohort, where each year the subjects received the same, novel H1N1 2009 pandemic vaccine strain. Repeated vaccination gradually enhanced receptor-blocking antibodies (HAI) to highly unmatched H1N1 strains within individuals with no initial memory recall against these historical viruses. An in silico model of affinity maturation in germinal centers integrated with a model of differentiation and expansion of memory cells provides insight into the mechanisms underlying these results and shows how repeated exposure to the same immunogen can broaden the antibody response against diversified targets.

Engaging an HIV vaccine target through the acquisition of low B cell affinity

Low affinity is common for germline B cell receptors (BCR) seeding development of broadly neutralizing antibodies (bnAbs) that engage hypervariable viruses, including HIV. Antibody affinity selection is also non-homogenizing, insuring the survival of low affinity B cell clones. To explore whether this provides a natural window for expanding human B cell lineages against conserved vaccine targets, we deploy transgenic mice mimicking human antibody diversity and somatic hypermutation (SHM) and immunize with simple monomeric HIV glycoprotein envelope immunogens. We report an immunization regimen that focuses B cell memory upon the conserved CD4 binding site (CD4bs) through both conventional affinity maturation and reproducible expansion of low affinity BCR clones with public patterns in SHM. In the latter instance, SHM facilitates target acquisition by decreasing binding strength. This suggests that permissive B cell selection enables the discovery of antibody epitopes, in this case an HIV bnAb site.

Imaging the different timescales of germinal center selection

Germinal centers (GCs) are the site of antibody affinity maturation, a fundamental immunological process that increases the potency of antibodies and thereby their ability to protect against infection. GC biology is highly dynamic in both time and space, making it ideally suited for intravital imaging. Using multiphoton laser scanning microscopy (MPLSM), the field has gained insight into the molecular, cellular, and structural changes and movements that coordinate affinity maturation in real time in their native environment. On the other hand, several limitations of MPLSM have had to be overcome to allow full appreciation of GC events taking place across different timescales. Here, we review the technical advances afforded by intravital imaging and their contributions to our understanding of GC biology.

System-Level Scenarios for the Elucidation of T Cell-Mediated Germinal Center B Cell Differentiation

Germinal center (GC) reactions are vital to the correct functioning of the adaptive immune system, through formation of high affinity, class switched antibodies. GCs are transient anatomical structures in secondary lymphoid organs where specific B cells, after recognition of antigen and with T cell help, undergo class switching. Subsequently, B cells cycle between zones of proliferation and somatic hypermutation and zones where renewed antigen acquisition and T cell help allows for selection of high affinity B cells (affinity maturation). Eventually GC B cells first differentiate into long-lived memory B cells (MBC) and finally into plasma cells (PC) that partially migrate to the bone marrow to encapsulate into long-lived survival niches. The regulation of GC reactions is a highly dynamically coordinated process that occurs between various cells and molecules that change in their signals. Here, we present a system-level perspective of T cell-mediated GC B cell differentiation, presenting and discussing the experimental and computational efforts on the regulation of the GCs. We aim to integrate Systems Biology with B cell biology, to advance elucidation of the regulation of high-affinity, class switched antibody formation, thus to shed light on the delicate functioning of the adaptive immune system. Specifically, we: i) review experimental findings of internal and external factors driving various GC dynamics, such as GC initiation, maturation and GCBC fate determination; ii) draw comparisons between experimental observations and mathematical modeling investigations; and iii) discuss and reflect on current strategies of modeling efforts, to elucidate B cell behavior during the GC tract. Finally, perspectives are specifically given on to the areas where a Systems Biology approach may be useful to predict novel GCBC-T cell interaction dynamics.

Linking signaling and selection in the germinal center

Germinal centers (GC) are sites of rapid B-cell proliferation in response to certain types of immunization. They arise in about 1 week and can persist for several months. In GCs, B cells differentiate in a unique way and begin to undergo somatic mutation of the Ig V regions at a high rate. GC B cells (GCBC) thus undergo clonal diversification that can affect the affinity of the newly mutant B-cell receptor (BCR) for its driving antigen. Through processes that are still poorly understood, GCBC with higher affinity are selectively expanded while those with mutations that inactivate the BCR are lost. In addition, at various times during the extended GC reaction, some GCBC undergo differentiation into either long-lived memory B cells (MBC) or plasma cells. The cellular and molecular signals that govern these fate decisions are not well-understood, but are an active area of research in multiple laboratories. In this review, we cover both the history of this field and focus on recent work that has helped to elucidate the signals and molecules, such as key transcription factors, that coordinate both positive selection as well as differentiation of GCBC.

Beyond Hot Spots: Biases in Antibody Somatic Hypermutation and Implications for Vaccine Design

The evolution of antibodies in an individual during an immune response by somatic hypermutation (SHM) is essential for the ability of the immune system to recognize and remove the diverse spectrum of antigens that may be encountered. These mutations are not produced at random; nucleotide motifs that result in increased or decreased rates of mutation were first reported in 1992. Newer models that estimate the propensity for mutation for every possible 5- or 7-nucleotide motif have emphasized the complexity of SHM targeting and suggested possible new hot spot motifs. Even with these fine-grained approaches, however, non-local context matters, and the mutations observed at a specific nucleotide motif varies between species and even by locus, gene segment, and position along the gene segment within a single species. An alternative method has been provided to further abstract away the molecular mechanisms underpinning SHM, prompted by evidence that certain stereotypical amino acid substitutions are favored at each position of a particular V gene. These "substitution profiles," whether obtained from a single B cell lineage or an entire repertoire, offer a simplified approach to predict which substitutions will be well-tolerated and which will be disfavored, without the need to consider path-dependent effects from neighboring positions. However, this comes at the cost of merging the effects of two distinct biological processes, the generation of mutations, and the selection acting on those mutations. Since selection is contingent on the particular antigens an individual has been exposed to, this suggests that SHM may have evolved to prefer mutations that are most likely to be useful against pathogens that have co-evolved with us. Alternatively, the ability to select favorable mutations may be strongly limited by the biases of SHM targeting. In either scenario, the sequence space explored by SHM is significantly limited and this consequently has profound implications for the rational design of vaccine strategies.

Cell Cycle-Associated CXCR4 Expression in Germinal Center B Cells and Its Implications on Affinity Maturation

Adaptation of antibody-mediated immunity occurs in germinal centers (GC). It is where affinity maturation, class switching, memory and plasma cell differentiation synergize to generate specific high-affinity antibodies that aid both to clear and protect against reinfection of invading pathogens. Within GCs, light and dark zone are two compartments instrumental in regulating this process, by segregating T cell-dependent selection and differentiation from generation of GC B cells bearing hypermutated antigen receptors. Spatial segregation of GC B cells into the two zones relies on the chemokine receptor CXCR4, with textbooks attributing high and low expression to a dark and light zone phenotype. Interestingly, this bipolarity is not reflected in the CXCR4 expression profile of GC B cells, which is highly variable and unimodal, indicating a continuum of intermediate CXCR4 levels rather than a binary dark or light zone phenotype. Here, analysis of published BrdU pulse-chase data reveals that throughout cell cycle, average CXCR4 expression in GC B cells steadily increases close to twofold, scaling with cell surface area. CXCR4 expression in recently divided GC B cells in G0/G1 or early S phase shows intermediate levels compared to cells in G2M phase, consistent with their smaller size. The lowest number of CXCR4 receptors are displayed by relatively aged GC B cells in G0/G1 or early S phase. The latter, upon progressing through S phase, however, ramp up relative CXCR4 expression twice as much as recently divided cells. Twelve hours after the BrdU pulse, labeled GC B cells, while initially in S phase, are desynchronized in terms of cell cycle and match the CXCR4 profile of unlabeled cells. A model is discussed in which CXCR4 expression in GC B cell increases with cell cycle and cell surface area, with highest levels in G2 and M phase, coinciding with GC B cell receptor signaling in G2 and immediately preceding activation-induced cytidine deaminase (AID) activity in early G1. In the model, GC B cells compete for CXCL12 expression on the basis of their CXCR4 expression, gaining a relative advantage as they progress in cell cycle, but loosing the advantage at the moment they divide.

Germinal center entry not selection of B cells is controlled by peptide-MHCII complex density

B cells expressing high affinity antigen receptors are advantaged in germinal centers (GC), perhaps by increased acquisition of antigen for presentation to follicular helper T cells and improved T-cell help. In this model for affinity-dependent selection, the density of peptide/MHCII (pMHCII) complexes on GC B cells is the primary determinant of selection. Here we show in chimeric mice populated by B cells differing only in their capacity to express MHCII (MHCII+/+ and MHCII+/-) that GC selection is insensitive to halving pMHCII density. Alone, both B cell types generate identical humoral responses; in competition, MHCII+/+ B cells are preferentially recruited to early GCs but this advantage does not persist once GCs are established. During GC responses, competing MHCII+/+ and MHCII+/- GC B cells comparably accumulate mutations and have indistinguishable rates of affinity maturation. We conclude that B-cell selection by pMHCII density is stringent in the establishment of GCs, but relaxed during GC responses.

Germinal center dynamics during acute and chronic infection

The ability of the immune system to clear pathogens is limited during chronic virus infections where potent long-lived plasma and memory B-cells are produced only after germinal center B-cells undergo many rounds of somatic hypermutations. In this paper, we investigate the mechanisms of germinal center B-cell formation by developing mathematical models for the dynamics of B-cell somatic hypermutations. We use the models to determine how B-cell selection and competition for T follicular helper cells and antigen influences the size and composition of germinal centers in acute and chronic infections. We predict that the T follicular helper cells are a limiting resource in driving large numbers of somatic hypermutations and present possible mechanisms that can revert this limitation in the presence of non-mutating and mutating antigen.

Computational Model Reveals Limited Correlation between Germinal Center B-Cell Subclone Abundancy and Affinity: Implications for Repertoire Sequencing

Immunoglobulin repertoire sequencing has successfully been applied to identify expanded antigen-activated B-cell clones that play a role in the pathogenesis of immune disorders. One challenge is the selection of the Ag-specific B cells from the measured repertoire for downstream analyses. A general feature of an immune response is the expansion of specific clones resulting in a set of subclones with common ancestry varying in abundance and in the number of acquired somatic mutations. The expanded subclones are expected to have BCR affinities for the Ag higher than the affinities of the naive B cells in the background population. For these reasons, several groups successfully proceeded or suggested selecting highly abundant subclones from the repertoire to obtain the Ag-specific B cells. Given the nature of affinity maturation one would expect that abundant subclones are of high affinity but since repertoire sequencing only provides information about abundancies, this can only be verified with additional experiments, which are very labor intensive. Moreover, this would also require knowledge of the Ag, which is often not available for clinical samples. Consequently, in general we do not know if the selected highly abundant subclone(s) are also the high(est) affinity subclones. Such knowledge would likely improve the selection of relevant subclones for further characterization and Ag screening. Therefore, to gain insight in the relation between subclone abundancy and affinity, we developed a computational model that simulates affinity maturation in a single GC while tracking individual subclones in terms of abundancy and affinity. We show that the model correctly captures the overall GC dynamics, and that the amount of expansion is qualitatively comparable to expansion observed from B cells isolated from human lymph nodes. Analysis of the fraction of high- and low-affinity subclones among the unexpanded and expanded subclones reveals a limited correlation between abundancy and affinity and shows that the low abundant subclones are of highest affinity. Thus, our model suggests that selecting highly abundant subclones from repertoire sequencing experiments would not always lead to the high(est) affinity B cells. Consequently, additional or alternative selection approaches need to be applied.

Germinal Center B Cell Dynamics

Germinal centers (GCs) are the site of antibody diversification and affinity maturation and as such are vitally important for humoral immunity. The study of GC biology has undergone a renaissance in the past 10 years, with a succession of findings that have transformed our understanding of the cellular dynamics of affinity maturation. In this review, we discuss recent developments in the field, with special emphasis on how GC cellular and clonal dynamics shape antibody affinity and diversity during the immune response.

The mutation patterns in B-cell immunoglobulin receptors reflect the influence of selection acting at multiple time-scales

During the several-week course of an immune response, B cells undergo a process of clonal expansion, somatic hypermutation of the immunoglobulin (Ig) genes and affinity-dependent selection. Over a lifetime, each B cell may participate in multiple rounds of affinity maturation as part of different immune responses. These two time-scales for selection are apparent in the structure of B-cell lineage trees, which often contain a 'trunk' consisting of mutations that are shared across all members of a clone, and several branches that form a 'canopy' consisting of mutations that are shared by a subset of clone members. The influence of affinity maturation on the B-cell population can be inferred by analysing the pattern of somatic mutations in the Ig. While global analysis of mutation patterns has shown evidence of strong selection pressures shaping the B-cell population, the effect of different time-scales of selection and diversification has not yet been studied. Analysis of B cells from blood samples of three healthy individuals identifies a range of clone sizes with lineage trees that can contain long trunks and canopies indicating the significant diversity introduced by the affinity maturation process. We here show that observed mutation patterns in the framework regions (FWRs) are determined by an almost purely purifying selection on both short and long time-scales. By contrast, complementarity determining regions (CDRs) are affected by a combination of purifying and antigen-driven positive selection on the short term, which leads to a net positive selection in the long term. In both the FWRs and CDRs, long-term selection is strongly dependent on the heavy chain variable gene family.

Visualizing antibody affinity maturation in germinal centers

Antibodies somatically mutate to attain high affinity in germinal centers (GCs). There, competition between B cell clones and among somatic mutants of each clone drives an increase in average affinity across the population. The extent to which higher-affinity cells eliminating competitors restricts clonal diversity is unknown. By combining multiphoton microscopy and sequencing, we show that tens to hundreds of distinct B cell clones seed each GC and that GCs lose clonal diversity at widely disparate rates. Furthermore, efficient affinity maturation can occur in the absence of homogenizing selection, ensuring that many clones can mature in parallel within the same GC. Our findings have implications for development of vaccines in which antibodies with nonimmunodominant specificities must be elicited, as is the case for HIV-1 and influenza.

Clonal and cellular dynamics in germinal centers

Germinal centers (GCs) are the site of antibody affinity maturation, a process that involves complex clonal and cellular dynamics. Selection of B cells bearing higher-affinity immunoglobulins proceeds via a stereotyped pattern whereby B cells migrate cyclically between the GC's two anatomical compartments. This process occurs in a timeframe that is well suited to analysis by intravital microscopy, and much has been learned in recent years by use of these techniques. On a longer time scale, the diversity of B cell clones and variants within individual GCs is also thought to change as affinity maturation progresses; however, our understanding of clonal dynamics in individual GCs is limited. We discuss recent progress in the elucidation of clonal and cellular dynamics patterns.

Multi Step Selection in Ig H Chains is Initially Focused on CDR3 and Then on Other CDR Regions

AFFINITY MATURATION OCCURS THROUGH TWO SELECTION PROCESSES

the choice of appropriate clones (clonal selection), and the internal evolution within clones, induced by somatic hyper-mutations, where high affinity mutants are selected for. When a final population of immunoglobulin sequences is observed, the genetic composition of this population is affected by a combination of these two processes. Different immune induced diseases can result from the failure of regulation of clonal selection or of the regulation of the within clone affinity maturation. In order to understand each of these processes separately, we propose a mixed lineage tree/sequence based method to detect within clone selection as defined by the effect of mutations on the average number of offspring. Specifically, we measure the imbalance in the number of leaves in lineage trees branches following synonymous and non-synonymous (NS) mutations. If a mutation is positively selected, we expect the number of leaves in the sub-tree below this mutation to be larger than in the parallel sub-tree without the mutation. The ratio between the number of leaves in such branches following NS mutations can be used to measure selection within a clone. We apply this method to the sampled Ig repertoire from multiple healthy volunteers and show that within clone selection is positive in the CDR2 region and either positive or negative in the CDR3 and FWR3 regions. Selection occurs already at the IgM isotype level mainly in the DH gene region, with a strong negative selection in the join region. This is followed in the later memory stages in the CDR2 region. We have not studied here the FWR1 and CDR1 regions. An important advantage of this method is that it is very weakly affected by the baseline mutation model or by sampling biases, as are most synonymous to NS mutations ratio based methods.

How oligoclonal are germinal centers? A new method for estimating clonal diversity from immunohistological sections

Background

The germinal center (GC) reaction leads to antibody affinity maturation and generation of memory B cells, but its underlying mechanisms are poorly understood. To assemble this puzzle, several key pieces of information are needed, one in particular being the number of participating B cell clones. Since this clonal diversity cannot be observed directly, earlier studies resorted to interpreting two types of available experimental data: Immunohistology of GCs containing two phenotypically distinct B-cell populations, and antibody gene sequences of small B-cell samples from GCs. Based on a simple model, investigators concluded that a typical GC was seeded by 2-8 B cells, endorsing the current notion that GCs are oligoclonal from the onset.

Results

A re-evaluation of these data showed that the used simple model is not statistically consistent with the original data. From an analysis of the experimental system, we propose a new model for estimating GC clonal diversity, including the initially neglected sampling and measurement errors, and making more general assumptions. Consistency analysis with the new model yielded an estimation of sampling and measurement errors in the experimental data of 10-11% for one B-cell population and 62-64% for the other population, and an average number of 19-23 seeder B cells. An independent analysis of antibody gene sequences of small B-cell samples from GCs, using an adapted Yule estimator of diversity, yielded a minimum estimation of 20-30 GC founder B cells, confirming the previous results.

Conclusions

Our new experimental-based model provides a highly improved method to estimate the clonal diversity of GCs from inmunohistochemistry data of chimeric animals. Calculations based on this model, and validated by an independent approach, indicate that GCs most likely contain broadly varying numbers of different B cell clones, averaging 5- to 10-fold more clones than previously estimated. These findings, in line with recent results showing that GC sizes and life times are also subject to high variability, dramatically change the picture of GC dynamics.

A theory of germinal center B cell selection, division, and exit

High-affinity antibodies are generated in germinal centers in a process involving mutation and selection of B cells. Information processing in germinal center reactions has been investigated in a number of recent experiments. These have revealed cell migration patterns, asymmetric cell divisions, and cell-cell interaction characteristics, used here to develop a theory of germinal center B cell selection, division, and exit (the LEDA model). According to this model, B cells selected by T follicular helper cells on the basis of successful antigen processing always return to the dark zone for asymmetric division, and acquired antigen is inherited by one daughter cell only. Antigen-retaining B cells differentiate to plasma cells and leave the germinal center through the dark zone. This theory has implications for the functioning of germinal centers because compared to previous models, high-affinity antibodies appear one day earlier and the amount of derived plasma cells is considerably larger.

Short-time evolution in the adaptive immune system

We exploit a simple model to numerically and analytically investigate the effect of enforcing a time constraint for achieving a system-wide goal during an evolutionary dynamics. This situation is relevant to finding antibody specificities in the adaptive immune response as well as to artificial situations in which an evolutionary dynamics is used to generate a desired capability in a limited number of generations. When the likelihood of finding the target phenotype is low, we find that the optimal mutation rate can exceed the error threshold, in contrast to conventional evolutionary dynamics. We also show how a logarithmic correction to the usual inverse scaling of population size with mutation rate arises. Implications for natural and artificial evolutionary situations are discussed.

Statistical mechanical concepts in immunology

Higher organisms, such as humans, have an adaptive immune system that usually enables them to successfully combat diverse (and evolving) microbial pathogens. The adaptive immune system is not preprogrammed to respond to prescribed pathogens. Yet it mounts pathogen-specific responses against diverse microbes and establishes memory of past infections (the basis of vaccination). Although major advances have been made in understanding pertinent molecular and cellular phenomena, the mechanistic principles that govern many aspects of an immune response are not known. We illustrate how complementary approaches from the physical and life sciences can help confront this challenge. Specifically, we describe work that brings together statistical mechanics and cell biology to shed light on how key molecular/cellular components of the adaptive immune system are selected to enable pathogen-specific responses. We hope these examples encourage physical chemists to work at this crossroad of disciplines where fundamental discoveries with implications for human health might be made.

Optimality of mutation and selection in germinal centers

The population dynamics theory of B cells in a typical germinal center could play an important role in revealing how affinity maturation is achieved. However, the existing models encountered some conflicts with experiments. To resolve these conflicts, we present a coarse-grained model to calculate the B cell population development in affinity maturation, which allows a comprehensive analysis of its parameter space to look for optimal values of mutation rate, selection strength, and initial antibody-antigen binding level that maximize the affinity improvement. With these optimized parameters, the model is compatible with the experimental observations such as the ∼100-fold affinity improvements, the number of mutations, the hypermutation rate, and the “all or none” phenomenon. Moreover, we study the reasons behind the optimal parameters. The optimal mutation rate, in agreement with the hypermutation rate in vivo, results from a tradeoff between accumulating enough beneficial mutations and avoiding too many deleterious or lethal mutations. The optimal selection strength evolves as a balance between the need for affinity improvement and the requirement to pass the population bottleneck. These findings point to the conclusion that germinal centers have been optimized by evolution to generate strong affinity antibodies effectively and rapidly. In addition, we study the enhancement of affinity improvement due to B cell migration between germinal centers. These results could enhance our understanding of the functions of germinal centers.

The antibodies in our immune system could efficiently improve their abilities in recognizing new antigens. This is done with the help of proliferation, mutation and selection of B cells which carry antibodies, but we have difficulties in developing a quantitative description of this adaptation process which is consistent with the various aspects of experimental observations. Based on the knowledge from experiments, here we present a theoretical model to calculate the numbers of B cells with different antigen recognizing abilities all the time, and look for the best possible design that improves the antigen recognizing ability most efficiently. We find that the best possible design is consistent with the experimental observations, pointing to the conclusion that the immune system has been optimized in evolution. We then study the trade-offs leading to the optimization of the design. The results will not only improve our understanding of the functions in immune system, but also reveal the design principles behind the details. In addition, the study enhances our understanding of the population dynamics in evolution.

Broad volume distributions indicate nonsynchronized growth and suggest sudden collapses of germinal center B cell populations

Immunization with a T cell-dependent Ag leads to the formation of several hundred germinal centers (GCs) within secondary lymphoid organs, a key process in the maturation of the immune response. Although prevailing perceptions about affinity maturation intuitively assume simultaneous seeding, growth, and decay of GCs, our previous mathematical simulations led us to hypothesize that their growth might be nonsynchronized. To investigate this, we performed computer-aided three-dimensional reconstructions of splenic GCs to measure size distributions at consecutive time points following immunization of BALB/c mice with a conjugate of 2-phenyl-oxazolone and chicken serum albumin. Our analysis reveals a broad volume distribution of GCs, indicating that individual GCs certainly do not obey the average time course of the GC volumes and that their growth is nonsynchronized. To address the cause and implications of this behavior, we compared our empirical data with simulations of a stochastic mathematical model that allows for frequent and sudden collapses of GCs. Strikingly, this model succeeds in reproducing the empirical average kinetics of GC volumes as well as the underlying broad size distributions. Possible causes of GC B cell population collapses are discussed in the context of the affinity-maturation process.

Exploration of factors affecting the onset and maturation course of follicular lymphoma through simulations of the germinal center

Genetic mutations frequently observed in human follicular lymphoma (FL) B-cells result in aberrant expression of the anti-apoptotic protein bcl-2 and surface immunoglobulins (Igs) which display one or more novel variable (V) region N-glycosylation motifs. In the present study, we develop a simulation model of the germinal center (GC) to explore how these mutations might influence the emergence and clonal expansion of key mutants which provoke FL development. The simulations employ a stochastic method for calculating the cellular dynamics, which incorporates actual IgV region sequences and a simplified hypermutation scheme. We first bring our simulations into agreement with experimental data for well-characterized normal and bcl-2(+) anti-hapten GC responses in mice to provide a model for understanding how bcl-2 expression leads to permissive selection and memory cell differentiation of weakly competitive B-cells. However, as bcl-2 expression in the GC alone is thought to be insufficient for FL development, we next monitor simulated IgV region mutations to determine the emergence times of key mutants displaying aberrant N-glycosylation motifs recurrently observed in human FL IgV regions. Simulations of 26 germline V(H) gene segments indicate that particular IgV regions have a dynamical selective advantage by virtue of the speed with which one or more of their key sites can generate N-glycosylation motifs upon hypermutation. Separate calculations attribute the high occurrence frequency of such IgV regions in FL to an ability to produce key mutants at a fast enough rate to overcome stochastic processes in the GC that hinder clonal expansion. Altogether, these simulations characterize three pathways for FL maturation through positively selected N-glycosylations, namely, via one of two key sites within germline V(H) region gene segments, or via a site in the third heavy chain complementarity-determining region (CDR-H3) that is generated from VDJ recombination.

Deriving a germinal center lymphocyte migration model from two-photon data

Recently, two-photon imaging has allowed intravital tracking of lymphocyte migration and cellular interactions during germinal center (GC) reactions. The implications of two-photon measurements obtained by several investigators are currently the subject of controversy. With the help of two mathematical approaches, we reanalyze these data. It is shown that the measured lymphocyte migration frequency between the dark and the light zone is quantitatively explained by persistent random walk of lymphocytes. The cell motility data imply a fast intermixture of cells within the whole GC in approximately 3 h, and this does not allow for maintenance of dark and light zones. The model predicts that chemotaxis is active in GCs to maintain GC zoning and demonstrates that chemotaxis is consistent with two-photon lymphocyte motility data. However, the model also predicts that the chemokine sensitivity is quickly down-regulated. On the basis of these findings, we formulate a novel GC lymphocyte migration model and propose its verification by new two-photon experiments that combine the measurement of B cell migration with that of specific chemokine receptor expression levels. In addition, we discuss some statistical limitations for the interpretation of two-photon cell motility measurements in general.

Recirculation of germinal center B cells: a multilevel selection strategy for antibody maturation

Optimization of antibody affinity is a hallmark of the humoral immune response. It takes place in hundreds of transient microstructures called germinal centers (GCs). Their function and time-dependent behavior are subjects of active investigation. According to a generally accepted notion, their individual kinetics follows the average kinetics of all GCs present in the observed lymphatic tissue. In this review, we challenge this view and point out, with the help of mathematical simulations, that inferring the kinetics of individual GCs from cross-sectional evaluation of GC kinetics is virtually impossible. Thus, the time course of individual GCs is open to conjecture. For instance, one possible interpretation is that GCs exist for a time span considerably shorter than that of the observed average kinetics. We explore the implications of different temporal organizations of GCs in the light of the hypothesis that GC B-cell emigrants recolonize GC niches. This assumption leads to a view where GCs work in parallel but are linked by recirculation of B-cell emigrants. In this view, interleaved global and local competition provide for an implementation of multiple levels of B-cell selection in affinity maturation. The concepts of iteration, all-or-none behavior, and phasic mutation schedule are discussed in the light of this hypothesis.

Germinal center-independent affinity maturation in tumor necrosis factor receptor 1-deficient mice

Germinal centers (GCs) have been identified as site at which the somatic mutation of immunoglobulins occurs.However, somatic mutations in immunoglobulins have also been observed in animals that normally do not harbor germinal centers. This clearly indicates that somatic mutations can occur in the absence of germinal centers. We therefore attempted to determine whether or not GCs exist in TNFR1-deficient mice, and are essential for the somatic mutation of immunoglobulins, using (4-hydroxy-3-nitropheny)acetyl-ovalbumin (NP-OVA). Both wild-type and TNFR1-deficient mice were immunized with NPOVA, and then examined with regard to the existence of GCs. No typical B-cell follicles were detected in the TNFR1-deficient mice. Cell proliferation was detected throughout all splenic tissue types, and no in vivo immunecomplex retention was observed in the TNFR1-deficient mice. All of these data strongly suggest that no GCs were formed in the TNFR1-deficient mice. Although TNFR1-deficient mice are unable to form GCs, serological analyses indicated that affinity maturation had been achieved in both the wild-type and TNFR1-deficient mice. We therefore isolated and sequenced several DNA clones from wild-type and the TNFR1-deficient mice. Eight out of 12 wild-type clones, and 11 out of 14 clones of the TNFR-1-deficient mice contained mutations at the CDR1 site. Thus, the wild-type and TNFR1-deficient mice were not extremely different with regard to types and rates of somatic mutation. Also, high-affinity antibodies were detected in both types of mice. Collectively, our data appear to show that affinity maturation may occur in TNFR1-deficient mice, which completely lack GCs.

Re-evaluating the recycling hypothesis in the germinal centre

Mathematical models have been used to study different aspects of the germinal centre reaction, in particular, affinity maturation of antibodies and the hypothesis of recycling. So far, interpretation of several theoretical and experimental results has pointed to the existence of recycling. However, theoretical models have seldom been compared with experimental data from specific immune responses and the potential relevance of recycling in the germinal centre is still an open problem. In this article, we propose a model without recycling that takes into account selection mechanisms that were previously uncovered experimentally. We apply the model to several experimental systems that use different Ag and compare the results with experimental data of affinity maturation whenever available. The results obtained for a primary immune response to the hapten (4-hydroxy-3-nitrophenyl)-acetyl show that recycling is not a necessary mechanism to achieve the level of affinity maturation observed in germinal centre reactions. Similar levels of affinity maturation are obtained for other responses, although for antibodies involving several affinity-enhancing mutations the affinity maturation obtained with the model is much lower. Interpretation of these results and consequences towards the concept of recycling are discussed.

Stochastic discrete event simulation of germinal center reactions

We introduce a generic reaction-diffusion model for germinal center reactions and perform numerical simulations within a stochastic discrete event approach. In contrast to the frequently used deterministic continuum approach, each single reaction event is monitored in space and time in order to simulate the correct time evolution of this complex biological system. Germinal centers play an important role in the immune system by performing a reaction that aims at improving the affinity between antibodies and antigens. Our model captures experimentally observed features of this reaction, such as the development of the remarkable germinal center morphology and the maturation of antibody-antigen affinity in the course of time. We model affinity maturation within a simple affinity class picture and study it as a function of the distance between the initial antibody-antigen affinity and the highest possible affinity. The model reveals that this mutation distance may be responsible for the experimentally observed all-or-none behavior of germinal centers; i.e., they generate either mainly output cells of high affinity or no high-affinity output cells at all. Furthermore, the exact simulation of the system dynamics allows us to study the hypothesis of cell recycling in germinal centers as a mechanism for affinity optimization. A comparison of three possible recycling pathways indicates that affinity maturation is optimized by a recycling pathway that has previously not been taken into account in deterministic continuum models.

Public, private and non-specific antibodies induced by non-cytopathic viral infections

Lymphocytic choriomeningitis virus (LCMV) represents a useful experimental model of murine infection with a non-cytopathic virus, bearing resemblance to HIV and hepatitis C virus (HCV) infections in humans. Recent data from the LCMV model indicate that the humoral immune response that is induced by non-cytopathic viruses is far more complex than previously appreciated. LCMV-induced IgG production is largely polyclonal, with more than 90% of the antibody repertoire constituting non-relevant specificities. A delayed virus-neutralizing antibody response is induced, including specificities directed not only against the parental LCMV-strain present in the host but also cross-specifically against LCMV-variants isolated from other hosts. These findings provide novel insights to aid our understanding of clinically relevant observations that are recorded following human infection with HIV, HCV and dengue viruses.

Analysis of mutational lineage trees from sites of primary and secondary Ig gene diversification in rabbits and chickens

Lineage trees of mutated rearranged Ig V region sequences in B lymphocyte clones often serve to qualitatively illustrate claims concerning the dynamics of affinity maturation. In this study, we use a novel method for analyzing lineage tree shapes, using terms from graph theory to quantify the differences between primary and secondary diversification in rabbits and chickens. In these species, Ig gene diversification starts with rearrangement of a single (in chicken) or a few (in rabbit) V(H) genes. Somatic hypermutation and gene conversion contribute to primary diversification in appendix of young rabbits or in bursa of Fabricius of embryonic and young chickens and to secondary diversification during immune responses in germinal centers (GCs). We find that, at least in rabbits, primary diversification appears to occur at a constant rate in the appendix, and the type of Ag-specific selection seen in splenic GCs is absent. This supports the view that a primary repertoire is being generated within the expanding clonally related B cells in appendix of young rabbits and emphasizes the important role that gut-associated lymphoid tissues may play in early development of mammalian immune repertoires. Additionally, the data indicate a higher rate of hypermutation in rabbit and chicken GCs, such that the balance between hypermutation and selection tends more toward mutation and less toward selection in rabbit and chicken compared with murine GCs.

Why are there so few key mutant clones? The influence of stochastic selection and blocking on affinity maturation in the germinal center

A small number of key somatic mutations lead to high-affinity binding in the anti-hapten immune responses to 2-phenyl-5-oxazolone (phOx) and (4-hydroxy-3-nitrophenyl)acetyl (NP). Affinity maturation models of the germinal center hold that B cells carrying these key mutations are preferentially selected for expansion within the germinal centers. However, additional factors are required to account for some quantitative aspects of affinity maturation in vivo. Radmacher et al. have shown that key mutants are observed in vivo significantly less frequently than expected by these models. To account for this finding, they propose that selection is a stochastic process where key mutants may be overlooked by positive selection or recruited out of the germinal center. While acknowledging that a minimal amount of stochastic selection is probably unavoidable in the germinal center, we instead propose a structural explanation for this key mutant discrepancy. This model is based on the existence of a large number of blocking mutations whose presence can prevent the ability of key mutations to confer high-affinity binding. Using mathematical modeling and computer simulation, we show that in addition to reconciling the key mutant discrepancy, the blocking model accounts for other aspects of experimental data that are not predicted by the stochastic selection model. In particular, the blocking model is consistent with the observation that key mutants generally exhibit a higher number of mutations per sequence in the phOx response, but a lower number in the NP response.

A spatial model of germinal center reactions: cellular adhesion based sorting of B cells results in efficient affinity maturation

Affinity maturation of humoral responses to T-cell-dependent antigens occurs in germinal centers (GC). In GCs antigen-specific B cells undergo rounds of somatic mutations that alter their affinity. High-affinity mutants take over GCs very soon after they appear; the replacement rate is as high as 4 per day (Radmacher et al., Immunol. Cell Biol. 76 (1998) 373). To gain more insight into this selection process, we present a spatial model of GC reactions, where B cells compete for survival signals from follicular dendritic cells (FDC). Assuming that high-affinity B cells have increased cellular adhesion to FDCs, we obtain an affinity-based sorting of B cells on the FDC. This sorting imposes a very strong selection and therefore results in a winner-takes-all behavior. By comparing our sorting model with "affinity-proportional selection models", we show that this winner-takes-all selection is in fact required to account for the fast rates at which high affinity mutants take over GCs. Another important feature of in vivo GC reactions is that they are non-mixed, i.e. GCs contain either no high-affinity cells at all or they are dominated by high-affinity cells. We here show that this all-or-none behavior can be obtained if B cells are sorted based on their affinity on the FDC surface. Affinity-proportional selection models, in contrast, always produce mixed GCs.

A mathematical model for germinal centre kinetics and affinity maturation

We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction. We show that antigen masking by antibodies which are produced by emerging plasma cells can drive affinity maturation and provide a feedback mechanism by which the reaction is stable against variations in the initial antigen amount over several orders of magnitude. This provides a possible answer to the long-standing question of the role of antigen reduction in driving affinity maturation. By comparing model predictions with experimental results, we propose that the selection probability of centrocytes and the recycling probability of selected centrocytes are not constant but vary during the GC reaction with respect to time. It is shown that the efficiency of affinity maturation is highest if clones with an affinity for the antigen well above the average affinity in the GC leave the GC for either the memory or plasma cell pool. It is further shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation. The impact on affinity maturation of simultaneous initiation of memory cell formation and somatic hypermutation vs. delayed initiation of memory cell formation is discussed.

B lymphocyte memory: role of stromal cell complement and FcgammaRIIB receptors

To dissect the influence of CD21/CD35 and FcgammaRIIB in antigen retention and humoral memory, we used an adoptive transfer model in which antigen-primed B and T lymphocytes were given to sublethally irradiated wild-type mice or mice deficient in CD21/CD35 (Cr2(-/-)) or FcgammaRIIB receptors (FcgammaRIIB(-/-)). Cr2(-/-) chimeras showed impaired memory as characterized by a decrease in antibody titer, reduced frequency of antibody secreting cells, an absence of affinity maturation, and significantly reduced recall response. The impaired memory in Cr2(-/-) chimeras corresponded with the reduced frequency of antigen-specific memory B cells. Interestingly, FcgammaRIIB(-/-) chimeras showed a differential phenotype with impaired splenic but normal bone marrow responses. These data suggest that CD21/CD35 on stroma, including follicular dendritic cells, is critical to the maintenance of long-term B lymphocyte memory.

Dominant, hierarchical induction of peripheral tolerance during foreign antigen-driven B cell development

We created mice expressing transgene-encoded BCRs with "dual reactivity" for the hapten Ars and nuclear autoantigens. Expression of transgene-encoded BCRs was not evident in the memory compartment despite observation of transgene-expressing B cells in germinal centers following Ars immunization. In contrast, dual reactive mAbs were readily obtained from mice with enforced expression of Bcl-2 following secondary Ars immunization. However, while these mAbs were hypermutated and displayed increased affinity for Ars, all had reduced avidity for DNA and intracellular autoantigens. Thus, Bcl-2 alters dominant-negative selection of dual reactive B cells during the Ars response, but this is restricted to those with lowered autoreactivity, demonstrating a hierarchy of peripheral tolerance during memory B cell development.

A mathematical model for the germinal center morphology and affinity maturation

During germinal center reactions, the appearance of two specific zones are observed: the dark and the light zone. Up to now, the origin and function of these zones are poorly understood. In the framework of a stochastic and discrete model, several possible pathways of zone development during germinal center reactions are investigated. The importance of the zones in the germinal center for affinity maturation, i.e. the process of antibody optimization is discussed.

Does recycling in germinal centres exist?

A general criterion is formulated to decide if the recycling of B cells exists in germinal centre (GC) reactions. The criterion is independent of the selection and affinity maturation process and based solely on total centroblast population arguments. An experimental test is proposed to verify whether the criterion is fulfilled.

Toward quantitative simulation of germinal center dynamics: biological and modeling insights from experimental validation

As models of immune system dynamics are developed, it is important to validate them with specific experimental data in order to understand their shortcomings and guide them toward becoming predictive. In this paper, we examine whether a particular mathematical model of germinal center dynamics, proposed by Oprea and Perelson, can reproduce experimental data from two specific primary responses, namely those directed against the haptens 2-phenyl-5-oxazolone and (4-hydroxy-3-nitrophenyl)acetyl. We develop formulas for estimating response-specific model parameters, as well as constraints for validating the model. In addition, we outline a general methodology for translating a continuous/deterministic model, expressed as a set of ordinary differential equations, into a discrete/stochastic framework. This methodology is used to create a new implementation of the Oprea and Perelson model that enables comparison with data on individual germinal centers. We conclude that while the model can reproduce the average dynamics of splenic germinal centers, it is at best incomplete and does not reproduce the distribution of individual germinal center behaviors. In addition to suggesting possible extensions to the model which can reconcile the dynamics with some aspects of the experimental data, we make a number of specific predictions that can be tested by in vivo experiments to obtain further insights and validation.

Recycling probability and dynamical properties of germinal center reactions

We introduce a new model for the dynamics of centroblasts and centrocytes in a germinal center. The model reduces the germinal center reaction to the elements considered as essential and embeds proliferation of centroblasts, point mutations of the corresponding antibody types represented in a shape space, differentiation to centrocytes, selection with respect to initial antigens, differentiation of positively selected centrocytes to plasma or memory cells and recycling of centrocytes to centroblasts. We use exclusively parameters with a direct biological interpretation such that, once determined by experimental data, the model gains predictive power. Based on the experiment of Han et al. (1995b) we predict that a high rate of recycling of centrocytes to centroblasts is necessary for the germinal center reaction to work reliably. Furthermore, we find a delayed start of the production of plasma and memory cells with respect to the start of point mutations, which turns out to be necessary for the optimization process during the germinal center reaction. The dependence of the germinal center reaction on the recycling probability is analysed.

Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood

The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.

Dissecting affinity maturation: a model explaining selection of antibody-forming cells and memory B cells in the germinal centre

Until recently, the relationship between apoptosis, selection in the germinal centre (GC) and production of high-affinity antibody-forming cells (AFCs) and memory B cells has been unclear. Here, Tarlinton and Smith present a model that accounts for the switch in GC production from high-affinity AFCs to memory B cells, and explain how Bcl-2, an inhibitor of apoptosis, can influence memory cells but not bone marrow AFCs.

Neonatal immunity and somatic mutation

Neonatal animals are able to mount an effective immune response, both humoral and cellular, when immunized using conditions that maximize stimulation of antigen presenting cells, T cells, and B cells. In adults, somatic mutation is a key feature of the humoral immune response because it contributes to the generation of high affinity memory B cells. Recent evidence that B cells in neonatal mice and human infants can somatically mutate their immunoglobulin heavy chains suggests that neonates can utilize somatic mutation not only to diversify their restricted germline antibody repertoire, but also to improve upon this repertoire by the generation of B cells which can produce higher affinity antibodies. By extrapolation, if vaccination of children early in life resulted in somatic mutation and affinity maturation, this could provide a more protective antibody response to childhood diseases.

bcl-2 transgene expression inhibits apoptosis in the germinal center and reveals differences in the selection of memory B cells and bone marrow antibody-forming cells

Immunization with T cell-dependent antigens generates long-lived memory B cells and antibody-forming cells (AFCs). Both populations originate in germinal centers and, predominantly, produce antibodies with high affinity for antigen. The means by which germinal center B cells are recruited into these populations remains unclear. We have examined affinity maturation of antigen-specific B cells in mice expressing the cell death inhibitor bcl-2 as a transgene. Such mice had reduced apoptosis in germinal centers and an excessive number of memory B cells with a low frequency of V gene somatic mutation, including those mutations encoding amino acid exchanges known to enhance affinity. Despite the frequency of AFCs being increased in bcl-2-transgenic mice, the fraction secreting high-affinity antibody in the bone marrow at day 42 remained unchanged compared with controls. The inability of BCL-2 to alter selection of bone marrow AFCs is consistent with these cells being selected within the germinal center on the basis of their affinity being above some threshold rather than their survival being due to a selective competition for an antigen-based signal. Continuous competition for antigen does, however, explain formation of the memory compartment.

Contrasting the In Situ Behavior of a Memory B Cell Clone During Primary and Secondary Immune Responses

Whether memory B cells possess altered differentiative potentials and respond in a qualitatively distinct fashion to extrinsic signals as compared with their naive precursors is a current subject of debate. We have investigated this issue by examining the participation of a predominant anti-arsonate clonotype in the primary and secondary responses in the spleens of A/J mice. While this clonotype gives rise to few Ab-forming cells (AFC) in the primary response, shortly after secondary immunization its memory cell progeny produce a massive splenic IgG AFC response, largely in the red pulp. Extensive clonal expansion and migration take place during the secondary AFC response but Ab V region somatic hypermutation is not reinduced. The primary and secondary germinal center (GC) responses of this clonotype are both characterized by ongoing V gene hypermutation and phenotypic selection, little or no inter-GC migration, and derivation of multiple, spatially distinct GCs from a single progenitor. However, the kinetics of these responses differ, with V genes containing a high frequency of total as well as affinity-enhancing mutations appearing rapidly in secondary GCs, suggesting either recruitment of memory cells into this response, or accelerated rates of hypermutation and selection. In contrast, the frequency of mutation observed per V gene does not increase monotonically during the primary GC response of this clonotype, suggesting ongoing emigration of B cells that have sustained affinity- and specificity-enhancing mutations.