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.     

Lineage tree analysis of immunoglobulin variable-region gene mutations in autoimmune diseases: chronic activation, normal selection

Autoimmune diseases show high diversity in the affected organs, clinical manifestations and disease dynamics. Yet they all share common features, such as the ectopic germinal centers found in many affected tissues. Lineage trees depict the diversification, via somatic hypermutation (SHM), of immunoglobulin variable-region (IGV) genes. We previously developed an algorithm for quantifying the graphical properties of IGV gene lineage trees, allowing evaluation of the dynamical interplay between SHM and antigen-driven selection in different lymphoid tissues, species, and disease situations. Here, we apply this method to ectopic GC B cell clones from patients with Myasthenia Gravis, Rheumatoid Arthritis, and Sj?gren's Syndrome, using data scaling to minimize the effects of the large variability due to methodological differences between groups. Autoimmune trees were found to be significantly larger relative to normal controls. In contrast, comparison of the measurements for tree branching indicated that similar selection pressure operates on autoimmune and normal control clones.     

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.     

Maturation of the immune response in germinal centers.

Germinal centers develop in peripheral lymphatic tissue during the primary immune response and may play a crucial role in affinity maturation. We have compared the diversification of the antigen-specific repertoire of B cells, both from within and from outside the germinal centers, during the murine response to 2-phenyloxazolone (phOx). By sequencing V kappa Ox1 L-chains characteristic of phOx-specific antibodies, we show that somatic mutations accumulate in germinal center B cells and that a mutation conferring high affinity binding is found with increasing frequency. An analysis of V/D/J rearrangements suggests that this mutation occurred independently in many B cells, which were then preferentially expanded. We conclude that, although the hypermutation mechanism may be activated before germinal centers develop, affinity maturation by hypermutation and selection takes place in the germinal centers.     

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.     

Mutation parameters from DNA sequence data using graph theoretic measures on lineage trees

MOTIVATION: B cells responding to antigenic stimulation can fine-tune their binding properties through a process of affinity maturation composed of somatic hypermutation, affinity-selection and clonal expansion. The mutation rate of the B cell receptor DNA sequence, and the effect of these mutations on affinity and specificity, are of critical importance for understanding immune and autoimmune processes. Unbiased estimates of these properties are currently lacking due to the short time-scales involved and the small numbers of sequences available. RESULTS: We have developed a bioinformatic method based on a maximum likelihood analysis of phylogenetic lineage trees to estimate the parameters of a B cell clonal expansion model, which includes somatic hypermutation with the possibility of lethal mutations. Lineage trees are created from clonally related B cell receptor DNA sequences. Important links between tree shapes and underlying model parameters are identified using mutual information. Parameters are estimated using a likelihood function based on the joint distribution of several tree shapes, without requiring a priori knowledge of the number of generations in the clone (which is not available for rapidly dividing populations in vivo). A systematic validation on synthetic trees produced by a mutating birth-death process simulation shows that our estimates are precise and robust to several underlying assumptions. These methods are applied to experimental data from autoimmune mice to demonstrate the existence of hypermutating B cells in an unexpected location in the spleen.     

Reconciling repertoire shift with affinity maturation: the role of deleterious mutations

The shift in Ab repertoire, from Abs dominating certain primary B cell responses to genetically unrelated Abs dominating subsequent "memory" responses, challenges the accepted paradigm of affinity maturation. We used mathematical modeling and computer simulations of the dynamics of B cell responses, hypermutation, selection, and memory cell formation to test hypotheses attempting to explain repertoire shift. We show that repertoire shift can be explained within the framework of the affinity maturation paradigm, only when we recognize the destructive nature of hypermutation: B cells with a high initial affinity for the Ag are less likely to improve through random mutations.     

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.     

Impaired affinity maturation in Cr2-/- mice is rescued by adjuvants without improvement in germinal center development

Cr2-/- mice have an impairment in humoral immunity, as shown by the decrease in the Ab titers against T cell-dependent Ags and abnormalities in germinal center formation. Germinal centers are present, but they are decreased in size and number, indicating problems in their development. In this study, we investigated whether this abnormality in germinal center development is associated with problems in the establishment of optimal affinity maturation and the generation of memory B cells, processes closely related to the germinal center reaction. We immunized the Cr2-/- animals with different Ags with or without adjuvants. We showed that, when immunized without adjuvants, complement receptors are absolutely required for optimal affinity maturation. Although limited affinity maturation is elicited in the Cr2-/- Ab response, it is decreased as compared with normal animals. Memory B cell generation is also impaired. In the presence of adjuvants, germinal center development in the Cr2-/- mice is still abnormal, as demonstrated by their decreased size and number. Surprisingly, adjuvants establish optimal affinity maturation and partially restore the amount of Ab produced during the primary response and memory B cell generation. However, adjuvants cannot improve the ability of follicular dendritic cells to retain Ags in the form of immune complexes. These observations indicate that immunization with inflammatory Ags offset some of the immunological abnormalities found in the Cr2-/- mice and show that optimal affinity maturation in the Cr2-/- mice can be achieved in the absence of normal germinal centers.     

Immune system learning and memory quantified by graphical analysis of B-lymphocyte phylogenetic trees

The immune system learns from its encounters with pathogens and memorizes its experiences. One of the mechanisms it uses for this purpose is the intra-individual evolution of antigen receptors on B lymphocytes, achieved via hypermutation and selection of antigen receptor variable region genes during an immune response. We have developed a novel method for analyzing the graphical properties of phylogenetic trees of receptor genes which have been mutated and selected during an immune response. In the study presented here, we address the artifacts introduced by experimental methods of cell collection for DNA analysis, the meaning of each parameter measured on the tree graphs, and the differences between the dynamics of the humoral immune response in different lymphoid tissues.     

Key mutations stabilize antigen‐binding conformation during affinity maturation of a broadly neutralizing influenza antibody lineage

Affinity maturation, the process in which somatic hypermutation and positive selection generate antibodies with increasing affinity for an antigen, is pivotal in acquired humoral immunity. We have studied the mechanism of affinity gain in a human B‐cell lineage in which two main maturation pathways, diverging from a common ancestor, lead to three mature antibodies that neutralize a broad range of H1 influenza viruses. Previous work showed that increased affinity in the mature antibodies derives primarily from stabilization of the CDR H3 loop in the antigen‐binding conformation. We have now used molecular dynamics simulations and existing crystal structures to identify potentially key maturation mutations, and we have characterized their effects on the CDR H3 loop and on antigen binding using further simulations and experimental affinity measurements, respectively. In the two maturation pathways, different contacts between light and heavy chains stabilize the CDR H3 loop. As few as two single‐site mutations in each pathway can confer substantial loop stability, but none of them confers experimentally detectable stability on its own. Our results support models of the germinal center reaction in which two or more mutations can occur without concomitant selection and show how divergent pathways have yielded functionally equivalent antibodies. Proteins 2014; 83:771–780. © 2014 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

The block in immunoglobulin class switch recombination caused by activation-induced cytidine deaminase deficiency occurs prior to the generation of DNA double strand breaks in switch mu region

Affinity maturation of the Ab repertoire in germinal centers leads to the selection of high affinity Abs with selected heavy chain constant regions. Ab maturation involves two modifications of the Ig genes, i.e., somatic hypermutation and class switch recombination. The mechanisms of these two processes are not fully understood. As shown by the somatic hypermutation and class switch recombination-deficient phenotype of activation-induced cytidine deaminase (AID)-deficient patients (hyperIgM type 2 syndrome) and mice, both processes require the AID molecule. Somatic DNA modifications require DNA breaks, which, at least for class switch recombination, lead to dsDNA breaks. By using a ligation-mediated PCR, it was found that class switch recombination-induced dsDNA breaks in S mu switch regions were less frequent in AID-deficient B cells than in AID-proficient B cells, thus indicating that AID acts upstream of DNA break induction.     

The T cell-dependent B cell immune response and germinal center reaction are intact in A-myb-deficient mice

Expression of the protooncogene A-myb is restricted to the developing CNS, adult testes, breasts in late pregnancy, and germinal centers of secondary B cell follicles. The functional relevance of A-myb expression at three of these sites has been demonstrated previously via the generation and analysis of A-myb-deficient mice, which display behavioral abnormalities, male sterility, and perturbed breast development during pregnancy. In contrast, here we show that the germinal center response driven by T cell-dependent Ag immunization and the associated processes of Ab V gene somatic hypermutation, affinity maturation, and heavy chain class switching are overtly normal in A-myb-deficient mice. Nonetheless, these mice display mild splenic white pulp hypoplasia and blunted primary serum Ab responses, suggesting that although A-myb is not directly involved in the regulation of the memory B cell response, it may play a role in enhancing peripheral B cell survival or proliferative capacity.     

Novartis Medal Lecture. Antibodies: a paradigm for the evolution of molecular recognition

Novel proteins have been elaborated over evolutionary time by an iterative alternation of mutation and selection. In a similar way, the humoral immune system also uses an iterative alternation of mutation and selection to generate novel antibodies that display a high affinity for their cognate antigen -- but this is achieved in a matter of a days. Gene rearrangement is used to produce a primary repertoire of antibodies and, on entering the body, antigen triggers the clonal expansion of those B lymphocytes that express a cognate antibody, albeit one of low affinity. Rapid and specific affinity maturation is then achieved by subjecting the immunoglobulin genes in the rapidly expanding B cells to a period of intense mutation. The intensity of this mutational assault is tolerated because it is targeted specifically to the immunoglobulin genes, causing relatively little damage to other loci. Antigen-mediated selection then allows the preferential expansion of those mutants expressing antibodies displaying improved binding characteristics. Here, studies are described that have been performed to glean insight into the mechanisms of the hypermutation and selection processes. Experiments are also described in which an attempt has been made to recapitulate aspects of physiological antibody generation in vitro, allowing the development of novel approaches to the generation of proteins with high-affinity binding sites.     

Gene conversion and hypermutation during diversification of VH sequences in developing splenic germinal centers of immunized rabbits

The young rabbit appendix and the chicken bursa of Fabricius are primary lymphoid organs where the B cell Ab repertoire develops in germinal centers (GCs) mainly by a gene conversion-like process. In human and mouse, V-gene diversification by somatic hypermutation in GCs of secondary lymphoid organs leads to affinity maturation. We asked whether gene conversion, somatic hypermutation, or both occur in rabbit splenic GCs during responses to the hapten DNP. We determined DNA sequences of rearranged heavy and light chain V region gene segments in single cells from developing DNP-specific GCs after immunization with DNP-bovine gamma-globulin and conclude that the changes at the DNA level that may lead to affinity maturation occur by both gene conversion and hypermutation. Selection was suggested by finding some recurrent amino acid replacements that may contribute increased affinity for antigen in the complementarity-determining region sequences of independently evolved clones, and a narrower range of complementarity-determining region 3 lengths at day 15. Some of the alterations of sequence may also lead to new members of the B cell repertoire in adult rabbits comparable with those produced in gut associated lymphoid tissues of young rabbits.     

Axon growth and guidance genes identify T-dependent germinal centre B cells

Selection of B cells subjected to hypermutation in germinal centres (GC) during T cell-dependent (TD) antibody responses yields memory cells and long-lived plasma cells that produce high affinity antibodies biased to foreign antigens rather than self-antigens. GC also form in T-independent (TI) responses to polysaccharide antigens but failed selection results in GC involution and memory cells are not generated. To date there are no markers that allow phenotypic distinction of T-dependent and TI germinal centre B cells. We compared the global gene expression of GC B cells purified from mice immunized with either TD or TI antigens and identified eighty genes that are differentially expressed in TD GC. Significantly, the largest cluster comprises genes involved in growth and guidance of neuron axons such as Plexin B2, Basp1, Nelf, Shh, Sc4mol and Sult4alpha. This is consistent with formation of long neurite (axon and dendrite)-like structures by mouse and human GC B cells, which may facilitate T:B cell interactions within GC, affinity maturation and B cell memory formation. Expression of BASP1 and PLEXIN B2 protein is very low or undetectable in resting and TI GC B cells, but markedly upregulated in GC B cells induced in the presence of T cell help. Finally we show some of the axon growth genes upregulated in TD-GC B cells including Basp1, Shh, Sult4alpha, Sc4mol are also preferentially expressed in post-GC B cell neoplasms.     

Memory in the B-cell compartment: antibody affinity maturation

In the humoral arm of the immune system, the memory response is not only more quickly elicited and of greater magnitude than the primary response, but it is also different in quality. In the recall response to antigen, the antibodies produced are of higher affinity and of different isotype (typically immunoglobulin G rather than immunoglobulin M). This maturation rests on the antigen dependence of B-cell maturation and is effected by programmed genetic modifications of the immunoglobulin gene loci. Here we consider how the B-cell response to antigen depends on the affinity of the antigen receptor interaction. We also compare and draw parallels between the two processes, which underpin the generation of secondary-response antibodies: V gene somatic hypermutation and immunoglobulin heavy-chain class switching.     

Antigen-induced somatic diversification of rabbit IgH genes: gene conversion and point mutation.

During T cell-dependent immune responses in mouse and human, Ig genes diversify by somatic hypermutation within germinal centers. Rabbits, in addition to using somatic hypermutation to diversify their IgH genes, use a somatic gene conversion-like mechanism, which involves homologous recombination between upstream VH gene segments and the rearranged VDJ genes. Somatic gene conversion and somatic hypermutation occur in young rabbit gut-associated lymphoid tissue and are thought to diversify a primary Ab repertoire that is otherwise limited by preferential VH gene segment utilization. Because somatic gene conversion is rarely found within Ig genes during immune responses in mouse and human, we investigated whether gene conversion in rabbit also occurs during specific immune responses, in a location other than gut-associated lymphoid tissue. We analyzed clonally related VDJ genes from popliteal lymph node B cells responding to primary, secondary, and tertiary immunization with the hapten FITC coupled to a protein carrier. Clonally related VDJ gene sequences were derived from FITC-specific hybridomas, as well as from Ag-induced germinal centers of the popliteal lymph node. By analyzing the nature of mutations within these clonally related VDJ gene sequences, we found evidence not only of ongoing somatic hypermutation, but also of ongoing somatic gene conversion. Thus in rabbit, both somatic gene conversion and somatic hypermutation occur during the course of an immune response.