A mathematical model for the germinal center morphology and affinity maturation

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.

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.

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.

Current State of Knowledge on Primary Sjögren's Syndrome, an Autoimmune Exocrinopathy

Primary Sjögren's syndrome (pSS) is a chronic systemic autoimmune rheumatic disease characterized by lymphoplasmacytic infiltration of the salivary and lacrimal glands, whereby sicca syndrome and/or systemic manifestations are the clinical hallmarks, associated with a particular autoantibody profile. pSS is the most frequent connective tissue disease after rheumatoid arthritis, affecting 0.3-3% of the population. Women are more prone to develop pSS than men, with a sex ratio of 9:1. Considered in the past as innocent collateral passive victims of autoimmunity, the epithelial cells of the salivary glands are now known to play an active role in the pathogenesis of the disease. The aetiology of the "autoimmune epithelitis" still remains unknown, but certainly involves genetic, environmental and hormonal factors. Later during the disease evolution, the subsequent chronic activation of B cells can lead to the development of systemic manifestations or non-Hodgkin's lymphoma. The aim of the present comprehensive review is to provide the current state of knowledge on pSS. The review addresses the clinical manifestations and complications of the disease, the diagnostic workup, the pathogenic mechanisms and the therapeutic approaches.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

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.

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

Affinity maturation is a Darwinian process in which B lymphocytes evolve potent antibodies to encountered antigens and generate immune memory. Highly mutable complex pathogens present an immense antigenic diversity that continues to challenge natural immunity and vaccine design. Induction of broadly neutralizing antibodies (bnAbs) against this diversity by vaccination likely requires multiple exposures to distinct but related antigen variants, and yet how affinity maturation advances under such complex stimulation remains poorly understood. To fill the gap, we present an in silico model of affinity maturation to examine two realistic new aspects pertinent to vaccine development: loss in B cell diversity across successive immunization periods against different variants, and the presence of distracting epitopes that entropically disfavor the evolution of bnAbs. We find these new factors, which introduce additional selection pressures and constraints, significantly influence antibody breadth development, in a way that depends crucially on the temporal pattern of immunization (or selection forces). Curiously, a less diverse B cell seed may even favor the expansion and dominance of cross-reactive clones, but only when conflicting selection forces are presented in series rather than in a mixture. Moreover, the level of frustration due to evolutionary conflict dictates the degree of distraction. We further describe how antigenic histories select evolutionary paths of B cell lineages and determine the predominant mode of antibody responses. Sequential immunization with mutationally distant variants is shown to robustly induce bnAbs that focus on conserved elements of the target epitope, by thwarting strain-specific and distracted lineages. An optimal range of antigen dose underlies a fine balance between efficient adaptation and persistent reaction. These findings provide mechanistic guides to aid in design of vaccine strategies against fast mutating pathogens.

Mathematical modeling of lymphocytes selection in the germinal center

Lymphocyte selection is a fundamental process of adaptive immunity. In order to produce B-lymphocytes with a target antigenic profile, mutation selection and division occur in the germinal center, a specific part of lymph nodes. We introduce in this article a simplified mathematical model of this phenomenon, taking into account the main mechanisms. This model is written as a non-linear, non-local, inhomogeneous second order partial differential equation, for which we develop a mathematical analysis. We assess, mathematically and numerically, in the case of piecewise-constant coefficients, the performance of the biological function by evaluating the duration of this production process as a function of several parameters such as the mutation rate or the selection profile, in various asymptotic regimes.

A Stochastic Model of the Germinal Center Integrating Local Antigen Competition, Individualistic T-B Interactions, and B Cell Receptor Signaling

The germinal center (GC) reaction underlies productive humoral immunity by orchestrating competition-based affinity maturation to produce plasma cells and memory B cells. T cells are limiting in this process. How B cells integrate signals from T cells and BCRs to make fate decisions while subjected to a cyclic selection process is not clear. In this article, we present a spatiotemporally resolved stochastic model that describes cell behaviors as rate-limited stochastic reactions. We hypothesize a signal integrator protein integrates follicular helper T (Tfh)- and Ag-derived signals to drive different B cell fates in a probabilistic manner and a dedicated module of Tfh interaction promoting factors control the efficiency of contact-dependent Tfh help delivery to B cells. Without assuming deterministic affinity-based decisions or temporal event sequence, this model recapitulates GC characteristics, highlights the importance of efficient T cell help delivery during individual contacts with B cells and intercellular positive feedback for affinity maturation, reveals the possibility that antagonism between BCR signaling and T cell help accelerates affinity maturation, and suggests that the dichotomy between affinity and magnitude of GC reaction can be avoided by tuning the efficiency of contact-dependent help delivery during reiterative T-B interactions.

Trade-offs in antibody repertoires to complex antigens

Pathogens vary in their antigenic complexity. While some pathogens such as measles present a few relatively invariant targets to the immune system, others such as malaria display considerable antigenic diversity. How the immune response copes in the presence of multiple antigens, and whether a trade-off exists between the breadth and efficacy of antibody (Ab)-mediated immune responses, are unsolved problems. We present a theoretical model of affinity maturation of B-cell receptors (BCRs) during a primary infection and examine how variation in the number of accessible antigenic sites alters the Ab repertoire. Naive B cells with randomly generated receptor sequences initiate the germinal centre (GC) reaction. The binding affinity of a BCR to an antigen is quantified via a genotype-phenotype map, based on a random energy landscape, that combines local and distant interactions between residues. In the presence of numerous antigens or epitopes, B-cell clones with different specificities compete for stimulation during rounds of mutation within GCs. We find that the availability of many epitopes reduces the affinity and relative breadth of the Ab repertoire. Despite the stochasticity of somatic hypermutation, patterns of immunodominance are strongly shaped by chance selection of naive B cells with specificities for particular epitopes. Our model provides a mechanistic basis for the diversity of Ab repertoires and the evolutionary advantage of antigenically complex pathogens.

A Network Model to Describe the Terminal Differentiation of B Cells

Terminal differentiation of B cells is an essential process for the humoral immune response in vertebrates and is achieved by the concerted action of several transcription factors in response to antigen recognition and extracellular signals provided by T-helper cells. While there is a wealth of experimental data regarding the molecular and cellular signals involved in this process, there is no general consensus regarding the structure and dynamical properties of the underlying regulatory network controlling this process. We developed a dynamical model of the regulatory network controlling terminal differentiation of B cells. The structure of the network was inferred from experimental data available in the literature, and its dynamical behavior was analyzed by modeling the network both as a discrete and a continuous dynamical systems. The steady states of these models are consistent with the patterns of activation reported for the Naive, GC, Mem, and PC cell types. Moreover, the models are able to describe the patterns of differentiation from the precursor Naive to any of the GC, Mem, or PC cell types in response to a specific set of extracellular signals. We simulated all possible single loss- and gain-of-function mutants, corroborating the importance of Pax5, Bcl6, Bach2, Irf4, and Blimp1 as key regulators of B cell differentiation process. The model is able to represent the directional nature of terminal B cell differentiation and qualitatively describes key differentiation events from a precursor cell to terminally differentiated B cells.

Generation of antibody-producing cells through terminal B cell differentiation represents a good model to study the formation of multiple effector cells from a progenitor cell type. This process is controlled by the action of several molecules that maintain cell type specific programs in response to cytokines, antigen recognition and the direct contact with T helper cells, forming a complex regulatory network. While there is a large body of experimental data regarding some of the key molecules involved in this process and there have been several efforts to reconstruct the underlying regulatory network, a general consensus about the structure and dynamical behavior of this network is lacking. Moreover, it is not well understood how this network controls the establishment of specific B cell expression patterns and how it responds to specific external signals. We present a model of the regulatory network controlling terminal B cell differentiation and analyze its dynamical behavior under normal and mutant conditions. The model recovers the patterns of differentiation of B cells and describes a large set of gain- and loss-of-function mutants. This model provides an unified framework to generate qualitative descriptions to interpret the role of intra- and extracellular regulators of B cell differentiation.

Evolutionary medicine and bone loss in chronic inflammatory diseases--A theory of inflammation-related osteopenia

OBJECTIVE

Bone loss is typical in chronic inflammatory diseases such as rheumatoid arthritis, psoriasis, ankylosing spondylitis, systemic lupus erythematosus, multiple sclerosis, inflammatory bowel diseases, pemphigus vulgaris, and others. It is also typical in transplantation-related inflammation and during the process of aging. While we recognized that bone loss is tightly linked to immune system activation or inflamm-aging in the form of acute, chronic active, or chronic smoldering inflammation, bone loss is typically discussed to be an "accident of inflammation."

METHODS

Extensive literature search in PubMed central.

RESULTS

Using elements of evolutionary medicine, energy regulation, and neuroendocrine regulation of homeostasis and immune function, we work out that bone waste is an adaptive, evolutionarily positively selected program that is absolutely necessary during acute inflammation. However, when acute inflammation enters a chronic state due to the inability to terminate inflammation (e.g., in autoimmunity or in continuous immunity against microbes), the acute program of bone loss is a misguided adaptive program.

CONCLUSIONS

The article highlights the complexity of interwoven pathways of osteopenia.

Manipulating the selection forces during affinity maturation to generate cross-reactive HIV antibodies

Generation of potent antibodies by a mutation-selection process called affinity maturation is a key component of effective immune responses. Antibodies that protect against highly mutable pathogens must neutralize diverse strains. Developing effective immunization strategies to drive their evolution requires understanding how affinity maturation happens in an environment where variants of the same antigen are present. We present an in silico model of affinity maturation driven by antigen variants which reveals that induction of cross-reactive antibodies often occurs with low probability because conflicting selection forces, imposed by different antigen variants, can frustrate affinity maturation. We describe how variables such as temporal pattern of antigen administration influence the outcome of this frustrated evolutionary process. Our calculations predict, and experiments in mice with variant gp120 constructs of the HIV envelope protein confirm, that sequential immunization with antigen variants is preferred over a cocktail for induction of cross-reactive antibodies focused on the shared CD4 binding site epitope.

Simulation of B cell affinity maturation explains enhanced antibody cross-reactivity induced by the polyvalent malaria vaccine AMA1

Polyvalent vaccines use a mixture of Ags representing distinct pathogen strains to induce an immune response that is cross-reactive and protective. However, such approaches often have mixed results, and it is unclear how polyvalency alters the fine specificity of the Ab response and what those consequences might be for protection. In this article, we present a coarse-grain theoretical model of B cell affinity maturation during monovalent and polyvalent vaccinations that predicts the fine specificity and cross-reactivity of the Ab response. We stochastically simulate affinity maturation using a population dynamics approach in which the host B cell repertoire is represented explicitly, and individual B cell subpopulations undergo rounds of stimulation, mutation, and differentiation. Ags contain multiple epitopes and are present in subpopulations of distinct pathogen strains, each with varying degrees of cross-reactivity at the epitope level. This epitope- and strain-specific model of affinity maturation enables us to study the composition of the polyclonal response in granular detail and identify the mechanisms driving serum specificity and cross-reactivity. We applied this approach to predict the Ab response to a polyvalent vaccine based on the highly polymorphic malaria Ag apical membrane antigen-1. Our simulations show how polyvalent apical membrane Ag-1 vaccination alters the selection pressure during affinity maturation to favor cross-reactive B cells to both conserved and strain-specific epitopes and demonstrate how a polyvalent vaccine with a small number of strains and only moderate allelic coverage may be broadly neutralizing. Our findings suggest that altered fine specificity and enhanced cross-reactivity may be a universal feature of polyvalent vaccines.

A one-shot germinal center model under protein structural stability constraints

The germinal center reaction is the process by which low-affinity B cells evolve into potent, immunoglobulin-secreting plasma and memory B cells. Since the recycling hypothesis was created, experimental studies have both tracked movement of a small population of B cells from the light zone into the dark zone, supporting the recycling model, and parallel to the light zone-dark zone interface, indicating a one-way trajectory. We present a novel, sequence-based ab initio model of protein stability and protein interactions. Our model contains a dark zone region of clonal expansion and somatic hypermutation and a light zone site of antigenic selection. We show not only that a one-shot model is sufficient to achieve biologically-realistic rates of affinity growth, population dynamics, and silent:non-silent mutation ratios in the complementary determining region and framework region of antibodies, but also that a stochastic recycling program with or without realistic constraints on the structural stabilities of GC antibodies cannot produce biologically-observed affinity growth, population dynamics or silent:non-silent mutation profiles. The effect of recycling erases affinity gains made by potent antibodies cycling back from the light zone and causes B cells to pool in the dark zone under high replication rates.

Evolutionary medicine and chronic inflammatory state--known and new concepts in pathophysiology

During the last 10 years, a series of exciting observations has led to a new theory of pathophysiology using insights from evolutionary biology and neuroendocrine immunology to understand the sequelae of chronic inflammatory disease. According to this theory, disease sequelae can be explained based on redirection of energy-rich fuels from storage organs to the activated immune system. These disease sequelae are highly diverse and include the following: sickness behavior, anorexia, malnutrition, muscle wasting–cachexia, cachectic obesity, insulin resistance with hyperinsulinemia, dyslipidemia, increase of adipose tissue near inflamed tissue, alterations of steroid hormone axes, elevated sympathetic tone and local sympathetic nerve fiber loss, decreased parasympathetic tone, hypertension, inflammation-related anemia, and osteopenia. Since these disease sequelae can be found in many animal models of chronic inflammatory diseases with mammals (e.g., monkeys, mice, rats, rabbits, etc.), the evolutionary time line goes back at least 70 million years. While the initial version of this theory could explain prominent sequelae of chronic inflammatory disease, it did not however address two features important in the pathogenesis of immune-mediated diseases: the time point when an acute inflammatory disease becomes chronic, and the appearance of hypertension in chronic inflammation. To address these aspects more specifically, a new version of the theory has been developed. This version defines more precisely the moment of transition from acute inflammatory disease to chronic inflammatory disease as a time in which energy stores become empty (complete energy consumption). Depending on the amount of stored energy, this time point can be calculated to be 19–43 days. Second, the revised theory addresses the mechanisms of essential hypertension since, on the basis of water loss, acute inflammatory diseases can stimulate water retention using a positively selected water retention system (identical to the energy provision system). In chronic smoldering inflammation, however, there is no increased water loss. In contrast, there is increased water generation in inflamed tissue and inflammatory cells, and the activation of the water retention system persists. This combination leads to a net increase of the systemic fluid volume, which is hypothesized to be the basis of essential hypertension (prevalence in adults 22–32%).

T cell responses in lymph nodes

Activation of T cells by antigen-presenting cells (APCs) in lymph nodes (LNs) is a key initiating event in many immune responses. Our understanding of this process has been both improved and complicated in recent years by evidence from techniques such as intravital microscopy that has revealed new levels of dynamism in the interaction of T cells and APCs. In particular, the complex motility of T cells within LNs, and their serial interactions with many APCs, imply that earlier static models of T cell activation need to be updated. Here we review the first attempts to model T cell interactions with APCs in LNs that incorporate simulations of T cell motility, based on experimental observations. We show that lattice-based modeling approaches are the dominant trend in these models, and then chart a possible course for development of these models toward spatially-resolved models of immune responses within LNs.

Cellular choreography in the germinal center: new visions from in vivo imaging

Germinal centers (GC) are large aggregates of proliferating B lymphocytes within follicles of lymphoid tissue that form during adaptive immune responses. GCs are the source of long-lived B cells that form the basis for pathogen-specific lifelong B cell immunity. The complex architecture of these structures includes subdomains that differ significantly in their stromal cell and T lymphocyte subset composition. In part due to their structural complexity and potential to generate some lymphomas, much interest and many theories about GC dynamics have emerged. Here, we review recent research employing in vivo imaging that has begun to untangle some of the mysteries.

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.

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.

Antigen-driven selection in germinal centers as reflected by the shape characteristics of immunoglobulin gene lineage trees: a large-scale simulation study

During the immune response, the generation of memory B lymphocytes in germinal centers involves affinity maturation of the cells' antigen receptors, based on somatic hypermutation of receptor genes and antigen-driven selection of the resulting mutants. Affinity maturation is vital for immune protection, and is the basis of humoral immune learning and memory. Lineage trees of somatically hypermutated immunoglobulin genes often serve to qualitatively illustrate claims concerning the dynamics of affinity maturation in germinal centers. Here, we derive the quantitative relationships between parameters characterizing affinity maturation dynamics (proliferation, differentiation and mutation rates, initial affinity of the Ig to the antigen, and selection thresholds) and the mathematical properties of lineage trees, using a computer simulation which combines mathematical models for all mature B cell populations, stochastic models of hypermutation and selection, lineage tree generation and measurement of graphical tree characteristics. We identified seven key lineage tree properties, and found correlations of these with initial clone affinity and with the selection threshold. These two parameters were found to be the main factors affecting lineage tree shapes in both primary and secondary response trees. The results also confirm that recycling from centrocytes back to centroblasts is highly likely.

A role for DRAK2 in the germinal center reaction and the antibody response

DAP-related apoptotic kinase-2 (DRAK2), a death-associated protein kinase family member, is highly expressed in B and T lymphocytes in the human and the mouse. To determine whether DRAK2 plays a role in B-cell activation and differentiation, we analyzed germinal centers (GCs) and the specific antibody response to NP in drak2-/- mice immunized with the thymus-dependent (TD) conjugated hapten NP16-CGG. In drak2-/- mice, spleen GCs were normal in size and morphology, but their number was reduced by as much as 5-fold, as compared to their wild-type littermates. This was not due to a defect in B-cell proliferation, as the BrdU uptake was comparable in DRAK2-deficient and wild-type B cells. Rather, the proportion of apoptotic GC B and T cells in drak2-/- mice was significantly higher than that in wild-type control mice, as shown by 7-AAD and terminal deoxynucleotide transferase dUTP nick end labeling (TUNEL) staining. In drak2-/- mice, the generation high affinity IgG antibodies was impaired in spite of the seemingly normal somatic hypermutation and class switch DNA recombination machineries in drak2-/- B cells. In NP16-CGG-immunized drak2-/- mice, T-cell-intrinsic Bcl-xL transgene expression increased the number of GCs and rescued the high affinity IgG response to NP. These findings suggest a novel role for DRAK2 in regulating the GC reaction and the response to TD antigens, perhaps through increased survival of T cells and enhanced B-cell positive selection. They also suggest that DRAK2-deficiency is not involved in regulating intrinsic B-cell apoptosis.

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.

The evolution of mathematical immunology

The types of mathematical models used in immunology and their scope have changed drastically in the past 10 years. Classical models were based on ordinary differential equations (ODEs), difference equations, and cellular automata. These models focused on the 'simple' dynamics obtained between a small number of reagent types (e.g. one type of receptor and one type of antigen or two T-cell populations). With the advent of high-throughput methods, genomic data, and unlimited computing power, immunological modeling shifted toward the informatics side. Many current applications of mathematical models in immunology are now focused around the concepts of high-throughput measurements and system immunology (immunomics), as well as the bioinformatics analysis of molecular immunology. The types of models have shifted from mainly ODEs of simple systems to the extensive use of Monte Carlo simulations. The transition to a more molecular and more computer-based attitude is similar to the one occurring over all the fields of complex systems analysis. An interesting additional aspect in theoretical immunology is the transition from an extreme focus on the adaptive immune system (that was considered more interesting from a theoretical point of view) to a more balanced focus taking into account the innate immune system also. We here review the origin and evolution of mathematical modeling in immunology and the contribution of such models to many important immunological concepts.

Are T cells at the origin of B cell lymphomas?

Lymphoma pathogenesis is at least in some cases related to transformed B cells (BCs) arising from germinal centre reactions (GCRs). In this article possible deregulations of GCRs are investigated using in silico simulations. It is found that the final differentiation of BCs as regulated by helper T cells (TCs) is the best candidate mechanism for such a deregulation. This shifts the paradigm of BC lymphoma pathogenesis from BC transformations to an emphasized role of TC-BC interactions.

Identification of B and T cells in human spleen sections by infrared microspectroscopic imaging

BACKGROUND

Infrared spectroscopy probes the chemical composition and molecular structure of complex systems such as tissue and cells. Infrared spectroscopic imaging combines this spectral information with lateral resolution near the single-cell level. We analyzed whether this method is competitive with classic immunohistochemical methods for immunologic tissue and cells.

METHODS

We recorded infrared microspectroscopic mapping datasets with a 90- x 90-microm2 aperture from a 3- x 3-mm2 unstained tissue area of human spleen. A secondary follicle containing a germinal center and a T zone were studied in more detail by infrared microspectroscopic imaging with lateral resolution near 5 mum. The results were compared with consecutive sections stained by immunoglobulin D antibodies. T and B lymphocytes were extracted from human blood and served as independent test samples.

RESULTS

Cluster analysis of infrared datasets produced images that distinguished anatomical features such as primary and secondary follicles, T zones, arteries, and spleen red pulp. The assignments could be confirmed in consecutive sections by immunohistochemical staining. Main spectral variances between T and B lymphocytes in high-resolution measurements were attributed to specific spectral contributions of DNA and cytosol.

CONCLUSIONS

Sensitivity and specificity of the infrared based methods are comparable to those of standard staining procedures for identification of B and T cells. However, infrared spectroscopic imaging can offer advantages in velocity, data throughput, and standardization because of minimal sample preparation. The results emphasize the potential of infrared spectroscopy as an innovative tool for the distinction of cell types, in particular in immunologic tissue.

Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model

We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next neighbors of the cells are provided by a weighted Delaunay triangulation with on average linear computational complexity. The cellular interactions include direct elastic forces and cell-cell as well as cell-matrix adhesion. The spatiotemporal distribution of two nutrients--oxygen and glucose--is described by reaction-diffusion equations. Viable cells consume the nutrients, which are converted into biomass by increasing the cell size during the G1 phase. We test hypotheses on the functional dependence of the uptake rates and use computer simulations to find suitable mechanisms for the induction of necrosis. This is done by comparing the outcome with experimental growth curves, where the best fit leads to an unexpected ratio of oxygen and glucose uptake rates. The model relies on physical quantities and can easily be generalized towards tissues involving different cell types. In addition, it provides many features that can be directly compared with the experiment.

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.

Cutting edge: back to "one-way" germinal centers

The present status of germinal center (GC) research is revisited using in silico simulations based on recent lymphocyte motility data in mice. The generally adopted view of several rounds of somatic hypermutations and positive selection is analyzed with special emphasis on the spatial organization of the GC reaction. We claim that the development of dark zones is not necessary for successful GC reactions to develop. We find that a recirculation of positively selected centrocytes to the dark zone is rather unlikely. Instead we propose a scenario that combines a multiple-step mutation and selection concept with a "one-way" GC in the sense of cell migration.

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.