Somatic mutation, affinity maturation and the antibody repertoire: a computer model

Antibody WN1 222-5 mimics Toll-like receptor 4 binding in the recognition of LPS

Escherichia coli infections, a leading cause of septic shock, remain a major threat to human health because of the fatal action to endotoxin (LPS). Therapeutic attempts to neutralize endotoxin currently focus on inhibiting the interaction of the toxic component lipid A with myeloid differentiating factor 2, which forms a trimeric complex together with Toll-like receptor 4 to induce immune cell activation. The 1.73-Å resolution structure of the unique endotoxin-neutralizing protective antibody WN1 222-5 in complex with the core region shows that it recognizes LPS of all E. coli serovars in a manner similar to Toll-like receptor 4, revealing that protection can be achieved by targeting the inner core of LPS and that recognition of lipid A is not required. Such interference with Toll-like receptor complex formation opens new paths for antibody sepsis therapy independent of lipid A antagonists.

How do we evaluate artificial immune systems?

The field of Artificial Immune Systems (AIS) concerns the study and development of computationally interesting abstractions of the immune system. This survey tracks the development of AIS since its inception, and then attempts to make an assessment of its usefulness, defined in terms of 'distinctiveness' and 'effectiveness.' In this paper, the standard types of AIS are examined--Negative Selection, Clonal Selection and Immune Networks--as well as a new breed of AIS, based on the immunological 'danger theory.' The paper concludes that all types of AIS largely satisfy the criteria outlined for being useful, but only two types of AIS satisfy both criteria with any certainty.

Deriving quantitative constraints on T cell selection from data on the mature T cell repertoire

The T cell repertoire is shaped in the thymus through positive and negative selection. Thus, data about the mature repertoire may be used to infer information on how TCR generation and selection operate. Assuming that T cell selection is affinity driven, we derive the quantitative constraints that the parameters driving these processes must fulfill to account for the experimentally observed levels of alloreactivity, self MHC restriction and the frequency of cells recognizing a given foreign Ag. We find that affinity-driven selection is compatible with experimental estimates of these latter quantities only if 1) TCRs see more peptide residues than MHC polymorphic residues, 2) the majority of positively selected clones are deleted by negative selection, 3) between 1 and 3.6 clonal divisions occur on average in the thymus after completion of TCR rearrangement, and 4) selection is driven by 103-105 self peptides.

A quantitative theory of affinity-driven T cell repertoire selection

Binding of the T cell antigen receptor (TCR) to peptides presented on molecules encoded by major histocompatibility complex (MHC) genes is the key event driving T cell development and activation. Selection of the T cell repertoire in the thymus involves two steps. First, positive selection promotes the survival of cells binding thymic self-MHC-peptide complexes with sufficient affinity. The resulting repertoire is self-MHC restricted: it recognizes foreign peptides presented on self, but not foreign MHC. Second, negative selection deletes cells which may be potentially harmful because their receptors interact with self-MHC-peptide complexes with too high an affinity. The mature repertoire is also highly alloreactive: a large fraction of T cells respond to tissues harboring foreign MHC. We derive mathematical expressions giving the frequency of alloreactivity, the level of self-MHC restriction, and the fraction of the repertoire activated by a foreign peptide, as a function of the parameters driving the generation and selection of the repertoire: self-MHC and self-peptide diversity, the stringencies of positive and negative selection, and the number of peptide and MHC polymorphic residues that contribute to T cell receptor binding. Although the model is based on a simplified digit string representation of receptors, all the parameters but one relate directly to experimentally determined quantities. The only parameter without a biological counterpart has no effect on the model's behavior besides a trivial and easily preventable discretization effect. We further analyse the role of the MHC and peptide contribution to TCR binding, and find that their relative, rather than absolute value, is important in shaping the mature repertoire. This result makes it possible to adopt different physical interpretations for the digit string formalism. We also find that the alloreactivity level can be inferred directly from data on the stringency of selection, and that, in agreement with recent experiments, it is not affected by thymic selection.

A Mathematical Model on Germinal Center Kinetics and Termination

We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics are extended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes, and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we study the role of GC T cells in GC kinetics, GC termination, and B cell selection. We find that GC T cells play a major role in GC formation, but that the maintenance of established GC reactions requires very few T cells only. The results therefore suggest that the termination of a GC reaction is largely caused by lack of Ag on the follicular dendritic cells and is hardly influenced by Th cells. Ag consumption by centrocytes is the major factor determining the decay rate of the antigenic stimulus during a GC reaction. Investigating the effect of the Ag dose on GC kinetics, we find that both the total size of the GC and its duration are hardly influenced by the initial amount of Ag. In the model this is due to a buffering effect by competition for limited T cell help and/or competition between proliferating centroblasts.

The Clonal Composition of a Peptide-Specific Oligoclonal CTL Repertoire Selected in Response to Persistent EBV Infection Is Stable Over Time

The TCR repertoire of a peptide-specific HLA A11-restricted CTL response to persistent infection with EBV was followed for a period of 57 mo. Sequencing of TCR Vα and Vβ chains and alanine scanning mutagenesis analysis of 83 CTL clones isolated in five reactivation experiments demonstrated that this repertoire is composed of at least four distinct CTL clonotypes that are constantly reactivated from donor’s blood and express structurally heterogeneous TCRs. Target cell recognition and CD8 blocking experiments indicate that the four clonotypes possess different avidity and TCR affinity for the specific Ag. This demonstrates that at least in some individuals a heterogeneous peptide-specific memory CTL repertoire selected by a persistent Ag can be remarkably stable in time and accommodate a range of TCR affinities and T cell avidities. Our results suggest that competition for the specific Ag may be not the major force driving the maintenance of memory CTLs and that the nature of the first antigenic challenge may largely determine the clonal composition of memory.

Epitope-dependent selection of highly restricted or diverse T cell receptor repertoires in response to persistent infection by Epstein-Barr virus

The T cell receptor (TCR) repertoires of cytotoxic responses to the immunodominant and subdominant HLA A11-restricted epitopes in the Epstein-Barr virus (EBV) nuclear antigen-4 were investigated in four healthy virus carriers. The response to the subdominant epitope (EBNA4 399-408, designated AVF) was highly restricted with conserved Vbeta usage and identical length and amino acid motifs in the third complementarity-determining regions (CDR3), while a broad repertoire using different combinations of TCR-alpha/beta V and J segments and CDR3 regions was selected by the immunodominant epitope (EBNA4 416-424, designated IVT). Distinct patterns of interaction with the A11-peptide complex were revealed for each AVF- or IVT-specific TCR clonotype by alanine scanning mutagenesis analysis. Blocking of cytotoxic function by antibodies specific for the CD8 coreceptor indicated that, while AVF-specific TCRs are of high affinity, the oligoclonal response to the IVT epitope includes both low- and high-affinity TCRs. Thus, comparison of the memory response to two epitopes derived from the same viral antigen and presented through the same MHC class I allele suggests that immunodominance may correlate with the capacity to maintain a broad TCR repertoire.

Inverse analysis of empirical matrices of idiotypic network interactions

The concept of shape space proposed by Perelson and Oster (1979, J. Theor. Biol. 81, 645-670) has been a useful tool for the theoretical immunologists, who have invoked it to model idiotypic binding, which plays a significant role in mathematical models of immune networks. The actual construction of such a space from its definition requires specialized experimental information, which is not completely available. In this article, we discuss, with illustrative examples, how graphical representations similar to the idea of shape space can be derived by analyzing real affinity matrices, and the relative merits of such representations to approximations that might be obtained by the approach of Perelson and Oster. We also give directions for future research with a view toward applications.

A Cayley tree immune network model with antibody dynamics

A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvist et al. (1989. Proc. natn. Acad. Sci. U.S.A. 86, 5074-5078), injection of Ab1 antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations of Ab1 and Ab2 antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvist et al. but not accounted for previously.

Pattern formation in one- and two-dimensional shape-space models of the immune system

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)

Size and connectivity as emergent properties of a developing immune network

The development of the immune repertoire during neonatal life involves a strong selection process among different clones. The immune system is genetically capable of producing a much more diverse set of lymphocyte receptors than are expressed in the actual repertoire. By means of a model we investigate the hypothesis that repertoire selection is carried out during early life by the immune network. We develop a model network in which possibly hundreds of B cell clones proliferate and produce antibodies following stimulation. Stimulation is viewed as occurring through receptor crosslinking and is modeled via a log bell-shaped dose-response function. Through secretion of free antibody B cell clones can stimulate one another if their receptors have complementary shapes. Receptor shapes are modeled as binary strings and complementarity is evaluated by a string matching algorithm. The dynamic behavior of our model is typically oscillatory and for some parameters chaotic. In the case of two complementary B cell clones, the chaotic attractor has a number of features in common with the Lorenz attractor. The networks we model do not have a predetermined size or topology. Rather, we model the bone marrow as a source which generates novel clones. These novel clones can either be incorporated into the network or remain isolated, mimicking the non-network portion of the immune system. Clones are removed from the network if they fail to expand. We investigate the properties of the network as a function of P(match), the probability that two randomly selected immunoglobulins have complementary shapes. As the model networks evolve they develop a number of self-regulatory features. Most importantly, networks attain a specific equilibrium size and generate a characteristic amount of "natural" antibody. Because the network reaches an asymptotic size even though the bone marrow keeps supplying novel clones, clones must compete for presence in the network, i.e. repertoire selection takes place. Networks comprised of cells with multireactive receptors remain small, whereas networks consisting of cells with specific receptors become much larger. We find an inverse relationship between n, the number of clones in a network, and P(match), and a linear relationship between n and M, the rate at which novel clones are produced in the bone marrow. We present a simple phenomenological model for the number of clones in the network that accounts for the inverse relationship between n and P(match), and that can account for the relationship between n and M. Additionally, the phenomenological model suggests that there are two qualitatively different network equilibria.(ABSTRACT TRUNCATED AT 400 WORDS)