Symposium paper

Shape space: an approach to the evaluation of cross-reactivity effects, stability and controllability in the immune system

One important feature of the mammalian immune system is the highly specific binding of antigens to antibodies. Antibodies generated in response to one infection may also provide some level of cross immunity to other infections. One model to describe this cross immunity is the notion of antigenic space, which assigns each antibody and each virus a point in ${\mathbb{R}}^n$. Past studies using hemagglutination data have suggested the dimensionality of antigenic space, n, is low. We propose that influenza evolution may be modeled as a Gaussian random walk. We then show that hemagluttination data would be consistent with a walk in very high dimensions. The discrepancy between our result and prior studies is due to the fact that random walks can appear low dimensional according to a variety of analyses including principal component analysis (PCA) and multidimensional scaling (MDS). A high dimensionality of antigenic space is of importance to modelers, as it suggests a smaller role for pre-existing immunity within the host population.

It is known that even if a ligand peptide is designed to bind to a target receptor on the surface of a pathogen such as viruses, bacteria or cancer cells, it is likely that some receptors are subject to random mutation and thus the ligand has a reduced ability to bind to these receptors. This issue is known as drug-resistant or escape mutants. In this paper, we present an idea to inhibit the evolving receptors by using an ensemble of all possible single- or double-point mutant sequences of the ligand peptide. Several mutant ligands in the ensemble are expected to bind to the mutant receptors, and then the ensemble may create a defensive wall surrounding the target receptors in receptor-sequence space. We examined the effectiveness of this “evolutionary containment” of the evolving receptors through eight peptide–protein complex systems, which were retrieved from the Protein Data Bank (PDB). As a result, we obtained a suggestion that the original (or parent) ligand sequence should be designed to have as high fitness as possible but to be not local optima, in order to maximize the rate of the evolutionary containment. This may be a strategy of the drug-design against evolving pathogens.

In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker–Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-of-equilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.

We present an approach to studying theoretically the regularities and the kinetic characteristics of influenza A virus (IAV) infection in man. The estimates of the "numbers" (Zinkernagel et al., 1985) characterizing evolutionary established interferon and immune responses in uncomplicated IAV infection are explored by developing a multiparameter mathematical model which allows direct quantitative references to the biological reality. The system of equations of the mathematical model of antiviral immune response, applied earlier to acute hepatitis B virus infection (Marchuk et al., 1991a, b), is modified and extended to describe the joint reaction of the interferon and immune systems in IAV infection. Macrophages infiltrating the airway's epithelium are considered to be the principal source of interferon that induces antiviral resistance in lung epithelial cells. The model is formulated as a delay-differential system with about 60 parameters characterizing the rates of various processes contributing to the typical course of IAV infection. The key aspect of the adjustment between the model and various data on the immunity to influenza is the derivation of a consistent data set—the generalized picture of uncomplicated IAV infection. It serves as a consistent theoretical definition of the structure of the normal course of the infection and the antiviral immune response suitable for model fitting. The parameter estimates for the processes considered in the model are carefully discussed. The quantitative model is used to study the organization and dynamic properties of the processes contributing to IAV infection. The threshold condition for immune protection of virus-free host to infection with IAV is analyzed. The relative roles of humoral, cellular and interferon reactions for the kinetics of the uncomplicated IAV infection are studied. The contribution of parameters of virus—sensitive tissue, interferon and IAV-specific immune processes to the variations of duration and severity of the infection is quantitatively estimated by sensitivity studies. It is shown that the variations in the parameters of a virus-epithelial cell system are more influential on the severity of the infection rather than that of the antiviral immune response. The need for fine co-ordination of the kinetics of the non-specific interferon response and the adaptive antigen-specific immune reactions to provide recovery from the infection is illustrated.

A unique feature of the immune system is that it possesses meta-dynamics: the process governing the removal of certain clones from the active population and the recruitment of new clones from the pool of lymphocytes freshly produced by the bone marrow. In this paper, we present a computer model which focuses on those aspects of the system that characteristically derive from the meta-dynamics as such. We observe that when a region of shape-space is densely populated, there is an emergence of dynamically quasi-stable configurations. Moreover, when the system develops in the presence of permanent self-antigens, the latter are systematically incorporated into such coherent configurations. We conclude that the metadynamics of the biological immune system may be such that it gives rise to the emergence of a connected, self-sustaining network that we call the Central Immune System: a coherent self-identity which incorporates the molecules of the somatic self and, more generally, reflects the history of its own development.

Simulations show that for a certain range of its free parameters, a model of the immune network including both cellular and humoral components is capable of self-sustained oscillations. The model also possesses a number of fixed points which appear to be unstable. These results, taken together, suggest the hypothesis that the immune network may be able to sustain a non-degenerate diversity of active clones which are actively connected to each other only on condition that the activities of these clones are oscillatory.