A theory of regulation and self-nonself discrimination in an immune network

Theories of immune recognition: Is anybody right?

The clonal selection theory (CST) is the centrepiece of the current paradigm used to explain immune recognition and memory. Throughout the past decades, the original CST had been expanded and modified to explain new experimental evidences since its original publication by Burnet. This gave origin to new paradigms that govern experimental immunology nowadays, such as the associative recognition of antigen model and the stranger/danger signal model. However, these new theories also do not fully explain experimental findings such as natural autoimmune immunoglobulins, idiotypic networks, low and high dose tolerance, and dual-receptor T and B cells. To make sense of these empirical data, some authors have been trying to change the paradigm of immune cognition using a systemic approach, analogies with brain processing and concepts from second-order cybernetics. In the present paper, we review the CST and some of the theories/hypotheses derived from it, focusing on immune recognition. We point out their main weaknesses and highlight arguments made by their opponents and believers. We conclude that, until now, none of the proposed theories can fully explain the totality of immune phenomena and that a theory of everything is needed in immunology.

Design Principles for Immunomodulatory Biomaterials

The immune system is imperative to the survival of all biological organisms. A functional immune system protects the organism by detecting and eliminating foreign and host aberrant molecules. Conversely, a dysfunctional immune system characterized by an overactive or weakened immune system causes life-threatening autoimmune or immunodeficiency diseases. Therefore, a critical need exists to develop technologies that regulate the immune system to ensure homeostasis or treat several diseases. Accumulating evidence shows that biomaterials─artificial materials (polymers, metals, ceramics, or engineered cells and tissues) that interact with biological systems─can trigger immune responses, offering a materials science-based strategy to modulate the immune system. This Review discusses the expanding frontiers of biomaterial-based immunomodulation, focusing on principles for designing these materials. This Review also presents examples of immunomodulatory biomaterials, which include polymers and metal- and carbon-based nanomaterials, capable of regulating the innate and adaptive immune systems.

Not by structures alone: Can the immune system recognize microbial functions?

A central question for immunology is: what does the immune system recognize and according to which principles does this kind of recognition work? Immunology has been dominated by the idea of recognizing molecular structures and triggering an appropriate immune response when facing non-self or danger. Recently, characterizations in terms of function have turned out to be more conserved and explanatory in microbiota research than taxonomic composition for understanding microbiota-host interactions. Starting from a conceptual analysis of the notions of structure and function, I raise the title question whether it is possible for the immune system to recognize microbial functions. I argue that this is indeed the case, making the claim that some function-associated molecular patterns are not indicative of the presence of certain taxa (''who is there'') but of biochemical activities and effects (''what is going on''). In addition, I discuss case studies which show that there are immunological sensors that can directly detect microbial activities, irrespective of their specific structural manifestation. At the same time, the discussed account puts the causal role notions of function on a more realist and objective basis.

A comprehensive review on the role of co-signaling receptors and Treg homeostasis in autoimmunity and tumor immunity

The immune system ensures optimum T-effector (Teff) immune responses against invading microbes and tumor antigens while preventing inappropriate autoimmune responses against self-antigens with the help of T-regulatory (Treg) cells. Thus, Treg and Teff cells help maintain immune homeostasis through mutual regulation. While Tregs can contribute to tumor immune evasion by suppressing anti-tumor Teff response, loss of Treg function can result in Teff responses against self-antigens leading to autoimmune disease. Thus, loss of homeostatic balance between Teff/Treg cells is often associated with both cancer and autoimmunity. Co-stimulatory and co-inhibitory receptors, collectively known as co-signaling receptors, play an indispensable role in the regulation of Teff and Treg cell expansion and function and thus play critical roles in modulating autoimmune and anti-tumor immune responses. Over the past three decades, considerable efforts have been made to understand the biology of co-signaling receptors and their role in immune homeostasis. Mutations in co-inhibitory receptors such as CTLA4 and PD1 are associated with Treg dysfunction, and autoimmune diseases in mice and humans. On the other hand, growing tumors evade immune surveillance by exploiting co-inhibitory signaling through expression of CTLA4, PD1 and PDL-1. Immune checkpoint blockade (ICB) using anti-CTLA4 and anti-PD1 has drawn considerable attention towards co-signaling receptors in tumor immunology and created renewed interest in studying other co-signaling receptors, which until recently have not been as well studied. In addition to co-inhibitory receptors, co-stimulatory receptors like OX40, GITR and 4-1BB have also been widely implicated in immune homeostasis and T-cell stimulation, and use of agonistic antibodies against OX40, GITR and 4-1BB has been effective in causing tumor regression. Although ICB has seen unprecedented success in cancer treatment, autoimmune adverse events arising from ICB due to loss of Treg homeostasis poses a major obstacle. Herein, we comprehensively review the role of various co-stimulatory and co-inhibitory receptors in Treg biology and immune homeostasis, autoimmunity, and anti-tumor immunity. Furthermore, we discuss the autoimmune adverse events arising upon targeting these co-signaling receptors to augment anti-tumor immune responses.

Stable isotope labeling approaches for NMR characterization of glycoproteins using eukaryotic expression systems

Glycoproteins are characterized by the heterogeneous and dynamic nature of their glycan moieties, which hamper crystallographic analysis. NMR spectroscopy provides potential advantages in dealing with such complicated systems, given that the target molecules can be isotopically labeled. Methods of metabolic isotope labeling in recombinant glycoproteins have been developed recently using a variety of eukaryotic production vehicles, including mammalian, yeast, insect, and plant cells, each of which has a distinct N-glycan diversification pathway. Yeast genetic engineering has enabled the overexpression of homogeneous high-mannose-type oligosaccharides with ¹³C labeling for NMR characterization of their conformational dynamics. The utility of stable isotope-assisted NMR spectroscopy has also been demonstrated using the Fc fragment of immunoglobulin G (IgG) as a model glycoprotein, providing useful information regarding intramolecular carbohydrate-protein interactions. Transverse relaxation optimization of intact IgG with a molecular mass of 150 kDa has been achieved by tailored deuteration of selected amino acid residues using a mammalian expression system. This offers a useful probe for the characterization of molecular interaction networks in multimolecular crowded systems typified by serum. Perspectives regarding the development of techniques for tailoring glycoform designs and isotope labeling of recombinant glycoproteins are also discussed.

Design specifications for cellular regulation

A critical feature of all cellular processes is the ability to control the rate of gene or protein expression and metabolic flux in changing environments through regulatory feedback. We review the many ways that regulation is represented through causal, logical, and dynamical components. Formalizing the nature of these components promotes effective comparison among distinct regulatory networks and provides a common framework for the potential design and control of regulatory systems in synthetic biology.

Immunity by equilibrium

The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.

Vaccination with endosomal unknown epitopes produces therapeutic response in rheumatoid arthritis patients and modulates adjuvant arthritis of rats

Background

Our previous results showed that intrasynovial Rifamycin SV caused the lysis of synoviocites and freed the autoantigens which in turn stimulated the immunoregulatory rather than autoreactive T cell response in rheumatoid patients. Here, we hypothesize that disruption in vitro of peripheral blood mononuclear cells, by freeze/thawing or by lytic action of Rifamycin SV, would induce the release of endosomal pathogenic autoantigens from APCs present in the circulation, which could then be isolated from degrading enzymes by ultrafiltration.

Methods

The preparation of the ultrafiltrates are based on the rupture of PBMCs (5 × 10⁶ cells/mL) by the addition of Rifamycin SV in culture (250 μg/mL), which causes the lysis of 90 % of the cells in 3 h, or by three cycles of freeze/thawing of the PBMC, from −80 °C to room temperature. The lysate and the fragmented cells were then centrifuged and ultrafiltered by passage through a filtration device with a cut-off of 10 kDa. Also the synovial fluid was subjected to ultrafiltration.

Results and conclusions

At clinical monitoring of the 30th day, 22/58 (38 %) patients subcutaneously treated with the autologous ultrafiltrate prepared by the freeze/thawing of PBMCs reached an ACR20. Comparable results were obtained with the other two ultrafiltrates.

Cell cultures The addition of ultrafiltrates to rheumatoid PBMCs cultures led to the upregulation of a marker for T-regulatory cells, and downregulation of a cell proliferation marker; changes that together have the meaning of a global immunomodulatory response and that only a specific antigen (ultrafiltrate UF-f/t) might induce in the rheumatoid patient, probably by activating pre-existing protective network.

Experimental arthritis All the ultrafiltrates except that prepared by Rifamycin SV were able to modulate the adjuvant arthritis in rats. In particular, longlasting synovial fluid induced a significant reduction of the severity of subsequent arthritis (p < 0.01) while SF from recent RA effusion (5–10 days after a previous complete extraction) and knee osteoarthrosis were ineffective. It is reasonable to assume there are at least two unknown endosomal immunoactive epitopes; one developing its immunotherapeutic property in RA, and the other, related to the molecule of HSP60, reduces the severity of oncoming arthritis. Both epitopes are present in humans, have a molecular weight of ≤10 kDa and do not appear to be bystander antigens. Please see Additional file 1 for the abstract in Italian.

Electronic supplementary material

The online version of this article (doi:10.1186/s12967-016-0908-7) contains supplementary material, which is available to authorized users.

Coevolutionary feedback elevates constitutive immune defence: a protein network model

Background

Organisms have evolved a variety of defence mechanisms against natural enemies, which are typically used at the expense of other life history components. Induced defence mechanisms impose minor costs when pathogens are absent, but mounting an induced response can be time-consuming. Therefore, to ensure timely protection, organisms may partly rely on constitutive defence despite its sustained cost that renders it less economical. Existing theoretical models addressing the optimal combination of constitutive versus induced defence focus solely on host adaptation and ignore the fact that the efficacy of protection depends on genotype-specific host-parasite interactions. Here, we develop a signal-transduction network model inspired by the invertebrate innate immune system, in order to address the effect of parasite coevolution on the optimal combination of constitutive and induced defence.

Results

Our analysis reveals that coevolution of parasites with specific immune components shifts the host’s optimal allocation from induced towards constitutive immunity. This effect is dependent upon whether receptors (for detection) or effectors (for elimination) are subjected to parasite counter-evolution. A parasite population subjected to a specific immune receptor can evolve heightened genetic diversity, which makes parasite detection more difficult for the hosts. We show that this coevolutionary feedback renders the induced immune response less efficient, forcing the hosts to invest more heavily in constitutive immunity. Parasites diversify to escape elimination by a specific effector too. However, this diversification does not alter the optimal balance between constitutive and induced defence: the reliance on constitutive defence is promoted by the receptor’s inability to detect, but not the effectors’ inability to eliminate parasites. If effectors are useless, hosts simply adapt to tolerate, rather than to invest in any defence against parasites. These contrasting results indicate that evolutionary feedback between host and parasite populations is a key factor shaping the selection regime for immune networks facing antagonistic coevolution.

Conclusion

Parasite coevolution against specific immune defence alters the prediction of the optimal use of defence, and the effect of parasite coevolution varies between different immune components.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0667-3) contains supplementary material, which is available to authorized users.

Topology driven modeling: the IS metaphor

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function [Formula: see text] with a particular functor of topological field theory-the generating function of the Betti numbers of the state manifold of the system-which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

The idiotypic network in the regulation of autoimmunity: Theoretical and experimental studies

The regulation of autoimmunity is a key issue in fundamental immunology. Despite outstanding achievements on this front, we currently have more questions than answers. The idea of an immune network as a regulatory mechanism is quite attractive, since it enables us to explain the selectivity (specificity), and moreover the clonality, of the regulation. Nevertheless it remains unclear how this mysterious network of immune cells is organized, how it operates, and how it exerts control over autoimmunity. This article presents an attempt to understand how the immune network functions and how it controls autoreactivity. We present a mathematical model of the immune network that is based on principles of immune network organization and function that we arrived at from a survey of the available literature. To test the principles on which the mathematical model is based, we studied the model and compared the different responses to antigen that it generated with the results obtained from experimental studies of immune response. The modeled kinetics of idiotype and anti-idiotype in response to the administration of antigen are in good agreement with the experimental kinetics of idiotypic and anti-idiotypic antibodies. To obtain evidence of the existence of idiotypic mechanisms for regulating autoimmunity, we studied a mathematical model containing autoclones and compared the model results with data from experimental studies in a model of autoimmune hemolytic anemia in mice. Because the results from the theoretical and the experimental studies coincide, there is justification to conclude that autoreactive lymphocytes are normal components of the immune network within which they are regulated. We discuss a possible molecular/cellular mechanism for negative control of autoreactive cells as affected by anti-idiotypic antibodies.

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.

Idiotypic networks: toward a renaissance?

Idiotypic networks, after being a dominating paradigm for more than a decade, have fallen out of fashion in parallel with the rapid success of molecular immunobiology. Today signs of a possible renaissance in idiotypic network studies are visible. For system biologists and also for physicists, the network idea remains attractive. Herein, a short account of the historical development of the paradigm is given. The necessary technical and conceptual ingredients for a theoretical description of idiotypic networks are briefly reviewed, and previous approaches are discussed. We also describe a minimalistic model developed in our group that allows for understanding the random evolution toward a highly non-trivial complex architecture. In the network, a connected large cluster of idiotype clones and many disconnected ones coexist, thus resembling the notion of central and peripheral parts proposed in the 'second-generation' version of the paradigm. The connected cluster consists of groups of idiotypic clones with clearly distinct statistical properties. The simplicity of the model allows for calculating the size of the groups and the number of inter- and intragroup links, which define the architecture. Aspects of idiotypic interactions in experimental medicine are discussed, along with the challenges to theory and experimentation.

The role of computational models of the immune system in designing vaccination strategies

Mathematical and computational models are designed to improve our understanding of biological phenomena, to confirm/reject hypotheses, and to find points of intervention by altering the behavior of the studied systems. Here we describe the role of mathematical/computational models of the immune system. In particular, we analyze some examples of how mathematical modeling can contribute to finding optimal vaccination strategies. Indeed, computational modeling offers an intriguing opportunity from the theoretical point of view, and it will be of interest for clinically oriented investigators who wish to find optimal therapeutic strategies and for pharmaceutical industries that want to produce effective and successful drugs.

Cytotoxic T-lymphocyte memory, virus clearance and antigenic heterogeneity

Cytotoxic T-lymphocyte (CTL) memory to viruses has traditionally been studied in an isolated setting. However, recent experiments have indicated that the presence of antigenically heterologous challenges can result in the attrition of CTL memory. Here we use mathematical models in order to explore the consequence of these dynamics for the ability of the immune system in controlling multiple infections. Mathematical models suggest that antigen-independent persistence of CTL memory is required in order to resolve and clear an infection. This ensures strong immunological pressure at low loads when the virus population declines towards extinction. If the number of antigenic stimuli exposed to the immune system crosses a threshold, we find that immunological pressure is significantly reduced at low loads and this can prevent virus clearance and reduces overall control of viral replication. Hence, exposure to many heterologous challenges reduces the ability of CTL memory to contribute to virus control. The higher the number of infections present in the host, the higher the overall virus load and the higher the total number of memory CTLs. Beyond a given threshold, addition of new viruses to the system results in accelerated loss of virus control which eventually leads to a reduction in the overall memory CTL population. These dynamics might contribute to the progressively weaker immunity observed as a result of ageing. In this context, antigenically variable pathogens expose the immune system to many heterologous challenges within a short period of time and this could result in accelerated ageing of the immune system. These results have important implications for vaccination and treatment strategies directed against viral infections.

Evolution of specificity in an immune network

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of specificity of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that specific and non-specific responses emerge as a function of antigen amounts. A specific response is observed with a fixed-point attractor, and a non-specific response is observed with a chaotic attractor for the lymphocyte population dynamics. The network topology also changes between fixed-point and chaotic attractors. For some antigen amounts, chaotic attractors will vanish or become long-lived super-transient states. A dynamic bell-shaped response function will thus emerge. The relevance of long-lived chaotic transient states embedded in fixed-point attractors is discussed with respect to immune functions.

The T cell receptor and AIDS pathogenesis

An idiotypic network model of AIDS pathogenesis is described in which the T cell receptor plays a role both in infection and as a target of autoimmunity. This is an extension of a previously published autoimmunity model, and provides explanations for several otherwise puzzling aspects of AIDS pathogenesis. In the model HIV-specific T cells are preferentially infected, and HIV, acting as an antigen, stimulates the expansion of the infectable pool of T cells. The HIV variants that are most strongly selected are those that are recognized by the most helper T cells. HIV and suppressor T cells are subject to the same selective environment, and consequently undergo a process of convergent selection to resemble each other more and more with time. Eventually immunity against HIV cross-reacts with suppressor T cell idiotypes, disrupting the normal regulation of helper T cells. Autoimmunity ensues. The model leads to novel vaccine and therapy approaches involving the targeting and elimination of HIV-specific T cells.

Memory capacity in large idiotypic networks

Many models of immune networks have been proposed since the original work of Jerne [1974, Ann. Immun. (Inst. Pasteur)125C, 373-389]. Recently, a limited class of models (Weisbuch et al., 1990, J. theor. Biol 146, 483-499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e., their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.

On the maternal transmission of immunity: a 'molecular attention' hypothesis

Maternally-derived antibodies can provide passive protection to their offspring. More subtle phenomena associated with maternal antibodies concern their influence in shaping the immune repertoire and priming the neonatal immune response. These phenomena suggest that maternal antibodies play a role in the education of the neonatal immune system. The educational effects are thought to be mediated by idiotypic interactions among antibodies and B cells in the context of an idiotypic network. This paper proposes that maternal antibodies trigger localized idiotypic network activity that serves to amplify and translate information concerning the molecular shapes of potential antigens. The triggering molecular signals are contained in the binding regions of the antibody molecules. These antibodies form complexes and are taken up by antigen presenting cells or retained by follicular dendritic cells and thereby incorporated into more traditional cellular immune memory mechanisms. This mechanism for maternal transmission of immunity is termed the molecular attention hypothesis and is contrasted to the dynamic memory hypothesis. Experiments are proposed that may help indicate which models are more appropriate and will further our understanding of these intriguing natural phenomena. Finally, analogies are drawn to attention in neural systems.

Co-selection in immune network theory and in AIDS pathogenesis

Co-selection is a term used to denote the mutual positive selection of individual members from within two diverse populations, such that selection of members within one population is dependent on interaction with (recognition of) one or more member(s) within the other population. Co-selection is a recurring theme of the idiotypic network model that my colleagues and I have developed. This paper discusses the role that co-selection plays in basic symmetrical network theory and in a network model that resolves the I-J paradox. It proposes that co-selection of helper T cells and HIV variants plays a role in the pathogenesis of AIDS. The AIDS model involves a role for the T cell receptor in the infection of T cells. Finally, a way in which a co-selection process may potentially be used in the prevention and therapy of harmful forms of immunity is described.

Memory in idiotypic networks due to competition between proliferation and differentiation

A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation precedes differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a "mexican-hat" effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively changed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.

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.

Immune network behavior--I. From stationary states to limit cycle oscillations

We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensionalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-type equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.

Modeling immune reactivity in secondary lymphoid organs

Models of the dynamical interactions important in generating immune reactivity have generally assumed that the immune system is a single well-stirred compartment. Here we explicitly take into account the compartmentalized nature of the immune system and show that qualitative conclusions, such as the stability of the immune steady state, depend on architectural details. We examine a simple model idiotypic network involving only two types of B cells and antibody molecules. We show, for model parameters used by De Boer et al. (1990, Chem. Eng. Sci. 45, 2375-2382), that the immune steady state is unstable in a one compartmental model but stable in a two compartment model that contains both a lymphoid organ, such as the spleen, and the circulatory system.

An idiotypic network model of AIDS immunopathogenesis

Considerations from a network theory of the immune system suggest that human immunodeficiency virus and allogeneic stimuli may act synergistically to cause AIDS. The immune responses to these stimuli include two components that are directed against each other. In some AIDS risk groups other antigens that mimic major histocompatibility complex antigens may substitute for allogeneic stimuli. Implications for the prevention of AIDS are discussed.

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)

Localized memories in idiotypic networks

The present paper investigates conditions under which immunological memory can be maintained by stimulatory idiotypic network interactions. The paper was motivated by the work of (De Boer & Hogeweg, 1989b, Bull. math. Biol. 51, 381-408.) which claimed that idiotypic memory is not possible because of percolation within the network. Here we reinvestigate the issue of percolation using both the previous model and a simpler one (Weisbuch, 1990, J. theor. Biol. 143, 507-522.) that allows analytic analysis. We focus on network topologies in which each Ab1 is connected to several Ab2s, which in turn are connected to several Ab3s. It is demonstrated that, for a considerable range of parameters, both models account for the existence of localized memory-states in which only the Ab1 and the Ab2 clones are activated and the clones of the Ab3 level remain virgin. The existence of localized memory-states seems to contradict the previous percolation result. This discrepancy will be shown to depend on the system dynamics. By simulation we explore the parameter regimes for which one finds percolation and those for which localized memory-states exists. We show that the conditions required for attaining the localized memory-state are considerably more stringent than those required for its existence and local stability. We conclude that both localized memory and percolation are possible in stimulatory idiotypic networks.

Immune network theory

Theoretical ideas have played a profound role in the development of idiotypic network theory. Mathematical models can help in the precise translation of speculative ideas into quantitative predictions. They can also help establish general principles and frameworks for thinking. Using the idea of shape space, criteria were introduced for evaluating the completeness and overlap in the antibody repertoire. Thinking about the distribution of clones in shape space naturally leads to considerations of stability and controllability. An immune system which is too stable will be sluggish and unresponsive to antigenic challenge; one which is unstable will be driven into immense activity by internal fluctuations. This led us to postulate that the immune system should be stable but not too stable. In many biological contexts the development of pattern requires both activation and inhibition but on different spatial scales. Similar ideas can be applied to shape space. The principle of short-range activation and long-range inhibition translates into specific activation and less specific inhibition. Application of this principle in model immune systems can lead to the stable maintenance of non-uniform distributions of clones in shape space. Thus clones which are useful and recognize antigen or internal images of antigen can be maintained at high population levels whereas less useful clones can be maintained at lower population levels. Pattern in shape space is a minimal requirement for a model. Learning and memory correspond to the development and maintenance of particular patterns in shape space. Representing antibodies by binary strings allows one to develop models in which the binary string acts as a tag for a specific molecule or clone. Thus models with huge numbers of cells and molecules can be developed and analyzed using computers. Using parallel computers or finite state models it should soon be feasible to study model immune systems with 10(5) or more elements. Although idiotypic networks were the focus of this paper, these modeling strategies are general and apply equally well to non-idiotypic models. Using bit string or geometric models of antibody combining sites, the affinity of interaction between any two molecules, and hence the connections in a model idiotypic network, can be determined. This approach leads to the prediction of a phase transition in the structure of idiotypic networks. On one side of the transition networks are small localized structures much as might be predicted by clonal selection and circuit ideas.(ABSTRACT TRUNCATED AT 400 WORDS)

Memory but no suppression in low-dimensional symmetric idiotypic networks

We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. non-idiotypic) antigens. Suppression is the dominant interaction, i.e. strong idiotypic interactions are always suppressive. This precludes reciprocal stimulation of large clones and thus infinite proliferation. Idiotypic interactions first evoke proliferation, this enlarges the clones, and may in turn evoke suppression. We investigate the effect of idiotypic interactions on normal proliferative immune responses to antigens (e.g. viruses). A 2-D, i.e. two clone, network has a maximum of three stable equilibria: the virgin state and two asymmetric immune states. The immune states only exist if the affinity of the idiotypic interaction is high enough. Stimulation with antigen leads to a switch from the virgin state to the corresponding immune state. The network therefore remembers antigens, i.e. it accounts for immunity/memory by switching between multiple stable states. 3-D systems have, depending on the affinities, 9 qualitatively different states. Most of these also account for memory by state switching. Our idiotypic network however fails to account for the control of proliferation, e.g. suppression of excessive proliferation. In symmetric networks, the proliferating clones suppress their anti-idiotypic suppressors long before the latter can suppress the former. The absence of proliferation control violates the general assumption that idiotypic interactions play an important role in immune regulation. We therefore test the robustness of these results by abandoning our assumption that proliferation occurs before suppression. We thus define an "escape from suppression" model, i.e. in the "virgin" state idiotypic interactions are now suppressive. This system erratically accounts for memory and never for suppression. We conclude that our "absence of suppression from idiotypic interactions" does not hinge upon our "proliferation before suppression" assumption.

Hyperreactivity of adult BALB/c mice tolerized at birth with TNP-ovalbumin

BALB/c mice injected with 0.2 mg TNP-ovalbumin (OA) within 24 hours after birth showed reduced levels of functionally active TNP-specific B cells and, accordingly, of plaque-forming cells (PFC) after challenge with carrier-bound TNP until the age of 8 weeks. Yet, when B cells of tolerized mice were cultured in the absence of antigen, a significant number of anti-TNP PFC were detected. Challenge of neonatally tolerized mice at older age with T-dependent or T-independent antigens led to a continuously increasing response towards TNP, which was dominated by IgG-producing B cells. At the age of 8 months, a five-fold augmentation of TNP-specific B cells and of anti-TNP antibodies (AB), as compared to animals treated accordingly as adults, was observed. Clonal analysis of regulatory cells revealed 2 populations of helper (Th1 and Th2) and suppressor (Ts1 and Ts2) T cells in spleen cells (SC) of tolerized mice. In SC of mice immunized as adults, Th1 and Th2, but only one Ts populations were observed. The frequencies of Th1 and Ts1 were in the same range in animals immunized neonatally or as adults. After challenge, frequencies of regulatory cells remained constant in animals immunized as adults. But, in neonatally tolerized mice, challenge resulted in increased frequencies of Th1 and Th2; Ts1 remained constant, and concomitantly the frequency of Ts2 declined significantly. The data are interpreted as newborn tolerance being due to transient B cell anergy via receptor blockade as well as inactivation of AB-producing cells. Neither deficiency in TNP-specific help nor dominance of TNP-specific suppression is involved in maintainance of tolerance, but tolerance appears to be sustained by interference of TNP-specific regulatory cells with anti-idiotypic regulatory cells (Th2, Ts2). Supposing a system of circular network interactions, activation of anti-idiotypic clones will be counterregulated/balanced by activation of antigen-specific clones. Thus, decreasing idiotypic connectivity during life may result in overshooting reactivity of neonatally tolerized mice at older age.

Model analysis of the bases of multistationarity in the humoral immune response

A formal analysis of the regulation of antibody production has been developed. It comprises two complementary approaches: a logical analysis in terms of discrete (boolean) variables and functions and a more classical analysis in terms of differential equations. A first paper dealt mostly with the logical description which provided global information on how complex the network needs to be in order to account for some main aspects of the immune response, without having to specify the details of the cellular interactions or to introduce a great number of parameters. Here we present the continuous approach and, in particular, a detailed study of the steady states and a discussion of their role in the dynamics of the immune response. The model subject to this analysis is a minimal one, which takes into account a small number of well-established facts concerning lymphocyte interactions and some reasonable assumptions. The core of the model is a negative feedback loop between the helper (TH) and suppressor (TS) T lymphocytes on which autocatalytic loops of the TH and TS populations on themselves are grafted. The salient feature of this minimal scheme is the prediction, for given environmental and parametrical conditions, of a multiplicity of steady states. This multistationarity occurs both in the absence of antigen or for constant antigen levels. Variations in the external constraints provoke switches among the steady states which might be related to the various modes of the humoral immune response, and depend on the doses of antigen injected and on the previous antigenic history of the system. In particular, high and low dose paralysis appear to be associated with two distinct steady state branches.

Modulation of T-suppressor cell activity by central nervous system catecholamine depletion

This study extends our previous findings, which indicate that depletion of CNS catecholamines has a marked inhibitory effect on humoral immune responsiveness. These data show that depletion of CNS catecholamines by injection of 6-hydroxydopamine (6-OHDA) into the cisterna magna in conjunction with immunization enhances the activity of a population of splenic T-suppressor cells as evidenced by the transfer of these cells to normal recipients. Increased suppressor cell activity does not result solely from 6-OHDA treatment, but rather requires concomitant immunization. Further characterization shows that these suppressor cells are not antigen specific. Hypophysectomy abrogates the effects of 6-OHDA injection suggesting that catecholamine depletion modulates immune function via the release of pituitary hormones. Thus, depletion of CNS catecholamines impairs immune responsiveness by inducing enhanced T-suppressor cell activity, providing additional evidence of the involvement of the CNS in regulation of immune responsiveness.

Detection of an IgM antiidiotype directed against anti-HBs in hepatitis B patients

An IgM-specific anti-[anti-HBs] antibody was detected by radioimmunoassay using anti-IgM-coated beads and 125I-labeled anti-HBs. This antiidiotype was found only in the sera of hepatitis B virus-infected patients, both acute and chronic. However, not all HBsAg-positive patients exhibited this reaction, and activity was correlated with the presence of HBeAg. Approximately 93% of sera that contained antiidiotype activity also contained HBeAg. Conversely, 70% of the sera positive for HBeAg reacted in the IgM assay. No correlation was observed between the presence of antiidiotype and rheumatoid factor or elevated SGPT levels. Two approaches were used to determine whether the reactive moiety was an IgM anti-[anti-HBs] as postulated or an IgM anti-HBs/HBsAg complex. It was shown that chicken anti-HBs sera, which does not share the common idiotype of human and other mammalian anti-HBs, did not block a positive reaction in this radioimmunoassay even though it specifically bound HBsAg. It was also demonstrated that treatment with polyethylene glycol, which will precipitate IgM anti-HBs/HBsAg activity, did not precipitate the reactive moiety in 6 of 7 sera tested, lending further evidence to the existence of an IgM antiidiotype in these patients. It is suggested that this antiidiotype directed against anti-HBs may be involved in a defective feedback mechanism resulting in the suppression of production of anti-HBs and maintenance of the carrier state.

Towards a logical analysis of the immune response

We present a new way to conceive, formalize and analyse models of the immune network. The models proposed are minimal ones, based essentially on the well-established negative feedback loop between helper and suppressor T cells. The occurrence of T-T interactions in both helper and suppressor circuits. These T-T interactions are represented here by autocatalytic feedback loops on TH and TS. The fact that immature B cells are sensitive to negative signaling, as was originally suggested by Lederberg (1959). There is a functional inactivation of immature B cells encountering antigen or anti-idiotypic antibody. This prevents further differentiation to a stage where the B cells become fully responsive. We describe the role of a logical method in the generation and analysis of the models, and the complementarity between this logical method and the more classical description by continuous differential equations. Logical analysis and numerical simulations of the differential equations show that the emerging model accounts for, the occurrence of multiple steady states (a virgin state, a memory state and a non-responsive state) in the absence of antigen, the kinetics of primary and secondary responses, high dose paralysis, low dose of paralysis. Its fit with real situations is surprisingly good for a model of this simplicity. Nevertheless, we give it as an example of what can now be done in the field rather than as a stable model.

Cluster formation in a symmetrical network: a dynamical system for the description of the suppression among non-immune T lymphocytes and its application to the effects of immunization

A mathematical model has been developed for the description of the suppressive regulation between polyclonally activated normal and immune T cells. The model assumes reversible cell-cell interactions to interpret results from limiting dilution experiments performed to determine the frequencies of precursor cells for antigen-specific T effector lymphocytes and to analyse mechanisms regulating the maturation of precursor into effector T cells. In particular, the model deals with the changes induced in the T lymphocytes population following immunization with antigens. In these limiting dilution experiments, T cells are placed in cultures at varying cell numbers with all other essential culture constituents kept in excess. After polyclonal activation of the T cells in culture they are supplied with growth and maturation factors so that they form daughter clones of functionally active T effector cells. The typical result observed was that effector T cells develop in cultures at low cell input but that this development is totally suppressed at high cell numbers. This result suggested that, at high cell numbers, the effector T cells are exposed to a sufficient number of other T cells of appropriate specificity to permit suppressive interactions. Whereas this is the case for non-immune T cells, T cells after immunization develop into effector cells both at high as well as at low cell concentrations, though with efficiencies less than proportional to their number of precursors. Our mathematical model is made up of a set of first order autonomous ordinary differential equations in many variables permitting the calculations of numbers of free cells and of cells engaged in cellular clusters of varying sizes. Free cells can develop into effector cells whereas cells engaged in clusters cannot. We calculate the consequences of several reasonable hypotheses concerning the effects of immunization. We consider the possibility that immunization modifies the growth behavior of the antigen-specific cells to permit an increased or accelerated clonal expansion in culture. Alternatively, we consider the possibility that immunization changes the interaction strength between cells specific for the immunizing antigen and other cells. Thirdly, we have connected both behaviors by calculating the case of an inverse relationship between growth rates and intensities of interaction between cells. Our model has been inspired by the symmetrical network model and can be interpreted in this framework. It proposes that immune regulation is a consequence of idiotype-anti-idiotype interactions.(ABSTRACT TRUNCATED AT 400 WORDS)

The X----Y----Z scheme after 23 years

Mathematical modelling of the course of the immune response is undoubtedly one of the most progressive and most promising areas of modern immunology. Mathematical models (along with computer programs) can be taken as "the only means of thoroughly testing and examining a large and intricate theory" (Partridge et al. 1984). The first phase of construction of mathematical models is the formulation of assumptions based on the knowledge of the facts to be modelled (manifested usually in a scheme of the presumed course of the modelled process). The first mathematical models of immune response were based on the hypothesis of a two-stage differentiation of cells participating in the humoral response, published in Prague 23 years ago (Sercarz and Coons 1962; Sterzl 1962) and illustrated by the X----Y----Z scheme. Many contemporary mathematical models still stem from this scheme which undoubtedly fits the fundamental data concerning the immune system.

Abrogation and reconstitution of nonresponsiveness: a correlation with high network connectivity

A monoclonal antibody (Fd-B2) to ferredoxin, which bears an idiotype scarcely expressed in any of a wide variety of mouse strains, is able to markedly enhance the response to ferredoxin of both high-responder and intermediate-responder strains. A rabbit anti-idiotype serum to Fd-B2 also specifically enhances the response to ferredoxin in such mice. Most remarkably, the treatment of nonresponder T cells by either the idiotype (Fd-B2) plus complement or anti-idiotype antiserum plus complement causes them to be responsive in adoptive transfer experiments. The two responding populations (idiotype-treated and anti-idiotype-treated) can then be combined to reconstitute the nonresponsive state. When the nonresponders are treated with either Fd-B2 idiotype plus complement or anti-idiotype plus complement and subsequently respond, the idiotype of the anti-ferredoxin antibody produced does not bear the Fd-B2 idiotype. We interpret the results as being consistent with a model in which the unresponsive state for ferredoxin is a state of high network connectivity of the ferredoxin-specific T cells.

Recognition of self and regulation of specificity at the level of cell populations

It is suggested that immunologic specificity and selective responsiveness, assayed by effector and memory cells, are, in part, determined by the existing repertoire of lymphocytes and, in part, by the dynamic nature of cellular growth. Clones within horizontal networks resemble competing species in a Darwinian world. Upon stimulation, the development of a clone is greatly affected, in a dynamic way, by factors that determine the balance between self-renewal and differentiation. Antigen is a major factor. The amount of antigen and the nature of encounter with the immune system (sudden, graded or continuous), through the selection of a particular subset of clones, can be correlated with a weak or a strong expression of effector function and with the generation of effective memory or of tolerance. The encounter with self antigens obeys the same rules. Thus, the distinction between self and non-self is a quantitative one, both at the single-cell level and at the systemic level. The encounter of developing lymphocytes with self antigens, and in particular with idiotypes and MHC-antigens, restricts the repertoire and imposes major constraints both on the mode of interaction with foreign antigens and on potential self-recognition networks. The proposed "dynamic scheme", differing from "structural schemes" in a number of fundamental aspects, calls for reevaluation of present concepts of immunoregulation and for reinterpretation of data.

Idiotypic networks and other preconceived ideas

The preceding section implies that the immune system (like the brain) reflects first ourselves, then produces a reflection of this reflection, and that subsequently it reflects the outside world: a hall of mirrors. The second mirror images (i.e., stable anti-idiotypic elements) may well be more complex than the first images (i.e., anti-self). Both give rise to distortions (e.g., mutations, gene rearrangements) permitting the recognition of nonself. The mirror images of the outside world, however, do not have permanency in the genome. Every individual must start with self. Paraphrasing Nicolas Schöffer (Schöffer 1982): those who always seek exterior pressures (e.g., microbes) to account for the evolution of the sets of V genes, would do well to turn their vision towards the interiors of themselves, and there discover the mystery, perhaps never completely revealable, of the immune system.