Size and connectivity as emergent properties of a developing immune network

Disease-related data patterns in cerebrospinal fluid diagnostics: medical quality versus analytical quantity

Cerebrospinal fluid (CSF) diagnostics is characterized by the biologically relevant combination of analytes in order to obtain disease-related data patterns that enable medically relevant interpretations. The necessary change in knowledge bases such as barrier function as a diffusion/CSF flow model and immunological networks of B-cell clones and pleiotropic cytokines is considered. The biophysical and biological principles for data combination are demonstrated using examples from neuroimmunological and dementia diagnostics. In contrast to current developments in clinical chemistry and laboratory medicine, CSF diagnostics is moving away from mega-automated systems with a constantly growing number of individual analyses toward a CSF report that integrates all patient data. Medical training in data sample interpretation in the inter-laboratory test systems ("EQA schemes") has become increasingly important. However, the results for CSF diagnostics (EQAS from INSTAND) indicate a crucially misguided trend. The separate analysis of CSF and serum in different, non-matched assays and extreme batch variations systematically lead to misinterpretations, which are the responsibility of the test providers. The questionable role of expensive accreditation procedures and the associated false quality expectations are discussed. New concepts that reintegrate the medical expertise of the clinical chemist must be emphasized along with the positive side effect of reducing costs in the healthcare system.

The role of promiscuous molecular recognition in the evolution of RNase-based self-incompatibility in plants

How do biological networks evolve and expand? We study these questions in the context of the plant collaborative-non-self recognition self-incompatibility system. Self-incompatibility evolved to avoid self-fertilization among hermaphroditic plants. It relies on specific molecular recognition between highly diverse proteins of two families: female and male determinants, such that the combination of genes an individual possesses determines its mating partners. Though highly polymorphic, previous models struggled to pinpoint the evolutionary trajectories by which new specificities evolved. Here, we construct a novel theoretical framework, that crucially affords interaction promiscuity and multiple distinct partners per protein, as is seen in empirical findings disregarded by previous models. We demonstrate spontaneous self-organization of the population into distinct "classes" with full between-class compatibility and a dynamic long-term balance between class emergence and decay. Our work highlights the importance of molecular recognition promiscuity to network evolvability. Promiscuity was found in additional systems suggesting that our framework could be more broadly applicable.

Shaping Polyclonal Responses via Antigen-Mediated Antibody Interference

Broadly neutralizing antibodies (bnAbs) recognize conserved features of rapidly mutating pathogens and confer universal protection, but they emerge rarely in natural infection. Increasing evidence indicates that seemingly passive antibodies may interfere with natural selection of B cells. Yet, how such interference modulates polyclonal responses is unknown. Here we provide a framework for understanding the role of antibody interference—mediated by multi-epitope antigens—in shaping B cell clonal makeup and the fate of bnAb lineages. We find that, under heterogeneous interference, clones with different intrinsic fitness can collectively persist. Furthermore, antagonism among fit clones (specific for variable epitopes) promotes expansion of unfit clones (targeting conserved epitopes), at the cost of repertoire potency. This trade-off, however, can be alleviated by synergy toward the unfit. Our results provide a physical basis for antigen-mediated clonal interactions, stress system-level impacts of molecular synergy and antagonism, and offer principles to amplify naturally rare clones.

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Multi-epitope antigens mediate antibody interference that couples B cell lineages

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Trade-off exists between repertoire potency and persistence of broad lineages

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Antigen-mediated synergy toward intrinsically unfit clones alleviates the trade-off

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Amplifying rare clones by leveraging molecular interference structure

MiStImm: an agent-based simulation tool to study the self-nonself discrimination of the adaptive immune response

BACKGROUND

There is an increasing need for complex computational models to perform in silico experiments as an adjunct to in vitro and in vivo experiments in immunology. We introduce Microscopic Stochastic Immune System Simulator (MiStImm), an agent-based simulation tool, that is designed to study the self-nonself discrimination of the adaptive immune system. MiStImm can simulate some components of the humoral adaptive immune response, including T cells, B cells, antibodies, danger signals, interleukins, self cells, foreign antigens, and the interactions among them. The simulation starts after conception and progresses step by step (in time) driven by random simulation events. We also have provided tools to visualize and analyze the output of the simulation program.

RESULTS

As the first application of MiStImm, we simulated two different immune models, and then we compared performances of them in the mean of self-nonself discrimination. The first model is a so-called conventional immune model, and the second model is based on our earlier T-cell model, called "one-signal model", which is developed to resolve three important paradoxes of immunology. Our new T-cell model postulates that a dynamic steady state coupled system is formed through low-affinity complementary TCR-MHC interactions between T cells and host cells. The new model implies that a significant fraction of the naive polyclonal T cells is recruited into the first line of defense against an infection. Simulation experiments using MiStImm have shown that the computational realization of the new model shows real patterns. For example, the new model develops immune memory and it does not develop autoimmune reaction despite the hypothesized, enhanced TCR-MHC interaction between T cells and self cells. Simulations also demonstrated that our new model gives better results to overcome a critical primary infection answering the paradox "how can a tiny fraction of human genome effectively compete with a vastly larger pool of mutating pathogen DNA?"

CONCLUSION

The outcomes of our in silico experiments, presented here, are supported by numerous clinical trial observations from the field of immunotherapy. We hope that our results will encourage investigations to make in vitro and in vivo experiments clarifying questions about self-nonself discrimination of the adaptive immune system. We also hope that MiStImm or some concept in it will be useful to other researchers who want to implement or compare other immune models.

Systems protobiology: origin of life in lipid catalytic networks

Life is that which replicates and evolves, but there is no consensus on how life emerged. We advocate a systems protobiology view, whereby the first replicators were assemblies of spontaneously accreting, heterogeneous and mostly non-canonical amphiphiles. This view is substantiated by rigorous chemical kinetics simulations of the graded autocatalysis replication domain (GARD) model, based on the notion that the replication or reproduction of compositional information predated that of sequence information. GARD reveals the emergence of privileged non-equilibrium assemblies (composomes), which portray catalysis-based homeostatic (concentration-preserving) growth. Such a process, along with occasional assembly fission, embodies cell-like reproduction. GARD pre-RNA evolution is evidenced in the selection of different composomes within a sparse fitness landscape, in response to environmental chemical changes. These observations refute claims that GARD assemblies (or other mutually catalytic networks in the metabolism first scenario) cannot evolve. Composomes represent both a genotype and a selectable phenotype, anteceding present-day biology in which the two are mostly separated. Detailed GARD analyses show attractor-like transitions from random assemblies to self-organized composomes, with negative entropy change, thus establishing composomes as dissipative systems-hallmarks of life. We show a preliminary new version of our model, metabolic GARD (M-GARD), in which lipid covalent modifications are orchestrated by non-enzymatic lipid catalysts, themselves compositionally reproduced. M-GARD fills the gap of the lack of true metabolism in basic GARD, and is rewardingly supported by a published experimental instance of a lipid-based mutually catalytic network. Anticipating near-future far-reaching progress of molecular dynamics, M-GARD is slated to quantitatively depict elaborate protocells, with orchestrated reproduction of both lipid bilayer and lumenal content. Finally, a GARD analysis in a whole-planet context offers the potential for estimating the probability of life's emergence. The invigorated GARD scrutiny presented in this review enhances the validity of autocatalytic sets as a bona fide early evolution scenario and provides essential infrastructure for a paradigm shift towards a systems protobiology view of life's origin.

Computational Nosology and Precision Psychiatry

This article provides an illustrative treatment of psychiatric morbidity that offers an alternative to the standard nosological model in psychiatry. It considers what would happen if we treated diagnostic categories not as causes of signs and symptoms, but as diagnostic consequences of psychopathology and pathophysiology. This reformulation (of the standard nosological model) opens the door to a more natural description of how patients present-and of their likely responses to therapeutic interventions. In brief, we describe a model that generates symptoms, signs, and diagnostic outcomes from latent psychopathological states. In turn, psychopathology is caused by pathophysiological processes that are perturbed by (etiological) causes such as predisposing factors, life events, and therapeutic interventions. The key advantages of this nosological formulation include (i) the formal integration of diagnostic (e.g., DSM) categories and latent psychopathological constructs (e.g., the dimensions of the Research Domain Criteria); (ii) the provision of a hypothesis or model space that accommodates formal, evidence-based hypothesis testing (using Bayesian model comparison); and (iii) the ability to predict therapeutic responses (using a posterior predictive density), as in precision medicine. These and other advantages are largely promissory at present: The purpose of this article is to show what might be possible, through the use of idealized simulations.

Towards a Neuronal Gauge Theory

Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics--based on approximate Bayesian inference--has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception.

Active inference, communication and hermeneutics

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others--during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions--both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then--in principle--they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa.

The Oral Tolerance as a Complex Network Phenomenon

The phenomenon of oral tolerance refers to a local and systemic state of tolerance induced in the gut after its exposure to innocuous antigens. Recent findings have shown the interrelationship between cellular and molecular components of oral tolerance, but its representation through a network of interactions has not been investigated. Our work aims at identifying the causal relationship of each element in an oral tolerance network, and also to propose a phenomenological model that's capable of predicting the stochastic behavior of this network when under manipulation. We compared the changes of a "healthy" network caused by "knock-outs" (KOs) in two approaches: an analytical approach by the Perron Frobenius theory; and a computational approach, which we describe within this work in order to find numerical results for the model. Both approaches have shown the most relevant immunological components for this phenomena, that happens to corroborate the empirical results from animal models. Besides explain in a intelligible fashion how the components interacts in a complex manner, we also managed to describe and quantify the importance of KOs that hasn't been empirically tested.

A mathematical approach to emergent properties of metabolic networks: partial coupling relations, hyperarcs and flux ratios

Emergent properties in systems biology are those which arise only when the biological system passes a certain level of complexity. In this study, we introduce some of the emergent properties which appear in the constraint-based analysis of metabolic networks. These properties generally appear as a result of existence of hfdeyperarcs and irreversible reactions in networks. Here, we present examples of metabolic networks in which there exist at least two reactions whose fluxes cannot be written as products and/or ratios of the stoichiometric coefficients of the network. We show that any such network contains at least one hyperarc. Additionally, we prove that partial coupling cannot appear in consistent metabolic networks with less than four reactions, or with less than three irreversible reactions, or without hyperarc(s).

Self-tolerance in a minimal model of the idiotypic network

We consider the problem of self-tolerance in the frame of a minimalistic model of the idiotypic network. A node of this network represents a population of B-lymphocytes of the same idiotype, which is encoded by a bit string. The links of the network connect nodes with (nearly) complementary strings. The population of a node survives if the number of occupied neighbors is not too small and not too large. There is an influx of lymphocytes with random idiotype from the bone marrow. Previous investigations have shown that this system evolves toward highly organized architectures, where the nodes can be classified into groups according to their statistical properties. The building principles of these architectures can be analytically described and the statistical results of simulations agree very well with results of a modular mean-field theory. In this paper, we present simulation results for the case that one or several nodes, playing the role of self, are permanently occupied. These self nodes influence their linked neighbors, the autoreactive clones, but are themselves not affected by idiotypic interactions. We observe that the group structure of the architecture is very similar to the case without self antigen, but organized such that the neighbors of the self are only weakly occupied, thus providing self-tolerance. We also treat this situation in mean-field theory, which give results in good agreement with data from simulation. The model supports the view that autoreactive clones, which naturally occur also in healthy organisms are controlled by anti-idiotypic interactions, and could be helpful to understand network aspects of autoimmune disorders.

The past, present, and future of immune repertoire biology - the rise of next-generation repertoire analysis

T and B cell repertoires are collections of lymphocytes, each characterized by its antigen-specific receptor. We review here classical technologies and analysis strategies developed to assess immunoglobulin (IG) and T cell receptor (TR) repertoire diversity, and describe recent advances in the field. First, we describe the broad range of available methodological tools developed in the past decades, each of which answering different questions and showing complementarity for progressive identification of the level of repertoire alterations: global overview of the diversity by flow cytometry, IG repertoire descriptions at the protein level for the identification of IG reactivities, IG/TR CDR3 spectratyping strategies, and related molecular quantification or dynamics of T/B cell differentiation. Additionally, we introduce the recent technological advances in molecular biology tools allowing deeper analysis of IG/TR diversity by next-generation sequencing (NGS), offering systematic and comprehensive sequencing of IG/TR transcripts in a short amount of time. NGS provides several angles of analysis such as clonotype frequency, CDR3 diversity, CDR3 sequence analysis, V allele identification with a quantitative dimension, therefore requiring high-throughput analysis tools development. In this line, we discuss the recent efforts made for nomenclature standardization and ontology development. We then present the variety of available statistical analysis and modeling approaches developed with regards to the various levels of diversity analysis, and reveal the increasing sophistication of those modeling approaches. To conclude, we provide some examples of recent mathematical modeling strategies and perspectives that illustrate the active rise of a "next-generation" of repertoire analysis.

The natural autoantibody repertoire in newborns and adults: a current overview

Antibody networks have been studied in the past based on the connectivity between idiotypes and anti-idiotypes-antibodies that bind one another. Here we call attention to a different network of antibodies, antibodies connected by their reactivities to sets of antigens-the antigen-reactivity network. The recent development of antigen microarray chip technology for detecting global patterns of antibody reactivities makes it possible to study the immune system quantitatively using network analysis tools. Here, we review the analyses of IgM and IgG autoantibody reactivities of sera of mothers and their offspring (umbilical cords) to 300 defined self-antigens; the autoantibody reactivities present in cord blood represent the natural autoimmune repertories with which healthy humans begin life and the mothers' reactivities reflect the development of the repertoires in healthy young adults. Comparing the cord and maternal reactivities using several analytic tools led to the following conclusions: (1) The IgG repertoires showed a high correlation between each mother and her newborn; the IgM repertoires of all the cords were very similar and each cord differed from its mother's IgM repertoire. Thus, different humans are born with very similar IgM autoantibodies produced in utero and with unique IgG autoantibodies found in their individual mothers. (2) Autoantibody repertoires appear to be structured into sets of reactivities that are organized into cliques-reactivities to particular antigens are correlated. (3) Autoantibody repertoires are organized as networks of reactivities in which certain key antigen reactivities dominate the network-the dominant antigen reactivities manifest a "causal" relationship to sets of other correlated reactivities. Thus, repertoires of autoantibodies in healthy subjects, the immunological homunculus, are structured in hierarchies of antigen reactivities.

Organization and evolution of synthetic idiotypic networks

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely, the interaction networks involving the B core of the immune system. Each node is endowed with a bit string representing the idiotypic specificity of the corresponding B cell, and the proper distance between any couple of bit strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit strings can yield fringes in the (weighted) degree distribution, small-world features, and scaling laws, in agreement with experimental findings. We also investigate the role of aging, thought of as a progressive increase in the degree of bias in bit strings, and we show that it can possibly induce mild percolation phenomena, which are investigated too.

Agent-based modeling of host-pathogen systems: The successes and challenges

Agent-based models have been employed to describe numerous processes in immunology. Simulations based on these types of models have been used to enhance our understanding of immunology and disease pathology. We review various agent-based models relevant to host–pathogen systems and discuss their contributions to our understanding of biological processes. We then point out some limitations and challenges of agent-based models and encourage efforts towards reproducibility and model validation.

Predicting and controlling the reactivity of immune cell populations against cancer

Heterogeneous cell populations form an interconnected network that determine their collective output. One example of such a heterogeneous immune population is tumor-infiltrating lymphocytes (TILs), whose output can be measured in terms of its reactivity against tumors. While the degree of reactivity varies considerably between different TILs, ranging from null to a potent response, the underlying network that governs the reactivity is poorly understood. Here, we asked whether one can predict and even control this reactivity. To address this we measured the subpopulation compositions of 91 TILs surgically removed from 27 metastatic melanoma patients. Despite the large number of subpopulations compositions, we were able to computationally extract a simple set of subpopulation-based rules that accurately predict the degree of reactivity. This raised the conjecture of whether one could control reactivity of TILs by manipulating their subpopulation composition. Remarkably, by rationally enriching and depleting selected subsets of subpopulations, we were able to restore anti-tumor reactivity to nonreactive TILs. Altogether, this work describes a general framework for predicting and controlling the output of a cell mixture.

How affinity influences tolerance in an idiotypic network

Idiotypic network models give one possible justification for the appearance of tolerance for a certain category of cells while maintaining immunization for the others. In this paper, we provide new evidence that the manner in which affinity is defined in an idiotypic network model imposes a definite topology on the connectivity of the potential idiotypic network that can emerge. The resulting topology is responsible for very different qualitative behaviour of the network. We show that using a 2D shape-space model with affinity based on complementary regions, a cluster-free topology results that clearly divides the space into distinct zones; if antigens fall into a zone in which there are no available antibodies to bind to, they are tolerated. On the other hand, if they fall into a zone in which there are highly concentrated antibodies available for binding, then they will be eliminated. On the contrary, using a 2D shape space with an affinity function based on cell similarity, a highly clustered topology emerges in which there is no separation of the space into isolated tolerant and non-tolerant zones. Using a bit-string shape space, both similar and complementary affinity measures also result in highly clustered networks. In the networks whose topologies exhibit high clustering, the tolerant and intolerant zones are so intertwined that the networks either reject all antigen or tolerate all antigen. We show that the distribution and topology of the antibody network defined by the complete set of nodes and links-an autonomous feature of the system-therefore selects which antigens are tolerated and which are eliminated.

Modeling regulation mechanisms in the immune system

We develop a mathematical framework for modeling regulatory mechanisms in the immune system. The model describes dynamics of key components of the immune network within two compartments: lymph node and tissue. We demonstrate using numerical simulations that our system can eliminate virus-infected cells, which are characterized by a tendency to increase without control (in absence of an immune response), while tolerating normal cells, which are characterized by a tendency to approach a stable equilibrium population. We experiment with different combinations of T cell reactivities that lead to effective systems and conclude that slightly self-reactive T cells can exist within the immune system and are controlled by regulatory cells. We observe that CD8+ T cell dynamics has two phases. In the first phase, CD8+ cells remain sequestered within the lymph node during a period of proliferation. In the second phase, the CD8+ population emigrates to the tissue and destroys its target population. We also conclude that a self-tolerant system must have a mechanism of central tolerance to ensure that self-reactive T cells are not too self-reactive. Furthermore, the effectiveness of a system depends on a balance between the reactivities of the effector and regulatory T cell populations, where the effectors are slightly more reactive than the regulatory cells.

Growing biological networks: Beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.

Control of Genotypic Allelic Inclusion through TCR Surface Expression

To gain insight into the molecular causes and functional consequences of allelic inclusion of TCR alpha-chains, we develop a computational model for thymocyte selection in which the signal that determines cell fate depends on surface expression. Analysis of receptor pairs on selected dual TCR cells reveals that allelic inclusion permits both autoreactive TCR and receptors not in the single TCR cell repertoire to be selected. However, in comparison with earlier theoretical studies, relatively few dual TCR cells display receptors with high avidity for thymic ligands because their alpha-chains compete aggressively for the beta-chain, which hinders rescue from clonal deletion. This feature of the model makes clear that allelic inclusion does not in itself compromise central tolerance. A specific experiment based on modulation of TCR surface expression levels is proposed to test the model.

Activation-threshold tuning in an affinity model for the T-cell repertoire

Naive T cells respond to peptides from foreign proteins and remain tolerant to self peptides from endogenous proteins. It has been suggested that self tolerance comes about by a 'tuning' mechanism, i.e. by increasing the T-cell activation threshold upon interaction with self peptides. Here, we explore how such an adaptive mechanism of T-cell tolerance would influence the reactivity of the T-cell repertoire to foreign peptides. We develop a computer simulation model in which T cells are tolerized by increasing their activation-threshold dependent on the affinity with which they see self peptides presented in the thymus. Thus, different T cells acquire different activation thresholds (i.e. different cross-reactivities). In previous mathematical models, T-cell tolerance was deletional and based on a fixed cross-reactivity parameter, which was assumed to have evolved to an optimal value. Comparing these two different tolerance-induction mechanisms, we found that the tuning model performs somewhat better than an optimized deletion model in terms of the reactivity to foreign antigens. Thus, evolutionary optimization of clonal cross-reactivity is not required. A straightforward extension of the tuning model is to delete T-cell clones that obtain a too high activation threshold, and to replace these by new clones. The reactivity of the immune repertoires of such a replacement model is enchanced compared with the basic tuning model. These results demonstrate that activation-threshold tuning is a functional mechanism for self tolerance induction.

Tolerance and immunity in a mathematical model of T-cell mediated suppression

Regulatory CD4+CD25+ T cells play a major role in natural tolerance to body components and therefore are relevant to understand the self-non-self discrimination by the immune system. The most pressing theoretical question, regarding the fact that these regulatory cells perform their function through linked recognition of the APCs, is how this "non-specific" mechanism permits a proper balance between tolerance and immunity that is compatible with an effective self-non-self discrimination. To tackle this issue, we develop a numerical simulation, which extends a previous mathematical model of T-cell-mediated suppression to include the thymic generation and the peripheral dynamics of many T cell clones. This simulation can mimic the capacity of the immune system to establish natural tolerance to self-antigens and reliably mount immune responses to foreign antigens. Natural tolerance is based on ubiquitous and constitutive self-antigens, which select and sustain clones of specific regulatory cells. Immune responses to foreign antigens are only achieved if they displace the self-antigens from the APCs, leading to a loss of the regulatory cells, and/or if the foreign antigen introduction entails a sharp increase in the total number of APCs. Meaningful behavior is obtained even if differentiation of regulatory cells in the thymus is antigen non-specific, but requires that a minimum number of new T cells enter the periphery per unit of time, and that the repertoire is selected so that anti-self-affinities are within a proper interval. We conclude that positive selection is required to generate a sufficiently high frequency of self-antigen specific regulatory cells that reliably mediate natural tolerance. Negative selection is required to avoid the emergence at the periphery of very high affinity anti-self-regulatory cells that will make the tolerant state so robust that it could no be broken by the introduction of a foreign antigen. This result highlights the importance of repertoire selection in dominant tolerance proposing a novel role for the processes of positive and negative selection within this framework.

The affirmation of self: a new perspective on the immune system

The fundamental concepts of autopoiesis, which emphasize the circular organization underlying both living organisms and cognition, have been criticized on the grounds that since they are conceived as a tight logical chain of definitions and implications, it is often not clear whether they are indeed a scientific theory or rather just a potential scientific vocabulary of doubtful utility to working scientists. This article presents the deployment of the concepts of autopoiesis in the field of immunology, a discipline where working biologists themselves spontaneously have long had recourse to "cognitive" metaphors: "recognition"; a "repertoire" of recognized molecular shapes; "learning" and "memory"; and, most striking of all, a "self versus non-self" distinction. It is shown that in immunology, the concepts of autopoiesis can be employed to generate clear novel hypotheses, models demonstrating these ideas, testable predictions, and novel therapeutic procedures. Epistemologically, it is shown that the self-non-self distinction, while quite real, is misleadingly named. When a real mechanism for generating this distinction is identified, it appears that the actual operational distinction is between (a) a sufficiently numerous set of initial antigens, present from the start of ontogeny, in conditions that allow for their participation in the construction of the system's organization and operation, and (b) single antigens that are first presented to the system after two successive phases of maturation. To call this a self-non-self distinction obscures the issue by presupposing what it ought to be the job of scientific investigation to explain.

Connectivity patterns in tuberculosis and leprosy patients are indistinguishable from that of healthy donors

Connectivity, the self-defined interactions between antigen-recognising molecules in a network system can in part be assessed by measuring the reactivity of a given serum against an ordered set of immunoglobulin (Ig)G F(ab')2 fractions, separated by means of isoelectric focusing so that, the serum reactivity against the whole set of fractions defines a characteristic pattern of connectivity. Deviations from the normal condition (healthy donors) have so far been documented for two autoimmune diseases: systemic lupus erythematosus (SLE) and pemphigus vulgaris, as well as for human immunodeficiency virus (HIV)-1 infection. We tested here if bacterial infections lead to alterations in connectivity. In addition, we wanted to test if two antigenically related bacteria would produce similar or otherwise distinctive connectivity patterns. Connectivity analysis was applied on the sera from tuberculosis and leprosy patients and the sera from healthy donors were used as control. No statistically significant differences between the three groups studied were found. These results have implications for theories that set the origin of autoimmune diseases in microbial infections. To the best of our knowledge, this is the first attempt to analyze the connectivity status in bacterial infections.

A mathematical method for investigating dynamic behavior of an idiotype network of the immune system. The time minimum optimal control theory

We proposed a mathematical method to investigate an integrated property of an idiotype immune network under the time minimum optimal control. The transient changes of amounts of B cell receptor bound antibodies and immune complex in the network system were expressed by detailed differential equations. The rate constant for binding the second Fab arm of antibody was set as a function of coulombic repulsive force to express the influence of redistribution of electrical charges in the ligand-receptor molecular complex. We proposed time minimum optimal control strategy as an organizing principle for rapid reactions of the immune system. Based on the rigorous mathematical foundations of the optimal control theory, we determined the differential equations for co-state variables for the state variables to compute the time minimum transient changes in the amount of the species. Biological parameters in the immune reactions were utilized from the reported experimental data. Numerical computation disclosed that influence of changes in a rate constant extended to all the species of the network. Changes in a rate constant in a different B cell system reinforced the collaborations among the idiotypes and lead them to set in motion the ejection of the antigen. Simulation of reported experimental data by the present method was successful. There were, however, some inevitable dissociations between reported experimental data and computed results. The present method will be available for evaluating the time minimum reaction of the immune network system.

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 immune system as a model for pattern recognition and classification

OBJECTIVE

To design a pattern recognition engine based on concepts derived from mammalian immune systems.

DESIGN

A supervised learning system (Immunos-81) was created using software abstractions of T cells, B cells, antibodies, and their interactions. Artificial T cells control the creation of B-cell populations (clones), which compete for recognition of "unknowns." The B-cell clone with the "simple highest avidity" (SHA) or "relative highest avidity" (RHA) is considered to have successfully classified the unknown.

MEASUREMENT

Two standard machine learning data sets, consisting of eight nominal and six continuous variables, were used to test the recognition capabilities of Immunos-81. The first set (Cleveland), consisting of 303 cases of patients with suspected coronary artery disease, was used to perform a ten-way cross-validation. After completing the validation runs, the Cleveland data set was used as a training set prior to presentation of the second data set, consisting of 200 unknown cases.

RESULTS

For cross-validation runs, correct recognition using SHA ranged from a high of 96 percent to a low of 63.2 percent. The average correct classification for all runs was 83.2 percent. Using the RHA metric, 11.2 percent were labeled "too close to determine" and no further attempt was made to classify them. Of the remaining cases, 85.5 percent were correctly classified. When the second data set was presented, correct classification occurred in 73.5 percent of cases when SHA was used and in 80.3 percent of cases when RHA was used.

CONCLUSIONS

The immune system offers a viable paradigm for the design of pattern recognition systems. Additional research is required to fully exploit the nuances of immune computation.

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.

Mathematical and computational challenges in population biology and ecosystems science

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

A new bell-shaped function for idiotypic interactions based on cross-linking

Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the "field," which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network. The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field. When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higher-affinity interactions. We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

A simple model for the statistics of events in idiotypic networks

A simple random graph model of idiotypic networks is introduced: this model allows (1) to evaluate the stability of the network dynamics' fixed points, and (2) to compute the statistics of events triggered in response to the arrival of new molecules (metadynamics) using a dynamic mean-field approximation based on the theory of branching processes. It is shown that (1) the network dynamics is unlikely to have many stable fixed points in a strict sense, but that (2) the reorganizations which the network undergoes owing to the metadynamics are always subcritical if plausible figures are injected into the model. In other words the distance between successive (unstable or weakly stable) fixed points is relatively small, so that the overall behavior is stable.

Contributions of memory B cells to secondary immune response

The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.

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.

Immune networks modeled by replicator equations

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function f (h), where the field h summarizes the effect of the network on a single clone. We show that by transforming into relative concentrations, the B-cell network equations can be brought into a form that closely resembles the replicator equation. We then show that when the total number of clones in a network is conserved, the dynamics of the network can be represented by the dynamics of a replicator equation. The number of equilibria and their stability are then characterized using methods developed for the study of second-order replicator equations. Analogies with standard Lotka-Volterra equations are also indicated. A particularly interesting result of our analysis is the fact that even though the immune network equations are not second-order, the number and stability of their equilibria can be obtained by a superposition of second-order replicator systems. As a consequence, the problem of finding all of the equilibrium points of the nonlinear network equations can be reduced to solving linear equations.

Central immune system, the self and autoimmunity

We model how auto-reactive B cells are kept under control by an idiotypic network. Autoimmunity occurs when the control is broken by an infection or not achieved through an abnormal ontogenetic evolution. We describe the idiotypic network, viz., the central immune system, by idiotype-anti-idiotype pairs which are coupled to a set of highly connected clones, which interact with each clone of the network. Some clones of the central immune system recognize self-antigen. We find a huge variety of fixed points which can be classified as tolerant, autoimmune, and neutral states according to the concentration of the auto-reactive antibody. Most significant are auto-reactive clones which are a member of an idiotype-anti-idiotype pair. In a healthy individual, an autoimmune disease is induced by an antigen infection which triggers a transition from a tolerant to an autoimmune state. Autoimmunity is induced more readily by an antigen coupling to the anti-idiotype than by one interacting with the auto-reactive clone itself. We indicate a possible therapy which simply reverses the processes that have lead to the autoimmune disease. In the early development of the central immune system its highly connected, core part serves to draw the more specific clones of idiotype-anti-idiotype pairs into the network. In order to avoid autoimmunity in ontogenetic evolution the anti-idiotype of an auto-reactive clone must be formed in advance by a sufficiently long period of time. Thus, a well ordered succession of the appearance of the more specific clones is required.

Capacity of a model immune network

The capacity of a model immune network in terms of the number of different antigens that can be vaccinated against without any memory lost is computed and tested by numerical simulations. We also investigate memory loss and failure to vaccinate due to overcrowding the network with too many antigens. The computations are done for two different strategies for proliferation, one implying all the antigen specific clones and the second one being more thrifty.

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.

Immune network behavior--II. From oscillations to chaos and stationary states

Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating.

Probability model for molecular recognition in biological receptor repertoires: significance to the olfactory system

A generalized phenomenological model is presented for stereospecific recognition between biological receptors and their ligands. We ask what is the distribution of binding constants psi(K) between an arbitrary ligand and members of a large receptor repertoire, such as immunoglobulins or olfactory receptors. For binding surfaces with B potential subsite and S different types of subsite configurations, the number of successful elementary interactions obeys a binomial distribution. The discrete probability function psi(K) is then derived with assumptions on alpha, the free energy contribution per elementary interaction. The functional form of psi(K) may be universal, although the parameter values could vary for different ligand types. An estimate of the parameter values of psi(K) for iodovanillin, an analog of odorants and immunological haptens, is obtained by equilibrium dialysis experiments with nonimmune antibodies. Based on a simple relationship, predicted by the model, between the size of a receptor repertoire and its average maximal affinity toward an arbitrary ligand, the size of the olfactory receptor repertoire (Nolf) is calculated as 300-1000, in very good agreement with recent molecular biological studies. A very similar estimate, Nolf = 500, is independently derived by relating a theoretical distribution of maxima for psi(K) with published human olfactory threshold variations. The present model also has implications to the question of olfactory coding and to the analysis of specific anosmias, genetic deficits in perceiving particular odorants. More generally, the proposed model provides a better understanding of ligand specificity in biological receptors and could help in understanding their evolution.