Qualitative dynamics of a network model of regulation of the immune system: a rationale for the IgM to IgG switch

COVID-19: Clinical laboratory diagnosis and monitoring of novel coronavirus infected patients using molecular, serological and biochemical markers: A review

COVID-19, a novel coronavirus disease, has provoked a variety of health and safety concerns, and socioeconomic challenges around the globe. The laboratory diagnosis of SARS-CoV-2 was quickly established utilizing nucleic acid amplification techniques (NAAT) after the disease causing virus has been identified, and its genetic sequence has been determined. In addition to NAAT, serological tests based on antibodies testing against SARS-CoV-2 were introduced for diagnostic and epidemiologic studies. Other biochemical investigations include monitoring of peripheral blood cells count, platelets/lymphocyte ratio, coagulation profile, cardiac, and inflammatory markers such as cytokines storm are also crucial in combating COVID-19 pandemic. Further, accurate and reliable laboratory results for SARS-CoV-2 play very important role in the initiation of early treatment and timely management of COVID-19 patients, provide support in clinical decision-making process to control infection, and detection of asymptomatic cases. The Task Force on Coronavirus-19 constituted by International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) has recognized informational framework for epidemiology, pathogenesis, and recommended the PCR-based analysis, serological and biochemical assays for analysis, monitoring, and management of disease. This literature review provides an overview of the currently used diagnostic techniques in clinical laboratories for the diagnosis, treatment monitoring, and management of COVID-19 patients. We concluded that each assays differ in their performance characteristics and the utilization of multiple techniques is necessary for the accurate diagnosis and management of SARS-CoV-2 infection.

Trends of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibody prevalence in selected regions across Ghana

Background: We set out to estimate the community-level exposure to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Ghana. Methods: Phased seroprevalence studies of 2729 participants at selected locations across Ghana were conducted. Phase I (August 2020) sampled 1305 individuals at major markets/lorry stations, shopping malls, hospitals and research institutions involved in coronavirus disease 2019 (COVID-19) work. The study utilized a lateral flow rapid diagnostic test (RDT) which detected IgM and IgG antibodies against SARS-CoV-2 nucleocapsid protein. Results: During Phase I, 252/1305 (19%) tested positive for IgM or IgG or both. Exposure was significantly higher at markets/lorry stations (26.9%) compared to malls (9.4%), with 41–60-year group demonstrating highest seropositivity (27.2%). Exposure was higher in participants with no formal education (26.2%) than those with tertiary education (13.1%); and higher in informally employed workers (24.0%) than those in the formal sector (15.0%). Results from phases II and III, in October and December 2020 respectively, implied either reduced transmissions or loss of antibody expression in some participants. The Upper East region showed the lowest seropositivity (2%). Phase IV, in February 2021, showed doubled seropositivity in the upper income bracket (26.2%) since August 2020, reflective of Ghana’s second wave of symptomatic COVID-19 cases. This suggested that high transmission rates had overcome the initial socioeconomic stratification of exposure risk. Reflective of second wave hospitalisation trends, the 21-40 age group demonstrated modal seropositivity (24.9) in Phase IV whilst 40-60 years and 60+ previously demonstrated highest prevalence. Conclusions: Overall, the data indicates higher COVID-19 seroprevalence than officially acknowledged, likely implying a considerably lower-case fatality rate than the current national figure of 0.84%. The data also suggests that COVID-19 is predominantly asymptomatic COVID-19 in Ghana. The observed trends mimic clinical trends of infection and imply that the methodology used was appropriate.

Immunoinformatics approach for multi-epitope vaccine design against P. falciparum malaria

Plasmodium falciparum (P. falciparum) is a leading causative agent of malaria, an infectious disease that can be fatal. Unfortunately, control measures are becoming less effective over time. A vaccine is needed to effectively control malaria and lead towards the total elimination of the disease. There have been multiple attempts to develop a vaccine, but to date, none have been certified as appropriate for wide-scale use. In this study, an immunoinformatics method is presented to design a multi-epitope vaccine construct predicted to be effective against P. falciparum malaria. This was done through the prediction of 12 CD4+ T-cell, 10 CD8+ T-cell epitopes and, 1 B-cell epitope which were assessed for predicted high antigenicity, immunogenicity, and non-allergenicity through in silico methods. The Human Leukocyte Antigen (HLA) population coverage showed that the alleles associated with the epitopes accounted for 78.48% of the global population. The CD4+ and CD8+ T-cell epitopes were docked to HLA-DRB1*07:01 and HLA-A*32:01 successfully. Therefore, the epitopes were deemed to be suitable as components of a multi-epitope vaccine construct. Adjuvant RS09 was added to the construct to generate a stronger immune response, as confirmed by an immune system simulation. Finally, the structural stability of the predicted multi-epitope vaccine was assessed using molecular dynamics simulations. The results show a promising vaccine design that should be further synthesised and assessed for its efficacy in an experimental laboratory setting.

COVID-19 Antibody Tests and Their Limitations

COVID-19, caused by the SARS-CoV-2 virus, has developed into a global health crisis, causing over 2 million deaths and changing people's daily life the world over. Current main-stream diagnostic methods in the laboratory include nucleic acid PCR tests and direct viral antigen tests for detecting active infections, and indirect human antibody tests specific to SARS-CoV-2 to detect prior exposure. In this Perspective, we briefly describe the PCR and antigen tests and then focus mainly on existing antibody tests and their limitations including inaccuracies and possible causes of unreliability. False negatives in antibody immunoassays can arise from assay formats, selection of viral antigens and antibody types, diagnostic testing windows, individual variance, and fluctuation in antibody levels. Reasons for false positives in antibody immunoassays mainly involve antibody cross-reactivity from other viruses, as well as autoimmune disease. The spectrum bias has an effect on both the false negatives and false positives. For assay developers, not only improvement of assay formats but also selection of viral antigens and isotopes of human antibodies need to be carefully considered to improve sensitivity and specificity. For clinicians, the factors influencing the accuracy of assays must be kept in mind to test patients using currently imperfect but available tests with smart tactics and realistic interpretation of the test results.

Evaluation of serum IgM and IgG antibodies in COVID-19 patients by enzyme linked immunosorbent assay

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is sweeping the world since the end of 2019. The titer change of antibodies against SARS-CoV-2 needs to be further clarified, the clinical and preventive value of antibodies still needs to be further investigated. An enzyme-linked immunosorbent assay (ELISA) was established by coating with SARS-CoV-2 recombinant spike protein and used to detect serum immunoglobulin M (IgM) and immunoglobulin G (IgG) antibodies against SARS-CoV-2 in coronavirus disease 2019 patients to evaluate the pattern of changes of antibodies. The specificity of the ELISA for detection SARS-CoV-2 IgM and IgG were 96% (144/150) and 100% (150/150), respectively. The sensitivity of ELISA was 100% (150/150) for IgM, and 99.3% (149/150) for IgG. SARS-CoV-2-SP-IgM and SP-IgG antibodies could be detected on Day 1 of hospitalization in 12.5% patients, and SP-IgM began to decrease after reaching its peak at around 22-28 days, and become negative at Month 3 in 30% patients and negative at Month 7 in 79% of these patients after onset; IgG reached its peak around Day 22-28 and kept at a high level within the longest observation period for 4 months, it dropped very sharply at 7 months. The positive rates of SP-IgM and SP-IgG were higher than those of reverse transcription-polymerase chain reaction on Day 7 and 4. The established indirect ELISA has good specificity and sensitivity. IgM and IgG against SARS-CoV-2 appeared almost simultaneously in the early stage, and the level of IgG antibodies could not maintain a high plateau in the observation period of 7 months. Our data will help develop the diagnosis and vaccine of SARS-CoV-2.

Molecular, serological, and biochemical diagnosis and monitoring of COVID-19: IFCC taskforce evaluation of the latest evidence

The global coronavirus disease 2019 (COVID-19) has presented major challenges for clinical laboratories, from initial diagnosis to patient monitoring and treatment. Initial response to this pandemic involved the development, production, and distribution of diagnostic molecular assays at an unprecedented rate, leading to minimal validation requirements and concerns regarding their diagnostic accuracy in clinical settings. In addition to molecular testing, serological assays to detect antibodies against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are now becoming available from numerous diagnostic manufacturers. In both cases, the lack of peer-reviewed data and regulatory oversight, combined with general misconceptions regarding their appropriate use, have highlighted the importance of laboratory professionals in robustly validating and evaluating these assays for appropriate clinical use. The International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) Task Force on COVID-19 has been established to synthesize up-to-date information on the epidemiology, pathogenesis, and laboratory diagnosis and monitoring of COVID-19, as well as to develop practical recommendations on the use of molecular, serological, and biochemical tests in disease diagnosis and management. This review summarizes the latest evidence and status of molecular, serological, and biochemical testing in COVID-19 and highlights some key considerations for clinical laboratories operating to support the global fight against this ongoing pandemic. Confidently this consolidated information provides a useful resource to laboratories and a reminder of the laboratory's critical role as the world battles this unprecedented crisis.

Evaluation of a COVID-19 IgM and IgG rapid test; an efficient tool for assessment of past exposure to SARS-CoV-2

COVID-19 is the most rapidly growing pandemic in modern time, and the need for serological testing is most urgent. Although the diagnostics of acute patients by RT-PCR is both efficient and specific, we are also crucially in need of serological tools for investigating antibody responses and assessing individual and potential herd immunity. We evaluated a commercially available test developed for rapid (within 15 minutes) detection of SARS-CoV-2-specific IgM and IgG by 29 PCR-confirmed COVID-19 cases and 124 negative controls. The results revealed a sensitivity of 69% and 93.1% for IgM and IgG, respectively, based solely on PCR-positivity due to the absence of a serological gold standard. The assay specificities were shown to be 100% for IgM and 99.2% for IgG. This indicates that the test is suitable for assessing previous virus exposure, although negative results may be unreliable during the first weeks after infection. More detailed studies on antibody responses during and post infection are urgently needed.

Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested.

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.

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.

Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B

The present approach to the mathematical modelling of infectious diseases is based upon the idea that specific immune mechanisms play a leading role in development, course, and outcome of infectious disease. The model describing the reaction of the immune system to infectious agent invasion is constructed on the bases of Burnet's clonal selection theory and the co-recognition principle. The mathematical model of antiviral immune response is formulated by a system of ten non-linear delay-differential equations. The delayed argument terms in the right-hand part are used for the description of lymphocyte division, multiplication and differentiation processes into effector cells. The analysis of clinical and experimental data allows one to construct the generalized picture of the acute form of viral hepatitis B. The concept of the generalized picture includes a quantitative description of dynamics of the principal immunological, virological and clinical characteristics of the disease. Data of immunological experiments in vitro and experiments on animals are used to obtain estimates of permissible values of model parameters. This analysis forms the bases for the solution of the parameter identification problem for the mathematical model of antiviral immune response which will be the topic of the following paper (Marchuk et al., 1991, J. theor. Biol. 15).

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)

Idiotypic networks incorporating T-B cell co-operation. The conditions for percolation

Previous work was concerned with symmetric immune networks of idiotypic interactions amongst B cell clones. The behaviour of these networks was contrary to expectations. This was caused by an extensive percolation of idiotypic signals. Idiotypic activation was thus expected to affect almost all (greater than 10(7] B cell clones. We here analyse whether the incorporation of helper T cells (Th) into these B cell models could cause a reduction in the percolation. Empirical work on idiotypic interactions between Th and B cells however, would suggest that two different idiotypic Th models should be developed: (1) a Th which recognises native B cell idiotypes, i.e. a non-MHC-restricted "ThId" model, and (2) a "classical" MHC-restricted helper T cell model. In the ThId model, the Th-B cell interaction is symmetric. A 2-D model of a Th and a B cell clone that interact idiotypically with each other accounts for various equilibria (i.e. one virgin and two immune states). Introduction of antigen does indeed lead to a state switch from the virgin to the immune state; such a system is thus able to "remember" its exposure to antigen. Idiotypic signals do however, percolate in ThId models via these "B-Th-B-Th" pathways: proliferating Th and B cell clones that interact idiotypically, will always activate each other reciprocally. In the MHC-restricted Th model, Th-B interactions are asymmetric. Because the B cell idiotypes are processed and subsequently presented by MHC molecules, the Th receptor and the native B cell receptor are not expected to be complementary. Thus the Th and the B cells are unable to activate each other reciprocally, and a 2-D Th-B cell model cannot account for idiotypic memory. In contrast to the ThId model, idiotypic activation cannot percolate via "B-Th-B-Th" interactions. Due to the assymmetry idiotypic activation stops at the first Th level. A Th clone cannot activate a subsequent B cell clone: if the B cells recognise the Th cells, they see idiotype but get no help; if the Th cells see the B cells, the B cells are helped but see no idiotype. The percolation along "B-B-B" pathways in these two models is next analysed. Two B cells clones, each helped by one Th clone, are connected by a symmetric idiotypic interaction. It turns out that in both models the second (i.e. anti-idiotypic) B cells (B2) never proliferate.(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.

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.

A neural network model based on the analogy with the immune system

The similarities between the immune system and the central nervous system lead to the formulation of an unorthodox neural network model. The similarities between the two systems are strong at the system level, but do not seem to be so striking at the level of the components. A new model of a neuron is therefore formulated, in order that the analogy can be used. The essential feature of the hypothetical neuron is that it exhibits hysteresis at the single neuron level. A network of N such neurons is modelled by an N-dimensional system of ordinary differential equations, which exhibits almost 2N attractors. The model has a property that resembles free will. A conjecture concerning how the network might learn stimulus-response behaviour is described. According to the conjecture, learning does not involve modifications of the strengths of synaptic connections. Instead, stimuli ("questions") selectively applied to the network by a "teacher" can be used to take the system to a region of the N-dimensional phase space where the network gives the desired stimulus-response behaviour. A key role for sleep in the learning process is suggested. The model for sleep leads to prediction that the variance in the rates of firing of the neurons associated with memory should increase during waking hours, and decrease during sleep.

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)

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.

Symmetry of effector function in the immune system network

Symmetry in antibody plus complement mediated killing between a T15 idiotype-bearing monoclonal antibody (HPC-M2) and an anti-T15 monoclonal antibody (B36-82) is demonstrated. The HPC-M2 antibody is also shown to be multispecific in its effector function, since it lyses both phosphorylcholine coated erythrocytes, and B36-82 Fab coated red blood cells. The symmetry and multispecificity in effector function are presented as new evidence against the concept that the paratope of antibody molecule exists as a uniquely defined site on the antibody variable region. A theoretical consequence for immune system network theory is that the anti-idiotypic set and the internal image are functionally equivalent, the results support symmetric network models of regulation, and are evidence against asymmetric models.