Verification of immune response optimality through cybernetic modeling

An immune response cascade that is T cell independent begins with the stimulation of virgin lymphocytes by antigen to differentiate into large lymphocytes. These immune cells can either replicate themselves or differentiate into plasma cells or memory cells. Plasma cells produce antibody at a specific rate up to two orders of magnitude greater than large lymphocytes. However, plasma cells have short life-spans and cannot replicate. Memory cells produce only surface antibody, but in the event of a subsequent infection by the same antigen, memory cells revert rapidly to large lymphocytes. Immunologic memory is maintained throughout the organism's lifetime. Many immunologists believe that the optimal response strategy calls for large lymphocytes to replicate first, then differentiate into plasma cells and when the antigen has been nearly eliminated, they form memory cells. A mathematical model incorporating the concept of cybernetics has been developed to study the optimality of the immune response. Derived from the matching law of microeconomics, cybernetic variables control the allocation of large lymphocytes to maximize the instantaneous antibody production rate at any time during the response in order to most efficiently inactivate the antigen. A mouse is selected as the model organism and bacteria as the replicating antigen. In addition to verifying the optimal switching strategy, results showing how the immune response is affected by antigen growth rate, initial antigen concentration, and the number of antibodies required to eliminate an antigen are included.     

Optimal strategies in immunology

After a first encounter with most antigens, the immune system responds to susequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part 1 of this paper, we examine the optimal strategy available to the immune system for B memory cell production. We again find that the strategy should be of the bang-bang variety. The model we consider assumes that antigen triggers a subpopulation of B-lymphocytes. These triggered lymphocytes can proliferate and secrete modest amounts of antibody, or differentiate into non-dividing plasma cells which secrete large amounts of antibody, or differentiate into non-antibody secreting memory cells. Given injections of antigen at two widely spaced times we compute the strategy which minimizes a linear combination of the primary and secondary response times. We find that for all biologically reasonable parameter values the best strategies are ones in which memory cells are produced at the end of the primary response. Exerimental results which bear on the actual strategies employed are discussed.     

Mathematical model of immune processes. II. Kinetic features of antigen-antibody interrelations

The dynamics of populations of self-replicating antigen and specific antibodies due to the antigen-stimulated antibody production and the antagonistic antibody-antigen interaction is treated in the framework of the mathematical model (Dibrov, Livshits &; Volkenstein, 1977). A special emphasis on the time lag in antibody production is made. The ability of the system to respond on the antigen challenge by antibody production is assumed to be constant during the reaction. The conditions of antigen elimination, of unlimited antigen multiplication, of self-sustaining oscillations and of stationary co-existence of antigen with specific antibodies are obtained. The discrete stochastic character of real birth and death processes enables the complete antigen elimination. A simple procedure for the evaluation of the probability of antigen extinction is proposed. The effect of therapy executed at different moments is examined.     

Dynamical analysis of a degenerate primary and secondary humoral immune response

Lymphocyte receptor response to antigen is degenerate. Each receptor can have a high affinity to more than one antigen. The optimal level of degeneracy was previously modeled using different methods; all showing that the degeneracy level should be inversely proportional to the probability that an antigen belongs to the self repertoire. Here we develop a new formalism, reproducing the results of previous models, which enables us to study the relation between receptor degeneracy and the pathogen-immune cell interaction dynamics, in primary and secondary response. We begin by developing a general formalismand reproducing the results obtained by Nemazee: (1) that an optimal immune system will have a capacity which is inversely proportional to the fraction of self-antigens and (2) that the number of self-reactive cells that the body destroys is tuned by this capacity optimization to be 63%. We then use our extended framework to relate the minimal number of B cell precursor required to mount an immune response to the naive B cell production rate. Finally, we analyze the dynamics of the interaction between the immune system and a pathogen and show that memory cells may be used as the first line of defense, while newly created cells are used later to refine the immune response.     

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.     

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

Somatic mutation has been implicated as a significant and possibly primary factor in the maturation of antibody affinity in the humoral immune response. B cells stimulated by antigen experience a hyper-mutation in the gene segments that code for the antigen-binding site of the antibody, creating antibody specificities that did not exist at the time of immunization. Although most of the mutations are likely to be disadvantageous, new specificities with a higher affinity for the antigen are sometimes created. These higher-affinity cells are preferentially selected for proliferation and eventual antibody secretion, resulting in a progressively higher average affinity over time. In this paper we present the results of an investigation of somatic mutation through the use of a computer model. At the basis of the model is a large repertoire of discrete antibodies and antigens, having three-dimensional structures, that exhibit properties similar to those of the real populations. The key factor is that the binding strength between any antibody/antigen pair can be calculated as a function of the complementarity of the (a) size, (b) shape and (c) functional groups that comprise the two structures. The created repertoires are imbedded in a dynamical system model of the immune response to directly evaluate the affect of somatic mutation on affinity maturation. We also present an expanded hypothesis of clonal selection and development to explain how the mutational restrictions imposed by the genetic code and the structure of the antibody repertoire, along with antigen concentration, affinity, and probabilistic factors may interact and contribute to the expansion of specific clones as the response develops over time.     

Immune reactions in polysaccharide media. The composition of the antigen–antibody complexes in the precipitin reaction

The precipitin reaction is enhanced in the presence of polysaccharides (Hellsing, 1966). This reaction has now been studied in detail with labelled antigen ((125)I-labelled human serum albumin) and antibody ((131)I-labelled rabbit anti-albumin immunoglobulin G). The relative proportions of antigen and antibody in the precipitates are unchanged by the addition of dextran in spite of the increased precipitation. The ratio of antibody to antigen in the soluble immune complexes decreases with increasing polysaccharide concentration. This can be interpreted as a decrease in the aggregate size of the complexes. At the same time the amount of free antigen in the solution increases. The results are consistent with a decrease in solubility, primarily of the large immune aggregates, together with a shift in the equilibrium between small and large complexes. The effect is in accord with a steric-exclusion phenomenon.     

Mathematical model of clonal selection and antibody production. II

Several modifications are proposed to a recent mathematical model (Bell, 1970) of the clonal selection and antibody production which take place when an adult animal is injected with an antigen. In the original model, antigen molecules were assumed univalent, i.e. to have only one combining site per molecule, and the first modification is an allowance for multivalent antigens by permitting an antigen molecule to interact with only one cell at a time. It is found that, for antigens with few (? 10) sites per molecule this modification is not important while for many sites per molecule, the modification will reduce the response as compared to that from the same number of independent antigenic sites. In section 3, it is seen that by restricting the number of cells which can arise in an immune response, much more realistic responses to high antigen doses are obtained. Moreover, the response is made more predictable by assuming that both target and proliferating cells are stimulated by antigen when a fraction of their receptors, between f_min and f_max, is bound to antigen. The parameter f_min is shown to determine the extent to which a molecule which can be recognized by antibodies will also serve as an immunogen giving rise to cellular proliferation and antibody production. In section 4, it is found that if more plasma cells than memory cells result from antigen stimulation, then weak stimulation will lead to a depletion of target plus memory cells and to at least partial immunological paralysis. Optimum antigen doses and times for the induction of such paralysis are examined. In section 5, precipitation of antigen-antibody mixtures is considered and it is shown that the number of doubly bound antibody molecules per antigen site determines whether precipitation will occur. This number is easily computed for heterogeneous bivalent antibodies.     

A mathematical model for germinal centre kinetics and affinity maturation

We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction. We show that antigen masking by antibodies which are produced by emerging plasma cells can drive affinity maturation and provide a feedback mechanism by which the reaction is stable against variations in the initial antigen amount over several orders of magnitude. This provides a possible answer to the long-standing question of the role of antigen reduction in driving affinity maturation. By comparing model predictions with experimental results, we propose that the selection probability of centrocytes and the recycling probability of selected centrocytes are not constant but vary during the GC reaction with respect to time. It is shown that the efficiency of affinity maturation is highest if clones with an affinity for the antigen well above the average affinity in the GC leave the GC for either the memory or plasma cell pool. It is further shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation. The impact on affinity maturation of simultaneous initiation of memory cell formation and somatic hypermutation vs. delayed initiation of memory cell formation is discussed.     

记忆T细胞平行分化模型的理论研究

为了从理论上讨论T细胞记忆维持机制的问题,基于T细胞的平行分化假说建立了非线性理论模型,利用此模型,在不同的抗原初值下得到了三种不同类型的应答。用优化剂量的抗原免疫生物体并且抗原存在时记忆能持续很长的时间,而失去抗原的同时将失去记忆,得出记忆T细胞平行分化模型确有记忆机制;并发现记忆强度与剩余抗原量有直接的关系,还进一步讨论了记忆细胞寿命的问题,并对体外情况作了预言。     

Antibody-mediated cell cytotoxicity in a defined system: regulation by antigen, antibody, and complement.

The use of a serum-free environment and target cells carrying defined amounts of radiolabeled antigen allowed a quantitative study of the role of antigen, antibody, and complement on antibody-mediated cell cytotoxicity (AbMC). For lysis to occure, a minimum number of antigen molecules must be present on the target cell. 51Cr release from target cells with lower antigen density requires larger concentration of effector cells and antibodies. Target cell-bound complement, itself unable to mediate cytotoxicity, reduces the number of IgG molecules required for lysis. The antibody and complement, however, have to be bound to the same target cell. Bystander complement-coated erythrocytes, present in the same reaction mixture with IgG-coated targets, are not lysed. Blocking of AbMC is effected only by antigen, either soluble or in immune complexes prepared in antigen excess. Antigen competes at the level of the target cell. Blocking at the level of the effector cell, by use of immune complexes prepared at equivalence or in antibody excess, is difficult to achieve. The large number of cells with Fc receptors contained in mouse spleens may explain this finding. Arming of effector cells by passive binding of immune complexes is poorly effective as a means of obtaining lysis of the target cells. In all situations, the outcome of the reaction is determined by the presence of free antibody-combining sites, alone, or in immune complexes, that are able to combine with the target cell membrane antigen. The requirements for lysis are rather stringent.     

Transfer Agent of Immunity

An immune ribonucleic acid (RNA) preparation was extracted with phenol from the spleens of guinea pigs immunized with diphtheria toxoid. Antibody-carrying cells were detected by immunocyte adhesion as rosette-forming cells. When germ-free rats, conventional guinea pigs or mice were injected intraperitoneally with this preparation, the rosette-formers were detected in either peritoneal exudate cells or spleen cells, whereas serum antibodies were unable to be detected thus far in such animals. Two injections with this preparation did not cause any remarkable increase in the number of rosette-formers, and serum antibody was also not detectable. By contrast, a high titer of serum antibody was demonstrated and the number of rosette-formers increased shortly after an injection of a small amount of diphtheria toxoid into guinea pigs which had previously received an injection with immune RNA. This reaction indicates a secondary response of antibody formation. However, secondary responses were not induced by injections of immune RNA preparations in guinea pigs primed with either diphtheria toxoid or immune RNA preparation. These facts suggest that immune RNA preparations did not contain antigens or fragments thereof and the immune response induced by RNA preparation is not the same as that induced by stimulation by the antigen itself. These results moreover can be accounted for by the notion that the immune RNA preparation is able to induce “memory” cells capable of responding to a secondary stimulus with an antigen and producing a high titer of serum antibody.     

Induction and monitoring of active delayed type hypersensitivity (DTH) in rats

Delayed type hypersensitivity (DTH) is an inflammatory reaction mediated by CCR7- effector memory T lymphocytes that infiltrate the site of injection of an antigen against which the immune system has been primed. The inflammatory reaction is characterized by redness and swelling of the site of antigenic challenge. It is a convenient model to determine the in vivo efficacy of immunosuppressants. Cutaneous DTH can be induced either by adoptive transfer of antigen-specific T lymphocytes or by active immunization with an antigen, and subsequent intradermal challenge with the antigen to induce the inflammatory reaction in a given skin area. DTH responses can be induced to various antigens, for example ovalbumin, tuberculin, tetanus toxoid, or keyhole limpet hemocyanin (KLH).Here we demonstrate how to induce an active DTH reaction in Lewis rats. We will first prepare a water-in-oil emulsion of KLH, our antigen of interest, in complete Freund's adjuvant and inject this emulsion subcutaneously to rats. This will prime the immune system to develop memory T cells directed to KLH. Seven days later we will challenge the rats intradermally on the back with KLH on one side and with ovalbumin, an irrelevant antigen, on the other side. The inflammatory reaction will be visible 16-72 hours later and the red and swollen area will be measured as an indication of DTH severity.     

Cellular aspects of tolerance. II. Unresponsiveness of B cells

The responsiveness of bone marrow cells from tolerant donors was examined by reconstitution of lethally irradiated tolerogen-free recipients. In these animals, stem cells from tolerant donors gave rise to immunologically competent antigen sensitive B cells. The antibody produced by these cells could be detected by a sensitive plaque assay in liquid and by antigen elimination. The antibody was not demonstrable by an assay which only detected plaque forming antibody which was highly avid or was formed in large quantity per cell. In lethally irradiated animals, partially purified B cells from a tolerant animal could not cooperate with T cells from normal donors to reconstitute immunological responsiveness to immunogenic doses of the tolerance inducing antigen. We concluded that antigen sensitive B cells in the bone marrow become unresponsive following administration of tolerogenic forms of antigen. Responsiveness of the reconstituted recipient animals was due to the differentiation of donor stem cells and subsequent antibody production by their descendants. Earlier contradictory findings could be unified in terms of these observations and conclusions.     

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.     

抗独特型抗体与T细胞记忆的关系

记忆T细胞作为人体免疫系统中的一个组成部分,在免疫应答中发挥着至关重要的作用,因此利用抗独特型抗体制备诱导产生记忆T细胞的疫苗是免疫学领域的一个重要方向。抗独特型抗体Fab段具有与特异性抗原相似的抗原决定簇的结构,其作为抗原替代物制备的疫苗所激发机体产生的记忆T细胞具有特异性强和安全性高的特点,成为一种比较理想的疫苗.就抗独特型抗体与T细胞记忆之间的联系及其应用效果作一简要综述。     

Antigen modulation of the immune response: IV. Selective triggering of antibody production and memory cell proliferation

When memory cells are transferred to syngeneic irradiated recipients and then challenged at various times after transfer, a precipitous decline in the ability of these cells to mount a secondary response is seen. Using this model we have investigated some of the influences which antigen can exert on the memory cell population. The results indicate that antigen may: 1) either stimulate the memory cells to proliferate and form new memory cells or stimulate memory cells to become antibody forming cells and 2) selectively trigger the memory cells for low or high affinity antibody production. This selective antigen triggering appeared to depend upon its concentration: high dose antigen challenge led to the production of large amounts of lower affinity antibody but stimulated less memory cell proliferation while low dose challenge showed just the opposite. Control experiments indicated that recruitment of new memory cells from a virgin precursor population was not responsible for these observations. Our results thus suggest that an asymmetrical division of memory cells is occurring in which antigen can exert selective influences in much the same way as seen with virgin precursor cells.     

Patterns of the forming of an immunologic memory to staphylococcal corpuscular antigen

The experiments carried out on inbred mice have revealed that the level of the immunological memory to staphylococci depends on the intensity of the antigenic stimulation; high priming dose of antigen proving to be the most effective one. The opposite character of immune responsiveness observed during primary antibody response to particulate staphylococcal antigen in C3H and A/Sn mice increased after the second immunization. It is established that immunological memory to staphylococci may be induced in genetically athymic mice. Many antibody-forming cells are found in the bone marrow of the secondary immunized mice. This phenomenon may be due to the repopulation of the bone marrow tissue by recirculating memory cells.     

Antigen modulation of the secondary immune response. VI. Contribution of cells recruited from precursor pool to expression of memory.

The adoptive transfer system has been used extensively to study the ability of antigen triggered memory cells to become antibody forming cells and/or to proliferate and expand the memory cell population. Selective antigen triggering of the memory cells for low and high affinity antibody formation has also been studied in this way. One of the main counter-arguments to the interpretation of these data is that the presence of antigen in the adoptive host may lead to recruitment of new memory cells from either a host or donor precursor population. In this paper we examined the contribution of both host and donor precursor cells to the total antibody response in adoptive secondary recipients. The following donor-host combinations were used in which the recipients were given 1 mg fluid antigen intravenously: (A) normal (non-immune) donors to normal irradiated recipients; (B) normal donors to carrier primed irradiated recipients; (C) carrier primed donors to normal irradiated recipients; (D) normal donors to carrier primed recipients with challenge and subsequent transfer to additional carrier primed recipients; (E) carrier primed donor to normal recipients to carrier primed recipients; (F) repeat of B and C above with multiple antigen administration; (G) purified immune (DNP-BGG) donor T cells mixed with normal B cells transferred to normal irradiated recipients. In most cases recruitment was seen but this represented less than 4% of the responses seen with immune cells. Thus we conclude that this level of recruitment does not compromise the use of the adoptive transfer system for studying selective antigen triggering of memory cells.     

Antigen-independent activation of memory cytotoxic T cells by interleukin 2

Culture supernatants from mitogen- or antigen-activated murine spleen cells are capable of causing reexpression of specific cytolytic activity from inactive memory cytotoxic T lymphocytes (CTL) in the absence of the original priming antigen. We have demonstrated that memory CTL from cytolytically inactive day 14 MLC cells are induced to reexpress high levels of specific cytotoxic activity after incubation with IL 2. Highly purified IL 2 was shown to induce levels of lytic activity comparable with that induced by supernatants from secondary mixed lymphocyte cultures (secondary MLC SN), suggesting that only IL 2 is necessary for the reactivation process. Moreover, only Lyt-2+ cells are necessary for reactivation inasmuch as inactive MLC cells depleted of Lyt-1+ cells by treatment with antibody and complement, followed by FACS selection of Lyt-2+ cells, were efficiently reactivated by IL 2. Because IL 2 is considered a proliferative signal, we examined whether proliferation was requisite for reactivation of memory CTL by IL 2. In the presence of cytosine arabinoside, which effectively inhibited proliferation, IL 2 was capable of reactivating memory CTL as efficiently as antigen, thus implying a differentiative role for IL 2 in secondary CTL activation. Reactivation of CTL by IL 2 and antigen appear to be functionally distinct events, because antigen but not IL 2 could trigger immune interferon release, although either IL 2 or antigen induced high levels of cytotoxicity. We propose that resting, memory CTL retain a heightened level of expression of IL 2 receptors as compared with naive CTL precursors, and thus are able to respond directly to exogenous IL 2. The consequences of this are proliferation and reexpression of specific killing activity, but this signal is not sufficient to induce immune interferon secretion. Rather, it appears that a signal via the antigen receptor is necessary for release of this lymphokine.