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R J De Boer

Publications and source records attributed to R J De Boer.

15 recordsLinked to original sources
PubMed1995

Towards a general function describing T cell proliferation.

A new function is proposed for describing the rate of T cell proliferation in response to peptides on antigen-presenting cells. The model improves an earlier model of ours by allowing for a true maximum proliferation rate of the T cells. This is achieved by a simple change of variables that markedly relaxes the conditions for a conventional quasi-steady-state assumption. The new model has the same "ecological" properties as the previous one. Thus the natural competition in the model allows for regulation of T cell population size in the presence of continuous stimulation by antigen. An important feature is the competitive exclusion of T cell clones recognizing the same peptide with different affinities allowing for "affinity selection". Models for the population dynamics of experienced, naïve and activated T cells are also developed. These T cell subpopulations compete with one another for antigen. In models with lymphokine production a "proliferation threshold" is obtained that allows for tolerance.

Animals↗
PubMed1995

A minimal model for T-cell vaccination.

We have developed a mathematical model for the regulation of the growth of autoreactive T cells (the T cells responsible for autoimmunity). The model is very simple in that it is based only on the fundamental properties of T cells. However, despite this simplicity, it can account for a variety of phenomena referred to as T-cell vaccination. The purpose of T-cell vaccination is to create resistance to autoimmunity. This can be achieved by injecting either a subpathogenic quantity of autoreactive T cells, or attenuated autoreactive cells, or cells that recognize the autoreactive cells. The results of our model are based on the assumption that the self antigens involved in T-cell vaccination are normally not expressed; thus the autoreactive T lymphocytes are neither activated nor negatively selected. Self tolerance, therefore, corresponds to a 'passive' state. T-cell vaccination induces a transition from this passive state of tolerance to an active state of tolerance. In this state the autoreactive cells are controlled by regulator cells which recognize the autoreactive cells. The model predicts a qualitative difference between vaccination with normal autoreactive cells and vaccination with attenuated autoreactive cells. Normal cells may give rise to a permanent switch to the vaccinated state; attenuated cells, however, can provide only transient protection, which is dose dependent. Preliminary experimental data confirm this prediction. Finally, we propose a speculative explanation for relapsing autoimmune disease.

Animals↗
PubMed1994

T cell repertoires and competitive exclusion.

Self-renewal is generally thought to play a major role in the maintenance of the T-cell repertoire. Here we develop a set of mathematical models for T-cell activation by peptides on antigen presenting cells (APCs). We show that competition between T cells is inherent to the processes involved in T cells binding APCs. We prove that for each dominant peptide only one T-cell clone can ultimately survive the competition. This is analogous to a classical result from theoretical ecology known as the principle of "competitive exclusion". These findings allow for three main results. First, competitive exclusion during an immune response to antigen implies that the clone(s) with the highest affinity for the dominant peptide(s) will outcompete all others. This allows for a form of "affinity selection". Second, the competition for binding antigen gives rise to regulation of T-cell numbers within a single clone. This allows for a regulated form of T-cell memory when T cells are continuously activated by a persisting antigen. Third, competitive exclusion implies that for each peptide only one T-cell specificity can be maintained in the repertoire. If the T-cell repertoire is largely maintained owing to cross-reactivities with various antigens, competitive exclusion means that the diversity of the T-cell repertoire is limited by the number of antigens stimulating the system. If the cross-reactivities were to involve activation by self antigens this would confirm an earlier result suggesting that the T-cell repertoire is diverse owing to the diversity of the self environment.

Animals↗
PubMed1992

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)

B-Lymphocytes↗
PubMed1991

Recent developments in idiotypic network theory.

A recent class of mathematical models of the immune network is reviewed. The models in this class are based upon the bell-shaped activation function that is known to be characteristic for receptor cross-linking. These network models have a large number of self-regulatory properties. This review discusses of number of these properties, i.e. immunological memory, suppression, and repertoire selection.

B-Lymphocytes↗
PubMed1990

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.

Animals↗
PubMed1989

Stability of symmetric idiotypic networks--a critique of Hoffmann's analysis.

Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis.

Animals↗
PubMed1989

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.

Animals↗
PubMed1989

Poor repertoire selection in symmetric idiotypic network models.

The selection of B and T cell repertoires is known to be influence by idiotypic interactions during early ontogeny. Early B cell clones are multi-specific, have numerous idiotypic interactions, produce IgM antibodies, and may constitute a separate cell lineage (characterised by the Ly1 or CD5 marker). Furthermore, because early B cells are self-reactive, self antigens should play a crucial role in the repertoire selection. Previously we developed a theoretical model of idiotypic B cell interactions. The model is based on a (symmetric) bell-shaped interaction function. The symmetry and the shape are a consequence of the process of receptor crosslinking. Assuming that early (i.e. IgM) B cell interactions are independent of helper T cell activation, we now apply this model to the problem of idiotypic repertoire selection. In the model the molecular structures of B cell receptors (i.e. of the idiotypes) and of self antigens are represented by random (bit)patterns. Interactions are based on complementary matches between these patterns. Therefore, the repertoire selection is brought about by stimulatory networks based upon complementary matches. These results show that the presence of a self antigen specifically shapes the B cell repertoire. The selection depends on the nature of the antigenic signal; we incorporate either stimulatory or inhibitory (i.e. tolerizing) self antigens. Clones stimulated by the self antigen tend to become aggressive in the network; tolerized self-reactive clones tend to become suppressed. Thus, idiotypic interactions play a facilitating role in self/non-self discrimination. However, since the idiotypic selection is only a tendency, the immune system should not rely on it. We next incorporate two classes of B cells. We call them the early, or "IgM", and the late, or "IgG", B cells (IgG B cells appear after the development of the IgM repertoire). IgG B cells may have only a few idiotypic interactions. We investigate whether the early IgM repertoire, which is (partly) selected by self antigen, influences the selection of the late IgG repertoire. It turns out that this influence can only be non-specific. Either we find a similar tendency in the IgG repertoire, or we find that the IgG repertoire influences the IgM repertoire non-specifically. Thus, despite the fact that this theoretical work readily confirms empirical results showing that the manipulation of early idiotypic interactions can have specific and long-lasting effects, the presupposed physiological role of these interactions, in terms of self-reactivity or repertoire selection, fails to develop in our models.

Animals↗
PubMed1986

Concomitant immunization by the fully antigenic counterparts prevents modulated tumor cells from escaping cellular immune elimination.

In a mathematical model of the cellular antitumor immune response, we studied the possible role of antigenic modulation as a tumor escape mechanism. Modulated tumor cells arise from normal (fully antigenic) tumor cells when the latter interact with antibodies. Modulated tumor cells demodulate when antibody concentrations are sufficiently low. Through modulation, tumor cells become less sensitive to cytotoxic macrophages (cell lysis) and contribute less to the stimulation of the immune system. These experimental data are incorporated in a model which we have analyzed previously. The model incorporates interactions between macrophages and T lymphocytes, which lead to cellular antitumor immune reactions (i.e., to cytotoxic macrophages). Parameters were derived from the immune resistance of DBA/2 mice to the SL2 tumor. Although all parameters were chosen deliberately to favor the modulation process (i.e., modulation proceeds fast, demodulation slowly, and the killing rate is reduced 50-fold), modulation is found to be a poor tumor escape mechanism. Heterogeneous populations of modulated and normal tumor cells are easily rejected. Homogeneous populations of modulated cells do escape, however. We conclude that the impact of modulation as an escape mechanism remains small because modulated tumor cells do not appear until the immune system has been stimulated (immunized) by the fully antigenic tumor cells. Thus, the elimination of modulated tumor cells generally occurs merely as a side effect of the immune response which is directed primarily against the fully antigenic tumor cells. Parameter sensitivity analysis shows that this conclusion holds true only for cellular immunity. Conversely, the parameter analysis suggests that antigenic modulation plays a deleterious role in cytotoxic antibody responses (e.g., monoclonal antibody therapy).

Animals↗
PubMed1985

Tumor escape from immune elimination: simplified precursor bound cytotoxicity models.

In this paper we present a series of models on cytotoxic T-cell activation derived, by successive simplifications, from the model for Tumor Escape from Immune Elimination of Grossman & Berke (1980). In their model Grossman & Berke (1980) investigate the "sneaking through" phenomenon, by which they mean that small tumors grow progressively, medium-sized tumors are rejected and large ones break through again. We define precursor bound cytotoxicity models as systems incapable of infinite proliferation. We show that sneaking through can occur in a broad class of very simple precursor bound cytotoxicity models due to the depletion of the precursor cells. The simplest process by which precursors can be depleted is long-lasting antigenic stimulation. We conclude that in precursor bound cytotoxicity models sneaking through does not need the rather intricate combination of counteracting feedback loops, memory and blocking described by Grossman & Berke (1980).

Antigens, Neoplasm↗
PubMed1985

Macrophage T lymphocyte interactions in the anti-tumor immune response: a mathematical model.

In this paper we present a model of the macrophage T lymphocyte interactions that generate an anti-tumor immune response. The model specifies i) induction of cytotoxic T lymphocytes, ii) antigen presentation by macrophages, which leads to iii) activation of helper T cells, and iv) production of lymphoid factors, which induce a) cytotoxic macrophages, b) T lymphocyte proliferation, and c) an inflammation reaction. Tumor escape mechanisms (suppression, antigenic heterogeneity) have been deliberately omitted from the model. This research combines hitherto unrelated or even contradictory data within the range of behavior of one model. In the model behavior, helper T cells play a crucial role: Tumors that differ minimally in antigenicity (i.e., helper reactivity) can differ markedly in rejectability. Immunization yields protection against tumor doses that would otherwise be lethal, because it increases the number of helper T cells. The magnitude of the cytotoxic effector cell response depends on the time at which helper T cells become activated: early helper activity steeply increases the magnitude of the immune response. The type of cytotoxic effector cells that eradicates the tumor depends on tumor antigenicity: lowly antigenic tumors are attacked mainly by macrophages, whereas large highly antigenic tumors can be eradicated by cytotoxic T lymphocytes only.

Animals↗