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Theoretical Immunology at Utrecht University

Rob J. De Boer

Theoretical Biology UU, Padualaan 8, 3584 CH Utrecht, The Netherlands


The immune system is a fascinating complex information processing system taking decisions on the appropriate immune response to a large variety of antigens Borghans & De Boer (2001); Borghans & De Boer (2002); Borghans et al. (1999a). Immunology has traditionally been a qualitative science describing the cellular and molecular components of the immune system and their functions. Theoretical immunology is maturing into a discipline where modeling helps to interpret experimental data, to resolve controversies, and -most importantly- to suggest novel experiments allowing for more conclusive and more quantitative interpretations.

In our group we aim to:
-- Go beyond qualitative descriptions and quantify the cellular immune response through a mathematical modeling approach
-- Integrate bioinformatic analysis of antigen presentation with mathematical modeling to characterize the epitopes and the onset of cellular immune responses to specific pathogens
Thus, we study population dynamics within the immune system to quantify the host-pathogen interaction of the cellular immune system.

We aim to understand how the system maintains its diversity of millions of lymphocyte populations, to understand how populations of naive and memory cells are maintained, to determine the turnover rates of various lymphocyte populations, and to understand the possible homeostatic mechanisms regulating lymphocyte population sizes. With our immunoinformatic approach we work on predicting the epitopes that are selected by antigen presentation. We aim to determine the specificity of the various steps in the antigen processing cascade from proteins to presented epitopes, and to quantify the number of foreign epitopes are to be expected among all the self epitopes.

Our group is active in the field of HIV dynamics because understanding the depletion of CD4 T cells requires a much better characterization of the population dynamics of these cells. This field has matured into a discipline with strong collaborations between experimentalists and theoreticians. HIV is also interesting from an immunoinformatics point of view because so much data is available on sequences and epitopes.

We work on decision making and information processing in the immune system. Antigenic stimulation typically selects a very small fraction of naive T cell clones that somehow have to decide on the most appropriate immune reaction. This decision is made from a distributed processes over many different cell types. The innate immune system provides information gathered on an evolutionary time scale. The adaptive immune system provides information by immunological memory, including regulatory anergic populations, from what the system learned during previous encounters with antigen.

Summarizing, we investigate fundamental properties of the immune system by the development and analysis of formal immune system models. Below we summarize our work in the following sections:

Lymphocyte population dynamics

The T cell repertoire consists of clones of naive and memory CD4 and CD8 T cells that are maintained by a source from the thymus and by density dependent renewal and death rates. One of our missions is to characterize the average life times, division rates, and daily production rates of T cells under normal circumstances. Determining the same parameters when T cell numbers are depleted should give us clues about the homeostasis regulating total T cell numbers.

BrdU. Labeling of dividing cells with BrdU is a widely used technique for estimating cellular turnover rates. We show that current estimates published in the literature are unreliable because they depend on the assumptions of the model used to fit the BrdU data (De Boer et al., 2003b). We develop a novel method by averaging the parameter estimates over the entire population, and obtain more reliable estimates for the average turnover rates of naive and memory, CD4 and CD8 T cells, NK cells, and B cells in SIV-infected and uninfected macaques (De Boer et al., 2003c).

Ki67. Measurements of Ki67+ T cells in lymphoid tissue suggest that under normal circumstances 0.2% of the CD8+ T cells and 0.5% of the CD4+ T cells is dividing (Fleury et al., 1998). Reviewing data on the numbers of dividing T cells, and the recovery rates of T cell populations following T cell depletion we have estimated the daily production rates for the various populations of T cells (Clark et al., 1999).

Telomeres. Telomeres shorten with each cell division and can therefore be used as a tool to study naive and memory CD4+ T cell replication. We have studied naive and memory CD4+ T cell dynamics with mathematical models. Because the memory T cell compartment is seeded from the naive compartment we find that, irrespective of the memory division rate, the rate at which memory T cells erode their telomeres should be similar to that of the naive T cells (De Boer & Noest, 1998). If naive T cells are seeded from a progenitor compartment, the same should be true for the naive T cells (De Boer & Noest, 1998; Wolthers et al., 1999). Otherwise naive T cells should reduce their average telomere lengths at a rate reflecting twice their cell division rate (De Boer & Noest, 1998; De Boer, 2002).

Production of naive T cells

TRECs. Thymic production can be studied using the DNA excision circles (TRECs) that are formed when the T cell receptor is recombined. We develop a novel mathematical model to analyze data on the TREC content, and fractions of dividing cells, in normal and depleted circumstances (Hazenberg et al., 2000b). We find that TREC contents are a poor tool for estimating thymic production because they are strongly biased by the increased cell division associated with T cell depletion (Hazenberg et al., 2003a). Tracking naive T cell numbers and TRECs in young children we have attempted to quantify the relative contributions of thymic production and peripheral renewal (Hazenberg et al., 2004). The fact that TREC contents decrease with age is caused by an age related decline of thymus production, but requires homeostatic regulation of division and/or death rates within the compartment of naive T cells (Dutilh & De Boer, 2003).

Thymus. The recovery of naive T cell numbers in HIV-1 infected patients in the presence of IL-2 treatment (Carcelain et al., 2003), and in its absence (Cohen Stuart et al., 2002), can be used to estimate thymic production in adults. The latter paper suggest that there is an age-dependent ongoing production of naive T cells in adults (Cohen Stuart et al., 2002). Indeed, TREC contents in CD4 and CD8 T-cell populations in HIV-1 infected patients indicate that thymus function in younger subjects is preserved at early stages of HIV infection (Nobile et al., 2004).

Primary immune response

Tetramer techniques and intracellular cytokine staining allows one to collect time series of the CD4 and CD8 T cell response to viruses. We have used a piece-wise linear model to estimate the parameters characterizing the CD8 immune response to LCMV (De Boer et al., 2001b). Similar data from the immunodominant and subdominant responses to various CD4 and CD8 epitopes have been modeled to characterize the kinetic differences between them (De Boer et al., 2003a).

Antigen presentation

Proteasome. The most important protease involved in generating the short peptides used in class I MHC antigen presentation is the (immuno)proteasome. We have identified differences in the cleavage patterns between the constitutive proteosome and the immunoproteosome, and have concluded that the peptides delivered by the immunoproteosome are better tailored for antigen presentation (Kesmir et al., 2003). The rate of proteasomal cleavage depends on the length of the substrate and follows Michaels-Menten kinetics, and the distribution of fragments depends on the gate size (Luciani et al., 2005).

Size of self. In collaboration with Nigel Burroughs we have enumerated all class I MHC peptides in the human proteome and in various pathogens to determine the likelihoods that immunodominant peptides overlap between self and non-self. Due to the apparently high information content of the 9-mers used in class I antigen presentation the overlaps are very small (Burroughs et al., 2004). This analysis also shows the co-evolution of the specificities of proteasome, TAP, and MHC molecules.

T cell competition

Competitive exclusion. Homeostasis is brought about by density dependent death and renewal rates that are due to competition between T cells for limited resources. Data suggest that T cell survival requires tickling by specific antigens. Thus, the T cell repertoire consists of a huge variety of clones competing ecologically for resources corresponding to specific antigens. Ecological principles of competitive exclusion, a clonal carrying capacity, and the natural selection of the best competitor can readily be found in models of T cell activation (De Boer & Perelson, 1995; De Boer & Perelson, 1997; De Boer & Perelson, 1994).

Intraspecific competition. Experimental data on the competition between a normal diverse repertoire and a transgenic less diverse repertoire suggested that diverse repertoires outcompete less diverse repertoires. By developing a mathematical model in terms of individual clones we provide a reinterpretation of these data. We find that there is more ``intraspecific'' competition within the less diverse repertoire than there is within a normal diverse repertoire (De Boer et al., 2001a). This explains the data without invoking competition between the two repertoires. Intraspecific competition is also required to explain the diversity of the immune response to HIV (Korthals Altes et al., 2003)

Renewal. If total T cell numbers are indeed regulated by resource competition at a clonal level, the diversity of T cells and the diversity of niches in the form of epitopes determine the total T cell numbers in the self-renewing T cell repertoire (De Boer & Perelson, 1997). This is similar to ecological relationships between productivity, diversity, and total biomass.

Functions. Changing T cell numbers and antigen availability, and measuring T cell proliferation, we found experimental support for proliferation functions involving T cell competition for antigenic sites (Borghans et al., 1999b). These functions are based upon an improved quasi steady state assumption (Borghans et al., 1996).

CD4+ T cell dynamics during HIV infection

Hyperactivation. HIV infection causes depletion of the CD4 T cell compartment and expansion of the CD8 T cell compartment. In both the CD4 and CD8 T cell compartment HIV-1 infection increases the percentages of naive and memory T cells that are in division several-fold (Hazenberg et al., 2000b; Hazenberg et al., 2000a). We think this is not due to homeostasis, but due to antigenic stimulation (Cohen Stuart et al., 2000; Hazenberg et al., 2000a). This limited increase in the division rates is not reflected in the average telomere length naive and memory CD4 T cells (Wolthers et al., 1999) but is responsible for the lower TREC content of CD4 cells in HIV-1 infected patients (Hazenberg et al., 2000b).

Thymus Although HIV readily infects the thymus we do not think this is important for the depletion of CD4 T cells in HIV infected patients (Hazenberg et al., 2003a). Thymic production in human adults had been estimated to decrease about 5% per year. We find similar results in HIV-1 infected patients on therapy (Cohen Stuart et al., 2002). The increased loss of naive T cells in patients having CXCR4-using HIV variants is due to increased death and activation (Hazenberg et al., 2003a).

Deactivation. Considering that target cell availability plays a role in limiting the HIV infection, a combination of immuno-suppressive and anti-retroviral therapy should be unexpectedly successful by preventing the outgrowth of drug-resistant variants (De Boer & Boucher, 1996). Trials combining hydroxyurea with DDI have confirmed this long-term effect (De Boer et al., 1998).

Oscillations. Mono-therapy with anti-retroviral drugs allows HIV to rapidly evolve a cascade of drug-resistant variants. This evolutionary sequence can be modeled assuming that HIV is limited by target cell availability (Stilianakis et al., 1997; De Jong et al., 1996). Both target-cell-limited and immune-controlled HIV models are classical predator-prey-models accounting for similar behavior however (De Boer & Perelson, 1998). Predator-prey type oscillations between CD4+ target cells and HIV-1 account for the large overshoots in HIV-1 viremia observed in patients stopping their therapy (De Jong et al., 1997).

Redistribution. Redistribution of T cells during anti-retroviral therapy plays an important role in the early recovery of the peripheral blood CD4 T cell count (Pakker et al., 1998). High recovery rates of naive, memory and total CD4+ T cells can however be achieved in children below 3 years of age (Cohen Stuart et al., 1998). Comparing HIV-1 infected patients with controls we have found that CD4 and CD8 T cells change their distributions over the peripheral blood and the lymphoid tissue during HIV-1 infection (Fleury et al., 1998).

Viral dynamics

Setpoint. Mathematical models incorporating an anti-HIV immune response have the unexpected result that only parameter determining the steady state viral during clinical latency is the reactivity of this immune response. Because there is so much variation between patients in this so-called viral set-point, patient would have to differ several orders of magnitude in this parameter. We think this is unrealistic and provide solutions by substituting processes for such parameters (Müller et al., 2001).

Breath of immune response. Current mathematical models all suffer from ``competitive exclusion'' and fail to explain how one can have a diverse immune response to a chronic infection like HIV-1. We have developed a novel model to study whether the diversity of the anti-viral immune response can explain the observed variation in viral setpoints between patients (Korthals Altes et al., 2003).

Fitness. In vivo measurements of HIV evolution suggest significant fitness differences between drug-resistant strains (Lukashov et al., 2001; Goudsmit et al., 1997; De Ronde et al., 2001). Most of the estimates published in the literature for the relative fitness of virus variants are wrong. We have developed a new model for the determination of the true relative fitness from viral competition experiments (Marée et al., 2000). This new method allows for non-exponential growth during the experiment, and is available on the Web. This method has recently been extended to allow the estimation of the relative fitness from time series data (Bonhoeffer et al., 2002).

Dynamics. The slopes with which the viral load decays during therapy and plasmapheresis have been used to estimate the clearance rates of viral particles ($c$) and of productively infected cells ($\delta$). We extend current models with a third compartment describing the bulk of virus located in the lymphoid tissue. This third compartment adds a third slope to the problem. We show that contradictions between the treatment data and the plasma apheresis data from HIV and HCV infected patients can be reconciled with this three compartment model (Müller et al., 2001).

The pretreatment viral load is a good predictor for the time it takes therapy to reduce the viral load to undetectable levels (Rizzardi et al., 2000). The HIV diversity threshold can better be defined as a threshold in the viral density which is equally determined by diversity and virulence (De Boer & Boerlijst, 1994).

Lymphocyte diversity and MHC polymorphism

Within host MHC diversity. The limited number of MHC loci in most species is conventionally explained by excessive negative selection when there are too many different MHC molecules per host. Using current parameter estimates for the chances of positive and negative selection in a new mathematical model we show that this consensus explanation is untenable (Borghans et al., 2003).

Population MHC diversity. There has been a long-standing debate whether the high degree of MHC polymorphism is due to overdominance or requires frequency dependent selection. We have shown that overdominance can only explain the observed degrees of MHC polymorphism when the fitness contributions of the various alleles are exceedingly similar (De Boer et al., 2004). The evolution of a high degree of MHC polymorphism can easily be explained by co-evolving pathogens that attempt to avoid antigen presentation. In a polymorphic population it is unpredictable which peptide from a pathogen is sampled to serve as the MHC-restricted epitope triggering an adaptive immune response (Borghans & De Boer, 2001; Beltman et al., 2002; Borghans et al., 2004).

Specificity and diversity. One conventionally thinks that the immune system is diverse to enable high affinity immune responses against a large variety of pathogens. We think that the acquired immune system is diverse to avoid inappropriate immune responses. Simple calculations indeed suggest that a lower bound for the diversity of the lymphocyte system is determined by the diversity of the self antigens the lymphocytes have to become tolerant to (Borghans & De Boer, 1998a; Borghans et al., 1999a; De Boer & Perelson, 1993). The innate system instructs the lymphocyte system to induce the appropriate immune response. We hypothesize that the acquired immune system is diverse to store specifically the instructions provided by the innate immune system. This requires even higher lymphocyte specificity (Borghans & De Boer, 2002; Borghans et al., 1999a). Self tolerance can also be brought about by tuning the T cell responsiveness, and this does not require optimization of T cell specificity (Scherer et al., 2004).

Current estimates for the diversity of the human T cell repertoire are about $2.4\times10^7$ different receptors. Because of the way this number was calculated, this estimate can only remain a lower bound; the true diversity could very well be much higher (Kesmir et al., 2000).

The evolution of individuality and polymorphisms is generally accounted for by a defense against pathogens or parasitic strains. However, in the absence of such parasites, compatibility molecules may evolve extensive polymorphisms to prevent clonal fusion (De Boer, 1995).

Germinal centers

B cell affinity maturation takes place in germinal centers and is extremely fast. The relative fitness of better mutants cannot be accounted for by conventional mathematical models. We develop a spatial germinal center model where affinity differences are translated into differential adhesion of antigen specific B cells to the follicular dendritic cells. This model accounts for the rapid selection of better mutants by an ``all-or-none'' behavior that is based upon the cellular sorting on the surface of the follicular dendritic cells (Kesmir & De Boer, 2003b). We are currently developing three-dimensional models of germinal centers.

T cell vaccination and Idiotypic regulation

T cell vaccination is a strategy to prevent auto-immune diseases by vaccinating with auto-aggressive T cells. Vaccination presumably elicits an idiotypic control. Assuming that a priori the auto-reactive T cells are ignorant of their self antigen a simple mathematical model can account for the experimental findings (Borghans et al., 1998; Borghans & De Boer, 1995). We have recently extended this model with Th1/Th2 regulation (ms. in prep.).

A whole series of B cell networks is based upon a bell-shaped interaction function (De Boer & Hogeweg, 1989b). These models account for memory (Weisbuch et al., 1990), chaotic and oscillatory behavior (De Boer et al., 1993c; De Boer et al., 1993b), steady state connectivity and total B cell numbers (De Boer & Perelson, 1991), and repertoire selection (Takumi & De Boer, 1996).

Importantly later models are based upon a novel bell-shaped function that seems more realistic than the previous one (Sulzer et al., 1996; De Boer et al., 1996). This new function strongly reduces the percolation observed in high dimensional networks (De Boer et al., 1996). The shape space concept is an interesting formalism for studying these network models. Immune repertoires arise by pattern formation in the form of Turing like bifurcations (Noest et al., 1997).


The mechanism explaining exhaustion of the dominant clones during an immune response remains illusive. We propose that the switching between the type of immune response may play a role (Kesmir & De Boer, 2003a).

Differences in the kinetics of the production of neutralizing antibodies against cytopathic and non-cytopathic viruses can be a consequence of the cytopathicity itself: non-cytopathic viruses infect a larger fraction of nAb producing B cells causing a delayed nAb response (Kesmir & De Boer, 1998).

Polly Matzinger's (1997) neonatal tolerance experiments can be reinterpreted by modeling the probability that T cells run into professional or non-professional APCs (Borghans & De Boer, 1998b).

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Rob de Boer 2005-09-13