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Biomedical subjects

R J De Boer

Publications and source records attributed to R J De Boer.

At least 19 recordsLinked to original sources
PubMed2001

Resource competition determines selection of B cell repertoires.

Previous experiments with mouse chimeras demonstrated that cellular competition for antigen-specific survival signals plays a crucial role in the maintenance of the naive B cell repertoire. Transgenic (Tg) B cell populations in these chimeras have a shortened lifespan and poor competitive abilities as compared to more diverse non-Tg populations in the same mice. We develop a mathematical model to investigate the mechanism of B cell competition. The model allows for various B cell clones, generated in the bone marrow, to go into the peripheral circulation, where they compete specifically for various ligands providing survival signals. In the model we also find the observed poor competitive abilities of the Tg repertoire. Investigating the nature of the competition in the model, we find that most of the competition is "intraspecific" occurring largely within the clone of truly Tg B cells, and within the repertoire of leaky Tg and non-Tg B cells. This is confirmed by analysing a simplified version of the model, which only allows for intraspecific competition, and resembles a simple ecological model with density-dependent death. The fact that our model accounts for the data, casts doubt on a previous interpretation of the same data arguing that more diverse repertoires outcompete repertoires of lower diversity. Here, we conclude that most of the data can be explained with intraspecific competition, and formulate an experimental prediction that allows one to distinguish between the previous interpretation of inter-specific competition between repertoires, and the current interpretation of intraspecific competition.

Animals↗
PubMed2001

Small variations in multiple parameters account for wide variations in HIV-1 set-points: a novel modelling approach.

Steady-state levels of HIV-1 viraemia in the plasma vary more than a 1,000-fold between HIV-positive patients and are thought to be influenced by several different host and viral factors such as host target cell availability, host anti-HIV immune response and the virulence of the virus. Previous mathematical models have taken the form of classical ecological food-chain models and are unable to account for this multifactorial nature of the disease. These models suggest that the steady-state viral load (i.e. the set-point) is determined by immune response parameters only. We have devised a generalized consensus model in which the conventional parameters are replaced by so-called 'process functions'. This very general approach yields results that are insensitive to the precise form of the mathematical model. Here we applied the approach to HIV-1 infections by estimating the steady-state values of several process functions from published patient data. Importantly, these estimates are generic because they are independent of the precise form of the underlying processes. We recorded the variation in the estimated steady-state values of the process functions in a group of HIV-1 patients. We developed a novel model by providing explicit expressions for the process functions having the highest patient-to-patient variation in their estimated values. Small variations from patient to patient for several parameters of the new model collectively accounted for the large variations observed in the steady-state viral burden. The novel model remains in full agreement with previous models and data.

HIV Infections↗
PubMed2001

Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus.

The specific CD8(+) T-cell response during acute lymphocytic choriomeningitis virus (LCMV) infection of mice is characterized by a rapid proliferation phase, followed by a rapid death phase and long-term memory. In BALB/c mice the immunodominant and subdominant CD8(+) responses are directed against the NP118 and GP283 epitopes. These responses differ mainly in the magnitude of the epitope-specific CD8(+) T-cell expansion. Using mathematical models together with a nonlinear parameter estimation procedure, we estimate the parameters describing the rates of change during the three phases and thereby establish the differences between the responses to the two epitopes. We find that CD8(+) cell proliferation begins 1 to 2 days after infection and occurs at an average rate of 3 day(-1), reaching the maximum population size between days 5 and 6 after immunization. The 10-fold difference in expansion to the NP118 and GP283 epitopes can be accounted for in our model by a 3.5-fold difference in the antigen concentration of these epitopes at which T-cell stimulation is half-maximal. As a consequence of this 3.5-fold difference in the epitope concentration needed for T-cell stimulation, the rates of activation and proliferation of T cells specific for the two epitopes differ during the response and in combination can account for the large difference in the magnitude of the response. After the peak, during the death phase, the population declines at a rate of 0.5 day(-1), i.e., cells have an average life time of 2 days. The model accounts for a memory cell population of 5% of the peak population size by a reversal to memory of 1 to 2% of the activated cells per day during the death phase.

Animals↗
PubMed2001

Release of virus from lymphoid tissue affects human immunodeficiency virus type 1 and hepatitis C virus kinetics in the blood.

Kinetic parameters of human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV) infections have been estimated from plasma virus levels following perturbation of the chronically infected (quasi-) steady state. We extend previous models by also considering the large pool of virus localized in the lymphoid tissue (LT) compartment. The results indicate that the fastest time scale of HIV-1 plasma load decay during therapy probably reflects the clearance rate of LT virus and not, as previously supposed, the clearance rate of virus in plasma. This resolves the discrepancy between the clearance rate estimates during therapy and those based on plasma apheresis experiments. In the extended models plasma apheresis measurements are indeed expected to reflect the plasma decay rate. We can reconcile all current HIV-1 estimates with this model when, on average, the clearance rate of virus in plasma is approximately 20 day(-1), that of LT virus is approximately 3 day(-1), and the death rate of virus-producing cells is approximately 0.5 day(-1). The fast clearance in the LT compartment increases current estimates for total daily virus production. Because HCV is produced in the liver, we let virus be produced into the blood compartment of our model. The results suggest that extending current HCV models with an LT compartment is not likely to affect current estimates for kinetic parameters and virus production. Estimates for treatment efficacy might be affected, however.

Anti-HIV Agents↗
PubMed2000

Estimating relative fitness in viral competition experiments.

The relative fitness of viral variants has previously been defined as the slope of the logarithmic ratio of the genotype or phenotype frequencies in time plots of pairwise competition experiments. Developing mathematical models for such experiments by employing the conventional coefficient of selection s, we demonstrate that this logarithmic ratio gives the fitness difference, rather than the relative fitness. This fitness difference remains proportional to the actual replication rate realized in the particular experimental setup and hence cannot be extrapolated to other situations. Conversely, the conventional relative fitness (1 + s) should be more generic. We develop an approach to compute the generic relative fitness in conventional competition experiments. This involves an estimation of the total viral replication during the experiment and requires an estimate of the average lifetime of productively infected cells. The novel approach is illustrated by estimating the relative fitness, i.e., the relative replication rate, of a set of zidovudine-resistant human immunodeficiency virus type 1 variants. A tool for calculating the relative fitness from observed changes in viral load and genotype (or phenotype) frequencies is publically available on the website at http://www-binf.bio.uu.nl/( approximately )rdb/fitness.html.

HIV-1↗
PubMed2000

Predicting the duration of antiviral treatment needed to suppress plasma HIV-1 RNA.

Effective therapeutic interventions and clinical care of adults infected with HIV-1 require an understanding of factors that influence time of response to antiretroviral therapy. We have studied a cohort of 118 HIV-1-infected subjects naive to antiretroviral therapy and have correlated the time of response to treatment with a series of virological and immunological measures, including levels of viral load in blood and lymph node, percent of CD4 T cells in lymph nodes, and CD4 T-cell count in blood at study entry. Suppression of viremia below the limit of detection, 50 HIV-1 RNA copies/mL of plasma, served as a benchmark for a successful virological response. We employed these correlations to predict the length of treatment required to attain a virological response in each patient. Baseline plasma viremia emerged as the factor most tightly correlated with the duration of treatment required, allowing us to estimate the required time as a function of this one measure.

Adult↗
PubMed1999

A mathematical model on germinal center kinetics and termination.

We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics are extended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes, and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we study the role of GC T cells in GC kinetics, GC termination, and B cell selection. We find that GC T cells play a major role in GC formation, but that the maintenance of established GC reactions requires very few T cells only. The results therefore suggest that the termination of a GC reaction is largely caused by lack of Ag on the follicular dendritic cells and is hardly influenced by Th cells. Ag consumption by centrocytes is the major factor determining the decay rate of the antigenic stimulus during a GC reaction. Investigating the effect of the Ag dose on GC kinetics, we find that both the total size of the GC and its duration are hardly influenced by the initial amount of Ag. In the model this is due to a buffering effect by competition for limited T cell help and/or competition between proliferating centroblasts.

Antigen-Antibody Complex↗
PubMed1999

Normal telomere lengths in naive and memory CD4+ T cells in HIV type 1 infection: a mathematical interpretation.

To study CD4+ T cell productivity during HIV-1 infection, CD4+ T cell telomere lengths were measured. Cross-sectional and longitudinal analysis of HIV-1-infected individuals with CD4+ T cells counts >300 cells/mm3 showed normal average telomeric restriction fragment (TRF) length and normal shortening rates of CD45RA+ naive and CD45RO+ memory CD4+ T cells. These TRF data were interpreted in terms of CD4+ T cell production by means of a mathematical model. This model resolves previous criticisms arguing that the normal TRF length of CD4+ T cells in HIV-1 clinical latency is due to the killing of dividing CD4+ T cells by the virus. Only an increased priming rate of naive CD4+ T cells to become memory cells may elongate the average TRF length of memory CD4+ T cells, and may therefore mask the shortening effect of increased turnover in the CD4+ memory T cell compartment. The data are more compatible with the notion that during HIV-1 clinical latency the turnover of CD4+ T cells is not markedly increased, however, and that HIV-related interference with renewal from progenitors plays a role in CD4+ T cell depletion. In such a "limited renewal" scenario disease progression is no longer a consequence of markedly increased CD4+ T cell production.

CD4-Positive T-Lymphocytes↗
PubMed1999

How specific should immunological memory be?

Protection against infection hinges on a close interplay between the innate immune system and the adaptive immune system. Depending on the type and context of a pathogen, the innate system instructs the adaptive immune system to induce an appropriate immune response. Here, we hypothesize that the adaptive immune system stores these instructions by changing from a naive to an appropriate memory phenotype. In a secondary immune reaction, memory lymphocytes adhere to their instructed phenotype. Because cross-reactions with unrelated Ags can be detrimental, such a qualitative form of memory requires a sufficient degree of specificity of the adaptive immune system. For example, lymphocytes instructed to clear a particular pathogen may cause autoimmunity when cross-reacting with ignored self molecules. Alternatively, memory cells may induce an immune response of the wrong mode when cross-reacting with subsequent pathogens. To maximize the likelihood of responding to a wide variety of pathogens, it is also required that the immune system be sufficiently cross-reactive. By means of a probabilistic model, we show that these conflicting requirements are met optimally by a highly specific memory lymphocyte repertoire. This explains why the lymphocyte system that was built on a preserved functional innate immune system has such a high degree of specificity. Our analysis suggests that 1) memory lymphocytes should be more specific than naive lymphocytes and 2) species with small lymphocyte repertoires should be more vulnerable to both infection and autoimmune diseases.

Animals↗
PubMed1998

T cell vaccination in experimental autoimmune encephalomyelitis: a mathematical model.

T cell vaccination (TCV) is a method to induce resistance to autoimmune diseases by priming the immune system with autoreactive T cells. This priming evokes an anti-idiotypic regulatory T cell response to the receptors on the autoreactive T cells. Hence resistance is induced. To prevent the inoculated autoreactive cells from inducing autoimmunity, cells are given in a subpathogenic dose or in an attenuated form. We developed a mathematical model to study how the interactions between autoreactive T cells, self epitopes, and regulatory cells can explain TCV. The model is based on detailed data on experimental autoimmune encephalomyelitis, but can be generalized to other autoimmune diseases. We show that all of the phenomena collectively described as TCV occur quite naturally in systems where autoreactive T cells can be controlled by anti-idiotypic regulatory T cells. The essential assumption that we make is that TCV generally involves self epitopes for which T cell tolerance is incomplete. The model predicts a qualitative difference between the two vaccination methods: vaccination with normal autoreactive cells should give rise to a steady state of long lasting protection, whereas vaccination with attenuated cells should only confer transient resistance. Moreover, the model shows how autoimmune relapses can occur naturally without the involvement of T cells arising due to determinant spreading.

Animals↗
PubMed1998

T cell renewal rates, telomerase, and telomere length shortening.

Measurements on the average telomere lengths of normal human naive and memory T cells suggested that 1) naive and memory human T cells have similar division rates, and 2) that the difference between naive and memory cells reflects the degree of clonal expansion during normal immune reactions. Here we develop mathematic models describing how the population average of telomere length depends on the cell division rates of naive and memory T cells during clonal expansion and normal renewal. The results show that 1) telomeres shorten with twice the cell division rate, 2) that the conventional approach of estimating telomere length shortening per mean population doubling gives rise to estimates that are 39% larger than the "true" loss per cell division, 3) that naive and memory T cells are expected to shorten their telomeres at rates set by the division rate of the naive T cells only, i.e., irrespective of the division rate of memory T cells, 4) that the measured difference in the average telomere length between naive and memory T cells may largely reflect the difference in renewal rates between these subpopulations rather than the clonal expansion, and 5) that full telomerase compensation during clonal expansion is consistent with all data on the shortening of telomere length in, and between, naive and memory T cells. Thus we reconcile the apparent contradictions between the demonstrated difference in division rates between human naive and memory T cells and their similar rates of telomere shortening, and the demonstrated telomere shortening in the presence of telomerase activity.

CD4-Positive T-Lymphocytes↗
PubMed1998

Target cell limited and immune control models of HIV infection: a comparison.

We develop various mathematical models of the clinical latency stage of HIV-1 infection assuming that HIV-1 infection is limited either by the availability of cells that HIV can infect or by a specific anti-HIV cellular immune response. The former models we call "target-cell-limited". Comparing the models by phase plane analysis we find that they all belong to the class of predator-prey models. In the target-cell limited models the virus is a predator feeding upon target cell prey, while in the immune-control models the virus is a prey that is controlled by an immune response predator. Because both classes of models are of predator-prey type they behave similarly in most circumstances. We find that both types of model can account for the generic picture of disease progression in which the CD4 T cell count slowly decreases and the viral load slowly increases. Additionally, we find that both types of models can adequately describe the clinically observed changes in the plasma HIV-1 RNA loads in response to retroviral therapies.

Antiviral Agents↗
PubMed1998

How does cytopathicity affect the production of neutralizing antibody?

Cytopathic viruses evoke an earlier neutralizing antibody (nAb) response than noncytopathic viruses do. This was previously explained by the elimination of infected B cells by the cytotoxic T cells (CTLs), which predominate during infections with noncytopathic viruses. Using a simple mathematical model we provide a much simpler explanation for this difference in the kinetics of neutralizing antibody production. The analysis of the model shows that the delay in nAb production during infections with noncytopathic viruses is a simple consequence of the cytopathic effect alone: noncytopathic viruses infect a larger fraction of nAb-producing B cells and as a result nAb response is delayed. Extending the model with CTLs, we find that a major effect of CTLs is to limit the antigenic stimulus of the nAb-producing B cells. Thus, by reducing the proliferation rate of nAb-producing B cells, CTLs further delay the production of neutralizing antibodies.

Animals↗
PubMed1997

Competitive control of the self-renewing T cell repertoire.

We develop a mathematical model for the self-renewing part of the T cell repertoire. Assuming that self-renewing T cells have to be stimulated by immunogenic MHC-peptide complexes presented on the surfaces of antigen-presenting cells, we derive a model of T cell growth in which competition for MHC-peptide complexes limits T cell clone sizes and regulates the total number of self-renewing T cells in the animal. We show that for a sufficient diversity and/or degree of cross-reactivity, the total T cell number hardly depends upon the diversity of the T cell repertoire or the diversity of the set of presented peptides. Conversely, for repertoires of lower diversity and/or cross-reactivity, steady-state total T cell numbers may be limited by the diversity of the T cells. This provides a possible explanation for the limited repertoire expansion in some, but not all, mouse T cell re-constitution experiments. We suggest that the competitive interactions described by our model underlie the normal T cells numbers observed in transgenic mice, germ-free mice and various knockout mice.

Animals↗
PubMed1997

Clinical data sets of human immunodeficiency virus type 1 reverse transcriptase-resistant mutants explained by a mathematical model.

Treatment of human immunodeficiency virus type 1 (HIV-1) infection during the clinical latency phase with drugs inhibiting reverse transcriptase (RT) reduces the HIV-1 RNA load and increases the CD4+ T-cell count. Typically, however, the virus evolves mutations in the RT gene that circumvent the drugs. We develop a mathematical model for this situation. The model distinguishes quiescent from activated CD4+ T cells, incorporates the fact that only activated cells can become productively infected by HIV-1, embodies empirical estimates for the drug resistance and the mutation frequency for each of the HIV-1 drug-resistant mutants, and assumes the antiviral immune response to remain constant over the course of the experiments. We analyze clinical data on the evolution of drug-resistant mutants for the RT inhibitors lamivudine and zidovudine. The results show that the evolutionary sequence of the drug-resistant mutants in both data sets is accounted for by our model, given that lamivudine is more effective than zidovudine. Thus, current empirical estimates of the mutation frequencies and the drug resistances of the mutants suffice for explaining the data. We derive a critical treatment level below which the wild-type HIV-1 RNA load can rebound before the first drug-resistant mutant appears. Our zidovudine data confirm this to be the case. Thus, we demonstrate in the model and the data that the rebound of the HIV-1 RNA load in the case of zidovudine is due to the outgrowth of wild-type virus and the first drug-resistant mutant, whereas that in the case of lamivudine can only be due to the drug-resistant mutants. The evolution of drug resistance proceeds slower in the case of zidovudine because (i) zidovudine is not as effective as lamivudine and (ii) the first zidovudine drug-resistant mutant is competing with the rebounding wild-type virus.

Drug Resistance, Microbial↗
PubMed1996

Self assertion modeled as a network repertoire of multi-determinant antibodies.

We study repertoire selection in a network of natural antibodies that is maintained by stimulatory idiotypic interactions. The natural antibody repertoire develops in an environment of self epitopes to which the self-reactive B cell clones are completely tolerant. For the modeling formalism, we extend the shape space framework so that each antibody is represented by several randomly chosen shapes. B cell clones are generated stochastically and are removed whenever their density falls below an extinction threshold. The idiotypic interactions are governed by a log bell-shaped interaction function. The natural antibody repertoire in the model is formed by percolation: the network is autonomously activated following a point stimulation. Our main conclusion is that the natural antibody repertoire organizes itself in such a way that most self epitopes are included in the repertoire. We find an over-representation of antibody determinants that are similar to self epitopes. We speculate that the network forms a "smoke screen" covering the somatic self.

Animals↗