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Contribution of CD8⁺ T Cells to Control of Mycobacterium tuberculosis Infection¹

Dhruv Sud^*,, Carolyn Bigbee, JoAnne L. Flynn and Denise E. Kirschner^2,*,

^* Department of Biomedical Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109; Department of Molecular Genetics and Biochemistry, University of Pittsburgh School of Medicine, Pittsburgh, PA 15261; and Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109

	Abstract

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
Tuberculosis is the number one cause of death due to infectious disease in the world today. Understanding the dynamics of the immune response is crucial to elaborating differences between individuals who contain infection vs those who suffer active disease. Key cells in an adaptive immune response to intracellular pathogens include CD8⁺ T cells. Once stimulated, these cells provide a number of different effector functions, each aimed at clearing or containing the pathogen. To explore the role of CD8⁺ T cells in an integrative way, we synthesize both published and unpublished data to build and test a mathematical model of the immune response to Mycobacterium tuberculosis in the lung. The model is then used to perform a series of simulations mimicking experimental situations. Selective deletion of CD8⁺ T cell subsets suggests a differential contribution for CD8⁺ T cell effectors that are cytotoxic as compared with those that produce IFN-. We also determined the minimum levels of effector memory cells of each T cell subset (CD4⁺ and CD8⁺) in providing effective protection following vaccination.

	Introduction

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
Tuberculosis (TB)³ is one of the most pervasive diseases today, with over one-third of the world population infected with Mycobacterium tuberculosis (Mtb) and 2 million deaths every year. The unique nature of Mtb pathogenesis results in only 5–10% of infected persons developing active tuberculosis within 1–5 years postinfection (1), whereas the remainder experience latent infection, which is generally accepted as a state of equilibrium between bacteria and host. Depending on the nature and extent of the host response to infection, there may be tissue damage, fluid accumulation in the lungs, and even death (2). Thus, it is of great interest to identify mechanisms that not only determine differences in infection outcome but also those that are most influential in controlling host damage.

A cell-mediated immune response is essential for control of Mtb infection. Mtb infection initiates in the lungs, where resident macrophages take up bacteria. Mtb can effectively evade killing processes in resting macrophages, thus avoiding elimination (3). Clearance of bacteria by macrophages is in part dependent on macrophage activation by the cytokine IFN- secreted by CD4⁺ T cells, CD8⁺ T cells, and NK cells (4, 5). Infected macrophages secrete other proinflammatory cytokines such as TNF and IL-12 as well as chemokines that recruit immune cells to the site of infection (2).

Several hypotheses have been proposed to explain different outcomes of infection (i.e., active tuberculosis vs latent infection), in part based on studies of isolated components of the host response to Mtb infection in animal models. In particular, many studies focus on genetic knockout (KO) studies and/or depletion experiments (6, 7, 8, 9, 10, 11, 12). Although such methods contribute significantly to our understanding of TB, it can be difficult to analyze the breadth of the entire immune response in such models, particularly when the KO mouse succumbs quickly to TB. In addition, there are limitations to animal models, including differences between certain molecules in humans and mice, difficulty in modeling latent infection, and the possibility of KO mutations affecting other pathways.

To offer another approach, our group previously developed mathematical models that track major elements of the cell-mediated immune response to Mtb infection (13, 14, 15). The first model accounts for the dynamics of six cell populations, including macrophages (resting, infected, and activated subpopulations) and CD4⁺ T cells (Th0, Th1 and Th2 effector subpopulations), four cytokines (IFN-, IL-12, IL-10, and IL-4), and two bacterial subpopulations (intracellular and extracellular mycobacteria) (15). Key regulatory mechanisms involving pathology and protection were identified, and the importance of a fine-tuned balance in immunity-regulating control of infection and tissue damage was discussed. The second model additionally considered the role of dendritic cells and the relevance of their trafficking between lung and lymph node in priming the immune response (13).

CD8⁺ T cells and TNF are believed to participate in the immune response to Mtb infection in humans (6, 7, 16, 17, 18, 19, 20, 21). The role of CD8⁺ T cells in immunity against Mtb infection has been controversial. However, there are data supporting a role for these cells in protection against TB (9, 22, 23, 24). It has been demonstrated repeatedly that mycobacteria-specific CD8⁺ T cells are induced in response to Mtb infection and that these cells can recognize Mtb-infected macrophages (22, 25). Cytotoxic activity of CD8⁺ T cells includes at least two separate mechanisms: apoptosis via the Fas-FasL pathway and killing via perforin and granulysin (26). In humans, CD8⁺ T cells can kill intracellular mycobacteria via the release of the antimicrobial peptide granulysin (27); however, this molecule is not present in the mouse. The fact that no mouse analog of granulysin exists may in part explain why CD8⁺ T cells are not as important in the control of infection in mouse models of TB (12). The cytotoxic potential of CD8⁺ T cells to kill infected cells (CTL activity) in vivo has been shown to be dependent on CD4⁺ T cells in the mouse model, suggesting that the susceptibility of CD4⁺ T cell KO mice to Mtb infection might be due in part to impaired CTL activity (10).

Mtb-specific CD8⁺ T cells are also involved in cytokine production, particularly that of IFN- and TNF (28, 29). Mechanisms that regulate relative cytokine or cytolytic activity of CD8⁺ T cells during Mtb infection are not yet known. Recent data from our laboratory indicate that there are different effector functions of CD8⁺ T cells depending on the stage of Mtb infection (30). In addition, data from viral systems as well as our own data support the idea that cells that produce perforin do not usually produce IFN- (30, 31). Finally, Ag load can influence the cytotoxic vs cytokine-producing phenotypes (31, 32).

In a previous study (15) we had included the effects of TNF and CD8⁺ T cells in an indirect (nonmechanistic) fashion. The objective of this work is to explicitly examine the effects of these two additional elements. We include both CD8⁺ T cells and TNF, but primarily focus our analysis on the role of CD8⁺ T cell dynamics. Other work analyzes the role of TNF in more detail (S. Marino, D. Sud, J. Chan, J. L. Flynn, and D. E. Kirschner, manuscript in preparation). We derive four additional equations describing the rate of change for each of these cell populations (including a precursor, T80 cells) and TNF. We add or modify terms in the existing model (15) to account for CD8⁺ T cell interactions.

We apply our updated model to simulate different infection outcomes (clearance, latent infection, and active tuberculosis) and validate cell numbers, bacterial numbers, and cytokine levels with experimental data. To further corroborate the model and test the role of CD8⁺ T cells, we perform virtual deletion studies mimicking gene KOs or depletion studies mimicking neutralization studies where a component can be eliminated for part of the infection or at specific time points. In addition, we examine the importance of each CD8⁺ T cell subset in control of infection, which is difficult to approach in an animal model. These results add to our understanding of TB and are not obtainable via standard experimental protocols. Based on these studies, we explore the role of both CD4⁺ and CD8⁺ T cells in a number of vaccination schemes.

In each of these situations, a mathematical modeling approach is advantageous to simulate a multitude of possible scenarios and to generate hypotheses that can then be tested in an experimental or clinical setting.

	Materials and Methods

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
Role of CD8⁺ T cells

The dynamics of recruitment, turnover, and effector and cytokine-producing functions of CD8⁺ T cells are illustrated in Fig. 1A. We define T8 as the class of effector CD8⁺ T cells that produce IFN- but do not exhibit cytotoxic activity, and TC is defined as those cells that have CTL activity but do not produce IFN-. CD8⁺ T cells are recruited in the majority as T80 cells (although a small percentage are recruited directly as T8 or TC cells). T80 cells undergo differentiation into T8s and TC cells. Although studies directly assessing cytotoxic capacity and IFN- production in the same cells are relatively rare, studies have indicated that perforin expression or cytotoxic function can coexist with IFN- expression (30, 31, 32). We allow for possible overlap of function via a parameter, m, which defines this percentage. The main roles of each of the subclasses are shown in Fig. 1A. The full equations with a complete explanation of the terms and how they are incorporated into the model are shown in the Appendix.

View larger version (21K): [in this window] [in a new window]   FIGURE 1. CD8+ T cell and TNF dynamics. A, Schematic showing CD8+ T cell dynamics and activities. CD8+ T cells are recruited by both TNF-dependent and independent pathways. They are killed by the apoptotic action of IFN- and also undergo natural death (based on their half-life; both apoptosis and natural death are indicated by the skull and cross-bones symbols in the cartoon). T80 cells can differentiate into TC or T8. We allow this to occur at the site of infection because we model only the lungs and not the corresponding lymph nodes. T8 and TC can both be recruited as well. Depending on the activity of CD8+ T cells, they may be classified as having effector CTL and apoptosis-inducing functions (TC cells) or a cytokine-secreting (TNF, IFN-, or IL-10 production) function (T8 cells). B, Schematic showing TNF dynamics and activities. TNF is produced by macrophages (infected and activated) as well as T cells (TH1, T8, and TC). TNF has a known half-life. Functions for TNF include macrophage and T cell recruitment, macrophage activation (along with IFN- and bacterial signal), and induction of apoptosis in infected macrophages.

For the purpose of focusing specifically on the CD8⁺ T cell response in this work, we only describe how we included TNF action in our updated model and present the results of TNF dynamics elsewhere (S. Marino, D. Sud, J. Chan, J. L. Flynn, and D. E. Kirschner, manuscript in preparation). Our previously published model of Mtb infection (15) simulated cell recruitment as a function of activated and infected macrophages, the main chemokine and TNF producers. We now include an equation representing the dynamics of TNF in the system (see Fig. 1B and Appendix). We include a TNF-dependent recruitment term for both macrophages and T cells (33). We maintain the previous terms that account for additional recruitment due to chemokines not dependent on TNF (33) (Equations 1 and 4–9 in Appendix). We also include the effect of TNF on macrophage activation, which was previously accounted for indirectly (Equations 1 and 3 in Appendix). Lastly, we add an extra term into both the infected macrophage and the bacterial equations to account for the appropriate gain/loss estimates (Equations 2, 15, and 16 in Appendix).

Effects of IL-10 on TNF production

To examine the effect of IL-10 on TNF production, in vitro experiments with wild-type and IL-10-deficient macrophages were performed. Bone marrow macrophages (2.5 x 10⁶ per well) were infected with Mtb strain Erdman (multiplicity of infection of 2), and TNF expression was determined at 2, 4, 8, and 24 h postinfection. Expression was measured by real-time RT-PCR for mRNA levels and by WEHI assay for TNF activity (Fig. 2). There was no difference in TNF mRNA expression or in protein production (ELISA data not shown) or activity between wild-type and IL-10^–/– macrophages. Addition of exogenous IL-10 (10 ng/ml) to the wild-type macrophages at the time of infection also had no effect on TNF expression or production. Thus, we have not included an effect of IL-10 on TNF production in our mathematical model.

View larger version (15K): [in this window] [in a new window]   FIGURE 2. TNF production by macrophages is not strongly influenced by IL-10 in the setting of Mtb infection. Bone marrow-derived macrophages (from C57BL/6 wild-type (WT) or IL-10–/– mice) were infected with Mtb in vitro (multiplicity of infection of 2). IL-10 was added exogenously to wild-type macrophages in one set of samples. Supernatants were harvested, and cells were used to prepare RNA at the time points indicated. mRNA expression of TNF was determined by quantitative real-time RT-PCR and expressed as the fold increase over uninfected macrophages. The supernatants were used in a bioactivity assay with WEHI cells, and the concentration of bioactive TNF was estimated based on a standard curve with recombinant TNF. There were no significant differences between wild-type and IL-10–/– macrophages with respect to TNF production, and exogenous IL-10 had no significant effect on TNF production by wild-type macrophages. Error bars represent SD. The experiment was repeated twice.

RNA was isolated from the cells using the TRIzol isolation protocol with modifications. The cells were lysed in TRIzol reagent (1 ml of TRIzol per 2 x 10⁶ cells), and then two chloroform extractions were performed. After an isopropanol precipitation, the RNA was washed with 70% ethanol and treated with RNase inhibitor (Applied Biosystems) for 45 min. After treatment at 65°C for 15 min (to fully resuspend the RNA), the RNA was cleaned, and DNA was removed with DNase using the Qiagen RNA isolation kit as directed by the manufacturer.

Real-time RT-PCR for TNF expression

RNA was reverse transcribed using the SuperScript II enzyme as directed by the manufacturer (Invitrogen Life Technologies). For real-time RT-PCR we used the relative gene expression method (34). Hypoxanthine phosphoribosyltransferase served as the normalizer, and macrophages served as the calibrator. Each primer and probe set was tested for efficiency (results were >97% efficiency for all primer/probe sets) as previously described (33). All samples were run in triplicate and with no reverse transcriptase controls on an ABI PRISM Sequence Detector 7700. Relative gene expression was calculated as 2(–cycle threshold (Ct)), where Ct = Ct (gene of interest) – Ct (normalizer) and Ct = Ct (sample) – Ct (calibrator). Results are expressed as relative gene expression to uninfected samples. The primer and probe concentrations were used as suggested by Applied Biosystems, with the final concentration of each primer at 400 nM and that of probe at 250 nM.

WEHI assay for TNF activity

In this assay, TNF induces death of WEHI cells in a dose-dependent manner (35, 36). Using this assay, the active TNF in a culture can be estimated. At indicated time points following Mtb infection, supernatants were removed and the filter was sterilized and frozen at –80°C. For the TNF activity assay, WEHI 164 subclone 13 (American Type Culture Collection) cells were placed in 96-well plates (1 x 10⁵ cells/well in 200 µl) and grown overnight at 37°C. Medium was removed, and 100 µl of fresh medium was added to each well. Then 100-µl samples, TNF standards, and controls were added. Samples were run in triplicate and incubated overnight at 37°C. The 100-µl medium was removed from the wells, and 50 µg of MTT was added. Following a 4-h incubation at 37°C, medium was removed from the wells, and 100 µl of 0.04 N HCl/isopropanol was added. OD₅₇₀ was read after 20 min, and TNF activity in samples was estimated by comparison with the standard curve generated using recombinant murine TNF. These controls were run concurrently for each assay.

The CD8⁺ T cell model

Based on our description above, we derived four nonlinear ordinary differential equations to describe the dynamics of three CD8⁺ T cell subpopulations (T80, T8, and TC) and TNF (see Appendix). Using similar mass action and kinetic law techniques as described (15), the interactions of these variables with other cells and cytokines were incorporated into the previous model equations (see Appendix and Ref.15). Parameter values for interactions are estimated as described in the Parameter Estimation section of the Appendix and in Table III.

IFN- dependent apoptosis of T cells

Recent studies suggest a host homeostatic mechanism whereby activated macrophages in the presence of IFN- induce apoptosis of T cells to prevent excessive IFN- production and further activation (37, 38, 39). The need for IFN- as well as activated macrophages for inducing T cell apoptosis seems redundant, but experimental data indicate that the effect of IFN- is indirect (likely via activated macrophages), although exact mechanisms are yet to be elucidated (38). We have now included IFN--induced apoptosis of T cells in the model.

Computer simulations

Our model is designed to represent the temporal immune response occurring dynamically in total lung. After deriving the model, we solve the nonlinear ordinary differential equation system to obtain temporal dynamics for each element of the model. For this purpose we use C code implementing the Runga-Kutta adaptive step-size solvers and appropriate finite difference methods. Finally, we validate our model output wherever possible with published experimental data.

As a marker of disease progression, we consider bacterial load as the most informative based on results from animal models (see a complete discussion of this in Refs.13, 14, 15). We observe two stable states with the model: latent infection (controlled and low bacterial numbers) and active tuberculosis (uncontrolled bacterial growth). Reactivation is consequently defined as the transition from latency to active disease. Because latency is a stable state, it logically follows that reactivation can only occur due to perturbations to the system, e.g., waning immune response due to aging, HIV infection, malnutrition, or immunotherapy, etc. (e.g., TNF neutralization).

Because all parameters exhibit a range of values, it is important to note that a single simulation is not a unique representation of a certain state (latency or disease). Differential equation models yield as their output a representation of a sample average dependent on the parameter values used. Parameters may trade off to attain these states in a variety of ways and exhibit variable cellular/cytokine compositions for each of these states (see below).

Given the temporal nature of the model, we are unable to track lung physiology to study the extent and localization of tissue damage. We assess damage by measuring the effector cell (i.e., effector CD4⁺ and CD8⁺ T cell subsets) to target cell (infected macrophage (M_I)) ratio. A very large ratio would indicate greater tissue damage and vice versa.

All dynamics are plotted as described (linear or log scale), and all numbers indicate cell numbers/cytokine concentration per whole lung, but we consider the primary effector functions to occur within the context of the tuberculous granuloma. We have used available experimental and/or clinical data to establish parameters of our models. There are available data on cytokine concentrations in bronchoalveolar lavage fluid from human TB studies, although such data are not available from whole lung tissue in human TB. However, because TB is a disease that is primarily manifested in the parenchyma, we assume that our modeling space represents whole lung. Additional data from mouse and nonhuman primate models of TB (Refs.6 , 10 , and 40 , and our unpublished data) have been incorporated where appropriate. All parameters are studied using a detailed uncertainty and sensitivity analysis (see below).

Deletion and depletion simulations

Simulations are performed mimicking in vivo experiments for the deletion of cells or effector molecules before infection (similar to a gene KO in a mouse model) and for the depletion of cells or effectors, where an element was removed from the system after latency had been achieved (day 500) (similar to Ab-mediated neutralization studies). Deletion experiments help us ascertain which elements of the system allow it to achieve latency, whereas depletion experiments help us understand which factors help maintain latency.

CD8⁺ T cell kinetic studies

To explore the contributions of different subclasses of CD8⁺ T cells on infection dynamics, we perform two experiments in which T8 and TC cells are differentially present, as suggested by Ref.30 . First, we allow only TC cells to be present for the first 200 days postinfection. Then we stop input of any further TC cells and allow those present to turn over naturally, based on their half-life. At that same day 200 time point we allow T8 cells to begin to develop, and they remain present until the end of the simulation. In another similar but opposite simulation we introduce T8 cells first, and then at day 200 postinfection we stop all further input of T8 cells and allow them to decay in two manners, fast or slow. At the same time point we allow TC cells to begin to develop, and they remain present until the end of the simulation. We track the effects to all model variables in the above simulations but only report the effects on total bacterial load.

Vaccine studies

To test what the model predicts about the effects of vaccination, we study four distinct scenarios. Each of these studies was performed with all parameters set to their latency values (Table III). First, we allow for only a class of CD4⁺ Th1 memory effector cells to be present at the time of first challenge with Mtb. We simulate this by varying a given background level of memory cells that theoretically could be present in the lungs upon challenge. Second, we repeat the previous scenario by adding a background level of memory T8 cells while fixing the value of memory CD4⁺ Th cells to a very small number that by itself would not lead to clearance. Third, we repeat this second scenario with TC cells rather than T8 cells. Values for memory cell levels used in each simulation are given in Table V. Finally, we include all three classes of memory cells in a number of simulations where we vary the levels of each subclass present to determine the effects of various combinations. In each of these simulations we assume that the input cells have a very long half-life, capturing their memory cell status. We track the effects of the presence of these memory cells for all model variables but only report them for total bacterial load.

Rates measured from in vivo or in vitro studies likely vary with each repeated experiment due to inherent differences among hosts, even when using inbred mice, as well as to intrinsic errors of measurement. Further, some interactions in the Mtb-host system are not currently measurable. To explore the effects of uncertainty in the model, we evaluate all of the parameters using our own C code based on Latin hypercube sampling (41, 42). The Latin hypercube sampling method is a stratified Monte Carlo sampling mechanism that allows simultaneous, random, and evenly distributed sampling of each defined parameter that we contrast over a wide range. We vary each parameter by a factor of 1000 above and below reported literature data or mathematical estimates to assess the effects of parameter variations on model outcome (total bacterial load in this case). We combine the resulting uncertainty data with a sensitivity analysis using partial rank correlation to ascertain the sensitivity of the outcome variable (total bacterial load) against variations in parameter values. The Student’s t test is then used to determine the significance of each partial rank correlation obtained, giving us a standard measure of sensitivity. Using these methods we are not only able to reveal key parameters that govern infection outcome but also able to evaluate temporal changes in the significance of these parameters as they relate to bacterial load. We provide only corresponding significance (p values) for brevity.

Control experiments

As a negative control the model simulates no infection, yielding an equilibrium value of resting macrophage population (3 x 10⁵ cells), and all other variables are zero (infected and activated macrophages, all T cell subsets, and cytokines). If the innate response is up-regulated so that the initial macrophage interaction kills the bacteria, the model indicates that it is indeed possible to clear an initial low dose (<10 bacilli) infection without any memory of the response and no damage to the host (data not shown) (1).

Qualitative behavior of the previous model (15) is recapitulated by this updated model. Virtual IFN- and IL-12 deletion experimental results are in agreement with the outcomes reported in literature and also agree with those presented previously (15). We discuss TNF deletion and depletion elsewhere (S. Marino, D. Sud, J. Chan, J. L. Flynn, and D. E. Kirschner, manuscript in preparation). Recent availability of data on Mtb infection studies in humans and nonhuman primates (Refs.43, 44, 45, 46, 47, 48, 49 and our unpublished data) have contributed to a more precise model of human infection.

	Results

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
Simulating latent infection and active disease

The model simulates both infection outcomes of latent and active TB depending on the parameter values. As discussed previously (15), we used an extracellular bacterial load as a marker of disease progression, where uncontrolled growth of extracellular bacteria is indicative of active TB. These extracellular bacteria are derived in two ways: 1) from intracellular bacteria when infected macrophages are killed by CTL action or burst due to high bacterial load; and 2) from bacteria dividing in the extracellular spaces (at a slower rate than intracellular bacteria) (50, 51, 52).

Latent infection

The various cell and cytokine profiles associated with latency can be seen in Fig. 3. Extracellular bacterial load is extremely low (Fig. 3A) (<40 bacteria per whole lung), and all intracellular bacteria reside within a small number of chronically infected macrophages (Fig. 3B). The relationship between infected macrophages and intracellular bacterial numbers implies that during latency there are on average 50 bacteria within each of 25 infected macrophages. Because some bacteria may be contained within resting and activated macrophages and thus quickly cleared, they are not included in this calculation. Resting macrophages maintain their numbers during latency due to the balance between their recruitment and subsequent activation or infection (Fig. 3B).

View larger version (24K): [in this window] [in a new window]   FIGURE 3. Simulations leading to latent infection. Shown are simulation results for all cells and cytokines in the model for the parameter values shown in Table III. Extracellular and intracellular bacterial populations are controlled by 200 days (A). Three subclasses of macrophages are shown (resting, infected, and activated) (B). All subclasses of T cells and cytokine dynamics are shown in C and D, respectively. Bacterial levels are controlled 7–8 mo postinfection, and all model elements stabilize over time, indicating latency. The axes for bacterial and macrophage dynamics are given on a log scale. Units are total lung levels except for cytokine, which is expressed as picograms per milliliter.

Simulated TNF levels are extremely low, because levels of infected and activated macrophages (the major TNF producers) are relatively low (Fig. 3D). This condition results in limited inflammation. Predicted ranges for IFN- and IL-10 correlate with studies measuring cytokine levels at the site of disease (47, 53, 54), whereas simulated IL-4 is present at essentially undetectable levels during latency (<0.1 pg/ml), possibly explaining why IL-4 is difficult to detect in humans with latent infection (54, 55). IL-12 levels in this particular latency simulation are higher than what might be found within the lungs, but this is likely due to the constraints of modeling within a single compartment, which means that priming of the T cell response occurs in the lungs instead of lymph nodes in this model. In other work from our group (14) involving a two-compartment system (lung and lymph node), IL-12 is higher in the lymphoid compartment.

Simulations indicate that latency is achieved by 7–8 mo, and bacterial numbers are controlled (Fig. 3). Depending on certain parameter values associated with bacterial turnover and infection as well as cytokine production, these time points can be manipulated to yield latent infection with different steady-state bacterial loads as well as cell and cytokine levels. Analysis of these parameters provides key insights into factors responsible for variations observed in patients infected with Mtb and also in regard to which parameters determine outcome. A subset of such parameters and their effect on the time to stabilized latent infection is shown in Table I.

Active tuberculosis

Only a subset of all model parameters can determine the infection outcome, i.e., latent infection or active tuberculosis. One other scenario that may occur under certain conditions is a system with oscillations, which is a less stable state than the latent state. This state allows for an enhanced chance of reactivation when any other small perturbation to the system is introduced. Our uncertainty and sensitivity analysis identifies which parameters have this property (Table II). By varying the parameters shown in Table II, the outcome is active tuberculosis rather than latent infection.

View larger version (24K): [in this window] [in a new window]   FIGURE 4. Simulations leading to active disease. Shown are simulation results for all cells and cytokines in the model for the parameter values shown in Table III; with one parameter different CTL activity is reduced (k52). Bacterial population dynamics are shown in A. Note that, in contrast to Fig. 2, at 1 year postinfection the extracellular bacteria are growing logarithmically, whereas intracellular levels saturate infected macrophages. Macrophages are shown in B, and the level of infected macrophages has increased four orders of magnitude compared with latency. T cells and cytokines respond by increases in their numbers and concentration, but infection is not controlled (C and D). The axes for bacterial and T cell dynamics are indicated on a log scale, whereas macrophage and cytokines dynamics are specified on a linear scale. Units are total lung levels except for cytokine, which is expressed as picograms per milliliter.

The total T cell population reaches a level comparable to that of the macrophage population (Fig. 4C). Because of the IFN--induced apoptosis of Th1 cells, we observe a transient delay (before attaining peak values) that also correlates inversely with activated macrophage dynamics. This observation compares well with available experimental data regarding the necessity of activated macrophages for T cell apoptosis (37, 57, 58). CD8⁺ T cell numbers are comparable to those of CD4⁺ T cells and show dynamics most similar to those of Th1 cells due to IFN- induced apoptosis (Fig. 4C).

All cytokine levels are significantly elevated during disease. TNF levels are increased by several orders of magnitude to >1000 pg/ml (Fig. 4D), which has been associated with severe pathology (59). Other cytokine levels correlate with experimental data (47, 60). In unpublished data from our nonhuman primate studies with active TB, CD4⁺ and CD8⁺ T cell production of IFN- increases substantially compared with that of latently infected monkeys. In addition, there is an increase in CD4⁺ and CD8⁺ T cells in the lungs of mice with fulminant TB compared with controlled infection (61) (our unpublished data).

Factors that determine infection outcome

The model consists of >100 parameters that govern rates and interactions between various components that can differ among individuals and potentially can affect progression to active tuberculosis or to latent infection (see Table III and Appendix). Varying each of these parameters over a large range simultaneously to perform sensitivity analyses demonstrates that changes in only a small subset of parameters are influential in distinguishing between infection outcomes (Table II). Logically, a tradeoff exists between these parameters; changing a parameter toward more stringent control can be compensated for by varying another to aggravate infection with no resulting change in outcome. For example, an increased extracellular bacterial reproduction rate (₂₀) can be controlled by increasing the rate of CTL activity (k₅₂).

IFN- is an important cytokine for macrophage activation and, not surprisingly, is relevant in determining infection outcome (Table II). The rate of production of IFN- from all three sources (CD4⁺ and CD8⁺ T cells and NK cells) has a positive effect on control of infection. However, the contribution of NK cells is particularly important in the initial phases of the infection (p < 0.01 for the first 50 days), whereas the contribution from T cells is important throughout the infection (p < 0.001). Related to the findings with respect to IFN- production, cytokine parameters that control the rate of macrophage activation (IFN- and TNF) determine the outcome of infection as well, with increased macrophage activation promoting establishment of latency. Parameters that influence IL-12 production by macrophages and dendritic cells (c₂₃, ₂₃, and c₂₃₀) and, therefore, the robustness of the type 1 response, can determine the outcome of infection and are important throughout the course of infection. Along these same lines, those parameters that inhibit a type 1 (IFN- producing) T cell response, such as IL-4 inhibition of IFN- effects (f₁) and IL-10 mediated inhibition of IL-12 production (s), have a negative effect on the establishment of latency. Increasing the rate of production of IL-10 from T cells (₁₈) results in progression to disease due to multiple effects of this cytokine, including inhibition of macrophage activation, IFN- production, and TNF-mediated apoptosis.

In addition to the IFN- production by CD8⁺ T cells, a parameter (k₅₂) that governs the perforin/granulysin-mediated cytotoxicity of infected macrophages with the subsequent killing of intracellular bacteria influences infection outcome. Decreasing the rate of these killing mechanisms leads to disease.

Bacterial factors that determine infection outcome include both the intracellular (₁₉) and extracellular (₂₀) bacterial replication rates, the ability of bacteria to be taken up into macrophages and destroyed by phagocytosis (k₁₈), the rate of bursting of infected macrophages due to bacterial overload (k₁₇), and the turnover of bacteria from intracellular to extracellular due to natural death of infected macrophages (µ_I) (Table II). This suggests that certain bacterial factors that are strain dependent can influence infection outcome. In particular, factors in the model that increase the extracellular bacterial load are all influential in infection outcome. Also suggested from these data is the idea that the growth rate inside macrophages, as well as perhaps cell wall factors that affect phagocytosis, should influence the ability of a strain to cause disease. This possibility is supported by literature comparing the virulence of different clinical strains of bacteria (62, 63, 64).

Recruitment of cells to the site of infection is clearly relevant to control of infection. Based on our previous data in animal models (33), we include both TNF-dependent and independent recruitment terms. There are several recruitment parameters in the model that are crucial in determining infection outcome (data not shown). Interestingly, those parameters that are most important are TNF-dependent. A full discussion of the predicted roles of TNF in TB from this mathematical model is the subject of another manuscript (S. Marino, D. Sud, J. Chan, J. L. Flynn, and D. E. Kirschner, manuscript in preparation).

Measuring immunopathology

Because we do not specifically track the lung tissue environment where infection is occurring, we define tissue damage based on the ratio of effector T cells to infected macrophages (see Materials and Methods). In other work (65) we focused on granuloma formation, examining the spatial aspects of infection together with the development of necrosis. An overexuberant immune response can lead to tissue damage, including necrosis. Caseous necrosis within a granuloma may actually contribute to control of infection (66), perhaps by creating anoxic (anaerobic) conditions (our unpublished data). In this work we specifically address the contribution of TNF and CD8⁺ T cells to immunopathology. Presented in Table IV are those factors that play a role in tissue damage, including those identified in our previous work (15). The model predicts that increased TNF production beyond a threshold level results in a high effector T cell to infected macrophage ratio, thereby causing tissue damage.

Cytokine dynamics

Shown in Fig. 5 are the infection outcomes following deletion (Fig. 5A) and depletion (Fig. 5B) for four key cytokines in the model. Note that TNF deletion or depletion results by far in the fastest progression to disease as compared with deletion of IL-12 or IFN-. IL-12 and IFN- deletion simulations both approach disease with similar kinetics, and IL-10 deletion is only slightly different from that of the latency control. Results are consistent across deletion and depletion studies, indicating that those cytokines that are important in establishment of latency are also relevant for maintaining the infection in a latent state.

View larger version (18K): [in this window] [in a new window]   FIGURE 5. Cytokine deletion and depletion. Shown are the simulation dynamics of total bacteria levels during deletion (indicated by –/–) (A) and depletion (indicated by –) (B). Deletions and depletions were performed for IFN- (thin, dark, solid lines), TNF (thick, dark, solid lines), IL-12 (gray dashed lines), and IL-10 (gray solid lines). Deletions imply that a cytokine was removed from the system at day 0, whereas for deletion it is removed at day 500. Simulations are shown compared with latency (wild type; dark dashed lines) as a positive control.

Our updated model is consistent with experimental data predicting that key immune components responsible for controlling initial and latent Mtb infection are CD8⁺ CTL activity and IFN- production (4, 30, 67, 68, 69). Cytotoxic activity of CD8⁺ T cells accounts for 80–90% of the killing of infected macrophages and up to 80% of the granulysin-mediated killing of bacteria within those macrophages; this activity is crucial to control of infection (k_52; Table II). The Fas-FasL apoptosis of infected macrophages induced by CD8⁺ T cells also appears to be important early in infection, in contrast to published in vitro studies (26, 70) that examined the effects of this pathway on killing intracellular mycobacteria.

T cell deletion studies

The updated model reflects the contribution of all of the major T cell subsets, which allows us to analyze the importance of each subset at different times in infection. Fig. 6 presents deletion (Fig. 6A) and depletion (Fig. 6B) simulations of various T cell population subsets. As stated previously, deletion simulates the loss of a component from the beginning of infection (similar to a KO mouse). Depletion studies simulate loss of a component during a latent infection (500 days postinfection), similar to Ab-mediated depletion or neutralization of cells or cytokines. Depletion studies closely match the deletion results (compare Fig. 6, A and B), supporting the hypothesis that similar factors are important for controlling both initial and latent infection.

View larger version (19K): [in this window] [in a new window]   FIGURE 6. T cell deletion and depletion. Simulations of total bacterial dynamics are shown for deletion (indicated by –/–) (A) and depletion (indicated by –) (B) simulations. For deletions, T cells were removed from the system at day 0. For depletions, cells were removed at day 500 after the system has achieved latency. Deletion and depletion simulations were performed for total CD4+ T cells, total CD8+ T cells, T8 cells, and TC cells. These were compared with latency (wild type) as a positive control.

Selective T8 or TC deletion

We exploit the model to specifically delete either T8 or TC subsets at day 0 to determine the relative contribution of each to control of infection. The resulting bacterial loads from selective T8 and TC deletion are shown in Fig. 6A. For T8 deletion, latent infection is achieved, although bacterial numbers are slightly higher than the standard latent infection values (wild type). In the absence of T8 cells, IFN- production by CD4 T cells (Th1) and NK cells increases to maintain total levels of IFN- (data not shown).

For TC deletion, latent infection is achieved; however, bacterial loads are an order of magnitude higher, and oscillations appear. The presence of oscillations in total bacterial numbers indicates a less stable state of latency. This result suggests that an additional, even minor, perturbation of the system could result in reactivation, whereas the same perturbation in the presence of TC cells would not affect the latency state. To test this hypothesis, an experiment was performed in which TC cells were deleted and the rate of IL-10 production by Th1 was increased (over a range of values) compared with the standard latency values. In this case, the outcome was always uncontrolled bacterial growth (data not shown). Varying the IL-10 values over the same range in the presence of TC cells (normal latency levels) did not affect the outcome of infection.

An unexpected result of the CD8⁺ T cell subset deletion simulations was the apparent synergy between these subsets that is important in the immune response to Mtb. When both T cell subsets were removed simultaneously, the system was driven to active disease. However, when T8 and TC were removed individually, latency was still achieved, but at a cost to either bacterial numbers or system stability, respectively. Taken together, these deletion and depletion studies support the view that T8 and TC cell subsets act in synergy to control infection.

T cell depletion

To explore the role of T cells in maintaining a latent infection, we performed depletions by removing CD4⁺ and CD8⁺ T cells as well as both functional subsets (T8 and TC cells) from our system at 500 days postinfection (while the system is in latency). Fig. 6B illustrates the dynamics of the total bacterial population in the lungs during latency (<500 days), depletion, and subsequent advancement to disease (>500 days). The results match those of the deletion cases (Fig. 6A). This finding implies that T cells are crucial in both establishing as well as maintaining latent infection.

CD8⁺ T cell subsets: dynamic changes during the course of infection

Experimental data from a C57BL/6 mouse model suggest that the functions of CD8⁺ T cells are differentially regulated during infection (30). Cytotoxic function was observed only during the initial phase of infection, whereas IFN- production by CD8⁺ T cells did not occur until the chronic phase of infection (see Fig. 7A, adapted from Ref.30). Until now, we assumed that the total CD8⁺ T cell population was comprised of equal numbers of T8 and TC cell subsets. We can now vary this assumption to test the experimental predictions of Lazarevic et al (30). In the murine system, the dynamics of infection occur on a faster time scale than that of humans and nonhuman primates. In the studies of Lazarevic et al. (30), the observed a switch in CD8⁺ T cell phenotype in < 50 days. In the simulations in this study, we allowed the system to evolve further for 200 days (just into the latent state; see Fig. 3) before we induced a switch. We first simulated the situation described in Lazarevic et al. (30) in which TC cells existed exclusively for 200 days and, as they declined, we introduced IFN--producing activity via T8 cells in an increasing and also exclusive fashion (Fig. 7B). In this case, the system no longer approaches latency as a steady state but instead reveals oscillations in bacterial numbers (Fig. 7C), suggesting a less stable latent state. Further, the average levels of bacteria during the course of infection in this simulation are higher than when both subclasses of CD8⁺ T cells are present throughout infection.

View larger version (32K): [in this window] [in a new window]   FIGURE 7. CD8+ T cell kinetic studies. A, Data from Ref.30 indicating the differential presence of T8 and TC populations a mouse model of TB. The progression time frame for a murine model is likely faster than that observed in humans. B–F, Simulations exploring the timing of CD8+ T cell kinetics. B, Dynamics of two subsets of CD8+ T cells when TC cells are present first and then, at the 200 day time point, they die off naturally and T8 cells are introduced and are allowed to increase. C, The corresponding bacterial subpopulations. Notice that oscillations are now present in the system as compared with latency (Fig. 3A). D and E, The opposite orientation, where T8 cells are present first for 200 days and are allowed to die off either fast (D) or slow (E) while the TC cell subset replaces the T8 cell subset. F, total bacterial dynamics during the fast (dashed line) and slow (solid line) T cell dynamics from D and E, respectively.

Vaccine strategies

Given the prevalence of Mtb worldwide, a clear need exists for an effective vaccine strategy to impart protective immunity against TB. Bacillus Calmette-Guérin, the vaccine against TB used for the last 80 years, has failed to control the TB scourge (71). Much of TB vaccine development has been empirical, because mechanisms of resistance to TB are incompletely understood. Using the model generated here, we address possible strategies that target different T cell subsets with the goal of illuminating vaccine approaches that will lead to the best control of infection.

Initially, we investigated the ability of single T cell subsets to provide protective immunity, assuming that effector memory cells of that phenotype were present in the lungs, poised to respond immediately to a challenge. When memory Th1 cells alone were present at levels of 10% of their peak values that lead to latency (Fig. 2; see 200 days postinfection), clearance of the challenge infection was observed (Fig. 8A and Table V). Similarly, when memory TC cells were present at 10% of the peak value of latency values (Fig. 2) (plus a few Th1 cells present that would be insufficient to clear the challenge; see Fig. 8A), clearance of challenge infection was observed (Fig. 8B and Table V). Conversely, if the memory response present at challenge was T8 cells (plus the same small number of Th1 cells as in the TC memory scenario), a large number of these cells (75% of peak values from latency) were necessary to observe clearance (Fig. 8C and Table V).

View larger version (23K): [in this window] [in a new window]   FIGURE 8. Vaccine strategies. In these simulations we test the effects of a cell-mediated vaccine by exploring the presence of different T cell subsets on infection progression. We vary the number of T cells of each subset in each simulation for 20 different values over a wide range (using the Latin hypercube sampling algorithm; see Materials and Methods) and show results for total bacterial loads. In A we show the total bacterial load when a range of Th1 cells are present at the time of infection at the site (values are shown in the left column of Table V). Of the 20 different values for numbers of Th1 cells (over a range of 1–35), only two did not lead to clearance (1 and 3). In B we set the level of Th1 cells to 3 and then input a range of T8 cells (values in the middle column of Table V range from 1 to 150). In this case, clearance of bacterial challenge is only possible when there are a great number of T8 cells present (>75). In C we set the levels of Th1 cells to 3 and then input a range of TC cells (values in the right column of Table V range from 1 to 150). Here, all but the lowest case (two TC cells) can lead to clearance. In D we input all three subsets (Th1, and T8, and TC) in two different combinations: case 1 presents three Th1 cells, two T8 cells, and three TC cells. Case 2 presents three Th1 cells, no T8 cells, and three TC cells.

From these data we hypothesize that induction of moderate Th1 and TC subsets should be sufficient as a vaccine against challenge, although retaining these cells in the lungs as effector memory cells is crucial to obtaining this outcome. In fact, if the memory cells do not arrive in the lungs within the first 3 days of infection, clearance is not observed (data not shown). The approach that could achieve this result may be related to mucosal routes of vaccination. In practice, it is not obvious how to vaccinate to modulate TC levels specifically, and, most likely, moderate levels of TC and T8 would be induced in any CD8-directed vaccine approach. Second, the percentages of T cells presented should be viewed simply as guidelines rather than as absolute numbers of cells that must be present, because these may be dependent on the genetic susceptibility of a particular person. Targeting both CD4⁺ and CD8⁺ T cell subsets will be the most efficient strategy for an effective vaccine, but a high peak response to the vaccine might be necessary to retain reasonable levels of these cells as effector memory cells in the lungs.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
In this study we extended our previous work in modeling the immune response to Mtb to examine the role of CD8⁺ T cells in the course of Mtb infection in humans. CD8⁺ T cell numbers were tracked in the course of infection, and we also incorporated both their cytokine-producing and CTL function. The model can easily simulate all possible infection outcomes: clearance, latency, disease, and reactivation. Clearance is achievable via an enhanced innate response or persistent activated macrophage action. We were able to ascertain critical parameters that govern infection outcome between latency and disease (Table II) and also determine parameters that control the time profile of these outcomes. Reactivation can be achieved by varying the parameters specified in Table II toward disease either slowly (representing aging or slow loss of immune function) or quickly (representing immunosuppressive therapy). Disease outcomes can be simulated for wild-type scenarios as well as for individuals with impaired macrophage (lower numbers) and/or impaired T cell responses. Tighter control of bacterial numbers may be achieved at the expense of tissue damage induced by excessive TNF production and a vigorous CTL response.

The data from these simulations strongly support the hypothesis that although IFN- is necessary for a protective immune response to Mtb, it is not sufficient. These results are supported, for example, by murine studies of acute and chronic infection of CD4⁺ T cell-deficient mice in which CD8⁺ T cells produced enough IFN- to match wild type levels in lung, yet the mice still succumbed to the infection (40, 72, 73). The data also support the belief that CD4⁺ T cells are very important for control of infection, as is generally accepted in the field, but highlight the finding that the contribution of CD4⁺ T cells to the control of Mtb infection is more than just production of IFN-. This can be most easily observed by comparing the CD4⁺ T cell and IFN- deletion or depletion scenarios (Figs. 5 and 6), where loss of CD4⁺ T cells is more detrimental in terms of time to active disease than loss of IFN-.

A consistent theme observed in all simulations performed was that mechanisms important in controlling initial infection also contributed to the maintenance of latent infection. This observation is supported by some (4, 5, 6, 40, 72, 73, 74, 75, 76) but not all (77) experimental findings in the literature. These results further suggest that there is continual need for dynamic control of infection rather than a special state attributed to latent infection. In the simulations where we study the mechanisms yielding different infection outcomes (using the uncertainty and sensitivity analysis), the values for all cells and cytokines adjust their levels slightly, yielding myriad different routes to latency or active disease for each combination of parameters. This variation could account for differences among individuals (and possibly between animals and humans) in response to infection and suggests that levels of effector cells and molecules necessary for achieving and maintaining latency may differ.

Using the updated model, we were able to assess the contributions of the various T cell subsets to the control of Mtb, both in the setting of natural infection and in a vaccinated individual. CD8⁺ T cells have at least two major functions that are important in control of Mtb infection: 1) cytotoxic activity, which can result in intracellular bacterial killing as well as killing of the infected macrophage; and 2) cytokine production. In this study we defined two subsets, TC (cytotoxic CD8⁺ T cells) and T8 (IFN- producing CD8⁺ T cells), based on literature indicating that these two subsets may be differentially regulated (1, 5, 6). This provided the opportunity to determine the contribution of each subset to control of infection. Although no human or primate TB data for such deletion/depletion experiments are available, we were able to compare our results to murine experiments involving T cell depletion via Ab treatment, as well as genetic KOs resulting in dysfunctional CD8⁺ T cells (12, 20, 78). However, in the mouse model it is technically challenging or impossible to selectively deplete either cytotoxic or IFN- producing subsets during chronic infection. In addition, KO mice can have dysregulated immune responses that prevent accurate analysis of the exclusive effects of the mutation. For example, we and others (9, 79) demonstrated previously that perforin KO mice (i.e., with CD8⁺ T cells impaired in cytotoxic potential) had dysregulated IFN- production (up to 4-fold higher) during Mtb infection, making it impossible to determine the true contribution of CTL to the control of the infection. In contrast, mathematical models are not subject to these complications. Finally, mice are lacking in what appears to be a crucial factor, granulysin, in the ability of CD8⁺ T cells to control Mtb infection. Using the mathematical model, we were able to include granulysin action in the CTL subset and directly study the effects of the actions of this molecule in the immune response to Mtb.

Our findings indicate that both subclasses of CD8⁺ T cells can play a role in the immune response to Mtb. Deletion or depletion of either subset can still allow the host to control the infection, but either total bacterial numbers during latency are slightly higher (in the case of absence of T8 cells) or total bacterial numbers oscillate (in the case of loss of TC), indicating a less stable latent state. The less stable latent state is more susceptible to minor perturbations, and small changes can lead to reactivation in this setting (data not shown). However, given the data regarding removal of a single CD8⁺ T cell subset, the surprising finding is that removal of both CD8⁺ T cell subsets together always results in active disease, suggesting that some contribution from either CD8⁺ T cell subset is necessary to control infection.

This model was used to explore the timing of CD8⁺ T cell effector functions. In the literature, Ag load or extent of priming in viral infections has been postulated to influence CD8⁺ T cell effector functions, with higher Ag load leading to a more cytokine-producing phenotype. Our group has published data (30) suggesting that, early in infection (in C57BL/6 mice), cytotoxic activity but little IFN- production from CD8⁺ T cells is observed in the lungs. When infection reaches the chronic stage there is a buildup of Ag in the lungs, and the CD8⁺ T cell phenotype appears to switch to IFN- production. Using the model, we compared the scenarios of first initiating TC function followed by T8 function (the naturally occurring situation) with the opposite orientation, i.e., T8 cells appearing first and then switching to TC cell function. In the first scenario (the early appearance and then decline of TC cells, with T8 cells appearing later in infection), the system could reach latency but with a higher and oscillating bacterial load (i.e., a less stable latent state). In contrast, if T8 cells were present initially but declined quickly as TC cells were introduced into the system, a stable latency was achieved. Furthermore, if the T8 cells were declining more slowly during the introduction of TC cells, clearance of the infection was achieved. This was the result of a higher bacterial load during the initiation of the response (caused by a lack of TC cells) and a stronger T cell response induced by increased Ag load in the system. This outcome was recapitulated by removing Th1 cells from the intact system for the first 100 days and then adding them back; this scenario also led to clearance due to higher total bacterial numbers (and Ag) during the priming phase of the response. These results confirm the importance of the TC subset in the control of infection but also suggest that a higher amount of Ag (perhaps more bacteria) in the system initially might lead to a stronger response and better protection against disease. The results further suggest that the low ID₅₀ of Mtb may serve as a key virulence strategy.

The updated model lends itself to the study of mechanisms of vaccine-induced protection. Vaccine development for TB has been mostly empirical because little is known about the protective mechanisms for this disease, and there are no useful surrogate markers of protection. In this work, we sought to define the requirements for protective vaccination against Mtb infection based on a T cell-mediated immune response. The model allows one to create scenarios that are impossible in animal models or human systems to elucidate key elements of protection. We identified the minimum level of memory TH1, T8, or TC cells that would be necessary to obtain clearance of a challenge infection. For Th1 alone or TC alone (with a small number of Th1 cells), effector memory populations at levels of 10% of the peak values (200 days in the latency scenario) would need to be maintained in the lungs to offer protection. In contrast, enormous numbers of memory T8 cells (75% of peak initial expansion) would need to be present in the lungs at time of challenge to lead to clearance. A combination of moderate levels of memory Th1 and TC cells were much more effective in achieving protection against challenge. In this situation, the minimum memory T cell percentages were 4 and 2%, respectively, of normal infection peak values, and no T8 cells were required. It is important to keep in mind that this may be true for infection with Mtb but that different levels of each of the three subsets may be necessary for control of different pathogens (80). These results strongly support the belief that vaccination strategies targeting both CD4⁺ and CD8⁺ T cells are likely to be most effective against Mtb infection.

We also determined that it is crucial that the memory T cells be present in the lungs at the time of infection (or shortly thereafter). If memory cells arrived in the lungs by 1 day postchallenge, the vaccination was effective. However, if cells arrived even by 3 days postchallenge, the vaccination was ineffective at clearing bacterial load but served to delay time to latency. There has been extensive mathematical modeling exploring the generation of CD8⁺ T cell immune memory (81). In our present work we have assumed that memory cells were already generated by a vaccine and only tested differences between numbers of cells in each subset present. Future work could include the generation as well as maintenance of memory T cell subsets for both CD4⁺ and CD8⁺ T cells directly into this model.

The current model incorporates IFN--induced apoptosis of Th1 and CD8⁺ T cells (both subsets) by activated macrophages and indicates that disease is always accompanied by a delayed Th1 and CTL response due to this activity. We also conclude that vigorous internalization of bacteria (macrophage infection rate) is imperative to infection control. Taken together, these two hypotheses provide a possible explanation of disease outcome, i.e., any mechanism that increases extracellular bacterial turnover beyond a critical point results in an enhanced infected and activated macrophage response. The augmented macrophage response feeds back and results in an excessive killing of Th1 and CTL cells that, in turn, further exacerbates infection. This cycle continues until bacterial load is high enough to overwhelm the system. That event is characterized by a decline in activated macrophage numbers and a simultaneous rise in Th1 and CD8⁺ T cell numbers to saturable levels. Evidently, extracellular bacterial turnover, macrophage activation, and T cell killing need to be tightly regulated to achieve control over infection.

The model, despite being updated from previous work, is still limited by several assumptions. Some suppositions of the earlier model (15) still hold for the current model, including whether bronchoalveolar lavage is a valid site for deriving experimental numbers for TB (for human data) and whether we model Ag presentation at the site of infection in the lungs instead of the lymph nodes. More importantly, although the model emulates disease progression in primate studies, parameter values include a hybrid of primate and mouse data. Results match well qualitatively with experimental outcomes, and we do observe quantitative differences in some cases. A key strength of the model, however, remains that parameter values can be easily updated when data are available while still providing important qualitative results.

In summary, the results from the updated and inclusive mathematical model provide the opportunity to address challenging and interesting questions regarding the immune response to Mtb. These results can guide vaccine development, provide data on basic immunologic mechanisms in the lung, and open up new avenues of study for experimentalists. In this context, the model can be used to test existing hypotheses as well as identify new factors for study in animal models and humans with tuberculosis.

	Acknowledgments

 
We are grateful to Dr. Vanja Lazarevic for providing data on CD8⁺ T cell function in the mouse. We thank Drs. John Chan and Simeone Marino for helpful discussions. We also thank Dr. Brian Murphy and Dongxiao Zhu for early efforts on this project.

	Disclosures

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
The authors have no financial conflict of interest.

	Appendix 1

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 
Model equations

In this section, we present the equations comprising the updated ordinary differential equations model of immune system-Mtb dynamics. The model simulates interactions between two bacterial subpopulations, eight cell populations, and five cytokines. Equations 7, 8, 9 and 10 are the new equations for T80, T8, TC, and TNF, respectively. Other equations are similar to those in the study by Wigginton and Kirschner (15 ), with some minor modifications where we included the affects of these new variables as well as updated biological information regarding IFN--induced apoptosis.

Macrophage dynamics. The equations describing rates of change for the macrophage subpopulations are given by Equations 1–3.

(1)

(2)

(3)

The rate of change of resting macrophages (Equation 1) includes a source term (sr_M) and a natural death term (–µ_MRM_R). This is reasonable, because even in the absence of infection, macrophages undergo constant turnover to maintain an equilibrium value, given by M_R = sr_M/µ_MR (negative control). In the course of infection, additional resting macrophages are recruited in a TNF-dependent fashion (33 ) at a rate of sr_4B, and this process is inhibited by IL-10 (88 ). We also account for the recruitment of macrophages due to TNF-independent mechanisms such as chemokines secreted primarily by activated and infected macrophages (33 ) at rates of _4A and w₂*_4A (0 < w₂ < 1), respectively.

Resting macrophages at the site of infection can become chronically infected at a maximum rate of k₂, which is dependent on the level of infection characterized by the extracellular bacterial load. Macrophages are activated at rate of k₃, which is dependent on two signals: the primary from IFN-, and the second either by bacteria or TNF (89 ). Note that because of the difference in measurement units, TNF is scaled by a factor . IFN--induced activation is inhibited by IL-4.

Infected macrophages (Equation 2) can be cleared by one of several different mechanisms. Given an average maximal intracellular bacterial carrying capacity of N, we assume that one-half of the infected macrophages burst when the intracellular bacterial load reaches NM_I. This mechanism has a maximal rate of k₁₇ and is described by a Hill process. Immune responses also contribute to infected macrophage killing by several mechanisms. Both CD8⁺ and CD4⁺ T cells can use the Fas-FasL apoptotic pathway to induce apoptosis in these cells at a maximum rate of k_14A. The half-saturation constant c₄ describes the effector-target ratio (T_total:M_I) at which this process is half-maximal. TNF can also induce apoptosis by binding to the 55-kDa TNF-receptor (90 ). This process is down-regulated by IL-10 and occurs at a rate of k_14B. Finally, CTL killing by CD8⁺ and CD4⁺ T cells happens at a rate of k₅₂. Specifically, CD4⁺ T cells have a limited contribution, and this is accounted for by scaling the CD4⁺ T cell numbers (0 < w₁ < 1). CD8⁺ T cell numbers are scaled by a term accounting for their indirect dependence on CD4⁺ T cells for effector capability (10 ).

Activated macrophages are generated from the term in Equation 1 and also undergo natural death at a rate proportional to their number (–µ_MAM_A). Activated macrophages can be deactivated (or lose activation status) by IL-10 (91 ) at a rate of k_4.

T cell dynamics. The equations for T cell dynamics are given by Equations 4–9.

(4)

(5)

(6)

(7)

(8)

(9)

Similar to resting macrophages, recruitment of T cells is both TNF-independent and TNF-dependent (33 ). The terms are similar, using different rates for the different T cell subsets (_1A, sr_1B for Th0 and T80 cells; _3A, sr_3B for Th1 and Th2 cells; and _3AC, sr_3BC for CD8⁺ T cells; respectively). We assume that CD4⁺ T cells can arrive at the site of infection either as Th0 (majority) or that a small fraction may arrive already differentiated into Th1 or Th2 cells (see Ref.15 for a complete discussion).

Upon arriving at the site of infection, Th0 cells (Equation 4) can proliferate further in response to signals released by activated macrophages at a rate ₂. Th0 cells can also differentiate into Th1 (Equation 5) and Th2 (Equation 6) cells. Th1 differentiation is controlled by IL-12 and IFN- and opposed by IL-4 and IL-10. Th2 differentiation is induced by IL-4 and inhibited by IFN-. Th0 cells undergo natural death at a rate of –µ_T0T₀). Th1 cells can be killed due to IFN--induced apoptosis in the presence of activated macrophages (37 38 39 ) at a rate of µ_T. Both Th1 and Th2 cells die naturally at rates µ_T1 and µ_T2, respectively.

As is the case for CD4⁺ T cells, we assume that CD8⁺ T cells can arrive at the site of infection either as T80 (majority) (Equation 7) or that a small fraction may arrive already differentiated into effector cells of either T8 (Equation 8) or TC (Equation 9) type. T80 cells are activated due to interaction with Th1 cells and cytokines and have a natural half-life.

CD8⁺ T cells also undergo IFN- induced apoptosis at a peak rate of µ_Tc and die at a rate of µ_Tc. Because the T8 cells (Equation 8) and Tc cells (Equation 9) are functional subsets of the CD8⁺ T cell population (see Introduction), the equations are identical for both. We introduce a parameter m that accounts for possible overlap between T8 and TC subsets. Although studies directly assessing cytotoxic capacity and IFN- production in the same cells are relatively rare, studies have indicated that perforin expression (or cytotoxic function) and IFN- expression can occur in the same cell (30 31 32 ). Thus, we allow for a small overlap (10%) here of cell types that perform both functions; hence the value of m is 60%. This assumption is studied further in the paragraph entitled Role of CD8⁺ T cells in Materials and Methods.

Cytokine dynamics. Equations 10–14 illustrate cytokine dynamics.

(10)

(11)

(12)

(13)

(14)

TNF (Equation 10) is produced primarily by infected macrophages (33 ) at a rate of ₃₀. Activated macrophages secrete TNF at a rate of ₃₁ in response to IFN- or bacteria, and this process is inhibited by IL-4. Other sources of TNF are Th1 cells (rate of ₃₂) and CD8⁺ T cells (rate of ₃₃) (92 ), and TNF has a given half-life.

IFN- (Equation 11) is produced by Th0, Th1, and CD8⁺ T cells in response to Ag presentation by activated macrophages (30 ) at rates of _5A and _5B, respectively. Production by Th0 and T80 cells is further enhanced by IL-12 and inhibited by IL-10. Other sources of IFN-, such as NK and NKT cells, are also believed to play a role in TB infection (24 93 94 ). Because these sources are not accounted for in the model, we include an extra source term (s_g) dependent on the extent of infection and the IL-12 level. Future work will include these cells to test the roles of NK and NKT cells in the dynamics of TB infection, both as IFN- producers and cytotoxic cells.

IL-12 (Equation 12) is produced by resting macrophages at a rate of ₂₃ in response to infection (95 ). Activated macrophages also produce IL-12, and this process is inhibited by IL-10 (95 ). Dendritic cells are the primary source of IL-12 upon Mtb infection (95 ) and are accounted for by an infection-dependent source term, s₁₂. Finally, there is a natural half-life for IL-12.

IL-10 (Equation 13) is produced mostly by activated macrophages (95 ), and this process is opposed by IFN- and IL-10 itself at a rate of ₇. Other sources such as Th1 cells, Th2 cells, and CD8⁺ T cells produce IL-10 at rates of ₁₆, ₁₇, and ₁₈, respectively.

IL-4 (Equation 14) is produced by Th0 cells at a rate of ₁₁, and Th2 cells at rate of ₁₂. IL-4 has a given half-life of µ_i4.

Bacterial dynamics. Equations 15 and 16 illustrate bacterial dynamics.

(15)

(16)

Intracellular bacteria (Equation 15) grow at a maximal rate of ₁₉ with logistic Hill kinetics accounting for a maximal carrying capacity of a macrophage. Extracellular bacteria (Equation 16) become intracellular when a macrophage becomes chronically infected at an assumed threshold of N/2 bacteria, and, hence, this represents a gain term for the intracellular bacteria. Bursting of macrophages (k₁₇) adds to the extracellular subpopulation. Intracellular bacteria are lost in various proportions due to different killing mechanisms. A corresponding gain in extracellular bacteria depends on the mechanism of killing. Whereas Fas-FasL-induced apoptosis (k_14A) releases all intracellular bacteria (N) (26 ), TNF-induced apoptosis (k_14B) eliminates 50% of the bacteria within the macrophage (90 96 ), and this is shown by the N_fraca multiplier in the BE equation. CTL activity (k₅₂) kills virtually all of the intracellular bacteria (N_fracc) due to granulysin action (26 ) and does not add to the BE population. Lastly, we assume that natural death of infected macrophages also releases all intracellular bacteria, and this assumption is modeled as a constant turnover of the bacteria (µ_IB_I) from intracellular to extracellular.

Extracellular bacteria grow at a maximum rate of ₂₀. They are taken up and killed by activated and resting macrophages at rates of k₁₅ and k₁₈, respectively.

Parameter estimation

Before simulations can be performed, parameters must be estimated from data or by mathematical means. Values for most model parameters are estimated from published experimental data or data generated by our group. Data from human studies and Mtb experiments are favored over mice and other mycobacterial species, respectively. We also use nonhuman primate data where available. Where no appropriate data are available for a given parameter, we conduct uncertainty analysis to obtain a range within orders of magnitude.

A detailed description of techniques used to evaluate model parameters, as well as a listing of parameters already estimated, can be found in work previously published by our group (15 ). All parameters newly estimated for the purpose of this work are listed in Table III and have been estimated using approaches similar to those described (15 ).

	Footnotes

 
The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

¹ This work was supported by National Institutes of Health Grants ROI HL62119 and ROI HL68526 (to D.E.K.) and AI37859 (to J.L.F.) and by a grant from the Ellison Medical Foundation (to J.L.F.).

² Address correspondence and reprint requests to Dr. Denise E. Kirschner, Department of Microbiology and Immunology, 6730 Medical Sciences Building II, University of Michigan, Ann Arbor, MI 48109-0620. E-mail address: kirschne{at}umich.edu

³ Abbreviations used in this paper: TB, tuberculosis; KO, knockout; Mtb, Mycobacterium tuberculosis.

Received for publication September 12, 2005. Accepted for publication December 2, 2005.

	References

Top Abstract Introduction Materials and Methods Results Discussion Disclosures Appendix 1 References

 

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