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Proc Natl Acad Sci U S A. 2009 Jul 7; 106(27): 11246–11251.
Published online 2009 Jun 22. doi:  10.1073/pnas.0904846106
PMCID: PMC2708732

Modeling the immune rheostat of macrophages in the lung in response to infection


In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the highly regulated nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters; these cells are typically activated by IFN-γ. CAM are far more effective than AAM in clearing the microbial load, producing proinflammatory cytokines and antimicrobial defense mechanisms necessary to mount an adequate immune response. Here, we are concerned with determining the first time when the population of CAM becomes more dominant than the population of AAM. This proposed “switching time” is explored in the context of Mycobacterium tuberculosis (MTb) infection. We have developed a mathematical model that describes the interactions among cells, bacteria, and cytokines involved in the activation of both AAM and CAM. The model, based on a system of differential equations, represents a useful tool to analyze strategies for reducing the switching time, and to generate hypotheses for experimental testing.

Keywords: alternatively activated macrophages, lung innate immunity, mycobacteria tuberculosis

The lungs encounter frequent challenges from inhaled particulates and microbes. Although this organ must effectively combat these invasions, it must also protect its delicate composition to ensure proper gas exchange. As a result, the lung environment is specialized to recognize and eliminate most invaders without causing excessive inflammation. However, this highly regulated inflammatory strategy can be detrimental to the host when a prompt, strong inflammatory response is needed to effectively eradicate pathogens. This limitation has led to the characterization of the lung as an immunosuppressive organ for respiratory pathogens (1).

Macrophages play a large role in the innate immune response of the lung. In general, macrophages can differentiate into subsets that exhibit distinct biological features in terms of receptor expression type, oxidative and nonoxidative antimicrobial defenses, cytokine production and antigen presentation (2, 3). For instance, classically activated macrophages (CAM) are the class of macrophages activated by IFN-γ and TNF-α, and they have been extensively studied in response to bacterial infection. Martinez and colleagues also refer to these as M1 macrophages, characterizing them as having elevated expression of MHC-II, CD80, and CD86 costimulatory molecules and promoting TH1 differentiation and IFN-γ production by T cells via the production of IL-12 (4). A different, more recently studied class of macrophages, is known as alternatively activated macrophages (AAM) (2, 58). Also referred to as M2a macrophages, these macrophages have a phenotype resembling macrophages activated by Interleukin-4 (IL-4) or IL-13 and are characterized by the up-regulation of scavenger receptors and the mannose receptor. Functionally, AAM facilitate tissue repair, stimulate cell growth, and produce both pro- and anti-inflammatory cytokines to generate a highly regulated immune response upon stimulation with a microbe (4). CAM are far more effective than AAM in killing intracellular pathogens although they do not take in bacteria as profusely as AAM. Alveolar macrophages, which are the resident macrophage population in the lung, have been classified as alternatively activated due to the receptor types they express and their balanced, regulated immune response (9). Hence, AAM are the dominant macrophage type in healthy lung tissue.

Because AAM have been classified as noninflammatory macrophages, they could be one important cause for the delay in the lung's protective immune response as reported in the literature. Consequently, one can ask whether this delayed immune response is related to a delayed entrance of CAM in the context of primary Mycobacterium tuberculosis (MTb) infection. MTb is transmitted by the airborne route and is a prototypic intracellular pathogen of macrophages. Much has been learned regarding the mechanisms for bacterial entry into these cells and the evasion strategies that enable its intracellular growth (10). Although over one-third of the world's population is infected with MTb, only 5–10% actually develops clinical symptoms of tuberculosis. For the others, the bacteria are merely contained, isolated and quarantined by other macrophages and T Cells in structures known as granulomas (11, 12).

During the very early stages of an MTb infection in the lung, AAM are the first macrophage type to encounter the pathogen. The role of AAM in tuberculosis infection is increasingly recognized (1315). Although CAM can reduce the bacterial load more effectively than AAM, there appears to be a delay before CAM become a governing force in the response, which may account for the early relatively unchecked bacterial growth observed in animal models (16, 17). Because the environment in the lung favors alternative activation of macrophages, it takes time for the cytokine milieu to change sufficiently enough for classical activation to occur, making the reason for the delay in CAM dominance most likely due to an initial lack of IFN-γ and TNF-α activation/function. We refer to this time delay as the “switching time,” i.e., the time when CAM begin to take over the macrophage population, and it could play an important role in disease progression and outcome in the lung. An earlier switching time may imply a more effective defense against the disease. In the absence of direct experimental measurements of this proposed switching time, the present article develops a mathematical model based on a system of nonlinear differential equations, which are able to estimate this time. The essential components in the model are the densities of AAM, infected AAM, CAM, dendritic cells, T cells, MTb, and the cytokines: IL-10, IL-12, IFN-γ, and TNF-α.

An earlier mathematical model of the human immune response to MTb in the lung based on 2 compartments (lung and lymph node) was developed by Marino and Kirschner (18). The present article builds on some of this work and on other models of tuberculosis (1921). However, these former models of tuberculosis infection do not specifically consider AAM and instead focus on the paradigm involving only macrophage populations (resting, activated, and infected) that are activated/primed by IFN-γ/TNF-α (i.e., CAM) Although it is clear that during the course of an MTb infection CAM are involved, the present work focuses on the fact that AAM are the first to encounter and respond to MTb. The aim is to investigate the different roles played by AAM versus CAM in the early stages of infection, and to identify a switching time; i.e., when CAM become more dominant than AAM. Although this work is in the context of MTb, the findings presented have potential relevance to all airborne pathogens, with the various switching times dependent on multiple factors specific to the pathogen of interest, such as host adaptiveness.

Results and Discussion

When MTb is inhaled into the airway, the AAM form the first line of cellular defense. AAM are not capable of effective elimination of the bacterium after phagocytosis. They become easily infected, allowing the bacterium an ideal intracellular environment in which to grow. Dendritic cells are recruited to the lung upon a cue from chemokines produced by infected AAM (2224), then travel to the lymph nodes in response to IL-12 and prime T cells to migrate from the lymph node into the lung (25, 26). Under signaling from IL-12 and major histocompatibility complex (MHC) molecules, T cells produce the cytokine IFN-γ, which, in conjunction with TNF-α, can then activate undifferentiated macrophages in the lung to become CAM as opposed to AAM. In addition, AAM and infected AAM can become activated to exhibit microbicidal properties.

This article develops a model based on a system of ordinary differential equations describing the interactions between cells and molecules during the early stages of an infection with tuberculosis. Fig. 1 is a pictorial representation of the descriptions given below for each equation. The model includes the following 11 variables: I10, I12, Ig, and Ia, concentrations of the cytokines IL-10, IL-12, IFN-γ, and TNF-α, respectively; A, density of alternatively activated macrophages; Ai, density of infected alternatively activated macrophages; C, density of classically activated macrophages; Be, density of extracellular bacteria; Bi, density of intracellular bacteria; D, density of dendritic cells; and TC, density of T cells (combination of CD4, CD8) The production and degradation of each species will be described by a differential equation, with parameter values that are known or estimated from the experimental literature or from the previously mentioned tuberculosis models. The parameter values, with references, are given in Table S1.

Fig. 1.
Diagram of interactions between various cell types and cytokines considered in the model equations, given by Eqs. 111 in the text. Explanations of the interactions displayed here can be found in the text descriptions of the equations.

Interleukin-10 (I10).

I10 is produced by Ai (5, 27) and D (2831). I10 inhibits its own production (to a lesser degree than it inhibits other processes) (32). A decay rate for I10 is also included so that:

equation image

Interleukin-12 (I12).

I12 is produced by Ai (27) and this production is assumed to increase as the number of Bi increases. In addition, I12 is produced by C, and Ig up-regulates this production. I12 is also produced by D (25, 30), and Ia up-regulates this production (33). I10 inhibits all 3 production sources of I12 (28, 32). With the inclusion of a decay term, the equation for I12 is:

equation image

IFN-γ (Ig).

Ig is produced by T cells upon cue from I12 and MHC displayed on the membrane of C. A inhibits production of Ig by T cells (7). Including an Ig decay term gives the following:

equation image

Tumor Necrosis Factor-α (Ia).

Ia is produced by Ai (27, 34, 35) and this production is assumed to increase as the number of Bi increases. In addition, Ia is produced by C and I10 inhibits the production of Ia by both Ai and C (32, 36). With a decay term, the Ia equation becomes:

equation image

Extracellular Bacteria (Be).

When an Ai cell bursts due to Bi growth, the Be population is increased, at least for a brief time, before being taken up by other macrophages. Similarly, when an Ai dies (via apoptosis or necrosis), it is assumed that only a small percentage of Bi are released and the Be population is also increased in this way (37, 38). Extracellular bacteria become intracellular bacteria when A phagocytose Be (13, 35). It is assumed that when C phagocytose bacteria, they effectively kill the bacteria, and when D phagocytose bacteria, they either effectively kill the bacteria or remove the bacteria from the lung upon migration to the lymph node. Thus, Be that are phagocytosed by C or D are effectively eliminated and do not become a part of the Bi population that we track. A small decay term for Be is added, but it can be neglected because Be does not remain free/unbound for very long.

equation image

Intracellular bacteria (Bi).

Bi are either extracellular bacteria that were directly phagocytosed by A, becoming intracellular bacteria (13, 35) or the result of bacterial growth of Bi in Ai. It is assumed that Bi grow in Ai according to a quadratic logistic growth (12, 21, 27, 35). In addition, through exposure to Ig and Ia, Ai can become activated to inhibit the growth of Bi (39). Ai have a limited carrying capacity for bacteria, after which they burst, thereby releasing all their intracellular bacterial load into the extracellular environment. As Ai die (via apoptosis or necrosis), it is assumed that most of their intracellular bacterial load is eliminated and only a small percentage is released into the extracellular environment (37, 38). As was the case with Be, a small decay rate of intracellular bacteria is included but can be neglected.

equation image

where β = β(Ig,Ia)

equation image

Alternatively Activated Macrophages (A).

This population originates from a constant source of newly immigrated macrophages (A0) coming from the bloodstream into the airspace before conversion into a particular macrophage phenotype. A0 transform into the alternatively activated phenotype as they enter the alveolar space due to locally produced, microenvironmental molecules, such as surfactant proteins (40). A0 can also differentiate into C in the presence of Ig and Ia, a process that is inhibited by I10. If not yet infected, it is assumed that A can also become (classically) activated by Ig and Ia, thereby leaving the A population and becoming a part of the C population (see Eq. 9 for C dynamics) (41, 42). It is assumed that the A population becomes infected immediately after phagocytosis of bacteria, thus subtracting from the A population and adding to the Ai population (13, 14, 35). A decay rate for A is included as well, giving the following equation:

equation image

where ε = ε(Ig, Ia, I10)

equation image

Infected Alternatively Activated Macrophages (Ai).

The Ai population increases when members of the A population phagocytose bacteria. The Ai population allows bacteria to grow (uninhibited) inside them, but after exceeding their carrying capacity for the bacteria, they burst and release their intracellular bacteria into the extracellular environment (14, 35). In addition, an Ai can die via apoptosis or necrosis (37), and this death is accounted for with the inclusion of a decay rate, giving:

equation image

Classically Activated Macrophages (C).

The C population originates from the same constant source of undifferentiated macrophages (A0) from which A come; however, in order for the macrophages to differentiate into C, a dual signal from Ig and Ia is necessary. Macrophages from the A population can also become (classically) activated in this way, adding to the C population (41, 42). This process is inhibited by I10 (6, 32). Including a decay rate, the C equation becomes:

equation image

where ε is given by Eq. 7.2.

Dendritic Cells (D).

This population originates from a constant source of dendritic cells (D0) (located in the lymph node and interstitial space), which are initially recruited to the lung by chemokines produced from Ai (2224). The recruitment of dendritic cells to the lung is inhibited by A (33, 43). The rate coefficient μD represents both the decay of dendritic cells and their migration rate from the lung to the lymph node (33); the model does not distinguish between populations of D in the lung and lymph node. Instead, μD is necessarily related to the coefficient k6, which controls the effects of D in the lymph node with respect to differentiating T0 into TC and enabling them (with the help of I12) to migrate into the lung. These effects appear in Eq. 11 for TC. As such, μD is also indirectly related to k5, the rate at which D are initially recruited to the lung:

equation image

T Cells (TC).

T cells originate from a constant source of undifferentiated T cells (T0) (a combination of CD4 and CD8 T cells) that are recruited and activated by a portion of the D population (25, 26). I12 is necessary for the migration of dendritic cells from the lung to the lymph node and for recruitment of TC to the lung from the lymph node (26). The first term below in Eq. 11 captures both these processes, with I10 (29, 28, 32) and A (33, 43) inhibiting them. Proliferation of TC is up-regulated by C (44) and inhibited by A (7). With the inclusion of a decay rate for TC, the equation is:

equation image

Baseline Simulation Results.

Using the initial conditions listed in Methods, the model outcome after 100 days, in terms of bacterial load, shows that both extra- and intracellular bacteria populations are not extinct yet are not growing out of control. This outcome is interpreted as a latent infection.

Fig. 2A shows that the density of Ai is increasing in the first few days, after which it drops, and is surpassed by the gradually increasing density of C at day 50, the “switching time.” (Fig. 2B shows the bacterial loads for the first 100 days.) The AAM not only ineffectively deal with the bacteria, but also prevent early recruitment of necessary effector cells, positioning their bacterial opponent at an unfair advantage. This immune battlefield may also negatively influence vaccine strategies in the lung microenvironment. Hence, if the switching time could be altered to occur earlier in the response, then, theoretically, tuberculosis therapies along with a more robust immune system may clear the disease more effectively, because a reduced switching time may imply reduced peak bacterial loads. The model can be used to develop hypotheses on how to shorten the switching time.

Fig. 2.
Baseline simulation results using parameter values given in Table S1. (A) Populations of infected alternatively activated macrophages (Ai) and classically activated macrophages (C) over 100 days revealing a switching time of 50 days when C begins to dominate ...

Validation and Sensitivity Analysis.

As an initial validation of the model, knockout simulations were conducted in which either IFN-γ or TNF-α was eliminated from the system, resulting in unrestrained bacterial growth, a consequence seen in the experimental literature (4549). In addition, patients suffering with AIDS are at an increased risk of developing active tuberculosis, due in part to a decrease in CD4 T Cells brought about by the disease (5052). As another model validation, we increased the decay rate (μT) of T Cells in the model to mimic this decrease, and an active tuberculosis scenario ensues, in which bacterial levels remain highly elevated.

In addition, sensitivity analysis was performed using the methods outlined in ref. 53, to determine those parameters that play a major role in affecting the switching time and related bacterial loads (see SI Text). Sensitivity analysis showed that out of the 12 parameters that we consider a priori to be involved in altering the switching time the parameters λ, k10, k17 were all significant in terms of switching time, peak bacterial loads, and residual bacterial loads and all had negative PRCC values in each case (see Table S2, Table S3, Table S4, and Table S5 and Fig. S1). Thus, increasing these parameters resulted in decreases in switching time, peak bacterial load, and residual bacterial load. The parameters k10 and λ are involved in the production of TNF-α and IL-12 by infected AAM (Ai) and k17 is the rate at which noninfected AAM (A) are sufficiently activated by TNF-α and IFN-γ to become CAM. These results imply that the early signaling from Ai is important in the development of protective immunity.

Generally speaking, reducing the switching time correlates with lower peak and residual bacterial loads. However, with respect to the parameter k16, which governs the strength of infected AAM (Ai) to inhibit the growth of their intracellular bacteria load (when stimulated by TNF-α and IFN-γ), an increase in k16 results in a decrease in peak and residual bacterial loads but an increase in the switching time (see Table S3, Table S4, and Table S5). Thus, greater inhibition of bacterial growth leads to reduced bacterial loads but an increase in the switching time, meaning that the presence of CAM in the lung is delayed. This is because inhibition of bacterial growth also reduces the population of infected AAM, which, in the model, is responsible for starting the signaling cascade, which recruits dendritic cells, which in turn recruit T cells, and so forth. Thus, a reduced Ai population reduces the strength of that signal and thus delays the entrance of CAM, lengthening the switching time. Hence, therapeutic strategies should reduce bacterial numbers but not reduce the signaling to downstream mediators. SI Text provide more detailed information regarding the sensitivity analysis.

IFN-γ Therapy Simulations.

The use of IFN-γ as a therapeutic agent to combat tuberculosis infections has been studied extensively and is considered to have greater potential compared with other cytokine therapies (54). In our model, the delay in the molecular switch from an AAM to CAM dominant environment is partly associated with a delay in optimal IFN-γ production at the site of infection. We use our model to determine how early introduction of IFN-γ may act as a therapeutic agent to shorten the switching time and lessen the bacterial loads. Two different IFN-γ treatment protocols were simulated, the details of which are described in Methods. Fig. 3 shows the simulation results of each protocol, both of which shorten the switching time and lessen peak bacterial loads and lower the residual bacterial loads at 100 days (compare with Fig. 2). These data support the idea that enhancing a TH1 immune response earlier in the lung and thereby shortening the switching time with concomitant reduction in bacterial load will reduce the number of residual bacteria following a primary TB infection. It is important to point out that the bacteria are not eradicated at 100 days. However, it is possible that by decreasing the residual pool of bacteria entering the latent phase of infection, the duration of treatment of latent infection, the likelihood of reactivation and the latent pool of resistant bacteria can be reduced. Our data also imply that IFN-γ alone is not sufficient to mediate a sterilizing immune response for tuberculosis. In agreement with this finding, clinical trials with IFN-g therapy, to date, have not proven to be highly efficacious, especially in the long term (54).

Fig. 3.
Simulated experiments using IFN-γ (Ig) therapy to decrease the switching time. (A) A constant dose of Ig is administered from Day 7 to Day 14 of the simulation to raise the concentration of Ig to 100 times that of the initial value. The switching ...


Model Assumptions.

The time course of the infection is marked in days, and units of cell populations are in terms of cells per milliliter. It is assumed that under normal, healthy conditions there are 1 × 106 alveolar macrophages per milliliter of extracellular lining fluid (ELF), which lines the alveolus and in which macrophages are bathed (refs. 18, 21, 55 and L.S. Schlesinger and M. Wewers, personal communication). In addition, it is assumed that an initial infection starts with very few total bacteria, say 5.0 Be. This initial bacterial population is quickly phagocytosed by alveolar macrophages and it is assumed that the bacteria grow uninhibited for 11 days. Assuming exponential growth and a doubling time of 20 h, after 11 days, there would be ≈47,000 total bacteria in the lung. It is assumed that all of these bacteria are intracellular and that on average each infected macrophage contains 25 bacteria. Thus, at the end of 11 days of unobserved bacterial growth there are ≈940 infected macrophages, assuming a total ELF of 1,000 mL (ref. 55, L.S. Schlesinger and M. Wewers, personal communication). This then implies that at the start of our simulation there is ≈1 Ai/mL and, hence, 25 Bi/mL. In addition, we estimated the amounts of cytokine production 11 days after infection from (L. S. Schlesinger, personal communication). Thus, the initial conditions of the simulations at “Day 0” (i.e., 11 days after infection) are

equation image

Simulation Methods.

All simulations were carried out with XPPAUT, courtesy of Bard Ermentrout of the University of Pittsburgh (available at www.math.pitt.edu/∼bard/xpp/xhtml) numerically integrated using Quality Step Runge-Kutta method with a step size of 0.01, over a period of 100 days. MATLAB (version R2008a Mathworks) was used to plot the data to generate the simulation figures included in this article. The numerical code can be used to determine ways by which to modify the switching time by adjusting the values of appropriate, experimentally feasible parameters.

IFN-γ Protocols.

Regarding IFN-γ treatment administration, whereas literature supports the use of IFN-γ as a treatment (54, 56), the direct comparison of our treatment with that in the literature would require modeling the pharmacokinetics/dynamics of the drug, which is beyond the scope of the article. Moreover, many of the studies included anti-tuberculosis treatment in addition to IFN-γ therapy, further hindering a direct comparison. As a preliminary exploration of the effect of IFN-γ on the switching time and bacterial loads, we simulated 2 different treatment schedules one of which is loosely based on a study that used aerosolized IFN-γ therapy. As a first exploration, Ig concentration in the model was simply increased to 100 times the initial amount from Day 7 through Day 14. This was accomplished via a constant source. In a second simulation, single injections of Ig treatment (at 100 pg of each) were given 3 times a week over a 33 day period starting on Day 7 (57). Future work will address the particulars mentioned above regarding IFN-γ drug properties and employ control algorithms to determine optimal dosing regimens.

Supplementary Material

Supporting Information:


We thank Dr. Mark Wewers for his helpful insights. This work was supported by National Science Foundation Agreements 0112050 (to A.F.) and 0635561 (to J.D.) and National Institutes of Health Grant AI059639 (to L.S.S.).


The authors declare no conflict of interest.

This article contains supporting information online at www.pnas.org/cgi/content/full/0904846106/DCSupplemental.


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