Conceived and designed the experiments: AB PJC. Performed the experiments: AB PJC. Analyzed the data: AB PJC. Contributed reagents/materials/analysis tools: AB PJC. Wrote the paper: AB PJC.
The authors have declared that no competing interests exist.
We present here a new 2D cellular automata model based on the concept of a multifunctional process that includes key factors such as the chemokine attraction of the cells; the role of innate immunity triggered by natural killers; the presence of neutrophils; apoptosis and necrosis of infected macrophages; the removal of dead cells by macrophages, which induces the production of foamy macrophages (FMs); the life cycle of the bacilli as a determinant for the evolution of infected macrophages; and the immune response.
The results obtained after the inclusion of two degrees of tolerance to the inflammatory response triggered by the infection shows that the model can cover a wide spectrum, ranging from highly-tolerant (i.e. mice) to poorly-tolerant hosts (i.e. mini-pigs or humans).
This model suggest that stopping bacillary growth at the onset of the infection might be difficult and the important role played by FMs in bacillary drainage in poorly-tolerant hosts together with apoptosis and innate lymphocytes. It also shows the poor ability of the cellular immunity to control the infection, provides a clear protective character to the granuloma, due its ability to attract a sufficient number of cells, and explains why an already infected host can be constantly reinfected.
The life cycle of the bacilli "in vitro" and its interaction with the alveolar macrophages, including how it interacts with the cytoplasm organelles and how these cells interact with the body as a whole by inducing the secretion of cytokines, is currently well-understood
The first intensive studies to evaluate the evolution of these lesions were performed by Kischner et al., who attempted to simulate the induction of solid and necrotic granulomas, corresponding to protective and deleterious responses respectively, in macaques infected with
The natural history of LTBI starts with inhalation of an infected aerosol, which allows the bacilli to reach the alveolar spaces and subsequently to be phagocytosed by the alveolar macrophages. The bacilli avoid the phagolysosome union
The presence of natural killers (NK)
In this scenario, approximately 10% of monocytes
The slow pace of bacillary growth results in a discrete pathological process at the beginning of the infection. Thus, in an experimental murine model, where infection is induced with a low-dose aerosol, infected lungs show a very limited and transient localised increase in the cellularity between the epithelia and the lamina propria rather than granulomatous lesions in the first three weeks post-infection despite the fact that the bacillary load increases up to 105 CFU
The bacillary life-cycle status
By using a cellular automata system, the aim of the current study is to bring all these concepts together in a rational manner by creating a model that can explain the dynamics of the onset of granuloma formation. This model is based on a murine experimental model as this is the "in vivo" model for which most information is available. Furthermore, the addition of data obtained from
Two criteria were followed to validate the model and fit it to the experimental data, namely progression of the bacillary load and granuloma size. The “in vivo” data used to validate the model were obtained from studies involving the low-dose (i.e. about 50 CFU) aerosol infection of immunocompetent (i.e. C57BL/6) and highly immunosuppressed mice, the latter of which lack specific lymphocytes (i.e. SCID mice). Both were infected with the virulent H37Rv strain of
The evolution of the viable bacilli in both scenarios (with or without adaptive immune response; see
Evolution of the infection without inducing an adaptative immune response in highly (HT) and poorly tolerant (PT) hosts according to the chemokine threshold above which a new cell can be attracted to a neighboring square (defined as 1000 arbitrary units (a.u.) and 650 a.u., respectively). A and B show the evolution of the bacillary load, and C and D the evolution of the different kind of macrophages. E and F show the evolution of natural killers (NK), neutrophils (PMN), and necrotic (NM) and apoptotic macrophages (APM).
Evolution of the infection, including the presence of an adaptive immune response, in highly (HT) and poorly tolerant (PT) hosts according to the chemokine threshold above which a new cell can be attracted to a neighboring square (defined as 1000 arbitrary units (a.u.) and 650 a.u., respectively). A and B show the evolution of the bacillary load, and C and D the evolution of the different kind of macrophages. E and F show the evolution of natural killers (NK), neutrophils (PMN), and necrotic (NM) and apoptotic macrophages (APM). Appearance of the immune response is marked with a dotted line.
To find the CT for a PT host, we assayed lower values, starting with a CT of 500 a.u. We did not obtain any difference between the predicted values with and without immune response at this level, a fact that does not fit with the current experimental and clinical data, therefore we gradually increased the CT value until we obtained a twofold reduction of the bacillary load with an immune response at CT = 650 a.u. (
Evolution of the infection was marked by an initial period of time with no bacillary growth, as the bacilli were in T
Control of the bacillary load depended on both the ability to necrotise macrophages and the ability to produce a sufficient number of activated macrophages (ACMs) to prevent the bacilli from growing intracellularly, either by killing them or leaving them in a non-replicating state (
The number of extracellular bacilli subsequently increased more quickly in the PT host (
This initial increase in NMs, PMNs and NK also induced a quicker increase in the concentration of foamy macrophages (FMs) in the PT host (
The entrance of specific T lymphocytes (Ts) was clearly related to the appearance of activated macrophages (ACMs) and increased the rate of bacillary killing in the HT host, whereas in the PT host it increased the presence of ACMs but did not affect that much the rate of bacillary destruction (
Progression of the granuloma size was the second parameter used to validate the current model.
Evolution of the cellular infiltration caused by viable macrophages in the four cases analyzed in terms of the host's tolerance and immunological status. Squares represent the whole lattice assayed, and show the evolution every week. Percentages show the ratio between the number of cells occupied by a viable macrophage divided by the total number of cells.
A more detailed view of the granuloma formation at the end of the evolution (i.e., 20,000 iterations, or 4 weeks post-infection) is given in
Characteristics of the granulomas taking into account the majority of the cells at week 4 post-infection in the four cases studied in terms of the tolerance and immune status. Squares represent the whole lattice assayed.
Remarkably, a high number of necrotized macrophages are also present in the lattice, with a large number of these being found outside the granuloma. A high accumulation of activated macrophages is clearly seen in the models with adaptive immunity, even outside the granuloma in the HT hosts. Furthermore, a high number of infected macrophages, which are non-activated and dispersed throughout the parenchyma, are found outside the granuloma in the models without adaptive immunity and even in HT hosts with adaptive immunity. The presence of resting macrophages (RMs) throughout the parenchyma in the PT hosts, which decreased in number once adaptive immunity appeared as they accumulated on the already existent granulomas, is also of importance. This finding is related to their ability to stimulate the presence of new cells with lower chemokine concentration.
Evolution of the chemokine concentration in the four cases analyzed in terms of the host's tolerance and immunological status. Squares represent the whole lattice assayed, and show the evolution every week.
Taken together, the above findings suggest that the individual production of chemokines is not sufficient for granuloma formation and that the random aggregation of cells with the capacity to excrete chemokines controls granuloma formation.
Previous experimental evidence (see
Effect of the availability time for specific T lymphocytes for HT and PT hosts (pictures A and B). Appearance of the change in the evolution of CFU counts is marked by a red dotted line; while the beginning of the usual immune response (10000 time-steps or iterations) is marked with a black hashed line.
This is followed by a period, at between 7000 and 10,000 iterations, that appears to result in some changes to the bacillary load, especially in the PT host, which is clearly more sensitive to the onset of the immune response as it react more quickly to the chemokine level. As the HT host needs higher chemokine concentrations (as shown in
Evolution of the bacillary load with respect to the physiological values of T
Remarkably, a chimera made by reducing the T
Our study of the ability of a single bacillus to generate an infection in both HT and PT hosts, including the induction of adaptive immunity, showed that the bacilli in our system had a high ability to generate an infection and that this ability was higher for a HT than for a PT host (93% and 87% respectively;
Importance of the initial bacillary load in the evolution of the infection. Pictures A and B show the evolution of 100 runs for HT and PT hosts with an immune response, respectively, inoculating with one bacillus in 100 naïve scenarios. Pictures C and D show the evolution of the total bacillary load when inoculated with different loads at one unique lattice.
The influence of the inoculum size was also studied and the HT host again found to be more sensitive to this factor than the PT host, which showed a similar bacillary load after 20,000 iterations assuming onset of the adaptive immunity at the same time point (10,000 iterations, i.e. 2 weeks) (
A re-infection process, which is a more similar scenario to a real-life situation whereby new infections usually arise in people living with the source of the infection (i.e. a patient with active TB who emits bacilli for two weeks before being diagnosed and then isolated and treated in a hospital, which means a hypothetical diagnostic delay of 15 days) was also considered. Thus, infecting every day for two weeks with 25 CFU (a total of 350 CFU) clearly resulted in a significant increase in the bacillary load (
A computational model that mimics the onset of
This scenario explains perfectly why a person with a specific cellular immunity can be reinfected by
This model also confirms the role of the innate immune response in controlling the infection, including both the presence of NK and an apoptosis mechanism, and highlights the role of FM drainage as a powerful mechanism for innate control of the infection in the lung, although this mechanism requires large alveolar spaces, which are only found in large mammals
Our study uses the same methodology as previous studies
Our model fits well with the best known animal model, which involves disease induction after a low-dose aerosol in mice. Published data clearly demonstrate that granulomas are rarely, if ever, seen before week 3
This simulation reproduces the initial evolution of the infection, including onset of the infection and of the adaptive immune response. Previous studies did not address this issue and focused in making predictions regarding the chronic phase (around 500 days post-infection). This can be considered to be a major drawback as this period is vital to understanding a key characteristic of
Our model also highlights the importance of the local milieu, in other words the chemokine factor that is needed to attract the specific lymphocytes to activate the infected macrophages. We have detected this problem in a very small ideal scenario (4 mm2) as the surface of an adult lung consists of up to 320,000 such scenarios (160 m2, around three-quarters of a tennis court)
Our model can also be used to study the whole lung instead of just a single lattice by considering one “naïve” lattice for each infective bacilli. The results suggest a significant role for the reinfection process, thereby supporting the “dynamic hypothesis” and enabling us to better understand the reality of scenarios with a high prevalence of active TB patients where there is a very high probability of constant exogenous reinfection. It is interesting to note that this is possible even in the presence of constantly available circulating specific T cells, which is the scenario found in LTBI patients, as can be seen with the recently developed range of diagnostic tools based on the detection of these cells in peripheral blood using the TIGRAS method.
At this point is important to highlight the limitations of our model. In the majority of cases we have only been able to make predictions up to four weeks post-infection as other factors, such as re-growth of the non-replicating bacilli inside the FM, as observed in the mouse model
Another limitation concerns the anatomic scenario. We have considered a “solid” organ, which is clearly not the case for the lungs with their alveolar spaces, alveolar wall, endothelial and other epithelial cells, including fibroblasts, which represent 30–40% of the total number of cells
This model also fails to take into account the role of the innate ability or the unspecifically activated macrophages to destroy new incoming bacilli from the very beginning, a factor that should be included to reduce the assumed 87% likelihood of a single bacillus initiating an infection. Indeed, it has been estimated that this value in humans is only around 30%
Furthermore, when recreating the “human model” as a PT host we have only assigned the higher reactivity to the presence of chemokines, which, of course, may not actually be the case. Our model therefore places significant emphasis on the NK and their ability to activate infected macrophages despite the likelihood that numerous other factors also play a part. Indeed, the properties of the macrophages themselves may differ from those found in mice and the activation percentages may also differ between the two species. We have only changed one factor despite the fact that this is highly likely to be a multifactorial process. However, we wanted to highlight how important this factor could be for controlling the infection and the fact that such control is clearly higher in humans than in mice as all infected mice die as a result of absolute infiltration of the lung, whereas, at most, only 40% of humans do so if active TB is triggered, which only occurs in 10% of cases. The differences found between the results obtained in the in silico model regarding the chemokine levels and their influence on infection control could be the explanation to explain this process.
Our representation of a generic chemokine and the “activation process” is necessarily an oversimplification of these highly complex processes as the addition of such complexity would make the model even less reliable. For this reason we have mainly focused on a relatively primitive process and tried to fit it to easily measureable parameters, such as granuloma size and bacillary counts in the murine experimental model.
On the basis of previous studies, we have attempted to develop a model to explain our current understanding of this disease process but which will nevertheless have to be modified in the future to take into account new experimental data. However, despite the current limitations of this model, we strongly believe that some basic elements, such as the impossibility of curtailing the initial growth of the bacilli, might help to structure current data regarding the infection process and to develop new tools and strategies to better understand and combat it.
Finally, our model also does not take into account the reinfection process resulting from the drainage of bacilli from infected lymph nodes, via the lymph ducts, to the right atrium and the pulmonary artery and from there back to the lung.
In conclusion, the data presented herein are an attempt to combine, in a limited scenario, the singularities of the cellularity and the infection process in a cellular automata model to simulate the infection process in mice and extrapolate it to a “human-like” model whilst also taking into account the life-cycle of the bacilli and the concept of “host tolerance”. Overall, this model helps to understand the mechanisms of
A two-dimensional 100×100 lattice of micro-compartments was constructed to mimic a granuloma. As the diameter of an alveolar macrophage is around 20 µm, each of these micro-compartments represents a square with dimensions 20×20 µm. A maximum of three live or dead cells can fit into each square, although only one living macrophage can be present at any one time (i.e. two living macrophages cannot be present in the same square;
Physical scenario of the cellular automata simulation system. A two-dimensional 100×100 lattice of micro-compartments has been built. As the diameter of an alveolar macrophage is around 20 µm, each of the micro-compartments in the lattice represents a square with dimensions 20×20 µm. A maximum of three live or dead cells can fit in each square, although only one living macrophage can be in a square at any one time (i.e. two living macrophages cannot be in the same square). The following pictures reproduce different phases in the evolution of the model. Picture
Time is one of the key dimensional parameters in any computational simulation. In this model, time is introduced by considering finite time-steps during which the rules are applied to all the cells in the grid to generate a totally new scenario. We decided to run a iteration (time-step) every two minutes of real time, which, according to Miller et al
Cell | Lifetime | Speed | ||
Time | Iterations | µm/minute | Iterations/compartment |
|
RM | 100 days | 72,000 | 1 | 10 |
IM | ||||
ICM | ||||
IRM | ||||
ISM | ||||
ACM | ||||
NM | N.A. | |||
APM | ||||
PMN | 3 hours | 90 | 10 | 1 |
NK | 3 days | 2160 | 10 | 1 |
Ts |
Macrophages = resting (RM); infected (MI); infected-consolidated (ICM); infected-at risk (IRM); infected-sentenced (ISM); activated (ACM); necrosed (NM); apoptosed (APM).
Neutrophils (PMN); Natural killers (NK).
Specific T lymphocytes (Ts).
N.A. = not applicable.
Iterations = Time-steps.
*number of iterations required to move the distance of one micro-compartment of the lattice.
Four groups of entities were considered: a generic chemokine, bacilli, macrophages and other cells (
Characterization of the macrophages according to the most advanced phase of the life cycle of the bacilli inside them. The bacillary life cycle evolution, as monitored using the optical density in a static liquid culture, is represented in the background. (Modified from Buchanan 1918
We decided to consider the macrophages as the only source of a hypothetical global chemokine and that the concentration of chemokines produced depended on the evolutive state of the macrophage (
Cell | Peak production | Continuous Production | ||
Transition to | Post bacterial | |||
Phagocytosis | Killing | |||
ICM | 100 | 100 | N.A. | 100 |
IRM | 500 | 500 | ||
ISM | 500 | 500 | ||
ACM | 0 | 0 | 100 | |
NM | 10,000 | N.A. | N.A. | N.A. |
Macrophages = infected-consolidated (ICM); infected-at risk (IRM); infected-sentenced (ISM); activated (ACM); necrosed (NM).
N.A. = not applicable.
We also assumed that all chemokines secreted diffuse throughout the network as assumed by others
The chemokine gradient attracts the cells towards the highest concentration, modifying their random movement accordingly, and induces the generation of a new cell in every square where the chemokine concentration is above a certain threshold (
In our model, we adapted the concept of host tolerance
At every time-step, the system checks the chemokine concentration in each micro-compartment. As indicated above, cells then move towards the highest concentration, and if this is above a determined
Cells | Immunity | |
Innate | Specific | |
RM | 90 | 99.74 |
PMN | 8 | 0.05 |
NK | 2 | 0.01 |
Ts | 0 | 0.2 |
RM = resting macrophages; PMN = neutrophils; NK = Natural killers; Ts = specific T lymphocytes.
According to observations in different experimental models, we have assumed that only intracellular bacilli residing in a non-activated macrophage are able to grow
We quantified the time that the bacilli remain in the extracellular milieu and considered that this should determine the length of their
Representation of the
Transformation of the macrophage status according to given probabilities, taking into account the number of cells (C) and bacilli (nB
When a
We also considered that the ability to phagocytose and kill
As stated above, the established rule was that both live and dead cells occupied the space until they moved or were phagocytosed, respectively. Each compartment could therefore contain three cells, either alive or dead. The only exclusion criterion was that a compartment could only hold one living macrophage (i.e. two living macrophages could not fit in a single compartment). Phagocytosis of dead cells took place once a cell entered the square where the dead cells were located or by being in one of the four squares that had a side in common.
Macrophages were classified according to the life-cycle status of the interior bacillus with the most active metabolism. There was no constitutive entrance of macrophages. Resting macrophages (
Once a macrophage was necrosed (
Once an NK cells or specific lymphocyte (
Although induction of adaptive immunity is thought to be triggered once a specific concentration of
If a specific lymphocyte (
Dead cells occupied space (as seen above) until phagocytosed by a macrophage. Each dead neutrophil represented one
We have not modified the speed capacity of the macrophages according to their status as others made before
Evolution of the drainage of Foamy Macrophages (FM) in poorly tolerant (PT) hosts, according their immunity status
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Photomicrographs of infected lungs in experimental models induced in mice (A to C) and mini-pigs (D to F) at weeks 3 and 5 respectively. Cuts were stained with haematoxylin-eosin (A to E) or visualized with a stereoscopic microscope, in the case of mini-pigs (F).
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Macrophage infiltration and chemokine concentration in the space at week 4 post-infection in the case of a poorly tolerant host with an immune response. A: macrophage infiltration; B: chemokine production; C: combined image.
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Evolution of the total amount of chemokines with time in all the cases studied.
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Influence of the apoptosis ratio on the bacillary concentration. The usual probability is compared with a 10-fold increase in the possibility of apoptosis, including the evolution of the numbers of necrotic and apoptotic macrophages in both cases (small squares).
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Evolution of dendritic cell (DC) formation in all the cases studied.
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Distribution of Tlag for the four cases studied. Data are presented as boxes showing the 25th and 75th percentiles, and the 10th and 90th percentiles with error bars. The median is shown as a horizontal line inside the boxes. Differences between groups were determined using an all pairwise multiple comparison procedure (Dunn's Method), and are marked with * when significant.
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The influence of Tdupli and extracellular growth on the evolution of the total bacillary load, showing the influence of different Tdupli values.
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Recreation of a bacillary "chimera" with Tdupli = 20 minutes.
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Role of reinfection in the evolution of the infection. Role of reinfection in the evolution of the infection. Picture A shows the standard inoculation in a PT host with immunity compared with the same host when constantly reinfected with 25 CFUs until t = 10,000 in the same lattice. Picture B shows the evolution of a whole lung of a person reinfected just 10 times with one bacillus in 10 different naïve lattices. The bacillary load is 5550.
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Presence of an hypothetical efficacious humoral response. Induction of a humoral response allowing the bacillus to be killed by any macrophage that phagocytes the opsonized bacillus, considering different percentages of activity (shown in the legend insert).
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Dissemination of a single chemokine peak through space at different time points.
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Simulation in a Highly tolerant host. Left window shows the evolution of the chemokine concentration; right window shows the evolution of the granuloma formation were entities are: RM (resting macrophage) in pink; ICM, IRM, ISM (infected consolidated, risk and sentenced macrophages) in green; NM (necrotic macrophages) in black; FM (foamy macrophages) in yellow; and ACM (activated macrophages) in red. Timing appears at the bottom right in steps.
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Simulation in a Highly tolerant host. Left window shows the evolution of the chemokine concentration; right window shows the evolution of the granuloma formation were entities are: RM (resting macrophage) in pink; ICM, IRM, ISM (infected consolidated, risk and sentenced macrophages) in green; NM (necrotic macrophages) in black; FM (foamy macrophages) in yellow; and ACM (activated macrophages) in red. Timing appears at the bottom right in steps.
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Simulation in a Poorly tolerant host showing the evolution of the granuloma formation were entities are: RM (resting macrophage) in blue; ICM, IRM, ISM (infected consolidated, risk and sentenced macrophages) in green; NM (necrotic macrophages) in black; FM (foamy macrophages) in yellow; ACM (activated macrophages) in red; and Ts (specific lymphocytes) in cerulean blue. Timing appears at the bottom right in steps.
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Simulation in a Poorly tolerant host showing the evolution of the granuloma formation were entities are: RM. ICM, IRM, ISM, ACM (resting, infected consolidated, risk and sentenced and activated macrophages) in green; NM (necrotic macrophages) in black; FM (foamy macrophages) in yellow; and Bextra (extracellular bacilli) in red. Timing appears at the bottom right in steps.
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To the students of our groups that constantly challenge us trying to better understand our hypothesis.