Front Microbiol. 2015 May 28;6:503. doi: 10.3389/fmicb.2015.00503.

Deciphering chemokine properties by a hybrid agent-based model of Aspergillus fumigatus infection in human alveoli

Johannes Pollmächer1,2 and Marc Thilo Figge1,2

1Applied Systems Biology, Leibniz-Institute for Natural Product Research and Infection Biology – Hans Knöll Institute, Jena, Germany

2Faculty of Biology and Pharmacy, Friedrich Schiller University Jena, Jena, Germany

 

Abstract

The ubiquitous airborne fungal pathogen Aspergillus fumigatus is inhaled by humans every day. In the lung, it is able to quickly adapt to the humid environment and, if not removed within a time frame of 4-8 hours, the pathogen may cause damage by germination and invasive growth. Applying a to-scale agent-based model of human alveoli to simulate early A. fumigatus infection under physiological conditions, we recently demonstrated that alveolar macrophages require chemotactic cues to accomplish the task of pathogen detection within the aforementioned time frame. The objective of this study is to specify our general prediction on the as yet unidentified chemokine by a quantitative analysis of its expected properties, such as the diffusion coefficient and the rates of secretion and degradation. To this end, the rule-based implementation of chemokine diffusion in the initial agent-based model is revised by numerically solving the spatio-temporal reaction-diffusion equation in the complex structure of the alveolus. In this hybrid agent-based model, alveolar macrophages are represented as migrating agents that are coupled to the interactive layer of diffusing molecule concentrations by the kinetics of chemokine receptor binding, internalization and re-expression. Performing simulations for more than a million virtual infection scenarios, we find that the ratio of secretion rate to the diffusion coefficient is the main indicator for the success of pathogen detection. Moreover, a subdivision of the parameter space into regimes of successful and unsuccessful parameter combination by this ratio is specific for values of the migration speed and the directional persistence time of alveolar macrophages, but depends only weakly on chemokine degradation rates.

PMID: 26074897

 

Supplement

Every day humans inhale an extensive amount of foreign substances and particles. The respiratory tract is able to remove most of them by a variety of filter mechanisms. Particles with a diameter below five micrometer are small enough to evade the lungs’ filter activity and to pass into lung alveoli, where oxygen diffuses into the bloodstream and carbondioxide is delivered back to the expiratory volume. Conidia of the airborne human-pathogenic fungus Aspergillus fumigatus are 2-3 µm in diameter and thus among the type of invading particles. This fungus quickly adapts to the humid and nutrient-rich conditions in the human lung. After 4-8 hours in the lung A. fumigatus germinates and is in the position to invade into the surrounding tissue to allow for nutrient acquisition and for further dissemination into the bloodstream.

The immune system of healthy individuals manages the time-limited task of pathogen detection and removal on a daily basis. Individuals with an altered or compromised immune system may encounter severe infections from A. fumigatus as this fungus has the ability to exploit weaknesses in their respective hosts. Invasive aspergillosis is the most severe systemic infection associated with A. fumigatus and leads to extremely high mortality rates (30-95%).

Alveolar macrophages (AM), also called dust-macrophages, are the predominant immune cells in alveoli and are primarily dedicated to clear the lower respiratory tract, i.e. lung alveoli, from all kinds of inhaled particles and microbes in order to maintain optimal gas-exchange. AM actively migrate on the inner surface of alveoli, which is a tissue composed of type I and type II alveolar epithelial cells. Studies with relation to speed values of alveolar macrophages showed strong condition-dependent variations up to 8 µm/min.

We studied the early immune response to conidia of A. fumigatus in a typical human alveolus performing agent-based computer simulations as shown in Fig. 1A. This method represented each conidium of A. fumigatus and each AM as a single virtual object in the computer. From literature data we were able to extract the spatial dimensions of all relevant cell types as well as the alveolus itself and created a virtual to-scale equivalent of this specific biological system. From daily A. fumigatus dosages we found that most of the 480 million alveoli are not associated with any conidium. Thus, the most interesting case for the system under consideration was to study the situation with one conidium in a typical alveolus. From an experimental point of view such a wet-lab study would not be conceivable as single conidia would induce immune responses that may be too weak to be detected with nowadays methods. Therefore computational approaches are highly valuable to simulate immune responses under physiological conditions.

 

Figure_1

Figure 1: Schematic overview of the alveolar environment implemented in the agent-based model. (A) Snapshot of the three-quarter alveolus including alveolar epithelial cells (AEC) of type I (yellow) and type II (blue), the pores of Kohn (black), alveolar macrophages (green) and an A. fumigatus conidium (red). (B) Overlay of cells with the distribution of chemokines (indicated by white isolines with thicker lines depicting higher concentration values) secreted by a type I AEC.

 

In a first study we analysed the time it takes for alveolar macrophages to establish a first physical contact with the conidium, which is a prerequisite for detection and elimination. This time period is called first-passage-time (fpt) and should ideally be well-below 6 h for fast AM detection due to quick germination and invasion of A. fumigatus. By variation of the speed and migration mode (random walk or chemotaxis) of alveolar macrophages as well as the underlying respiration condition of the individual (resting condition, heavy exercise, static condition) we were in the position to predict the requirements for successful elimination of conidia by alveolar macrophages. The random walk migration mode was ruled out as the fraction of fpt above six hours was generally above 15%, even for a relatively high speed value of 10 µm/min. In the case of macrophage chemotaxis in the direction of the conidium, speed values of at least 4 µm/min lead to a fraction of fpt above six hours below 5% (see Figure 2).

 

Figure_2Figure 2: First-passage-time distributions for the migration modes (A) random walk and (B) chemotaxis of alveolar macrophages at a speed of 4 µm/min.

 

On the basis of these findings we refined our model to explicitly account for the diffusion of a chemokine responsible for chemoattraction of alveolar macrophages. We included chemokine secretion by the alveolar epithelial cell that was in contact with the conidium at the start of a simulation (see Figure 1B). In order to determine the chemokine distribution in space over time including the interaction with chemokine receptors on AM we numerically solved the reaction-diffusion equation on the curved surface of the alveolus. Thus the agent-based model of our first study was transformed into a hybrid agent-based model as we extended the agent layer that represented individual cells by the scale of molecules which were modeled by concentration values on a triangular grid. From our computer simulations we were able to predict potential regimes of chemokine parameters like diffusion coefficient, degradation rate and secretion rate as well as the speed of macrophages in order to successfully find the pathogen before the onset of invasive growth. Our results suggest an important role for the ratio of secretion rate to the diffusion coefficient and a minor role for the degradation rate (see Figure 3). Higher macrophage speeds generally increased the regime of successful parameter combinations. Interestingly we found that even for relatively low speeds of 2 µm/min alveolar macrophages were able to find the conidium before germination started.

 

 Figure_3Figure 3: Potential parameter regimes of the alveolar macrophage chemoattractant conducted for the macrophage speeds vAM 2, 4 and 6 µm/min. D is the diffusion coefficient, sAEC the secretion rate and λ the degradation rate.

 

The present studies are the first to model the early immune response in a three-dimensional dynamic human alveolus. State of the art hybrid agent-based modeling and simulation was used to predict the migration mode of alveolar macrophages and the potential regime of parameters that are coupled to the detection of A. fumigatus conidia in time. Our studies complement the classical wet-lab approaches as in infection studies typically millions of conidia are administered to individual animals in order to determine mortality rates. Our predictions require experimental verification, which is not an easy task to tackle due to the delicate and sensitive morphology of alveoli as well as the vital function of the lung. On validation or falsification of our predictions we would be in the position to iteratively refine our model with the ultimate goal to provide a comprehensive picture of the A. fumigatus infection process.

 

References:

Pollmächer J, Figge MT (2015): Deciphering chemokine properties by a hybrid agent-based model of Aspergillus fumigatus infection in human alveoli. Front. Microbio. 6:503. doi:10.3389/fmicb.2015.00503

Pollmächer J, Figge MT (2014): Agent-based model of human alveoli predicts chemotactic signaling by epithelial cells during early Aspergillus fumigatus infection. PLoS One 9(10), e111630. doi:10.1371/journal.pone.0111630

 

 

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