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

Pollmächer J, Figge MT - Front Microbiol (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Applied Systems Biology, Leibniz-Institute for Natural Product Research and Infection Biology - Hans Knöll Institute Jena, Germany ; Faculty 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 h, 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.

No MeSH data available.


Related in: MedlinePlus

Schematic overview and structural relations between different components of the hybrid agent-based model. (A) Close-to-equidistant discretization of the three-quarter alveolus with 10,000 grid points. Grid points with label alveolar surface point (orange spheres) are connected with their neighboring grid points (orange lines) and those with label boundary point (blue spheres) correspond to either pores of Kohn or the alveolar entrance ring. (B) To-scale reconstruction of the human three-quarter alveolus from Pollmächer and Figge (2014) including alveolar epithelial cells (AEC) of type I (yellow) and type II (blue) as well as the pores of Kohn (black). (C) Receptor kinetics model that drives the chemotaxis of alveolar macrophages (AM). Free chemokine receptors [R] bind to chemokine ligands [L] located at grid points associated with the AM. Bound receptors [LR] are processed into internalized receptors [R*] and are re-expressed subsequently. (D) Snapshot of a virtual infection scenario where AM (green) aim to find a conidium of A. fumigatus (red). The information contained in the molecule layer is integrated using chemokine concentration isolines (white), which are plotted proportional to their respective values with different sizes.
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Figure 1: Schematic overview and structural relations between different components of the hybrid agent-based model. (A) Close-to-equidistant discretization of the three-quarter alveolus with 10,000 grid points. Grid points with label alveolar surface point (orange spheres) are connected with their neighboring grid points (orange lines) and those with label boundary point (blue spheres) correspond to either pores of Kohn or the alveolar entrance ring. (B) To-scale reconstruction of the human three-quarter alveolus from Pollmächer and Figge (2014) including alveolar epithelial cells (AEC) of type I (yellow) and type II (blue) as well as the pores of Kohn (black). (C) Receptor kinetics model that drives the chemotaxis of alveolar macrophages (AM). Free chemokine receptors [R] bind to chemokine ligands [L] located at grid points associated with the AM. Bound receptors [LR] are processed into internalized receptors [R*] and are re-expressed subsequently. (D) Snapshot of a virtual infection scenario where AM (green) aim to find a conidium of A. fumigatus (red). The information contained in the molecule layer is integrated using chemokine concentration isolines (white), which are plotted proportional to their respective values with different sizes.

Mentions: Mathematical models of chemotaxis typically set focus on one of the three key aspects that are associated with the directed migration of cells: gradient-sensing, polarization and motility. While integrative models combining all three aspects are still rare today (Iglesias and Devreotes, 2008), a chemotaxis model including the processes of gradient-sensing and motility was developed by Guo and Tay (2008). In this approach, a hybrid ABM (hABM) was used to simulate the migration behavior of leucocytes and to compare with experimental results of under-agarose assays. A hABM is a multi-scale model where cells are represented as migrating and interacting agents that are coupled to the interactive layer of diffusing molecule concentrations by the kinetics of chemokine receptor binding, internalization and re-expression (see Figure 1). From a technical point of view, this requires the implementation of a solver for the spatio-temporal reaction-diffusion equation of molecule concentrations in the complex alveolar structure with spherical symmetry and peculiar boundary conditions as imposed by the pores of Kohn and the alveolar entrance ring. This is achieved by generating a Delaunay triangulation of the alveolar surface for close-to-equidistant surface points. The geometric quantities of the corresponding Voronoi tesselation, i.e., the dual graph of the Delaunay triangulation, can then be used to solve the reaction-diffusion equation by a finite difference method on unstructured grids (Sukumar, 2003). We perform a numerical study of the steady state behavior of molecules for typical values of the diffusion coefficient, chemokine secretion rate and the rate of molecular degradation. Furthermore, performing statistical analyses of first-passage-time distributions we narrow down the regime of characteristic parameters required for the time-limited detection of A. fumigatus conidia by AM.


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

Pollmächer J, Figge MT - Front Microbiol (2015)

Schematic overview and structural relations between different components of the hybrid agent-based model. (A) Close-to-equidistant discretization of the three-quarter alveolus with 10,000 grid points. Grid points with label alveolar surface point (orange spheres) are connected with their neighboring grid points (orange lines) and those with label boundary point (blue spheres) correspond to either pores of Kohn or the alveolar entrance ring. (B) To-scale reconstruction of the human three-quarter alveolus from Pollmächer and Figge (2014) including alveolar epithelial cells (AEC) of type I (yellow) and type II (blue) as well as the pores of Kohn (black). (C) Receptor kinetics model that drives the chemotaxis of alveolar macrophages (AM). Free chemokine receptors [R] bind to chemokine ligands [L] located at grid points associated with the AM. Bound receptors [LR] are processed into internalized receptors [R*] and are re-expressed subsequently. (D) Snapshot of a virtual infection scenario where AM (green) aim to find a conidium of A. fumigatus (red). The information contained in the molecule layer is integrated using chemokine concentration isolines (white), which are plotted proportional to their respective values with different sizes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4446573&req=5

Figure 1: Schematic overview and structural relations between different components of the hybrid agent-based model. (A) Close-to-equidistant discretization of the three-quarter alveolus with 10,000 grid points. Grid points with label alveolar surface point (orange spheres) are connected with their neighboring grid points (orange lines) and those with label boundary point (blue spheres) correspond to either pores of Kohn or the alveolar entrance ring. (B) To-scale reconstruction of the human three-quarter alveolus from Pollmächer and Figge (2014) including alveolar epithelial cells (AEC) of type I (yellow) and type II (blue) as well as the pores of Kohn (black). (C) Receptor kinetics model that drives the chemotaxis of alveolar macrophages (AM). Free chemokine receptors [R] bind to chemokine ligands [L] located at grid points associated with the AM. Bound receptors [LR] are processed into internalized receptors [R*] and are re-expressed subsequently. (D) Snapshot of a virtual infection scenario where AM (green) aim to find a conidium of A. fumigatus (red). The information contained in the molecule layer is integrated using chemokine concentration isolines (white), which are plotted proportional to their respective values with different sizes.
Mentions: Mathematical models of chemotaxis typically set focus on one of the three key aspects that are associated with the directed migration of cells: gradient-sensing, polarization and motility. While integrative models combining all three aspects are still rare today (Iglesias and Devreotes, 2008), a chemotaxis model including the processes of gradient-sensing and motility was developed by Guo and Tay (2008). In this approach, a hybrid ABM (hABM) was used to simulate the migration behavior of leucocytes and to compare with experimental results of under-agarose assays. A hABM is a multi-scale model where cells are represented as migrating and interacting agents that are coupled to the interactive layer of diffusing molecule concentrations by the kinetics of chemokine receptor binding, internalization and re-expression (see Figure 1). From a technical point of view, this requires the implementation of a solver for the spatio-temporal reaction-diffusion equation of molecule concentrations in the complex alveolar structure with spherical symmetry and peculiar boundary conditions as imposed by the pores of Kohn and the alveolar entrance ring. This is achieved by generating a Delaunay triangulation of the alveolar surface for close-to-equidistant surface points. The geometric quantities of the corresponding Voronoi tesselation, i.e., the dual graph of the Delaunay triangulation, can then be used to solve the reaction-diffusion equation by a finite difference method on unstructured grids (Sukumar, 2003). We perform a numerical study of the steady state behavior of molecules for typical values of the diffusion coefficient, chemokine secretion rate and the rate of molecular degradation. Furthermore, performing statistical analyses of first-passage-time distributions we narrow down the regime of characteristic parameters required for the time-limited detection of A. fumigatus conidia by AM.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Applied Systems Biology, Leibniz-Institute for Natural Product Research and Infection Biology - Hans Knöll Institute Jena, Germany ; Faculty 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 h, 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.

No MeSH data available.


Related in: MedlinePlus