Spatiotemporal modeling quantifies cellular contributions to uptake of Aspergillus fumigatus in the human lung

Abstract

The human lung is confronted daily with thousands of microbial invaders reaching the lower respiratory tract. An efficient response by the resident type 1 and type 2 alveolar epithelial cells (AECs) and alveolar macrophages (AMs) cells during the early hours of innate immunity is a prerequisite to maintain a non-inflammatory state, but foremost to rapidly remove harmful substances. One such human-pathogenic invader is the opportunistic fungus Aspergillus fumigatus. If the spherical conidia are not cleared in time, they swell reaching approximately twice of their initial size and germinate to develop hyphae around six hours post-infection. This process of morphological change is crucial as it enables the pathogen to invade the alveolar epithelium and to reach the bloodstream, but also makes it conspicuous for the immune system. During this process, conidia are first in contact with AECs then with migrating AMs, both attempting to internalize and clear the fungus. However, the relative contribution of AMs and AECs to uptake of A. fumigatus remains an open question, especially the capabilities of the barely investigated type 1 AECs. In this study, we present a bottom-up modeling approach to incorporate experimental data on the dynamic increase of the conidial diameter and A. fumigatus uptake by AECs and AMs in a hybrid agent-based model (hABM) for the to-scale simulation of virtual infection scenarios in the human alveolus. By screening a wide range of parameters, we found that type 1 AECs, which cover approximately 95% of the alveolar surface, are likely to have a greater impact on uptake than type 2 AECs. Moreover, the majority of infection scenarios across the regime of tested parameters were cleared through uptake by AMs, whereas the contribution to conidial uptake by AECs was observed to be limited, indicating that their crucial support might mostly consist in mediating chemokine secretion for AM recruitment. Regardless, as the first host cell being confronted with A. fumigatus conidia, our results evidence the large potential impact of type 1 AECs antimicrobial activities, underlining the requirement of increasing experimental efforts on this alveolar constituent.

Fig. 1. Bottom-up approach to model the immune response against A. fumigatus lung infection.

A–C Based on experimental phagocytosis assays between A. fumigatus conidia and type 2 AECs (A), we fitted a Verhulst ODE model to the increase of conidial diameter (B), and an extended Malthus ODE model to uptake indexes resulting in an increasing chance of uptake from non-swelling to swelling conidia. The dotted arrow denotes the transition from a resting to a swelling conidium that is taken up with a higher probability (C). D–F Including the fitted ODEs into a previously developed hybrid agent-based model (hABM) of one human alveolus, we were able to simulate millions of virtual infection scenarios. The hABM comprises one alveolus as a ¾ sphere consisting of type 1 AECs (yellow) and type 2 AECs (light blue). The entrance ring (dark blue) and pores of Kohn (PoK) (black) are the boundaries of the system (see Supplementary Video S1). The migration of AMs (green) is directed by the chemokine signal (white isolines) to locate the A. fumigatus conidia (red). The conidium can be taken up by AMs, type 1 and type 2 AECs, as demonstrated in the Supplementary Video S2. G By training a surrogate infection model (SIM) on the hABM output, we were able to predict uptake indexes by AMs and AECs for an interpolated parameter space.

Fig. 2. Modeling the conidial swelling and size-dependent uptake by type 2 AECs.

A The Verhulst ODE model (blue dashed lined) exhibits the experimental conidial diameter in µm (blue points, mean values as big blue points) in the first 12 h. The blue shaded area represents the 95% confidence bands of the model prediction. B The Verhulst ODE model as the relative increase in area compared to $t=0\min$ (blue dashed lined). The dark red dots represent the conidial size at $t=0\min$ and the red dots represent the swollen conidial part over time. C The extended Malthus ODE model (dark red dashed line) fitting the experimental size-dependent conidial uptake by type 2 AECs (red points, mean values as big red points). The orange dashed line represents the normal Malthus ODE model. The red shaded area represents the 95% confidence bands of the model prediction. D The extended Malthus ODE to model the theoretical uptake index for different uptake rates $r_{up0}$. Different opacity values for different values of $r_{up0}$ for more (blue dotted lines) or less (green dotted lines) efficient uptake than type 2 AECs.

Fig. 3. Simulation results of the extended hABM.

A The hABM simulations results without AMs. The light blue line shows the relative uptake by type 2 AECs matching the analytical solution from the extended Malthus ODE Model (dark red dotted). The green curves show the relative uptake by type 1 AECs, and the orange lines show the overall uptake by AECs. Different line styles denote different values of $r_{up0}^{AEC1}$. B The spatial distribution of conidia being confronted with type 1 or type 2 AECs averaged over all hABM simulations. C–F The blue lines denote the uptake by AMs, and the green lines denote the uptake by type 1 and type 2 AECs combined. The orange lines denote the overall uptake. The corresponding parameter combination is written at the top. In (C), different line styles denote different values of $r_{up0}^{AM}$. In (D) different line styles denote varied delayed chemokine secretion $t_{s_{AEC}}$ scenarios. In (E) different line styles denote different AM numbers $n_{AM}$. In (F) different line styles denote different values of $r_{up0}^{AEC1}$. In (A, C–F) error bars represent the 95% confidence interval as obtained from the standard error of independent Bernoulli trials.

Fig. 4. Sobol sensitivity analysis of the hABM with the SIM.

A Relative impact of the input parameters on the uptake index of AECs $U{I}_{AEC}$ in the hABM is denoted with the Sobol index. B Relative impact of the input parameters on the uptake index of AMs $U{I}_{AM}$ in the hABM denoted with the Sobol index.

Fig. 5. Predictions with the SIM for varying onsets of chemokine secretion.

A, B Uptake comparisons and indexes at the onset of germination at $t=360\min$. All plots denote on the x-axis the time-dependent uptake rate $r_{up}^{AEC1}\left(t\right)=r_{up0}^{AEC1}\cdot S\left(t\right)$ for varying $r_{up0}^{AEC1}$ for type 1 AECs and on the y-axis the time-dependent uptake rate $r_{up}^{AM}\left(t\right)=r_{up0}^{AM}\cdot S\left(t\right)$ for varying $r_{up0}^{AM}$. The plots are displayed for low $t_{s_{AEC}}=0\min ,$ medium $t_{s_{AEC}}=90\min$ and high $t_{s_{AEC}}=180\min$ onsets of chemokine secretion for an average AM number of $n_{AM}=12$. Predicted $UI$ and $UC$ values are rounded to integers dividable by five for better visibility of $UI$ and $UC$ structures. A The color-coded uptake comparison $UC$ denotes in green (positive values) that AECs take up more conidia and in blue (negative values) that AMs take up more conidia. B The color-coded uptake index $UI$ denoting in blue a low and in yellow a high overall uptake index of 100% by AMs and AECs combined.

Fig. 6. Predictions with the SIM for varying AM numbers.

A, B Uptake comparisons and indexes at the onset of germination at $t=360\min$. All plots denote on the x-axis the time-dependent uptake rate $r_{up}^{AEC1}\left(t\right)=r_{up0}^{AEC1}\cdot S\left(t\right)$ for varying $r_{up0}^{AEC1}$ type 1 AECs and on the y-axis the time-dependent uptake rate $r_{up}^{AM}\left(t\right)=r_{up0}^{AM}\left(t=0\right)\cdot S\left(t\right)$ for varying $r_{up0}^{AM}.$ The plots are displayed for low ($n_{AM}=4$), average ($n_{AM}=12$), and high $\left(n_{AM}=28\right)$ AM numbers and onsets of chemokine secretion at $t_{s_{AEC}}=60\min$. Predicted $UI$ and $UC$ values are rounded to integers dividable by five for better visibility of $UI$ and $UC$ structures. A The color-coded uptake comparison $UC$ denotes in green (positive values) that AECs take up more conidia and in blue (negative values) that AMs take up more conidia. B The color-coded uptake index $UI$ denoting in blue a low and in yellow a high overall uptake index of 100% by AMs and AECs combined.

Fig. 7. Predictions with the SIM for the clearance contributions of the hABM.

A, B Uptake contribution of AMs compared to AECs (y-axis) given on the x-axis the time-dependent uptake rate $r_{up}^{AEC1}\left(t\right)=r_{up0}^{AEC1}\cdot S\left(t\right)$ for varying $r_{up0}^{AEC1}$ for type 1 AECs. Different opacities of the blue and green curves stand for high (dark) down to low (bright) values of the time-dependent uptake rate $r_{up}^{AM}\left(t\right)=r_{up0}^{AM}\cdot S\left(t\right)$ for varying $r_{up0}^{AM}$ AMs. The blue curves denote the relative uptake contribution by AMs, and the green curves denote the relative uptake contribution by type 1 and type 2 AECs combined. The values are normalized, such the sum of two curves for the same value of $r_{up0}^{AM}$ adds up to 100. A Predictions for $n_{AM}=12$ $t_{s_{AEC}}=0\min$ (left) and $t_{s_{AEC}}=120\min$ (right). B Predictions for low AM numbers and early onset of chemokine secretion $n_{AM}=4,$ $t_{s_{AEC}}=0\min$ (left) and for high AM numbers and late onset of chemokine secretion $n_{AM}=28$, $t_{s_{AEC}}=120\min$.