As can be seen in Figure 1, the alveoli for human and mouse have been implemented as to-scale models that are composed of AEC of type I and II, as well as PoK. Given the differences in the size and composition of alveoli for the two organisms (see Table 1 and Supplementary Table 1), it can be expected that infections may be cleared with different efficiency. For example, the surface area of the human alveolus is about 20 times larger compared to that of the murine alveolus and the number of AM per alveolus is about 6 times higher in the human alveoli. This gives rise to a scanning area per AM, which is about three times higher in humans suggesting that mice could cope much better with the detection of alveolar pathogens. However, the situation is complicated by the fact the number of PoK per alveolar area is higher by a factor 5.7 in the mouse alveolus, which together with the alveolar entrance ring gives rise to an increase of the relative alveolus' open boundary length by a factor 3.4 compared to the human alveolus. On the one hand, since AM can enter and leave the alveolus only across these boundaries (28, 29), this may result in a faster infection dynamics of the murine system. On the other hand, chemotactic signaling molecules can as well flow out of the alveolus via these boundaries implying that their increased length in the murine alveolus may be of disadvantage with regard to establishing an efficient chemokine gradient. Again, this argument may only be valid for a low pathogen density in the alveolus, because for high pathogen densities the induced chemokine profile may provide an ambiguous signal for AM guidance. For the same fungal burden in mice and humans, the pathogen density is much higher in the murine alveolus, due to their much lower number and smaller size. Therefore, A. fumigatus may be much more efficiently cleared from the human lung. Taken together, these considerations imply that the efficiency of the infection dynamics will depend on the combination of the alveolar morphometry and the fungal burden that together impact on the chemokine profile for AM migration in a way, which is impossible to quantitatively predict without performing comparative computer simulations of to-scale models.

We first consider the case of low fungal burden, which we define as the case where one A. fumigatus conidium per alveolus is the highest alveolar occupation number (AON) that is statistically expected to occur in the whole lung. The corresponding fungal burden can be derived from the binomial distribution (see Methods section for details) and is 2.5 × 10³ in mice and 3 × 10⁴ in humans (see Figure 2). This implies that the limit of low fungal burden covers the dose of daily inhalation for humans, but is relatively low for experimental conditions in typical mice experiments. Examples of the infection dynamics can be seen for humans and mice in Supplementary Videos 1, 2, respectively.

Our previous work on A. fumigatus infection in human alveoli for low fungal burden revealed that a high secretion rate s_AEC of chemotactic molecules combined with a low diffusion coefficient D of the chemokine is beneficial for a small infection score IS^H in humans (27). In the present study, we screened the diffusion coefficient and the secretion rate in the regimes, respectively, D = [20, 6 × 10³] μm²/min and sAEC=[1.5 × 103, 5×105] min-1 for alveoli of mice and humans. The numerical results for the quantitative comparison between human and mouse is shown by the infection scores IS^H,M in Figure 3A. It can be observed that, for all combinations of D and s_AEC, the infection score in mice is significantly smaller: IS^M < IS^H. Furthermore, it can be seen that the relation of a high secretion rate and a low diffusion coefficient also leads to a more efficient infection clearance in mice. The relative difference in the infection scores of the two organisms, ΔIS = 1 − IS^M/IS^H, is in the range 50−90 %, indicating that the murine system performs always better than the human system in the limit of a low fungal burden.

To dissect whether the infection dynamics is governed by the chemotaxis or the alveolar size, we compared the probability of directed AM migration resulting from one conidium in the alveolus of mice and humans. The chemokine concentration itself falls off with the distance from the source AEC, i.e., the AEC in contact with the conidium. In order to avoid that AM perform mostly random walk migration, the chemokine gradient (i) must not exceed a certain value to avoid saturation of AM chemokine receptors and (ii) must not fall below a certain value to provide a detectable signal. As a qualitative measure of gradient efficiency we calculated the probability that AM follow the gradient depending on the distance to the source AEC. This probability reflects the impact of the chemokine gradient on AM migration and was computed as explained in Supplemantary Methods (see section on AM Migration) for optimal chemokine parameters (Dopts¯, sAECopts¯) in the human (s = H) and mouse (s = M) system. The optimal parameters were computed from the 36 scanned parameter combinations, {D₁…D₆} × {s_AEC1…s_AEC6}, for the diffusion coefficient and the secretion rate as follows: Based on the simulation results in terms of the infection score IS_Di,sAECi and the limits of its respective 95%-confidence interval, we computed the optimal diffusion coefficient as Dopt¯=1∑iwi·∑iwi·Di with weights w_i = 1−IS_Di,sAECi for all those parameter combinations that had infection scores not exceeding the minimal upper limit of all confidence intervals (see Supplementary Video 3). The optimal secretion rate sAECopt¯ was determined in the same way yielding for the human host DoptH¯=34μm2 min-1 and  sAECoptH¯=1.5×104min-1 and for the murine host DoptM¯=61μm2min-1 and sAECoptM¯=4.9×104min-1 as the optimal parameters in the limit of low fungal burden.

The probability of directed AM migration for both host systems and for their respective optimal chemokine parameters is plotted in Figure 3B. The two curves exhibit quantitative similarity suggesting that the infection dynamics in the case of a low fungal burden is mainly governed by the size of the alveolus rather than the chemokine profile itself. Thus, in contrast to the significantly larger human alveolus, AM in the murine counterpart will typically perform directed migration across the entire alveolus.

Increasing the AON from one to higher conidia numbers, we again performed computer simulations for various infection scenarios that differ in the parameters for chemokine secretion s_AEC and diffusion coefficient D. However, multiple conidia within the alveolus can lead to more complex chemokine profiles derived from the various conidia-associated AEC that are simultaneously serving as sources of chemokine secretion. In Figure 4A the infection scores IS obtained from 10³ simulations are summarized for AON between one and six and for selected secretion rates s_AEC, while the numerical results for the full range of studied parameter values is shown for human and mouse in Supplementary Figure 1. Parameter regimes of efficient infection clearance in these plots resemble those previously found for one conidium in the human alveolus (27), indicating that low ratios D/s_AEC are as well preferred in the mouse system.

Extending the computation of optimal chemokine parameters for one conidium to larger AON enables computing for both systems the average optimal parameter set (see Supplementary Figure 2). We obtain for one to six conidia per alveolus the averaged optimal values DoptH¯=26±6.6 μm2min-1 and  sAECoptH¯=1.1×104 ±6×103 min-1 for the human host and DoptM¯=74±22.4 μm2min-1 and sAECoptM¯=8.0×104±4,1×104 min-1 for the murine host. In Figure 4B, we show that the resulting infection score IS as a function of the AON is always significantly lower in mice compared to humans.

Due to morphometric differences between the lungs of mice and humans, the AON is not directly related to the fungal burden. This follows from our earlier statistical considerations on the highest AON that is expected to occur in the whole lung for a given fungal burden (see Figure 2) exhibiting a significant quantitative difference between mice and humans. Since the number of more than 10⁸ alveoli in the human lung exceeds that of mice by more than two orders of magnitude, even in the case of an extremely high fungal burden with 10⁶ conidia in the lung, the maximal AON for humans does not exceed two. In contrast, the same fungal burden in the lung of mice yields a maximal AON between five and six conidia in one alveolus. It thus follows that a comparison between mice and humans for the same fungal burden requires contrasting infection scenarios with different AON. Of note, our analysis focuses on the maximal AON for a given fungal burden, because it is argued that this configuration will be directly correlated with the estimated time needed to clear all occupied alveoli from the pathogen. In Figures 4C,D the numerical results for the infection score IS are shown for mice and humans as a function of the fungal burden, respectively, for identical chemokine parameters and for the respective optimal chemokine parameters. Supplementary Figure 3 shows the infection score IS as a function of the fungal burden for all the scanned parameter combinations. It can be seen by the smaller infection scores in the murine host that infections are still more efficiently cleared for the entire experimentally relevant range of 10³−10⁵ conidia in the lung. In Supplementary Video 3 we indicated all combinations of chemokine parameters for which the infection score reaches values below the threshold of IS_t = 5%.

However, as we have mentioned before, administration of conidia based on liquid solutions is reported to be associated with higher local fungal burdens due to a more non-uniform distribution of conidia (33). It can be seen in Figure 2 for a uniform distribution of conidia that a high fungal burden in the range 10⁵−10⁶ conidia per lung is associated with an AON of two in the human system, whereas this value ranges between three and six for the murine system. Consequently, for a non-uniform distribution of conidia, such high AON can be reached in the murine lung and these can result in infection scores that are much higher than for the human system with AON of two, even if the respective optimal chemokine parameters are applied (see Figure 4B). Our spatio-temporal computer simulations of the infection scenarios reveal that higher AON are associated with chemokine profiles that deteriorate clearance efficiency. Since the mouse alveolus contains more than 10 times fewer AEC compared to the human alveolus (see Table 1), multiple randomly positioned conidia will occupy most of the alveolus' AEC associated with chemokine secretion from various source AEC. First of all, this can lead to chemokine saturation that will turn directed AM migration into random walk migration. Secondly, if the number of conidia is increased further, this will not alter the chemokine gradient anymore. Consequently, AM will perform the inefficient random walk migration until a sufficient number of conidia is detected, such that AM migration becomes again dominated by the chemokine gradient. Obviously, this complex interplay between the morphometry of the alveolus and the chemokine profile will be much less pronounced for the larger human alveolus that consists of many more AEC. To validate this hypothesis, we computed the mean values of the chemokine concentration across all alveolar surface grid points in the simulations and found that significant deviations arise between the human and mouse alveolus starting at AON of four. As can be seen in Figure 5, for AON above four the mean concentration value in the murine alveolus does change only slightly providing no additional chemotactic guidance to AM, whereas it is still increasing in the human alveolus and can provide chemotactic guidance associated with lower infection scores IS in the human alveolus and in the limit of fungal burdens well above the typical experimental range.

In the quantitative comparison of infection scenarios in mice and humans, we so far assumed the same values for the model parameters. For example, we assumed that the chemokine secretion rates from human and murine alveolar epithelial cells are similar. However, it may be argued that this does not reflect the physiological reality correctly, since murine AEC are effectively about 33% smaller in area and may thus exhibit a reduced potential of chemokine secretion. Similarly, it is an open question today whether the postulated chemotactic signals in human and mice are transmitted by chemokines that are structural homologs and can therefore be expected to have similar diffusion coefficients in the surfactants of mice and humans. While these uncertainties cannot be avoided, we estimated the impact of variations in these parameters on the infection score in humans and mice. To this end, we calculated the relative infection score between the human and murine model ΔIS = 1−IS^M/IS^H, over all simulated parameter combinations in the experimental range of fungal burdens. Setting both diffusion parameters in humans and mice to identical values, the mouse shows lower relative infection scores with a median value of ΔIS = 0.49.

Next, we analyzed the robustness of the infection outcome with regard to the diffusion coefficient and the secretion rate. To this end, we compared the infection scores for humans and mice for those simulated parameter combinations that obey the scaling factors fD=  DH/DM  for the diffusion coefficient and fsAEC=  sAECH/sAECM for the chemokine secretion rate. For example, comparing diffusion coefficients with scaling factor fD=3-1 (i.e., D^H = (20, 200, 2000) μm²/min, D^M = (60, 600, 6000) μm²/min) revealed a reduction in the median value of the relative infection score to ΔIS = 0.27 over the scanned fungal burdens. This indicates that the infection score in mice is higher in >50% of all selected parameter combinations, even if the diffusion coefficient is three times higher in the murine alveolus (see Figure 6). The scaling factor of the secretion rate f_sAEC has a reversed impact on the relative infection score reflecting that a high ratio s_AEC/D induces low infection scores (see Figure 6).

Taken together, our simulation results imply that our main conclusions are qualitative robust against variations in the chemotaxis parameters. As long as the associated scaling factors have values fD>10-1 or f_sAEC < 10, the murine system still shows better infection scores in more than half of all screened fungal burdens, even if chemotactic signaling becomes deteriorated. We therefore conclude that within these limits our simulation results are qualitatively robust against variations in the chemotaxis parameters.

A comprehensive literature research was performed to design the virtual infection model of the mouse alveolus as realistic as possible. The most important morphology parameters are summarized and compared with the human alveolus in Table 1, from which other characteristics can be derived (see for examples Supplementary Table 1). For example, it can be seen that the radius (surface area) of a typical human alveolus is about 4.5 (20)-fold larger compared to a murine alveolus. The numbers of AEC of type 1 and 2 differ significantly in both organisms, i.e., a human alveolus contains about 12.0-fold more type 1 and 21-fold more type 2 AEC. Furthermore, the number of PoK is about 3.4 times higher in the human alveolus. A video of both model alveoli is provided in the (Supplementary Videos 1, 2).

The ABM was adjusted for the implementation of the mouse alveolus with parameters as summarized in Table 1 and Supplementary Table 1. This also required changes in the algorithm for cell positioning on the alveolar surface. Type 1 AEC were placed as described before around the three-quarter sphere (see Supplementary Material for details). Previously, type 2 AEC and PoK were placed at the borders between type 1 AEC. However, due to the larger ratio of type 2 AEC and PoK with respect to type 1 AEC in mice, the positioning of PoK and type 2 AEC had to be changed. We adjusted the position of type 2 AEC and PoK uniformly across the whole border of the type 1 AEC. While these changes in the cell positioning were required for realistic configurations of mouse alveolus morphometries, quantitative results of the ABM for the human alveolus remained within the 95%-confidence interval. Moreover, the smaller size of the mouse compared to the human alveolus required adjustment of the Delaunay-triangulated grid, on which the diffusion equation is solved (27). The number of grid points could be reduced from 10⁴ in the human alveolus to only 5.1 × 10², keeping the spatial resolution in the mouse alveolus the same as in the human system (see Supplementary Table 1).

As a measure of fungal clearance we compute for various infection scenarios the first-passage-time (FPT) of AM, i.e., the time required for migrating AM to find all conidia in a particular alveolus (26, 27). The relation between the FPT and the time point of conidia germination, which corresponds to about 6 h post conidia arrival, is obtained from repeating the simulation of each infection scenario 10³ times. From the corresponding FPT distribution, we then compute an infection score, IS, as the percentage p of simulations with FPT above 6 h: IS^{s = H,M} = p(FPT > 6 h), where the superscript refers to the human (s = H) or mouse (s = M) system and IS^{s = H,M} = 0 (IS^{s = H,M} = 1) implies that conidia were cleared in each (none) of the 10³ simulations. The various infection scenarios correspond to scanning the parameter space in terms of AM migration, chemokine secretion, and diffusion, as well as conidia infection doses in alveoli of mice and humans.

For a given fungal burden δ, the conidia are distributed across all alveoli n_alv of the host's lung. Assuming an independent and uniform distribution of these conidia, we can describe the probability of having n_con conidia present in one alveolus by the Binomial distribution B_con(δ, p, n_con) with probability of p=1nalv  for δ repeats. To estimate the maximal AON that is associated with a specific fungal burden, we computed n_con from the 1-1nalv-quantile of the distribution B_con(δ, p, n_con). The resulting number corresponds to the maximal AON that can be expected to occur in the whole lung for a specific fungal burden (see Figure 2). The corresponding IS was determined by linear interpolation of the results from our simulations for various AON.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.