S. aureus induces specific immune response pattern in whole-blood infection assays

In our previous studies, we performed whole-blood infection assays with either C. albicans or C. glabrata and observed that infection outcomes strongly depend on the pathogen [1, 2]. In this study, we additionally performed whole-blood infection assays with the bacterial pathogen S. aureus. During the time course of four hours, we measured the viability of the pathogens by survival assays as well as the association of the pathogens to PMNs and monocytes using flow cytometry. The experimentally measured kinetics of pathogen association and viability are depicted in Fig 2 for S. aureus (orange lines) together with the kinetics from infection with C. albicans (pink lines) or C. glabrata (blue lines). Similar to C. albicans and C. glabrata, most S. aureus cells were killed in the whole-blood infection assay during four hours. A fraction of only 5.0% ± 2.4% alive S. aureus cells was measured four hours post infection (see Fig 2A). The time course of alive S. aureus cells in the whole-blood infection was qualitatively similar to that of alive C. glabrata cells, but in comparison to alive C. albicans cells a much faster dynamics was observed. The flow cytometry analysis revealed association of S. aureus cells to PMNs and monocytes, but no interaction with lymphocytes. Similar to infections with the fungal pathogens, association to immune cells increased with time and the majority of S. aureus cells was associated with PMNs (76.7% ± 6.5%), whereas a smaller fraction was associated with monocytes (20.1% ± 6.4%) at four hours post infection. However, the dynamics of S. aureus interaction with both immune cell types were faster compared to the two fungal pathogens, resulting in a smaller population of extracellular S. aureus cells after four hours of infection, and showed a markedly higher association to monocytes. (see Fig 2B).

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Fig 2. Experimental data acquired from whole-blood infection assays with C. albicans, C. glabrata and S. aureus.

Experimental data from whole-blood infection assays infected with either C. albicans (pink line), C. glabrata (blue line) or S. aureus (orange line). Survival assays were performed to measure fractions of alive pathogens (A) and flow cytometry was used to determine the distribution of pathogens in human blood, shown as extracellular pathogens (B), pathogens associated with PMN (C) and with monocytes (D).

https://doi.org/10.1371/journal.pone.0249372.g002

Taken together, we found that, similar to the fungal pathogens, also S. aureus could not be cleared completely from human blood, which is a strong evidence for the existence of immune-evasive S. aureus cells at four hours post infection. Furthermore, we found that the immune response to S. aureus showed pathogen-specific properties, such as the greater impact of monocytes and the larger elimination of pathogens from whole blood in comparison to C. albicans and C. glabrata.

Rejection of pre-IE model by image-based systems biology approach

Since we observed for all three types of pathogens that microbial cells can remain extracellular (see Fig 2B) and can remain alive, we investigated the hypothesis of a pre-existing immune-evasive phenotype in a proportion of the initial population used for infection (see Fig 1C). In the pre-IE model, we set the population of immune-evasive cells to a constant value that does not change over time (see Methods). This pre-existing subpopulation of immune-evasive cells can consist of alive and/or killed cells. In order to test whether this model captures the immune response as measured in the whole-blood infection assays with any of the three pathogens, we applied the parameter estimation algorithm Simulated Annealing based on the Metropolis Monte Carlo scheme (see S2 Fig of S1 File). This algorithm minimizes the least-square error (LSE); i.e. it determines the model parameter values for the best fit between model simulations and experimental data by minimizing the LSE. The resulting parameter values are given in S3 Table of S1 File. We observed that the corresponding model simulations matched the experimental data for all three infection scenarios. As shown in S10, S18 and S26 Figs of S1 File, respectively, for infection with C. albicans, C. glabrata and S. aureus, the model simulations were close to the mean values of the experimental data and within their corresponding standard deviations.

In the following we focus on model simulations for extracellular pathogens and alive pathogens. For infection with C. albicans cells, the pre-IE model predicted that four hours post infection a fraction of 15.85% ± 0.0% pathogens was remaining in extracellular space (see Fig 3B) and that most of these cells were immune-evasive (15.81% ± 0.0%, see S10 Fig of S1 File). Furthermore, the model predicted that this fraction of evasive cells is composed of 7.1% ± 0.0% killed evasive cells and 8.7% ± 0.0% alive evasive cells. Thus, the model predicted that at the time point of infection (t = 0 min) a fraction of 7.1 ± 0.0% pathogens were already dead, i.e. not all pathogens were alive initially. This can be seen in Fig 3A, where the fraction of alive C. albicans cells was 92.9% ± 0.0% at t = 0 min. Similarly, the simulated dynamics of alive pathogens for infection with C. glabrata and S. aureus, respectively, started at t = 0 min with 10.3 ± 0.1% and 1.6 ± 0.01% killed evasive pathogens (see Fig 3C) and hence with 89.7% ± 0.1% and 98.4% ± 0.1% alive pathogens (see Fig 3A). Taken together, the pre-IE model predicted fractions of alive cells and killed cells that are immune-evasive before infection for all three infection scenarios.

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Fig 3. Kinetics of combined units for C. albicans, C. glabrata or S. aureus infection simulated by the pre-IE model.

The thickness of the solid lines indicates the mean ± standard deviation (SD) of 50 simulations with transition rate values that were randomly sampled within their respective SD. Dashed lines correspond to the experimental data to which the model was fitted. The simulation results of the pre-IE model are depicted for an infection with C. albicans (pink line), C. glabrata (blue line) or S. aureus (green line). The time course of alive pathogens is shown at the top (A), the time course of extracellular pathogens in the middle (B) and the predicted time course total of immune-evasive (P_IE), alive immune-evasive (P_AIE) and killed immune-evasive cells (P_KIE) is shown at the bottom (C).

https://doi.org/10.1371/journal.pone.0249372.g003

So far, it is not possible to experimentally determine the fraction of immune-evasive cells before infection. However, we can test the model prediction by quantifying the amount of dead pathogens before infection using the live/dead staining with propidium iodide (PI) and subsequent microscopy imaging (see Methods). Example microscopy images for the three types of pathogens are shown in S27 Fig of S1 File. In order to count the number of alive and dead cells in these images, we applied the automated segmentation algorithm implemented in the framework AMIT (Algorithm for Migration and Interaction Tracking) [14], as described in Methods. In total, we analyzed six samples with C. albicans cells, six samples with C. glabrata cells and nine samples with S. aureus cells. Independent of the type of pathogen, we found that almost all cells in a viable pathogen inoculum were alive and that the number of dead pathogens was vanishingly small (see S28 Fig of S1 File): on average 0.0% ± 0.0% C. albicans cells, 0.2 ± 0.4% C. glabrata cells and 0.13% ± 0.07% S. aureus cells were dead before infection.

Taken together, for all three types of pathogens the experimentally determined fractions of dead pathogens before infection are vanishingly small and much smaller than the fractions of killed evasive pathogens that were predicted by the pre-IE model. These results strongly suggest that no dead pathogens are present at the beginning of the infection assays. On the other hand, since it cannot be excluded that alive evasive pathogens do exist before infection, we replace the pre-IE model by the alivePre-IE model. The latter model allows for the existence of an initial subpopulation of evasive pathogens that are all alive (see Methods). However, since dead cells do exist after four hours of infection (see Fig 2), the alivePre-IE model can only be considered in combination with other mechanisms of immune evasion. This conclusion motivated us to perform a comparative analysis of virtual infection models.

Comparative analysis of virtual infection models for whole-blood assays

In order to find the most realistic immune-evasion model from the set of eight immune evasion models (see Table 1), we calibrated these models to the experimental data of all three types of pathogens using the global parameter estimation algorithm Simulated Annealing based on the Metropolis Monte Carlo scheme (see Methods section and S2 Fig of S1 File). Afterwards, we comparatively analyzed different model characteristics such as the estimated model parameter values and the goodness of the models, using the Akaike information criterion (AIC) in addition to the LSE. In the following paragraphs, we compare the predictions of the different immune-evasion models for each type of pathogen separately. Here, we first focus on the comparison of the alivePre-IE model with the other two base models that contain solely one way to acquire immune evasion, i.e. the spon-IE model and the PMNmed-IE model (see Fig 1A, 1B and 1D, Table 1 and Methods). Afterwards, we comparatively analyze the predictions made by the combined models, where three of them contain two evasion mechanisms (the spon-PMNmed-IE model, the spon-alivePre-IE model and the PMNmed-alivePre-IE model) and one model with all three potential evasion mechanisms, the spon-PMNmed-alivePre-IE model.

Whole-blood infection with C. albicans

By fitting the immune-evasion models to data from whole-blood infection assays with the fungal pathogen C. albicans [1], we could estimate values of the model parameters and thereby quantify the immune reaction rates. The resulting parameter values are given in S1 Table of S1 File and depicted in Fig 4 for each immune-evasion model. We observed that the alivePre-IE model predicted larger phagocytosis rates of neutrophils (Φ_N) and monocytes (Φ_M) in comparison to the spon-IE model (, ) and the PMNmed-IE model (, ). The combined units that were directly influenced by these rates are P_N and P_M, respectively, representing pathogens in neutrophils and in monocytes. Despite these differences in the phagocytosis rates between the base models, the dynamics of P_N and P_M were similar during the first 60 minutes post infection and differed only slightly at four hours post infection (see Fig 5B and 5C). However, the phagocytosis rates were larger in the alivePre-IE model, because at t = 0 min the fraction of 12.7% ± 0.4% pathogens were alive evasive pathogens and 87.3% ± 0.4% of non-evasive pathogens in extracellular space were accessible for phagocytosis, which is a value that is smaller in comparison to the two other base models. In the spon-IE and the PMNmed-IE model, no evasive cells were present before infection. Thus, 100% of the infected pathogens were in extracellular space and could be phagocytosed. In comparison to the spon-IE model and PMNmed-IE model, the alivePre-IE model predicted a smaller fraction of extracellular pathogens (P_E) at t = 240 min and nearly all of them were alive and evasive (see S3C Fig of S1 File for spon-IE model, S4C Fig of S1 File for PMNmed-IE model and S5C Fig of S1 File for alivePre-IE model). Furthermore, we observed differences between models in rates of killing. Compared to the spon-IE model and the PMNmed-IE model, the alivePre-IE model predicted a larger value for the rate of intracellular killing by neutrophils (κ_N) (see Fig 4B), whereas the rate for extracellular killing by antimicrobial peptides (κ_EK(t)) was smaller (see Fig 4C). This inverted ratio of intracellular and extracellular killing rates between the alivePre-IE model and the two other base models seems to compensate the effect on the dynamics of the combined unit for killed pathogens (P_K). Consequently, the course of P_K during 60 minutes post infection was similar for each of these three base models (see Fig 5A). At four hours post infection, the alivePre-IE model predicted a smaller fraction of killed pathogens (P_K = 87.3 ± 0.4%) and a larger fraction of alive pathogens (P_A = 12.7 ± 0.4%) in comparison to the spon-IE model with P_K = 88.6 ± 0.6% and P_A = 11.4 ± 0.6%, and the PMNmed-IE model with P_K = 88.9 ± 0.9% and P_A = 11.1 ± 0.9%.

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Fig 4. Resulting transition rate values from calibrating the potential immune evasion models to whole-blood infection scenarios with either C. albicans, C. glabrata or S. aureus.

Mean values (data points) and standard deviations (error bars and line thickness) of transition rates were quantified by the global parameter estimation algorithm Simulated Annealing based. Dots depict the transition rate values for the spon-IE model (light green), PMNmed-IE model (pink), alivePre-IE model (dark blue), spon-alivePre-IE model (light blue), PMNmed-alivePre-IE model (orange), spon-PMNmed-IE model (red) and spon-PMNmed-alivPre-model (dark green). The transition rates for phagocytosis are defined by ϕ_N for PMN and by ϕ_M for monocytes. Intracellular killing rates are defined by κ_N for PMN and κ_M\ for monocytes. Transition rates γ and determine the time-dependent extracellular killing rate κ_EK(t). Depending on the chosen model, the transition rates ρ, and γ_IE determine the immune-evasion rate over time (ρ(t)). Transition rate values for infection scenario with C. albicans for phagocytosis (A), intracellular killing (B), time course of the extracellular killing rate (C) and the time course of the immune-evasion rate (D). Transition rate values for infection scenario with C. glabrata infection for phagocytosis (E), intracellular killing (F), time course of the extracellular killing rate (G) and time course of the immune-evasion rate (H). Transition rate values for infection scenario with S. aureus infection for phagocytosis (I), intracellular killing (J), time course of the extracellular killing rate (K) and time course of the immune-evasion rate (L). Transition rates and start populations quantified for all base and combined models for each pathogen infection are also shown in S1-S3 Tables of S1 File.

https://doi.org/10.1371/journal.pone.0249372.g004

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Fig 5. Kinetics of combined units of each immune-evasion model for infection scenario with C. albicans.

Experimental data from whole-blood infection assays (dashed lines) with corresponding standard deviations (SDs) are compared to the simulated data (solid lines) for infection scenario with C. albicans. The simulated kinetics by the spon-IE model (light green line), PMNmed-IE model (pink line), alivePre-IE model (dark blue line), spon-alivePre-IE model (light blue line), PMNmed-alivePre-IE model (orange line), spon-PMNmed-IE model (red line) and spon-PMNmed-alivePre-IE model (dark green line) are shown in their corresponding color. The thickness of solid lines indicates the mean ± SD of 50 simulations with transition rate values that were randomly sampled within their respective SD. Simulated kinetics of killed cells (A), pathogens associated with monocytes (B), pathogens associated with PMN (C) and immune-evasive cells (D).

https://doi.org/10.1371/journal.pone.0249372.g005

Taken together, the alivePre-IE model predicted parameter values, especially for Φ_N, Φ_M, κ_N and κ_EK(t), that differed in comparison to the spon-IE and the PMNmed model. Furthermore, we observed differences between these models in the simulation of the combined units P_E, P_K and P_A (see Fig 5A–5C and S3-S5 Figs of S1 File). As described above, these differences in the parameter values and the combined units were a direct consequence of the initial presence of alive evasive pathogens at time t = 0 min. Furthermore, by comparing the degree of agreement of model simulations with the experimental data using the LSE (see Methods), we found that the alivePre-IE model simulations had the largest LSE (see Fig 6A) and, moreover, this was mainly caused by deviations in the combined units P_E and P_A, which were shown to be mainly affected by the presence of evasive pathogens that are alive. In other words, the model could not fill in the gap between extracellular pathogens (15.0±5.8%) and alive pathogens (6.5±4.2%) at t = 240 min post infection. In addition to the LSE, we compared the goodness of the models using the AIC_C (corrected Akaike information criterion, see Methods), which involves not only the deviation to the experimental data but also the number of model parameters (see Methods). We observed that the spon-IE model not only had the smallest LSE, among the three base models (see Figs 6 and 7A), but also showed the smallest AIC_C (see Fig 7A). The goodness of the two other base models was evaluated by their ΔAIC_C, which is defined as the absolute difference to the model with the smallest AIC_C, i.e. the spon-IE model. The differences ΔAIC_C = 4.78 for the PMNmed-IE model and ΔAIC_C = 5.86 for the alivePre-IE model show that these models are in the category of models with considerably less support in comparison to the spon-IE model (see Methods).

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Fig 6. LSE values of immune evasion models resulting from calibration to infection scenarios with the different pathogens.

Each bar refers to the mean LSE value ± SD of 50 simulations with transition rate values that were randomly sampled within their respective SD by the spon-IE model (light green line), PMNmed-IE model (pink line), alivePre-IE model (dark blue line), spon-alivePre-IE model (light blue line), PMNmed-alivePre-IE model (orange line), spon-PMNmed-IE model (red line) and spon-PMNmed-alivePre-IE model (dark green line). The LSE is compared for a simulated infection scenario with C. albicans (A), C. glabrata (B) and S. aureus (C).

https://doi.org/10.1371/journal.pone.0249372.g006

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Fig 7. Distribution of LSE values and the AIC_C values for each immune evasion model.

The LSE distribution of 50 simulations for each immune evasion model with transition rate values that were randomly sampled within their respective standard deviation are depicted in the left column. The colors refer to the spon-IE model (light green), PMNmed-IE model (pink bars), alivePre-IE model (dark blue), spon-alivePre-IE model (light blue), PMNmed-alivePre-IE model (orange), spon-PMNmed-IE model (red) and spon-PMNmed-alivePre-IE model (dark green). The mean of the LSE was used to calculate the corresponding AIC_C value for each model (same color as in the left column). The most supported model achieves the lowest AIC_C value and for every other model the ΔAIC_C value is calculated and depicted. Areas colored by different shades of grey represent the different categories of ΔAIC_C that are defined in the Methods section. The white regions indicate the areas between the ΔAIC_C categories. The horizontal red line depicts the median LSE of all LSE values. The subfigures show the LSE distribution and the AIC_C values for each model, respectively, for C. albicans infection (A, B), C. glabrata infection (C, D) and S. aureus infection (E, F).

https://doi.org/10.1371/journal.pone.0249372.g007

By involving the results of the four combined immune-evasion models into the comparative analysis, we observed that the PMNmed-alivePre-IE model predicted killing rates that have also an inverse relationship to the other combined models (see Fig 4B and 4D), but the resulting dynamics of P_K was not affected (see Fig 5A).

However, similar to the alivePre-IE model, the PMNmed-alivePre-IE model predicted a smaller fraction of immune-evasive cells (P_IE) in comparison to the other models (see Fig 5D). This resulted in much larger LSEs of these two models (see Fig 6A). For example LSEs of the alivePre-IE model (P′ < 0.001) and PMNmed-alivePre-IE model (P′ < 0.001) are significantly different in comparison to the LSE of the PMNmed-IE model and this is also the case when comparing to the other models. Since the complexity of the PMNmed-alivePre-IE is also large (nine parameters), the difference ΔAIC_C to the model with the smallest AIC_C, which is the spon-IE model, indicates that this model is in the category of models that have essentially no support (see Methods for the respective categorization). The spon-alivePre-IE model simulations caused a similar LSE to the spon-IE model simulations and the corresponding ΔAIC_C is the smallest among the compared models. The other combined models have an LSE similar to the spon-IE model, but are either close to or within the category of models that have essentially no support according to their ΔAIC_C values.

Taken together, we observed that the immune-evasion models can be calibrated to the experimental data of whole-blood infection with C. albicans. However, differences in the parameter values caused differences in the goodness of the fit with respect to the LSE and the AIC_C. We found that the spon-IE model simulations caused the smallest LSE and the best AIC_C. Since no killed evasive cells are allowed in the alivePre-IE model, the simulated kinetics causes the highest LSE. The PMNmed-alivePre-IE model and the spon-PMNmed-alivePre-IE model are the evasion models with the largest complexity, i.e. with the largest number of model parameters, causing the highest AIC_C values. The respective difference to the best AIC_C value, the ΔAIC_C, indicates that these models belong to the category of models with essentially no support.

Whole-blood infection with C. glabrata

In our previous study, we found remarkable differences in the model predictions for C. glabrata infection regarding the transition rate values–especially for the rate of extracellular killing–from the spon-IE model and the PMNmed-IE model. In this study, we additionally compared the predictions from the alivePre-IE model and found its transition rate values to be either similar to or between the respective values quantified by the two other base models (see Fig 4F–4J). For example, the phagocytosis rate of neutrophils (Φ₀) was predicted to be highest in the spon-IE model, followed by the alivePre-IE model and lowest in the PMNmed-IE model (). Consequently, this led to a quicker increase in the dynamics of P_N for the spon-IE model in comparison to the alivePre-IE model and the PMNmed-IE model, which is also visible by comparing the fraction of P_N at ten minutes post infection (, , ) as shown in Fig 8C. However, four hours post infection with C. glabrata, the fraction of P_N was largest in the model with the smallest phagocytosis rate, i.e. the PMNmed-IE model. This was caused by additionally predicting a lower immune evasion rate in comparison to the spon-IE and the alivePre-IE model (see Fig 4H), which consequently gave the neutrophils and monocytes more time to phagocytose C. glabrata cells.

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Fig 8. Kinetics of combined units of each immune-evasion model for infection scenario with C. glabrata.

Experimental data from whole-blood infection assays (dashed lines) with corresponding standard deviations (SDs) are compared to the simulated data (solid lines) for C. glabrata infection scenario. The simulated kinetics by the spon-IE model (light green line), PMNmed-IE model (pink line), alivePre-IE model (dark blue line), spon-alivePre-IE model (light blue line), PMNmed-alivePre-IE model (orange line), spon-PMNmed-IE model (red line) and spon-PMNmed-alivePre-IE model (dark green line) are shown in their corresponding color. The thickness of solid lines indicates the mean ± SD of 50 simulations with transition rate values that were randomly sampled within their respective SD. Simulated kinetics of killed cells (A), pathogens associated with monocytes (B), pathogens associated with PMN (C) and immune-evasive cells (D) for a C. glabrata infection.

https://doi.org/10.1371/journal.pone.0249372.g008

Despite the fact that the model dynamics of the combined units appear similar for the base models, the quantitative differences in the transition rate values are associated with somewhat different LSEs (see Fig 6B). The LSE of the alivePre-IE model is smaller than the LSE of the PMNmed-IE model and larger than the LSE of the spon-IE model. By additionally involving the model complexity into the model assessment using the AIC_C (see Methods), we found that the spon-IE model had the lowest AIC_C, which indicates that the corresponding LSE is small enough to compensate for the higher number of parameters in the spon-IE model (see Table 1) in comparison to the alivePre-IE model. Moreover, the absolute difference between AIC_C values of the alivePre-IE model and the spon-IE model () indicates that the alivePre-IE model has less support than the spon-IE model (see Fig 7D). The PMNmed-IE model not only showed a larger LSE value than the spon-IE model, but also a higher number of parameters. Thereby, the AIC_C is larger and, moreover, the corresponding lies between the two categories referred to as considerably less support and essentially no support.

Interestingly, the four combined models of immune evasion predicted values for Φ_N, Φ_M and κ_N that were markedly different from the values predicted by the two base models, alivePre-IE and PMNmed-IE model (see Fig 4E–4G). By comparing the LSE, we found that simulations of all four combined models have LSEs that differ from the spon-IE model, which is the base model with the lowest LSE. The statistical analysis revealed that this difference is significant with P′ < 0.01 for the spon-alivePre-IE model and with P′ < 0.001 for the PMNmed-alivePre-IE model, the spon-PMNmed-IE model and the spon-PMNmed-alivePre-IE model. However, the combined models contain more model parameters and, therefore, their AIC_C values are larger in comparison to that of the spon-IE model. The spon-alivePre-IE model has a lower LSE and thus the larger model complexity was compensated in comparison to the spon-IE model. The corresponding ΔAIC_C = 2.7 clearly shows the proximity to the category of models with substantial support. All other combined models failed to compensate for their model complexity with a better fit and are either close to or within the category of models with essentially no support (see Fig 7D).

Taken together, the alivePre-IE model made predictions that are quantitatively between those of the two other base models regarding transition rate values, LSE and AIC_C. The largest differences were found for the rates of intracellular killing, extracellular killing and immune evasion. The spon-IE model was the best according to the AIC_C and the spon-alivePre-IE model was comparable with this model according to the categorization of the ΔAIC_C (see Methods). All other combined models contain more parameters and this larger complexity could not be compensated by a better fit to experimental data, leading to a larger difference ΔAIC_C.

Whole-blood infection with S. aureus

Extending to the infection scenario with S. aureus in this study, the immune reaction rates were quantified by calibrating the models to the observed association and killing kinetics of S. aureus cells. We found that the optimal reaction rate values of the spon-IE model and the alivePre-IE model showed a smaller deviation from each other than in comparison to the rates of the PMNmed-IE model. As can be seen in Fig 4I, the phagocytosis rates of monocytes (Φ_M) and PMNs (Φ_N) are smaller for the PMNmed-IE model in comparison to the other base models. Furthermore, the rate for immune evasion is smaller in the PMNmed-IE model (see Fig 4L). The evasion rate in this model is dependent on the first-phagocytosis events by PMNs, which mainly occurred during the first hour post infection, resulting in an immune-evasion rate close to zero at one hour post infection. At later times, extracellular pathogens (P_AE and P_KE) were phagocytosed predominantly by immune cells, i.e. mainly by neutrophils. This led to a larger fraction of P_N for the PMNmed-IE model in comparison to the spon-IE model and the alivePre-IE model (see Fig 9). Additionally, the PMNmed-IE model predicted an optimal value for the intracellular killing rate for monocytes (κ_M) that was the smallest compared to the other base models, whereas the rate of extracellular killing (κ_EK(t)) was the largest. However, these differences do not have an effect on the resulting model dynamics with regard to the killed pathogens (P_K), which is almost equal for all three base models (see Fig 9A). The LSE is larger for the PMNmed-IE model in comparison to the spon-IE model (P′ < 0.001) and the alivePre-IE model (P′ < 0.001). The three base models have similar LSE values that are not significantly different (P′ > 0.05) (see Fig 6C). However, in comparison to the other infection scenarios (see Fig 6A and 6B), the differences between the LSEs of the base models are smaller. Simulations of the alivePre-IE model led to the smallest AIC_C value being similar to the AIC_C of the spon-IE model with difference ΔAIC_C = 0.09, indicating that this model belongs to the category of models with substantial support (see Fig 7E and 7F). We observed a difference of ΔAIC_C = 4.19 for the PMNmed-IE model, indicating that this model belongs to the category of models with considerably less support than the alivePre-IE model with the smallest AIC_C value.

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Fig 9. Kinetics of combined units of each immune-evasion model for infection scenario with S. aureus.

Experimental data from whole-blood infection assays (dashed lines) with corresponding standard deviations (SDs) are compared to the simulated data (solid lines) for the S. aureus infection scenario. The simulated kinetics by the spon-IE model (light green line), PMNmed-IE model (pink line), alivePre-IE model (dark blue line), spon-alivePre-IE model (light blue line), PMNmed-alivePre-IE model (orange line), spon-PMNmed-IE model (red line) and spon-PMNmed-alivePre-IE model (dark green line) are shown in their corresponding color. The thickness of solid lines indicates the mean ± SD of 50 simulations with transition rate values that were randomly sampled within their respective SD. Simulated kinetics of killed cells (A), pathogens associated with monocytes (B), pathogens associated with PMN (C) and immune-evasive cells (D) for a S. aureus infection.

https://doi.org/10.1371/journal.pone.0249372.g009

The combined models of immune evasion could be calibrated to the whole-blood infection assays with S. aureus, resulting in LSEs that are not significantly different from those of the model with the smallest LSE, i.e. the spon-alivePre-IE model. Considering the AIC_C score, we observed that this model is better than the other combined models, because the difference ΔAIC_C classifies the model in the category of considerably less supported models, whereas the other combined models where classified in the category of models with essentially no support.

Taken together, for the infection scenario with S. aureus, we observed similar dynamics for all models with predicted reaction rates that are mostly similar. We found only minor differences in the predictions from the PMNmed-IE model. Furthermore, we observed that for S. aureus whole-blood infection the alivePre-IE model simulation led to the smallest AIC_C, being close to the AIC_C of the spon-IE model.

Patterns of immune reaction rates for the three infection scenarios are highly model-specific

After comparing the predictions by the various models for each infection scenario, we compared the predictions for all infection scenarios for each model separately. This is helpful in order to identify pathogen-specific patterns that differ between the immune evasion models. First, we compared the values of the rate of extracellular killing by antimicrobial peptides for the infection with C. albicans, C. glabrata and S. aureus at specific time points post infection. As shown in Fig 10A, the spon-IE model predicted the largest value of the extracellular killing rate for C. glabrata infection and the smallest value for C. albicans infection ( at t = 10 min) ten minutes post infection. In contrast, the PMNmed-IE model predicted a larger value of the extracellular killing rate for infection with S. aureus in comparison to C. albicans and C. glabrata infection, while the latter two rates are not significantly different from each other ( at t = 10 min0) (see Fig 10B). The third base model, the alivePre-IE model, also predicted that the infection by S. aureus cells leads to the largest extracellular killing rate, but the values for infection by C. glabrata and C. albicans are significantly different ( at t = 10 min) (see Fig 10C).

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Fig 10. Kinetics of extracellular killing rates estimated by immune evasion models for the three infection scenarios.

The predicted extracellular killing rate κ_EK(t) is shown for an infection with C. albicans (pink line), C. glabrata (blue line) or S. aureus (orange line). The subfigures show the time course of extracellular killing for the spon-IE model (A), the PMNmed-IE model (B), the alivePre-IE model (C), the spon-alivePre-IE model (D), the PMNmed-alivePre-IE model (E), the spon-PMNmed-IE model (F) and the spon-PMNmed-alivePre-IE model (G). The thickness of the lines indicates the mean ± standard deviations obtained by 50 simulations with normally distributed transition rates.

https://doi.org/10.1371/journal.pone.0249372.g010

As shown in Fig 10D–10G, the various combined immune evasion models predicted strikingly similar relations of the extracellular killing rates between the infection scenarios at ten minutes post infection. Similar to the pattern predicted by the spon-IE model, infection with C. glabrata induced a larger extracellular killing rate than infection with S. aureus, which in turn is larger than the value for C. albicans infection, i.e. at t = 10 min. However, additional evaluation of the relation of extracellular killing rates between the pathogens at one hour post infection revealed that the spon-PMNmed-IE model predicted another pattern than the other four models. The extracellular killing rate is larger for infection with C. albicans in comparison to infection with C. glabrata (with P′ < 0.001) (Fig 10F). The other three combined immune evasion models (Fig 10D, 10E and 10G) and the spon-IE model (Fig 10A) predicted similar values for C. albicans and C. glabrata at one hour post infection. Therefore, we conclude that the rate for extracellular killing provides a marker that enables to differentiate between three immune evasion models, i.e. the PMNmed-IE model, the alivePre-IE model and the spon-PMNmed-IE model. Moreover, the other four models predicted a unique pattern, which in turn is distinct from the previous three models.

By comparing the relation of immune evasion rates between the models, we identified more model-specific patterns. Since the PMNmed-IE model, the alivePre-IE model and the spon-alive-IE model can be clearly differentiated based on the rate for extracellular killing, we here focus on the four models that have a unique pattern for extracellular killing, i.e. the spon-IE model (Fig 11A), the spon-alivePre-IE model (Fig 11C), the PMNmed-alivePre-IE model (Fig 11D) and the spon-PMNmed-alivePre-IE model (Fig 11F). The spon-IE model and the spon-alivePre-IE model have immune evasion rates that are constant during infection and the predicted patterns for the relation between the infection scenarios are similar. However, because of the constant nature of the immune evasion rate, these models can be differentiated from the PMNmed-alivePre-IE model and the spon-PMNmed-alivePre-IE model with their time-dependent immune evasion rates (see Fig 11D and 11F). Additionally, we observed for the spon-PMNmed-alivePre-IE model that the order of the immune evasion rates for the different infection scenarios was constant during infection, while the PMNmed-alivePre-IE model predicted that this order changed during infection. As can be seen in Fig 11D, ten minutes post infection the rate for C. albicans infection is the smallest in comparison to C. glabrata and S. aureus infection, while from 70 minutes post infection, the rate is the largest for C. albicans.

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Fig 11. Kinetics of the immune-evasion rate estimated immune evasion models for the three infections scenarios.

The predicted immune-evasion rate is shown for an infection with C. albicans (pink line), C. glabrata (blue line) or S. aureus (orange line). The subfigures show the results for the spon-IE model (A), the PMNmed-IE model (B), the alivePre-spon-IE model (C), the PMNmed-alivePre-IE model (D), the spon-PMNmed-IE model (E) and the spon-PMNmed-alivePre-IE model (F). Note that the alivePre-IE model does not contain a rate for the acquisition of immune evasion and therefore it is not included in this figure.

https://doi.org/10.1371/journal.pone.0249372.g011

Additionally, we compared the relation of the other transition rates between the infection scenarios and we found that either all models predicted a similar pattern, such as for Φ_M and Φ_N with Φ^S.a. > Φ^c.g. > Φ^c.a., or the differences are not sufficient to differentiate between the spon-IE model and the spon-alivePre-IE model.

Taken together, the analysis of the relation of immune reaction rates between the three infection scenarios separately for each immune evasion model enabled us to identify distinct patterns for most immune evasion models. We found unique patterns for the PMNmed-IE model, the alivePre-IE model and the spon-PMNmed-IE model by analyzing the model predictions for the rate of extracellular killing. While the spon-IE model and the spon-alivePre-IE model predict similar patterns for all immune reaction rates, evaluating the rate for immune evasion revealed unique patterns for the PMNmed-alivePre-IE model and the spon-PMNmed-alivePre-IE model. This means that five out of seven immune-evasion models showed unique patterns for the rates of extracellular killing and immune evasion.

Fungal strains and culture

C. albicans wild-type strain SC5314 [32], GFP-expressing C. albicans strain (CaGFP) [1], C. glabrata wild-type strain ATCC2001 [33] and C. glabrata expressing GFP (CgGFP) [34] were routinely seeded in YPD medium (2% D-glucose, 1% peptone, and 0.5% yeast extract, in water) and grown overnight at 30°C (C. albicans strains) and 37°C (C. glabrata strains), respectively, in a shaking incubator. Fungal cells were reseeded 1:50 in fresh YPD medium, grown until they reach the mid-log phase (OD₆₀₀ ~ 1) followed by harvesting in HBSS.

Killing of C. albicans wild-type strain SC5314 or C. glabrata wild-type strain ATCC2001 was performed after staining with Cell Tracker^™Green (Invitrogen) for 1 hour using 0.1% thimerosal (Sigma-Aldrich) at 37°C for 1 hour and followed by extensively washing with HBSS.

Staphylococcus aureus strains and culture

S. aureus wild-type strain ATCC25923 and GFP-expressing S. aureus (SaGFP) [35, 36] were cultivated overnight in lysogeny broth (LB) medium (10 g/l tryptone, 5 g/l yeast extract, 10 g/l sodium chloride, pH 7) at 37°C in a shaking incubator. In case of SaGFP the lysogeny broth medium was supplemented with 10 μg/ml chloramphenicol. Bacterial cells were reseeded 1:100 in fresh lysogeny broth medium, grown until they reach the mid-log phase (OD₆₀₀ = 0.6–0.7) followed by harvesting in HBSS containing 10% heat-inactivated human serum (hiHS, Sigma-Aldrich).

Killing of S. aureus wild-type strain ATCC25923 was performed after staining with Cell Tracker^™Green for 30 minutes using 50% ethanol for four hours at 37°C and followed by extensively washing with HBSS+10%hiHS.

Human whole-blood infection assay

This study was conducted in accordance with the Declaration of Helsinki and all protocols were approved by the Ethics Committee of the University Hospital Würzburg (permit number: 37/17). Human peripheral blood was collected from healthy donors with written informed consent. The whole-blood infection assay was performed as described previously [1]. Briefly, alive GFP-expressing C. albicans, C. glabrata or S. aureus cells were added to Hirudin-anti-coagulated blood (1x10⁶ fungal or bacterial cells per milliliter of blood) and incubated at 37°C on a rolling mixer for indicated time points. Treatment of blood with either HBSS or HBSS containing 10% hiHS served as mock-infected control samples. After incubation, the samples were immediately placed on ice and subjected to flow cytometric analyses.

Flow cytometry

Analyses of immune cell populations in whole blood with regard to phagocytosis of fungal or bacterial cells were performed using differential FACS staining and subsequent measurement with a FACS Canto II (BD Bioscience). To distinguish different immune cells, whole blood was stained with mouse anti-human CD3 (clone SK7, T cells), CD19 (clone HIB19, B cells), CD56 (clone B159, NK-cells) and CD66b (clone G10F5, PMN) obtained from BD Biosciences. Monocytes were labeled with mouse anti-human CD14 antibody (clone 47-3D6, Abcam). The stained samples were treated with FACS Lysing solution (BD Biosciences) that lyses erythrocytes while preserving and fixing leukocytes, followed by washing and harvesting cells in CellWASH solution (BD Biosciences).

Detailed data analysis including gating of relevant immune cell populations was performed using FlowJo 7.6.4 software. The strategy used to evaluate the association of microorganisms to immune cells in human blood was shown for CaGFP in Hünniger et al. [1].

Propidium iodide staining and imaging

To evaluate the amount of dead CaGFP, CgGFP or SaGFP cells in a fresh induction culture, microorganisms were stained with 2.5 ng/ml of propidium iodide (Sigma-Aldrich). Propidium iodide (PI) is widely used as a vital dye that is not permeant to live cells, but labels the nucleus in dying cells, which lack an intact plasma membrane. Thimerosal-killed Cell Tracker^™Green-labeled C. albicans or C. glabrata and ethanol-killed Cell Tracker^™Green-labeled S. aureus cells, respectively, served as controls for a positive PI staining. Fluorescence images of C. albicans and C. glabrata samples were acquired with the Zeiss AxioObserver Z.1 microscope using a 40x objective (EC Plan-Neofluar 40x/0,75) and processed using the ZEN 2.3 software (Carl Zeiss). Images of S. aureus samples were acquired with the LSM 780 confocal microscope using a 63x objective (Plan-Apochromat 63x/1.4 Oil DIC) and processed using the ZEN 2.3 software.

Automated image analysis

The microscopy images consist of two different channels: the green fluorescence channel with GFP-labeled pathogens and the red fluorescence channel for pathogen live/dead PI staining (S27 Fig of S1 File). The microscopy images with either C. albicans cells or C. glabrata cells were analyzed and counted by the automated segmentation algorithm that is integrated within the framework AMIT (Algorithm for Migration and Interaction Tracking) [14, 37, 38]. In brief, the green fluorescence images were segmented and cell clusters were split into their constituent cells using the implemented cluster splitting algorithm that is based on the method of Farhan et al. [39]. Here, a cluster was split after identifying the concave contour regions between the borders of neighboring convex cells. Since the parameters of this cluster splitting method are strongly dependent on pathogen specific properties, such as the average diameter of the respective cells, we adapted these parameters individually for each type of pathogen following the guidelines given by Brandes et al. [14]. The respective parameter values are given in S4 Table of S1 File. In case of C. albicans cells and C. glabrata cells, we observed reproduction by budding where small outgrowths are formed. These smaller daughter cells adhere to the mother cell and are only evaluated as a new cell if they reach the size of an average cell. The cluster splitting algorithm detected cells with a large bandwidth of different area sizes. To prevent daughter cells from being counted as single cells, these were excluded by a histogram threshold method over the area sizes (see S4 Table of S1 File).

In the case of S. aureus cells with sizes of only 1 μm in diameter–corresponding to five pixels à 0.2 μm–an alternative segmentation approach was applied involving a pixel-based thresholding approach. Since the illumination was varying from image to image, handling of S.aureus images was done in the following way: Images showing local inhomogeneities with a small contrast between the cell border and the background intensity were pre-processed by a contrast enhancement, where the image intensity was stretched over the whole range of intensity values. In order to remove background noise and emphasize the cells itself, a median filter with kernel size 4 × 4 px was used. Finally, a global thresholding was performed on the image intensity histogram to reduce noise in the images. The number of S.aureus cells was then determined by dividing the amount of foreground pixels through the average cell size. In order to determine the total number of dead cells, the resulting segmented image was applied as a binary mask for the PI stained channel that was processed by the same three methods, i.e. thresholding, median filtering and contrast enhancement.

Whole-blood infection modeling

In this study, we generated mathematical models with different mechanisms for immune evasion of pathogens in whole blood. These state-based models (SBMs) were derived from our previous models of whole-blood infection [1, 12]. In order to compare the dynamics of the SBMs with the time-resolved experimental measurements, we defined the five combined units P_E, P_M, P_N, P_A and P_K as variables that combine specific states, which represent specific cell populations. The combined unit P_E is defined by (1) and incorporates all states that represent extracellular pathogens, i.e. states for extracellular pathogens that are alive (P_AE) or killed (P_KE), or immune-evasive pathogens that are alive (P_AIE) or killed (P_KIE). Pathogens phagocytosed by PMN or monocytes are respectively recorded within the combined units (2) and (3)

Here, the states N_i,j and M_i,j represent neutrophils and monocytes respectively, with the number of i alive pathogens and j killed pathogens. We limit the maximal number of phagocytosed pathogen cells to nine (i.e. j<10), a value far above what has been observed in experiments [1]. The combined unit P_A contains all states that represent alive pathogens and is defined by (4) whereas the combined unit of killed pathogens is given by (5)

Note that the total number of pathogens is given by P ≡ P_E + P_N + P_M and P ≡ P_A + P_K. Biological processes that take place during the immune response to the pathogens are represented by state transitions characterized by transition rates. All SBMs contain at least four types of state transitions that are the phagocytosis by PMN or monocytes, the intracellular killing by PMN or monocytes and the extracellular killing of pathogens (see S5 Table of S1 File). The implementation of the immune-evasion mechanism of pathogens differs between the SBMs as described in the next subsection.

The SBMs were applied to simulate the immune response to 1 × 10⁶ pathogens in 1 ml blood containing 5 × 10⁶ PMN and 5 × 10⁵ monocytes; thus, the initial conditions of the model simulation are P_A(t = 0) = 1 × 10⁶, N_0,0(t = 0) 5 × 10⁶, M_0,0(t = 0) 5 × 10⁵. The time-evolution of the SBMs is calculated by the random selection simulation algorithm using a time-step driven, synchronous update scheme [40] (see S1 Fig of S1 File for the flow chart of the algorithm). In this simulation algorithm, the simulation time is divided into discrete time-steps with distance Δt and at each simulation time-step a transition from state S to state S′ can be performed with probability P_S→S′ = r_S→S′ × Δt, where r_S→S′ denotes the corresponding transition rate. In S5 Table of S1 File, a complete list of transition rates of the SBMs is given. Here it can be seen that the SBMs contain common transition rates for the following transitions: phagocytosis by PMN or monocytes, intracellular killing by PMN or monocytes as well as extracellular killing. The killing of pathogens in the extracellular space is caused by antimicrobial peptides released during the first-time phagocytosis of PMN. Therefore, the rate for extracellular killing κ_EK(t) is defined by (6) and describes the time-dependent effect of antimicrobial peptides by the constant rate , a half-life time characterized by the rate γ and the number of first-phagocytosis events (N_PE) per PMN (N_0,0).

For further information about the model structure, the simulation algorithm as well as the estimation of transition rate values using the global optimization algorithm Simulated Annealing we refer to our previous studies by Hünniger et al. [1] and Lehnert et al. [12].

In order to investigate the unresolved mechanism of immune evasion of pathogens, we generated various SBMs that differ in the implementation of the rate for the acquisition of an immune-evasive state. We implemented two models with solely one immune-evasion mechanism, two models without an evasion mechanism but instead with either populations of alive and killed pre-existing evasive cells or with only alive pre-existing cells. We refer to these models as base models in the following. Additionally, we implemented four so called combined models that are composed of at least two base models and thereby contain more than one option for the acquisition of immune evasion. The representation of the different immune-evasion mechanisms in the SBMs is described in the following section and an overview is given in Table 1. The source code of all models is available in the Immune evasion repository at https://asbdata.hki-jena.de/LehnertEtAl_PLOS/.

Modeling immune evasion of pathogens

The population of pathogens that can evade the immune response in whole blood was first described in our studies by Hünniger et al. [1] and Lehnert et al. [12]. In these studies, experimental measurements revealed that at four hours post infection alive and extracellular pathogens are present. These observations gave rise to define the transitions (7) and (8) where extracellular pathogens that are alive (P_AE) or killed (P_KE) can become immune-evasive pathogens that are alive (P_AIE) or killed (P_KIE) and thereby cannot be phagocytosed by immune cells and/or killed. The corresponding transition rate was defined by (9) since there were no information about this mechanism known and we consequently assumed that the process occurs spontaneously (see Fig 1A). In the following, we refer to this model as spon-IE model.

In the subsequent study by Prauße et al. [2], we took advantage of the strength of mathematical modeling and implemented the PMNmed-IE model to test the hypothesis that the acquisition of immune evasion is mediated by PMN. More precisely, we speculated that during first-time phagocytosis by PMNs not only molecules causing extracellular killing will be released but also specific molecules that aims at protecting pathogens against the immune system (see Fig 1B). In the PMNmed-IE model, we replaced the constant transition rate of the spon-IE model and defined the time-dependent rate for the acquisition of immune evasion by (10)

Similar to the time-dependent rate for extracellular killing κ_EK(t) (see Eq 6), this rate represents the time-dependent effect of specific molecules that were secreted upon the first-time phagocytosis events by PMN (P_PE). The effect of these molecules is specified by the constants and γ_IE and decreases exponentially.

In addition, we investigated the hypothesis that immune-evasive cells do not develop during immune response to pathogens but instead are present before infection as pre-existing immune-evasive cells (see Fig 1C). To this end, we implemented two models that do not contain the transition from the extracellular state to the immune-evasive state (see Eqs 7 and 8), but rather contain constant populations of immune-evasive cells that are present during the infection time. In the pre-IE model, we assume that both alive and killed evasive pathogens are present before infection and therefore set the number of alive and killed immune-evasive cells at time point of infection t = 0 to P_AIE > 0 and P_KIE > 0. The alivePre-IE model contains exclusively alive evasive pathogens (see Fig 1D) and therefore, we set P_AIE > 0 and P_KIE > 0 at time point of infection t = 0.

Thereby, the number of a priori unknown transition rates decreased in these two models in comparison to the spon-IE and the PMNmed-IE models. However, the numbers of alive and killed immune-evasive cells at time t = 0 min are additional a priori unknown values and have to be estimated in the course of the parameter estimation. The total number of parameters of each SBM that has to be estimated is given in Table 1. As a starting value of evasive cells, the algorithm randomly chooses a value in the range of the mean ± standard deviation of experimentally measured pathogens that are free in extracellular space and not associated with immune cells at four hours post infection (see Fig 2B).

Furthermore, we implemented four SBMs with more than one of the above described evasion mechanisms in order to investigate the possibility that immune evasion of pathogens could be developed in various ways. As given in Table 1, we implemented not only three SBMs with two evasion mechanisms, i.e. the spon-PMNmed-IE model, the spon-alivePre-IE model and the PMNmed-alivePre-IE model, but also one SBM with three immune-evasion mechanisms, the spon-PMNmed-alivePre-IE model.

Model parameter estimation by Simulated Annealing

The estimation of optimal values for the transition rates of the different immune evasion mechanism was rformedperformed by the global optimization method Simulated Annealing based on the Metropolis Monte Carlo scheme [41]. Starting with a random position in the parameter space, the algorithm performs a random walk and decides for the next step based on a score of the deviations between the model simulation with model parameters and experimental data, i.e. the weighted sum of least-square errors (LSE) (11)

Here, ω_c is defined as the specific weight of the LSE (12) which is defined as the sum of the squared difference between the experimental data () and the comparable simulated data (), which forms the combined unit c, for each time point k. The definition of each combined unit is provided in the methods section “Whole-Blood Infection Modeling”. The weights used for the infection scenarios with C. albicans and C. glabrata were taken over from our previous studies [1, 2]. For infection with S. aureus, we used the same weights as for C. albicans infection.

In course of the random walk through the parameter space, the next step will be performed by accepting a parameter set with a smaller in comparison to , the score of the current parameter set , i.e. . However, the Metropolis Monte Carlo scheme enables that also parameter sets with a larger LSE are accepted with a certain probability, the acceptance probability, which is dependent on the Boltzmann distribution and decreases with the increasing number of fitting steps f. The acceptance function plays the role of the “system’s temperature”, which decreases during the annealing process. The flowchart in S2 Fig of S1 File shows the algorithm. For a detailed description of this algorithm we refer to our previous studies of Hünniger et al. [1] and Lehnert et al. [12]. The source code of this algorithm is available in the Immune evasion repository at https://asbdata.hki-jena.de/LehnertEtAl_PLOS/.

We repeated the whole fitting procedure to increase the statistical robustness of this procedure. Furthermore, we performed this procedure for different system sizes by starting with P = 100 cells, M_0,0 = 50 cells and N_0,0 = 500 cells and stepwise increasing the number of cells by a factor of ten, while keeping the ratio of pathogens and immune cells constant. The optimal parameter set of a system size was used as starting point for the fitting procedure of the next larger system size until the system size of 1 ml blood with P = 10⁶ cells, M_0,0 = 5 · 10⁵ cells and M_0,0 = 5 · 10⁶ cells is reached.

Model comparison based on information criterion

In order to compare the different mathematical models for the immune evasion of pathogens, we applied the Akaike information criterion (AIC) [13]. This score aims to rank the different models by including not only the agreement of the model kinetics with the experimental data, like the LSE (see Eq 12), but also by incorporating the complexity of the models regarding the number of parameters. For least-square estimation, the AIC is defined by (13) as described by Burnham et al. [42]. Here, K denotes the number of parameters that is directly proportional to the penalty defined in the second term. The first term of Eq 13 represents the penalty by the number of independent experimental data points n and by the deviation of the model and the experimental data in terms of the sum of squared residuals (14)

This variable is calculated by the sum of the squared differences between experimental data (x^exp) and simulated data () resulting from simulating the model with the optimal parameter set at each of the ith experimentally measured data points (i = 1, 2, 3, …, 27). The corrected version of the AIC, the (15) must be applied if n/K ≤ 40, i.e. the number of model parameters is large relative to the number of experimental data points n [42]. For each of the m models, the AIC_C value was calculated and, subsequently, the relative measure (16) was used to rank the models. Here, denotes the relative AIC_C difference of the ith model with to the model with the smallest AIC_C (). Based on this difference the models were categorized by means of the following assessment guidelines [43]

Statistical analysis

Statistical analysis was performed by applying the following steps. First, we test whether the underlying data is normally distributed using the Shapiro-Wilk test. If the data was normally distributed, the unpaired t-test was used to test for significant differences. If the data was not normally distributed the Mann-Whitney U test (Wilcoxon rank-sum test) was applied to test unpaired samples for significant differences. If comparisons were made between several data sets, a multiple comparison correction (Bonferroni’s correction) was performed afterwards. The corrected P-value is given by P′. Significance is shown as *P′ < 0.05, **P′ < 0.001, ***P′ < 0.001.