Dynamic Interplay of Host and Pathogens in an Avian Whole-Blood Model

Microbial survival in blood is an essential step toward the development of disseminated diseases and blood stream infections. For poultry, however, little is known about the interactions of host cells and pathogens in blood. We established an ex vivo chicken whole-blood infection assay as a tool to analyze interactions between host cells and three model pathogens, Escherichia coli, Staphylococcus aureus, and Candida albicans. Following a systems biology approach, we complemented the experimental measurements with functional and quantitative immune characteristics by virtual infection modeling. All three pathogens were killed in whole blood, but each to a different extent and with different kinetics. Monocytes, and to a lesser extent heterophils, associated with pathogens. Both association with host cells and transcriptional activation of genes encoding immune-associated functions differed depending on both the pathogen and the genetic background of the chickens. Our results provide first insights into quantitative interactions of three model pathogens with different immune cell populations in avian blood, demonstrating a broad spectrum of different characteristics during the immune response that depends on the pathogen and the chicken line.

RNA was isolated from 100 μl whole blood of each animal, infection, and time point, and aliquots of the eluted RNA were used for subsequent RT-PCR. Due to variations in leucocyte numbers (see Supplementary Table 1 and Figure 2) resulting in variations in RNA content, some variation was expected and observed for GAPDH Ct values (mean ± SD):

Model Parameter Estimation
In order to estimate the values of the a priori unknown transition rate, we applied the method Simulated Annealing based on Metropolis Monte Carlo [REF: Kirkpatrick 1983]. This global parameter estimation algorithm is able to find optimal model parameter values that yield the best fit of the simulated model kinetics to experimental measurements. The algorithm performs a random walk through the multi-dimensional parameter space. At each position on this walk, the set of model parameters ⃗ is scored by calculating the distance of the model simulation with ⃗ to the experimental data. This is performed by calculating the weighted sum of the least squares errors (LSE) where the weight is specific for each combined unit . The least squares error (LSE) is given by and is defined as the sum of the squared difference between the experimental data ( , ) and the comparable simulated data ( , ), which forms the combined unit , for each time point . The definition of each combined unit is provided in the main manuscript in section 2.8. Mathematical Modeling.
Based on the current position ⃗ in the parameter space, the next potential position ′ ���⃗ is calculated by varying ⃗ in the range of 0 to 10%. Whether this parameter set is accepted and thereby, this step will Here, ∈ [0,1] is a uniformly distributed random number that and ( ) plays the role of the inverse 'system temperature'. If the annealing process starts and the temperature decreases with continuing fitting steps , the inverse temperature ( ) increases according the Hill function where the Hill exponent and the parameter K denote the smooth increase of ( ) from 0 to ∞ with increasing . Thereby, the acceptance probability of worse parameter sets, i.e. those with a larger score, decrease with continuing fitting steps. By accepting worse parameters by means of the Metropolis criterion, local minima can be passed and the global minimum can be found.
In order to increase the statistical robustness of this procedure, we repeated the whole procedure starting at randomly chosen positions in the parameter space and calculated the mean and the standard deviations. Furthermore, we performed the fitting procedure for different system sizes. We stepwise increased the number of cells in the system by factor 10 until the real system size is reached.
Since the more realistic system sizes are associated with increasing computational effort, we adapted the number of fitting steps to avoid computational overload. The settings of the estimation algorithm for the different system sizes are provided in Supplementary Material.

Model comparison based on Akaike Information Criterion
The different mathematical models of avian whole-blood infection were compared using the Akaike information criterion (4). This score aims at ranking the different models by not only including the agreement of the models with experimental data, like the LSE (see Eq 8), but also by incorporating the complexity of the models regarding the number of parameters. As described in Burnham et al. 2014 (5), in the special case of least squares estimation, the AIC is defined by Here, the second term represents the penalty by the number of model parameters , which increases proportionally with . The first term of Eq. 5 determines the influence by the number of independent experimental data points and the agreement of the model with the experimental data by the sum of squared residuals This variable is calculated by sum of the squared differences between experimental data ( ) and simulated data ( � ⃗ �) resulting from simulating the model with the optimal parameter set ⃗ at each of the ℎ experimentally measured data points ( = 1, 2, 3, … , 48). If the number of experimental data points is small relative to the number of model parameters , i.e. when ≤ 40, then the corrected version of the AIC, the must be applied (5). After calculating the AIC c value for each of the models, the models were ranked according a relative measure the Here, the relative AIC c distance of the ℎ model with to the best model, i.e. the model with the smallest AIC c ( ), is calculated.
This distance is used to categorize the models by means of the following assessment guidelines (6)

Supplementary Figure 4: Total least squares error (LSE) and corrected Akaike information criterion ( ) of the SBMs for different infection scenarios.
The LSE scores the agreement between experimental data and simulated data by the SEK-SBM (single extracellular killing mechanism of pathogens) and the MEK-SBM (multiple extracellular killing mechanisms of pathogens). The data points and error bars depict the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. The model simulations were calibrated to experimental data of whole-blood infection of samples from WLA and R11 chicken with C. albicans (A), E. coli (B) and S. aureus (C). The corrected AIC ( ) additionally involves the model complexity of the SBMs and is calculated for simulations of whole-blood infection with C. albicans (D), E. coli (E) and S. aureus (F). (A, B), E. coli (C, D) and S. aureus (E, F) that were injected into whole-blood samples from WLA chickens (left column) and R11 chickens (right column). The thickness of the solid lines represents the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. Experimental data are represented by black data points that are connected by dashed lines as guide for the eye.

Supplementary Figure 6: Time course of the rate for extracellular killing by antimicrobial peptides predicted by the SEK-SBM (single extracellular killing mechanism of pathogens) and the MEK-SBM (multiple extracellular killing mechanisms of pathogens).
The thickness of the solid lines represents the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. These rates were predicted by calibrating the models to experimental data of whole-blood samples from WLA chickens (left column) and R11 chickens (right column) that were infected with C. albicans (A, B), E. coli (C, D) and S. aureus (E, F). cells (A, B), E. coli cells (C, D) and S. aureus cells (E, F) that were injected into whole-blood samples from WLA chickens (left column) and R11 chickens (right column). The thickness of the solid lines represents the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. Experimental data are represented by black data points that are connected by dashed lines as guide for the eye.

Supplementary Figure 8: Rates for phagocytosis of pathogens by heterophils ( ) and monocytes ( ) predicted by the SEK-SBM (single extracellular killing mechanism of pathogens) and the MEK-SBM (multiple extracellular killing mechanisms of pathogens).
The models were calibrated to experimental data of infection scenarios with C. albicans cells (left column), E. coli cells (middle column) and S. aureus cells (right column) that were injected into whole-blood samples from WLA chickens (A-C) and R11 chickens (D-E). cells (A, B), E. coli cells (C, D) and S. aureus cells (E, F) that were injected into whole-blood samples from WLA chickens (left column) and R11 chickens (right column). The thickness of the solid lines represents the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. Experimental data are represented by black data points that are connected by dashed lines as guide for the eye. Figure 11: Comparisons of kinetics of heterophils simulated by the SEK-SBM (single extracellular killing mechanism of pathogens) and the MEK-SBM (multiple extracellular killing mechanisms of pathogens). Model simulations (solid lines) of infection scenarios with C. albicans cells (A, B), E. coli cells (C, D) and S. aureus cells (E, F) that were injected into whole-blood samples from WLA chickens (left column) and R11 chickens (right column). The thickness of the solid lines represents the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. Experimental data are represented by black data points that are connected by dashed lines as guide for the eye.

Supplementary Figure 12: Time course of the heterophil number during infection simulated by the MEK-SBM without immune cell killing by extracellular mechanisms induced by pathogens with rate
for heterophils and rate for monocytes. The model was calibrated to experimental data on whole-blood infection of samples from WLA chickens (A) and R11 chickens (B). Experimental data are represented by data points that were connected by dotted lines as guide for the eye. The resulting decrease of heterophils in WLA chicken is caused by killing due to the experimental setup with rate .
Supplementary Figure 13: Time course of the monocyte number during infection simulated by the MEK-SBM without immune cell killing by extracellular mechanisms induced by pathogens with rate for heterophils and rate for monocytes. The model was calibrated to experimental data on whole-blood infection of samples from WLA chickens (left column) and R11 chickens (right column). Experimental data are represented by data points that are connected by dotted lines as guide for the eye.

Supplementary Figure 14: Total least squares error (LSE) and corrected Akaike information criterion (
) of varius SBMs. The LSE scores the agreement between experimental data and simulated data of the SEK-SBM (single extracellular killing mechanism of pathogens), the MEK-SBM (multiple extracellular killing mechanisms of pathogens) and the MEK-SBM with additional immune cell killing mechanism of lysis by pathogens. The data points and error bars depict the mean ± standard deviation of simulation results observed from 50 simulations for normally distributed transition rates. The model simulations were calibrated to experimental data of whole-blood samples from WLA and R11 chicken that were infected with C. albicans (A), E. coli (B) and S. aureus (C). The corrected AIC ( ) additionally involves the model complexity of the SBMs and is calculated for simulations of whole-blood infection with C. albicans (D), E. coli (E) and S. aureus (F).