Pneumonia is a highly prevalent disease that kills almost 1 million children annually (McIntosh, 2002). The most frequent cause of pneumonia is infection with a strain of Streptococcus pneumoniae (S.p. or pneumococcus) (Sharma et al., 2007). Elderly and immunosuppressed people are high-risk groups because S.p. is an opportunistic pathogen (El-Solh et al., 2001; Wong and Evans, 2017). Although its virulence is limited, the pathogen achieves high morbidity because it is able to spread from permanent reservoirs in the nasopharyngeal airways which it colonizes asymptomatically in 15% of the general population and in about 40% of children (Tuomanen and Masure, 1997; Sjöström et al., 2006; de Lastours et al., 2016). Nasopharyngeal colonies are also more resistant to antibiotics compared to colonies in the lung (Perez et al., 2014), which makes controlling or eradicating the disease in the population a highly complex endeavor. Vaccination against S.p. is possible, but the efficacy of the vaccine is low in the risk groups (children, the elderly, and immunosuppressed people) due to the limited immune response triggered by the vaccine in these groups (Sjöström et al., 2006; Nguyen et al., 2017). Bacterial pneumonia begins with an infection of the alveolar cavities, but nasopharyngeal colonization precedes alveolar infection (Mandell, 2009). When the alveolar infection is recognized by the host, the immune system triggers an acute response culminating in substantial inflammation of the surrounding tissue. The inflammation itself compromises the alveolar gas exchange and potentially endangers the life of the patient (Henriques-Normark and Tuomanen, 2013). The disease can also worsen into septicaemia or bacterial encephalitis, increasing the patient's mortality risk (Henriques-Normark and Tuomanen, 2013; Iovino et al., 2016). Under these circumstances, optimum protection of high-risk patients would encompass preventing or impeding the initial alveolar infection, i.e., at the asymptomatic stage of the disease.

Streptococcus pneumoniae is able to generate an asymptomatic biofilm structure with high antibiotic resistance in the nasopharyngeal tissue (Simell et al., 2012; Perez et al., 2014). This structure is a prerequisite for a successful infection of the alveolar tissue (Simell et al., 2012). Nasopharyngeal co-infections, for instance by Haemophilus influenzae, can lead to immune stress on S.p. and thus trigger the release of bacteria from the biofilm to the lower airways, from where they can reach the alveoli and initiate infection (Chao et al., 2015). This stage likewise involves phenotypic transition of the bacteria from an unencapsulated, avirulent phenotype to a virulent one with a capsule (Simell et al., 2012; Weiser et al., 2015). It has been established that S.p. in the biofilm adopts a transparent appearance due to the lack of a capsule, which makes them more adherent but less invasive (Brueggemann et al., 2004; Kadioglu et al., 2008). Further, some studies have found that encapsulated bacteria are better able to colonize the alveolar surface and other tissues (Brueggemann et al., 2004; Hammerschmidt et al., 2005). Apart from the capsule (Jedrzejas, 2001), it has not yet been established which specific virulence factors permit S.p. to colonize the lower airways. Though gene expression differences between the biofilm and the virulent phenotype have been recorded (Lanie et al., 2007), the availability of these data has not led to an understanding of the early stages of alveolar infection.

When bacteria enter the alveolar lumen, they are exposed to a set of immunological barriers that prevent or impede infection. During initiation of the infection, the most relevant barriers are the tightly sealed epithelium, the alveolar lining fluid, and the alveolar macrophages (Sherman and Ganz, 1992). The epithelial cell layer with its tight junction-mediated intercellular adhesion acts as a physical barrier (Knight and Holgate, 2003). Furthermore, the epithelial cells are able to recognize the pathogens and release chemokines and cytokines that recruit and activate immune cells (Diamond et al., 2000). The primary role of the chemokines thus produced, such as MCP-1, is to attract resident alveolar macrophages to the site of infection (Deshmane et al., 2009), but in later stages other pro-inflammatory cytokines and chemokines recruit and activate neutrophils, monocytes, and leucocytes from the blood (Craig et al., 2009; Shi and Pamer, 2011; Hickey and Westhorpe, 2013). In the lining fluid, there are many factors that can inactivate pathogens, for instance complement proteins (Kadioglu and Andrew, 2004; Martin and Frevert, 2005). Also, the lining fluid acts as a means for the clearing of particles (including pathogens) from the alveolus, as the fluid is continuously produced and flows outwards toward the alveolar opening, dragging suspended bacteria along (Lindert et al., 2007). Finally, the macrophages serve as a mobile defense mechanism against the first stages of bacterial infection (Moldoveanu et al., 2008; Wilson et al., 2015). These cells follow and phagocytise bacteria, eliminating them before the infection becomes productive.

To recruit other immune cells, the resident cells in the alveoli produce pro-inflammatory cytokines, such as IL-8 and IL-1β, as well as chemokines (Standiford et al., 1990; Descamps et al., 2012). The phagocytic function of alveolar macrophages is then sequentially supplemented in later phases of the infection by other phagocytic cells, namely neutrophils and monocyte-derived macrophages (Mizgerd, 2002; Goto et al., 2004; Craig et al., 2009). Much later, the adaptive immune system controls the disease in a targeted manner.

The response to bacterial infection in the lung alveoli involves interactions between several types of immune and epithelial cells. The activation of key phenotypes in these cells is driven by intracellular molecular networks, each of which is distinctively activated in the course of the infection (Eberhardt et al., 2016; Cantone et al., 2017). Interestingly, this biological system contains multiple intracellular and paracrine positive and negative feedback loops that regulate the immune response (Hoffmann et al., 2002; Ashall et al., 2009). This type of regulatory loop can generate counter-intuitive, non-linear behavior (Tyson et al., 2003). Deriving hypotheses on the pathogenesis of lung infection that acknowledge these different levels of regulation, or integrating different types of experimental data accounting for the pathogenesis, is a difficult and onerous task even for a well-trained researcher.

A feasible approach to the integration of data linking tissue, cellular and intracellular events, the derivation of hypotheses and experiment design is the use of mathematical model simulations (Vera and Wolkenhauer, 2008; Cantone et al., 2017). This approach proceeds by collection of biomedical knowledge from publications and databases and its conversion into a graphical representation that connects the relevant processes, cells and molecules. On the basis of specific heuristic rules, this representation is encoded in a mathematical model that consists of equations, computational rules and other mathematical entities. Quantitative experimental data are used to characterize the mathematical model by assigning values to the parameters in the model equations in a process termed calibration. In a biomedical context, a calibrated model combined with experimental data can be used to dissect the fine tuning of regulatory pathways in immune cells or bacteria in the course of infection (Shih et al., 2012; Ben-Jacob et al., 2014), find new biomarkers for disease prognosis (Khan et al., 2017), analyse the feasibility of conventional or personalized treatments or detect new drug targets (Schoeberl et al., 2009; Passante et al., 2013), and gain understanding of complex ecological interactions between bacterial species during upper respiratory tract infection (Lysenko et al., 2010; Margolis et al., 2010; Mukherjee et al., 2014). In addition to this, models and their simulations can also be used to generate new hypotheses about the molecular and cellular pathophysiology of lung infection. Schultz et al. derived a mathematical model, calibrated with quantitative time series data, accounting for the interplay between macrophages and lung epithelial cells during L. pneumophila infection. They used simulation-based sensitivity analysis to conceive the hypothesis of a paracrine mechanism of macrophage-secreted IL-1β able to induce a prolonged degradation of the signaling factor IRAK-1 in lung epithelial cells. This model-based prediction was then corroborated with additional experiments (Schulz et al., 2017).

In line with this approach, we constructed, and characterized with available experimental data, a multi-level mathematical model derived to simulate the interactions between the host and S.p. inside a single alveolus during the first 10 h of infection. Previous work on multi-level modeling in the lung has sought to understand some key molecular interactions in fungal infections (Cilfone et al., 2013; Pollmächer and Figge, 2014, 2015; Oremland et al., 2016; Pollmächer et al., 2016). Our model combines ordinary differential equations (ODE) to simulate the activation of intracellular pathways in lung epithelial cells and an agent-based model to simulate the cell-to-cell interactions between bacteria, epithelial cells and macrophages. We confirmed that our mathematical model has predictive abilities by simulating the effect of removing some components of the model and comparing it with experimental observations. Next, we combined mathematical modeling-based simulations with data analysis techniques to derive phenotypic-genotypic signatures associated with bacterial infectivity. This methodology is an extension and adaptation of a previous workflow employed in the detection of cancer gene signatures (Vera et al., 2013; Santos et al., 2016; Khan et al., 2017). With our results, we constructed falsifiable hypotheses about the key molecular and cellular events in the early phase of lung S.p. infection and discuss them in the context of existing experimental evidence.

Streptococcus pneumoniae may prove a threat to life for immunocompromised patients, children and elderly people. An interesting strategy for the protection of these high-risk groups would be preventative interventions that stop the infection in its earliest stages, thus avoiding a systemic immune response; such interventions could be administered during periods of high infection risk (Cheng et al., 2015). Here, we propose harnessing the predictive ability of a mathematical model on the time course of infection in a single alveolus. The underlying idea is to make efficient use of modeling and simulations in order to conceive hypotheses on key physiological and bacterial parameters that distinguish between a successful infection and one rapidly cleared. Experiments can then be designed to test these hypotheses. Multi-level models allow for the integration of different temporal and spatial scales into a single mathematical model. This is particularly interesting in our context because alveolar infection involves interactions between the pathogen and the host cells at both the tissue and intracellular levels. In this work we have focused on the initial stages, an infection phase that involves essentially three types of cells (bacteria, epithelial cells, and macrophages) and a well-defined intracellular pathway.

Logistic regression analysis combined with systematic model perturbations and simulations provides a method for ranking model parameters and their associated processes in terms of their significance for the outcome of an early alveolar infection. The processes associated with the most important parameters could be investigated as targets for drug modulation in a preventative strategy.

At the tissue level, the most influential bacterial parameter predicted by the model and the logistic regression is the probability that the bacteria will remain in the same layer of the lining fluid. Transition between layers can be seen as a random process that alters the composition of the bacteria's capsule, thereby modifying adherence to the epithelial cells (Hammerschmidt et al., 2005); the higher the probability of this transition, the higher the turnover of the bacterial surface receptors that modify its adherence. Our model simulations suggest that a low rate of change to bacterial adherence to the epithelial cell surface is important for producing successful infection. Interestingly, this model prediction correlates with the function of a known S.p. virulence factor, the Pneumococcal surface protein C, which is involved in adherence to the epithelial surface (Iannelli et al., 2004).

It is important to highlight at this point that the model assumes a trade-off for the bacteria between adherence and clearance to the epithelial cell layer. Floating bacteria can be easily removed from the alveolus by the lining fluid. Conversely, attached bacteria can quickly be recognized by the epithelial cells, which will then produce MCP-1 to attract macrophages and promote clearance. Our model predicts that, during the very early stages of alveolar infection, the accumulation of a minimal biomass inside the alveolus by prevention of the lining fluid-driven removal of bacteria is critical to a productive infection. According to our simulations, this can be achieved by keeping bacteria attached to the epithelial cell layer. This choice would produce a more robust macrophage response through the MCP-1 produced by the epithelial cells. For the bacteria, fine tuning of the dwelling parameter can promote dispersion of the bacteria through the alveolus in such a way that some bacteria clusters could escape from macrophages without being washed out by the lining fluid.

In our analysis, increased proliferation of pneumococci promotes infection of the alveolar tissue. This suggests that faster growth can be beneficial for the establishment of infection. In previous studies, it has been observed that the capsule production efficacy can impose a delay in bacterial growth, and this effect influences virulence (Hathaway et al., 2012); in our model we observe a similar correlation via the effect of doubling time on infectivity. The number of initial bacteria entering the alveolus is another important parameter promoting infection. This is in line with the observation that nasopharyngeal colonization precedes alveolar infection. The experimental evidence in the literature suggests that, in order to achieve successful bacterial infection in the lung, pneumococci first need to accumulate in the higher respiratory tract, to then be released to the lower respiratory tissue (Mandell, 2009). Our simulations support this idea.

The capsule is a polysaccharide layer that protects bacteria from phagocytosis by macrophages. Bacteria colonizing the nasopharyngeal tissue produce low levels of capsule (Hammerschmidt et al., 2005). The model includes the hypothesis that, in order to invade the lung, bacteria trigger capsule production to protect themselves from macrophages. This hypothesis is supported by in vitro observations (AlonsoDeVelasco et al., 1995). In line with this, we considered in our model a dynamic ability of bacteria to produce capsule, triggered upon invasion of the alveolus. The results suggest that the adherence effect of the capsule could actually impair its protective effect during the initial phases of infection. This result may explain why some highly invasive strains of S.p. display lower efficiency in capsule production (Weinberger et al., 2009).

Resident macrophages are the first immunological barrier in the alveolar tissue; their task is to quickly clear invading pathogens and remove other particles without activating other branches of the innate and adaptive immune response. According to our analysis, two parameters accounting for the features of the alveolar macrophages play an important role in early infection: the number of resident macrophages and their speed of movement. Promisingly, these results provide an explanation for the higher susceptibility of infants to pneumococcal infections (O'Brien et al., 2009): in infants, alveolar macrophages tend to be insufficiently mature (Saito et al., 2008), and this lack of maturation impairs the movement of the resident macrophages through the alveolar lumen.

Moving to the intracellular level of the model, one of the most significant parameters in the analysis is related to the molecular stability of the MCP-1 mRNA (kmmpc1deg), which is consistent with some experimental observations (Rose et al., 2003). The analysis shows that high stability of the MCP-1 mRNA increases bacterial numbers at the end of the simulation. From the model (Figure 3), we can observe that local increases in the production of MCP-1 can act as chemokine traps in which macrophages are retained after they clear the bacteria cluster that triggered MCP-1 production. This arises from the fact that the rate of chemokine decay is much smaller than the velocity of macrophages (which can also be observed in time-lapse videos of the simulations available at http://sysbiomed-erlangen.weebly.com/resources.html).

A second influential parameter is the stability of IKK, an upstream kinase mediator in the NF-κB signaling pathway. Specifically, this kinase phosphorylates and thus marks for degradation IκB, a major inhibitor of NF-κB activation and nuclear shuttling (Jacobs and Harrison, 1998). Strikingly, our model predicts that high stability of the IKK protein increases the success rate of early alveolar infection (Figure 8). Long-term NF-κB activation provoked by a more stable IKK would increase the duration of MCP-1 release after a transient stimulation. This long-term signal would again trap the macrophages after clearance of bacteria, thereby delaying the elimination of bacteria at other sites.

The above two parameters were responsible for almost half of the variability of the regression model. If we add to them the production rate of NF-κB (knfkbgain) and the degradation rate of the mRNA of the NF-κB inhibitor IκBa (kmikbadeg), we see four parameters accounting for 70% of variability. The degradation of the IκBa mRNA is higher in the high load group, again increasing the duration of MCP-1 production because NF-κB cannot be re-sequestered efficiently if the stability of the IκBa mRNA is low. Finally, the production rate of NF-κB is lower in the high load group, a situation that would represent a low intracellular total amount of NF-κB. It has to be noted that this is the only parameter that refers to a production rate rather than a degradation rate. Our model simulations suggest that with a low total amount of intracellular NF-κB, the system is not able to trigger MCP-1 production and promote rapid, macrophage-mediated control of the infection.

Decision tree analysis is a methodology for finding subpopulations within defined groups. In the context of our analysis, we were looking for subpopulations of solutions within the high load and low load groups. We obtained five subpopulations with high infectivity and two with low infectivity (Figures 10A–D). Interestingly, the subpopulations differ depending on the macrophages' state of maturation. If the velocity of the macrophages is low we can differentiate four subpopulations, but if velocity is high, we can observe only three.

Further, the number and nature of subpopulations identified depend on the values of bacterial doubling time and adherence (doub and dwel, respectively). The final outcome of the subpopulations will also depend on the number of initial bacteria (nbac). We note that all three parameters relate to bacteria phenotypes. The decision tree analysis indicates that the strategies available to the bacteria depend on a single immunological parameter of the host, the velocity of their macrophages (macm). If the host is immunocompetent and has “quick” macrophages, the bacteria can only attain a highly infective phenotype in one of two ways: either by having a very high dwelling probability and a high initial number of colonizing bacteria, or by having very high proliferation with lower dwelling probability. Conversely, if the host macrophages move slowly, three out of the four identified bacterial phenotypes achieve high infectivity. In this case, a high number of bacteria can be reached for intermediate to high values of both proliferation and dwelling probability, with a reduced need for high initial numbers of colonizing bacteria. Analogously, if the initial number of bacteria is high, a strain with low proliferation and intermediate dwelling probability or with low dwelling probability and high proliferation is able to establish a productive infection. In our opinion, these subpopulations, distinguished by only three bacterial parameters (dwel, doub, and nbac), can explain observations of diversity in the infectivity of different S.p. serotypes (Serrano et al., 2006).

In Table 2, we link our model predictions to published experimental observations that support them, at least partially. For example, our model simulations suggest that dwelling probability and bacterial adherence play a key role in the establishment of infection. Specifically, the model predicts that adherence to epithelial cells facilitates bacterial infection. Since the capsule decreases the adherence of pneumococci, we hypothesize that the bacterial capsule is an obstacle during early infection (Figure 11). The invading bacteria originate from the upper airway colonies and are metabolically adapted to high capsule production and low proliferation (Hathaway et al., 2012). Our results indicate that, in order to succeed in infecting the alveolus, the bacteria have to switch to a higher proliferative profile and decrease capsule production to strengthen their adherence to the epithelial cells. In line with this, Iannelli et al. (2004) found in S.p. infection experiments with mice that bacterial adherence factors such as pneumococcal surface protein C can act as virulence factors, increasing the risk of severe infection and sepsis (Iannelli et al., 2004), although the authors did not succeed in fully unraveling the mechanism. Our model predictions provide a mechanistic explanation for Iannelli's results. In our view, our hypothesis can be tested in animal models using an antibody binding to one of the adherence factors of the bacteria, such as pneumococcal surface proteins. Preliminary studies have pointed to the utility of this approach (Ferreira et al., 2009).

This paper proposes a multilevel mathematical model to the end of unraveling pathogen-host interactions during the first 10 h of alveolar invasion. Combining simulations and techniques of statistical analysis, we identified various bacterial strategies for infection of the lower airways. These predicted strategies explain experimental differences observed in S.p. serotype infectivity. We propose that certain human pneumococci isolate phenotypes can be explained, at least in part, by differences in bacterial proliferation rates and adherence capabilities. On the basis of these findings, we hypothesize that interventions based on decreasing the adherence of pneumococci to alveolar epithelial cells would be able to protect high-risk populations before the disease is established.

GS, XL, ME, and JV created the model; GS analyzed the model; GS, XL, ME, and JV discussed the results and wrote the manuscript.