Mathematical Model for MRSA Nasal Carriage

Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical-experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth-conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

The ups and downs of S. aureus nasal carriage

Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model's behaviour were made including interacting effects of the bacteria's growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.

Robust Phagocyte Recruitment Controls the Opportunistic Fungal Pathogen Mucor circinelloides in Innate Granulomas In Vivo

Mucormycosis is an emerging fungal infection with extremely high mortality rates in patients with defects in their innate immune response, specifically in functions mediated through phagocytes. However, we currently have a limited understanding of the molecular and cellular interactions between these innate immune effectors and mucormycete spores during the early immune response. Here, the early events of innate immune recruitment in response to infection by Mucor circinelloides spores are modeled by a combined in silico modeling approach and real-time in vivo microscopy. Phagocytes are rapidly recruited to the site of infection in a zebrafish larval model of mucormycosis. This robust early recruitment protects from disease onset in vivoIn silico analysis identified that protection is dependent on the number of phagocytes at the infection site, but not the speed of recruitment. The mathematical model highlights the role of proinflammatory signals for phagocyte recruitment and the importance of inhibition of spore germination for protection from active fungal disease. These in silico data are supported by an in vivo lack of fungal spore killing and lack of reactive oxygen burst, which together result in latent fungal infection. During this latent stage of infection, spores are controlled in innate granulomas in vivo Disease can be reactivated by immunosuppression. Together, these data represent the first in vivo real-time analysis of innate granuloma formation during the early stages of a fungal infection. The results highlight a potential latent stage during mucormycosis that should urgently be considered for clinical management of patients.IMPORTANCE Mucormycosis is a dramatic fungal infection frequently leading to the death of patients. We know little about the immune response to the fungus causing this infection, although evidence points toward defects in early immune events after infection. Here, we dissect this early immune response to infectious fungal spores. We show that specialized white blood cells (phagocytes) rapidly respond to these spores and accumulate around the fungus. However, we demonstrate that the mechanisms that enable phagocytes to kill the fungus fail, allowing for survival of spores. Instead a cluster of phagocytes resembling an early granuloma is formed around spores to control the latent infection. This study is the first detailed analysis of early granuloma formation during a fungal infection highlighting a latent stage that needs to be considered for clinical management of patients.

Combining Two Methods of Global Sensitivity Analysis to Investigate MRSA Nasal Carriage Model

We apply two different sensitivity techniques to a model of bacterial colonization of the anterior nares to better understand the dynamics of Staphylococcus aureus nasal carriage. Specifically, we use partial rank correlation coefficients to investigate sensitivity as a function of time and identify a reduced model with fewer than half of the parameters of the full model. The reduced model is used for the calculation of Sobol' indices to identify interacting parameters by their additional effects indices. Additionally, we found that the model captures an interesting characteristic of the biological phenomenon related to the initial population size of the infection; only two parameters had any significant additional effects, and these parameters have biological evidence suggesting they are connected but not yet completely understood. Sensitivity is often applied to elucidate model robustness, but we show that combining sensitivity measures can lead to synergistic insight into both model and biological structures.