Bifurcation analysis of a tuberculosis progression model for drug target identification.

Tuberculosis (TB) is a major cause of morbidity and mortality worldwide. The emergence and rapid spread of drug-resistant M. tuberculosis strains urge us to develop novel treatments. Experimental trials are constrained by laboratory capacity, insufficient funds, low number of laboratory animals and obsolete technology. Systems-level approaches to quantitatively study TB can overcome these limitations. Previously, we proposed a mathematical model describing the key regulatory mechanisms underlying the pathological progression of TB. Here, we systematically explore the effect of parameter variations on disease outcome. We find five bifurcation parameters that steer the clinical outcome of TB: number of bacteria phagocytosed per macrophage, macrophages death, macrophage killing by bacteria, macrophage recruitment, and phagocytosis of bacteria. The corresponding bifurcation diagrams show all-or-nothing dose-response curves with parameter regions mapping onto bacterial clearance, persistent infection, or history-dependent clearance or infection. Importantly, the pathogenic stage strongly affects the sensitivity of the host to these parameter variations. We identify parameter values corresponding to a latent-infection model of TB, where disease progression occurs significantly slower than in progressive TB. Two-dimensional bifurcation analyses uncovered synergistic parameter pairs that could act as efficient compound therapeutic approaches. Through bifurcation analysis, we reveal how modulation of specific regulatory mechanisms could steer the clinical outcome of TB.

Medical Systems Biology.

The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.

Modeling Procedures.

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

Case Studies.

The aim of this chapter is to illustrate the modeling procedures discussed in the previous chapter via three well-chosen examples.

Mathematical Modeling of Streptococcus pneumoniae Colonization, Invasive Infection and Treatment.

Streptococcus pneumoniae (Sp) is a commensal bacterium that normally resides on the upper airway epithelium without causing infection. However, factors such as co-infection with influenza virus can impair the complex Sp-host interactions and the subsequent development of many life-threatening infectious and inflammatory diseases, including pneumonia, meningitis or even sepsis. With the increased threat of Sp infection due to the emergence of new antibiotic resistant Sp strains, there is an urgent need for better treatment strategies that effectively prevent progression of disease triggered by Sp infection, minimizing the use of antibiotics. The complexity of the host-pathogen interactions has left the full understanding of underlying mechanisms of Sp-triggered pathogenesis as a challenge, despite its critical importance in the identification of effective treatments. To achieve a systems-level and quantitative understanding of the complex and dynamically-changing host-Sp interactions, here we developed a mechanistic mathematical model describing dynamic interplays between Sp, immune cells, and epithelial tissues, where the host-pathogen interactions initiate. The model serves as a mathematical framework that coherently explains various in vitro and in vitro studies, to which the model parameters were fitted. Our model simulations reproduced the robust homeostatic Sp-host interaction, as well as three qualitatively different pathogenic behaviors: immunological scarring, invasive infection and their combination. Parameter sensitivity and bifurcation analyses of the model identified the processes that are responsible for qualitative transitions from healthy to such pathological behaviors. Our model also predicted that the onset of invasive infection occurs within less than 2 days from transient Sp challenges. This prediction provides arguments in favor of the use of vaccinations, since adaptive immune responses cannot be developed de novo in such a short time. We further designed optimal treatment strategies, with minimal strengths and minimal durations of antibiotics, for each of the three pathogenic behaviors distinguished by our model. The proposed mathematical framework will help to design better disease management strategies and new diagnostic markers that can be used to inform the most appropriate patient-specific treatment options.

Mathematical modeling of atopic dermatitis reveals "double-switch" mechanisms underlying 4 common disease phenotypes.

BACKGROUND: The skin barrier acts as the first line of defense against constant exposure to biological, microbial, physical, and chemical environmental stressors. Dynamic interplay between defects in the skin barrier, dysfunctional immune responses, and environmental stressors are major factors in the development of atopic dermatitis (AD). A systems biology modeling approach can yield significant insights into these complex and dynamic processes through integration of prior biological data. OBJECTIVE: We sought to develop a multiscale mathematical model of AD pathogenesis that describes the dynamic interplay between the skin barrier, environmental stress, and immune dysregulation and use it to achieve a coherent mechanistic understanding of the onset, progression, and prevention of AD. METHODS: We mathematically investigated synergistic effects of known genetic and environmental risk factors on the dynamic onset and progression of the AD phenotype, from a mostly asymptomatic mild phenotype to a severe treatment-resistant form. RESULTS: Our model analysis identified a "double switch," with 2 concatenated bistable switches, as a key network motif that dictates AD pathogenesis: the first switch is responsible for the reversible onset of inflammation, and the second switch is triggered by long-lasting or frequent activation of the first switch, causing irreversible onset of systemic TH2 sensitization and worsening of AD symptoms. CONCLUSIONS: Our mathematical analysis of the bistable switch predicts that genetic risk factors decrease the threshold of environmental stressors to trigger systemic TH2 sensitization. This analysis predicts and explains 4 common clinical AD phenotypes from a mild and reversible phenotype through to severe and recalcitrant disease and provides a mechanistic explanation for clinically demonstrated preventive effects of emollient treatments against development of AD.