Concepts of multi-level dynamical modelling: understanding mechanisms of squamous cell carcinoma development in Fanconi anemia.

Fanconi anemia (FA) is a rare disease (incidence of 1:300,000) primarily based on the inheritance of pathogenic variants in genes of the FA/BRCA (breast cancer) pathway. These variants ultimately reduce the functionality of different proteins involved in the repair of DNA interstrand crosslinks and DNA double-strand breaks. At birth, individuals with FA might present with typical malformations, particularly radial axis and renal malformations, as well as other physical abnormalities like skin pigmentation anomalies. During the first decade of life, FA mostly causes bone marrow failure due to reduced capacity and loss of the hematopoietic stem and progenitor cells. This often makes hematopoietic stem cell transplantation necessary, but this therapy increases the already intrinsic risk of developing squamous cell carcinoma (SCC) in early adult age. Due to the underlying genetic defect in FA, classical chemo-radiation-based treatment protocols cannot be applied. Therefore, detecting and treating the multi-step tumorigenesis process of SCC in an early stage, or even its progenitors, is the best option for prolonging the life of adult FA individuals. However, the small number of FA individuals makes classical evidence-based medicine approaches based on results from randomized clinical trials impossible. As an alternative, we introduce here the concept of multi-level dynamical modelling using large, longitudinally collected genome, proteome- and transcriptome-wide data sets from a small number of FA individuals. This mechanistic modelling approach is based on the "hallmarks of cancer in FA", which we derive from our unique database of the clinical history of over 750 FA individuals. Multi-omic data from healthy and diseased tissue samples of FA individuals are to be used for training constituent models of a multi-level tumorigenesis model, which will then be used to make experimentally testable predictions. In this way, mechanistic models facilitate not only a descriptive but also a functional understanding of SCC in FA. This approach will provide the basis for detecting signatures of SCCs at early stages and their precursors so they can be efficiently treated or even prevented, leading to a better prognosis and quality of life for the FA individual.

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.

A combination approach of pseudotime analysis and mathematical modeling for understanding drug-resistant mechanisms.

Cancer cells acquire drug resistance through the following stages: nonresistant, pre-resistant, and resistant. Although the molecular mechanism of drug resistance is well investigated, the process of drug resistance acquisition remains largely unknown. Here we elucidate the molecular mechanisms underlying the process of drug resistance acquisition by sequential analysis of gene expression patterns in tamoxifen-treated breast cancer cells. Single-cell RNA-sequencing indicates that tamoxifen-resistant cells can be subgrouped into two, one showing altered gene expression related to metabolic regulation and another showing high expression levels of adhesion-related molecules and histone-modifying enzymes. Pseudotime analysis showed a cell transition trajectory to the two resistant subgroups that stem from a shared pre-resistant state. An ordinary differential equation model based on the trajectory fitted well with the experimental results of cell growth. Based on the established model, it was predicted and experimentally validated that inhibition of transition to both resistant subtypes would prevent the appearance of tamoxifen resistance.

Personalized prediction of daily eczema severity scores using a mechanistic machine learning model.

BACKGROUND: Atopic dermatitis (AD) is a chronic inflammatory skin disease with periods of flares and remission. Designing personalized treatment strategies for AD is challenging, given the apparent unpredictability and large variation in AD symptoms and treatment responses within and across individuals. Better prediction of AD severity over time for individual patients could help to select optimum timing and type of treatment for improving disease control. OBJECTIVE: We aimed to develop a proof of principle mechanistic machine learning model that predicts the patient-specific evolution of AD severity scores on a daily basis. METHODS: We designed a probabilistic predictive model and trained it using Bayesian inference with the longitudinal data from two published clinical studies. The data consisted of daily recordings of AD severity scores and treatments used by 59 and 334 AD children over 6 months and 16 weeks, respectively. Validation of the predictive model was conducted in a forward-chaining setting. RESULTS: Our model was able to predict future severity scores at the individual level and improved chance-level forecast by 60%. Heterogeneous patterns in severity trajectories were captured with patient-specific parameters such as the short-term persistence of AD severity and responsiveness to topical steroids, calcineurin inhibitors and step-up treatment. CONCLUSIONS: Our proof of principle model successfully predicted the daily evolution of AD severity scores at an individual level and could inform the design of personalized treatment strategies that can be tested in future studies. Our model-based approach can be applied to other diseases with apparent unpredictability and large variation in symptoms and treatment responses such as asthma.

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.

Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes.

Atopic dermatitis (AD) is a common inflammatory skin disease, whose incidence is currently increasing worldwide. AD has a complex etiology, involving genetic, environmental, immunological, and epidermal factors, and its pathogenic mechanisms have not yet been fully elucidated. Identification of AD risk factors and systematic understanding of their interactions are required for exploring effective prevention and treatment strategies for AD. We recently developed a mathematical model for AD pathogenesis to clarify mechanisms underlying AD onset and progression. This model describes a dynamic interplay between skin barrier, immune regulation, and environmental stress, and reproduced four types of dynamic behaviour typically observed in AD patients in response to environmental triggers. Here, we analyse bifurcations of the model to identify mathematical conditions for the system to demonstrate transitions between different types of dynamic behaviour that reflect respective severity of AD symptoms. By mathematically modelling effects of topical application of antibiotics, emollients, corticosteroids, and their combinations with different application schedules and doses, bifurcation analysis allows us to mathematically evaluate effects of the treatments on improving AD symptoms in terms of the patients' dynamic behaviour. The mathematical method developed in this study can be used to explore and improve patient-specific personalised treatment strategies to control AD symptoms.

Computational design of treatment strategies for proactive therapy on atopic dermatitis using optimal control theory.

Atopic dermatitis (AD) is a common chronic skin disease characterized by recurrent skin inflammation and a weak skin barrier, and is known to be a precursor to other allergic diseases such as asthma. AD affects up to 25% of children worldwide and the incidence continues to rise. There is still uncertainty about the optimal treatment strategy in terms of choice of treatment, potency, duration and frequency. This study aims to develop a computational method to design optimal treatment strategies for the clinically recommended 'proactive therapy' for AD. Proactive therapy aims to prevent recurrent flares once the disease has been brought under initial control. Typically, this is done by using an anti-inflammatory treatment such as a potent topical corticosteroid intensively for a few weeks to 'get control', followed by intermittent weekly treatment to suppress subclinical inflammation to 'keep control'. Using a hybrid mathematical model of AD pathogenesis that we recently proposed, we computationally derived the optimal treatment strategies for individual virtual patient cohorts, by recursively solving optimal control problems using a differential evolution algorithm. Our simulation results suggest that such an approach can inform the design of optimal individualized treatment schedules that include application of topical corticosteroids and emollients, based on the disease status of patients observed on their weekly hospital visits. We demonstrate the potential and the gaps of our approach to be applied to clinical settings.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

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.

Gene regulatory network underlying the immortalization of epithelial cells.

BACKGROUND: Tumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of spontaneous immortalization. This process is characterized by a series of cell-state transitions, in which normal epithelial cells acquire first a senescent state which is later surpassed to attain a mesenchymal stem-like phenotype with a potentially tumorigenic behavior. In this paper we aim to provide a system-level mechanistic explanation to the emergence of these cell types, and to the time-ordered transition patterns that are common to neoplasias of epithelial origin. To this end, we first integrate published functional and well-curated molecular data of the components and interactions that have been found to be involved in such cell states and transitions into a network of 41 molecular components. We then reduce this initial network by removing simple mediators (i.e., linear pathways), and formalize the resulting regulatory core into logical rules that govern the dynamics of each of the network components as a function of the states of its regulators. RESULTS: Computational dynamic analysis shows that our proposed Gene Regulatory Network model recovers exactly three attractors, each of them defined by a specific gene expression profile that corresponds to the epithelial, senescent, and mesenchymal stem-like cellular phenotypes, respectively. We show that although a mesenchymal stem-like state can be attained even under unperturbed physiological conditions, the likelihood of converging to this state is increased when pro-inflammatory conditions are simulated, providing a systems-level mechanistic explanation for the carcinogenic role of chronic inflammatory conditions observed in the clinic. We also found that the regulatory core yields an epigenetic landscape that restricts temporal patterns of progression between the steady states, such that recovered patterns resemble the time-ordered transitions observed during the spontaneous immortalization of epithelial cells, both in vivo and in vitro. CONCLUSION: Our study strongly suggests that the in vitro tumorigenic transformation of epithelial cells, which strongly correlates with the patterns observed during the pathological progression of epithelial carcinogenesis in vivo, emerges from underlying regulatory networks involved in epithelial trans-differentiation during development.

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.

Resistance to water diffusion in the stratum corneum is depth-dependent.

The stratum corneum (SC) provides a permeability barrier that limits the inflow and outflow of water. The permeability barrier is continuously and dynamically formed, maintained, and degraded along the depth, from the bottom to the top, of the SC. Naturally, its functioning and structure also change dynamically in a depth-dependent manner. While transepidermal water loss is typically used to assess the function of the SC barrier, it fails to provide any information about the dynamic mechanisms that are responsible for the depth-dependent characteristics of the permeability barrier. This paper aims to quantitatively characterize the depth-dependency of the permeability barrier using in vivo non-invasive measurement data for understanding the underlying mechanisms for barrier formation, maintenance, and degradation. As a framework to combine existing experimental data, we propose a mathematical model of the SC, consisting of multiple compartments, to explicitly address and investigate the depth-dependency of the SC permeability barrier. Using this mathematical model, we derive a measure of the water permeability barrier, i.e. resistance to water diffusion in the SC, from the measurement data on transepidermal water loss and water concentration profiles measured non-invasively by Raman spectroscopy. The derived resistance profiles effectively characterize the depth-dependency of the permeability barrier, with three distinct regions corresponding to formation, maintenance, and degradation of the barrier. Quantitative characterization of the obtained resistance profiles allows us to compare and evaluate the permeability barrier of skin with different morphology and physiology (infants vs adults, different skin sites, before and after application of oils) and elucidates differences in underlying mechanisms of processing barriers. The resistance profiles were further used to predict the spatial-temporal effects of skin treatments by in silico experiments, in terms of spatial-temporal dynamics of percutaneous water penetration.

Risk factor-dependent dynamics of atopic dermatitis: modelling multi-scale regulation of epithelium homeostasis.

Epithelial tissue provides the body with its first layer of protection against harmful environmental stimuli by enacting the regulatory interplay between a physical barrier preventing the influx of external stimuli and an inflammatory response to the infiltrating stimuli. Importantly, this interdependent regulation occurs on different time scales: the tissue-level barrier permeability is regulated over the course of hours, whereas the cellular-level enzymatic reactions leading to inflammation take place within minutes. This multi-scale regulation is key to the epithelium's function and its dysfunction leads to various diseases. This paper presents a mathematical model of regulatory mechanisms in the epidermal epithelium that includes processes on two different time scales at the cellular and tissue levels. We use this model to investigate the essential regulatory interactions between epidermal barrier integrity and skin inflammation and how their dysfunction leads to atopic dermatitis (AD). Our model exhibits a structure of dual (positive and negative) control at both cellular and tissue levels. We also determined how the variation induced by well-known risk factors for AD can break the balance of the dual control. Our model analysis based on time-scale separation suggests that each risk factor leads to qualitatively different dynamic behaviours of different severity for AD, and that the coincidence of multiple risk factors dramatically increases the fragility of the epithelium's function. The proposed mathematical framework should also be applicable to other inflammatory diseases that have similar time-scale separation and control architectures.

Transforming growth factor-ß/SMAD Target gene SKIL is negatively regulated by the transcriptional cofactor complex SNON-SMAD4.

The human SKI-like (SKIL) gene encodes the SMAD transcriptional corepressor SNON that antagonizes TGF-ß signaling. SNON protein levels are tightly regulated by the TGF-ß pathway: whereas a short stimulation with TGF-ß decreases SNON levels by its degradation via the proteasome, longer TGF-ß treatment increases SNON levels by inducing SKIL gene expression. Here, we investigated the molecular mechanisms involved in the self-regulation of SKIL gene expression by SNON. Bioinformatics analysis showed that the human SKIL gene proximal promoter contains a TGF-ß response element (TRE) bearing four groups of SMAD-binding elements that are also conserved in mouse. Two regions of 408 and 648 bp of the human SKIL gene (∼2.4 kb upstream of the ATG initiation codon) containing the core promoter, transcription start site, and the TRE were cloned for functional analysis. Binding of SMAD and SNON proteins to the TRE region of the SKIL gene promoter after TGF-ß treatment was demonstrated by ChIP and sequential ChIP assays. Interestingly, the SNON-SMAD4 complex negatively regulated basal SKIL gene expression through binding the promoter and recruiting histone deacetylases. In response to TGF-ß signal, SNON is removed from the SKIL gene promoter, and then the activated SMAD complexes bind the promoter to induce SKIL gene expression. Subsequently, the up-regulated SNON protein in complex with SMAD4 represses its own expression as part of the negative feedback loop regulating the TGF-ß pathway. Accordingly, when the SNON-SMAD4 complex is absent as in some cancer cells lacking SMAD4 the regulation of some TGF-ß target genes is modified.