Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

A Multicellular Model of Intestinal Crypt Buckling and Fission

Crypt fission is an in vivo tissue deformation process that is involved in both intestinal homeostasis and colorectal tumourigenesis. Despite its importance, the mechanics underlying crypt fission are currently poorly understood. Recent experimental development of organoids, organ-like buds cultured from crypt stem cells in vitro, has shown promise in shedding light on crypt fission. Drawing inspiration from observations of organoid growth and fission in vivo, we develop a computational model of a deformable epithelial tissue layer. Results from in silico experiments show the stiffness of cells and the proportions of cell subpopulations affect the nature of deformation in the epithelial layer. In particular, we find that increasing the proportion of stiffer cells in the layer increases the likelihood of crypt fission occurring. This is in agreement with and helps explain recent experimental work

Simplified mathematical model of proton exchange membrane fuel cell based on horizon fuel cell stack

This paper presents a simplified zero-dimensional mathematical model for a self-humidifying proton exchange membrane (PEM) fuel cell stack of 1 kW. The model incorporates major electric and thermodynamic variables and parameters involved in the operation of the PEM fuel cell under different operational conditions. Influence of each of these parameters and variables upon the operation and the performance of the PEM fuel cell are investigated. The mathematical equations are modeled by using Matlab–Simulink tools in order to simulate the operation of the developed model with a commercial available 1 kW horizon PEM fuel cell stack (H-1000), which is used for the purposes of model validation and tuning of the developed model. The model can be extrapolated to higher wattage fuel cells of similar arrangements. New equation is presented to determine the impact of using air to supply the PEM fuel cell instead of pure oxygen upon the concentration losses and the output voltage when useful current is drawn from it

Combined changes in Wnt signalling response and contact inhibition induce altered proliferation in radiation treated intestinal crypts

Curative intervention is possible if colorectal cancer is identified early, underscoring the need to detect the earliest stages of malignant transformation. A candidate biomarker is the expanded proliferative zone observed in crypts before adenoma formation, also found in irradiated crypts. However, the underlying driving mechanism for this is not known. Wnt signaling is a key regulator of proliferation, and elevated Wnt signaling is implicated in cancer. Nonetheless, how cells differentiate Wnt signals of varying strengths is not understood. We use computational modeling to compare alternative hypotheses about how Wnt signaling and contact inhibition affect proliferation. Direct comparison of simulations with published experimental data revealed that the model that best reproduces proliferation patterns in normal crypts stipulates that proliferative fate and cell cycle duration are set by the Wnt stimulus experienced at birth. The model also showed that the broadened proliferation zone induced by tumorigenic radiation can be attributed to cells responding to lower Wnt concentrations and dividing at smaller volumes. Application of the model to data from irradiated crypts after an extended recovery period permitted deductions about the extent of the initial insult. Application of computational modeling to experimental data revealed how mechanisms that control cell dynamics are altered at the earliest stages of carcinogenesis

Indoor Contamination with Hexabromocyclododecanes, Polybrominated Diphenyl Ethers, and Perfluoroalkyl Compounds: An Important Exposure Pathway for People?

This review underlines the importance of indoor contamination as a pathway of human exposure to hexabromocyclododecanes (HBCDs), polybrominated diphenyl ethers (PBDEs), and perfluoroalkyl compounds (PFCs). There is ample evidence of substantial contamination of indoor dust with these chemicals and that their concentrations in indoor air exceed substantially those outdoors. Studies examining the relationship between body burden and exposure via indoor dust are inconsistent while some indicate a link between body burdens and PBDE and HBCD exposure via dust ingestion, others find no correlation. Likewise, while concentrations in indoor dust and human tissues are both highly skewed, this does not necessarily imply causality. Evidence suggests exposure via dust ingestion is higher for toddlers than adults. Research priorities include identifying means of reducing indoor concentrations and indoor monitoring methods that provide the most ""biologically-relevant"" measures of exposure as well as monitoring a wider range of microenvironment categories. Other gaps include studies to improve understanding of the following: emission rates and mechanisms via which these contaminants migrate from products into indoor air and dust; relationships between indoor exposures and human body burdens; relevant physicochemical properties; the gastrointestinal uptake by humans of these chemicals from indoor dust; and human dust ingestion rates.</p

Autism Spectrum Disorder Among US Children (2002–2010): Socioeconomic, Racial, and Ethnic Disparities

Objectives. To describe the association between indicators of socioeconomic status (SES) and the prevalence of autism spectrum disorder (ASD) in the United States during the period 2002 to 2010, when overall ASD prevalence among children more than doubled, and to determine whether SES disparities account for ongoing racial and ethnic disparities in ASD prevalence

One-year urinary and sexual outcome trajectories among prostate cancer patients treated by radical prostatectomy: A prospective study

BACKGROUND: To examine one-year trajectories of urinary and sexual outcomes, and correlates of these trajectories, among prostate cancer patients treated by radical prostatectomy (RP). METHODS: Study participants were recruited from 2011 to 2014 at two US institutions. Self-reported urinary and sexual outcomes were measured at baseline before surgery, and 5 weeks, 6 months and 12 months after surgery, using the modified Expanded Prostate Cancer Index Composite-50 (EPIC-50). Changes in EPIC-50 scores from baseline were categorized as improved (beyond baseline), maintained, or impaired (below baseline), using previously-reported minimum clinically important differences. RESULTS: Of the 426 eligible participants who completed the baseline survey, 395 provided data on at least one EPIC-50 sub-scale at 5 weeks and 12 months, and were analyzed. Although all mean EPIC-50 scores declined markedly 5 weeks after surgery and then recovered to near (incontinence-related outcomes) or below (sexual outcomes) baseline levels by 12 months post-surgery, some men experienced improvement beyond their baseline levels on each sub-scale (3.3-51% depending on the sub-scale). Having benign prostatic hyperplasia (BPH) at baseline (prostate size ≥ 40 g; an International Prostate Symptom Index Score ≥ 8; or using BPH medications) was associated with post-surgical improvements in voiding dysfunction-related bother at 5 weeks (OR = 3.9, 95% CI: 2.1-7.2) and 12 months (OR = 3.3, 95% CI: 2.0-5.7); and in sexual bother at 5 weeks (OR = 5.7, 95% CI:1.7-19.3) and 12 months (OR = 3.0, 95% CI: 1.2-7.1). CONCLUSIONS: Our findings provide additional support for considering baseline BPH symptoms when selecting the best therapy for early-stage prostate cancer

Feeding graded levels of dried Sea buckthorn (Hippophaes rhamnoides) berries to broiler chickens

The aim of this study was to assess the effects of graded levels (0, 3, 6, 9 and 12 g/kg) of dry Sea buckthorn (SB) berries on growth performance, gastrointestinal tract (GIT) development, jejunal histomorphology, bird antioxidant status and caecal short-chain fatty acid concentration when fed to female Ross 308 broiler chickens. In addition, expression of cytokine biomarker genes in the jejunum was evaluated. The five experimental diets were fed from 7 to 21 days age to 8 pens (two birds in each) following randomisation. Feeding SB did not influence bird growth performance (p > .05). There was a linear decrease in butyric, acetic and valeric acid concentrations in caecal digesta (p  .05). Feeding dry SB berries up to 12 g/kg of diet did not improve the zootechnical variables of healthy commercial-strain broilers in this study

Application of fuzzy logic to assess the quality of BPMN models

© Springer International Publishing AG, part of Springer Nature 2018. Modeling is the first stage in a Business Process’s (BP) lifecycle. A high-quality BP model is vital to the successful implementation, execution, and monitoring stages. Different works have evaluated BP models from a quality perspective. These works either used formal verification or a set of quality metrics. This paper adopts quality metric and targets models represented in Business Process Modeling and Notation (BPMN). It proposes an approach based on fuzzy logic along with a tool system developed under eclipse framework. The preliminary experimental evaluation of the proposed system shows encouraging results

Co-methylation network analysis of Psychosis in Alzheimer’s disease

Background: Psychosis (broadly delusions and hallucinations) has a cumulative disease prevalence of around 40% in Alzheimer’s disease (AD). The epigenomic, genomic, and neuropathological data provide powerful evidence that AD+P has a distinct neurobiological profile. Here, we used the weighted gene co-expression network analysis (WGCNA) method to investigate DNA methylation associated with AD+P in the dorsolateral prefrontal cortex of 153 post-mortem brain samples. Method: Our primary analysis focused on applying WGCNA to the PITT-ADRC cohort, followed by subsequent replication of its findings in the BDR cohort. The genotype data from PITT-ADRC and the WGCNA results were further utilized to identify the most significant methylation Quantitative Trait Loci (mQTLs) associated with psychosis. Subsequently, we explored RNA sequencing data from PITT-ADRC to identify genes affected by the replicated findings uncovered in our primary analysis. Result: We identified five AD+P-related modules in the PITT-ADRC cohort, with one of them being replicated in the BDR cohort. This replicated AD+P-related module exhibits a high enrichment in the T cell receptor signalling pathway. According to the colocalization analysis results, this module shares significant SNPs in some regions that are also significantly associated with Schizophrenia and Educational Attainment. Conclusion: Understanding molecular differences between AD and Psychosis at the genetic and epigenetic levels could guide us in discovering appropriate treatments for AD+P cases. To this end, we initiated a comprehensive, large sample-sized network analysis study based on genetic and epigenetic data