MacLean, Adam L.; Harrington, Heather A.; Stumpf, Michael P. H.; Byrne, Helen M.(Methods in Molecular Biology, Springer Nature, 2015-12-16)[Book Chapter]
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.
MacLean, Adam L.; Rosen, Zvi; Byrne, Helen M.; Harrington, Heather A.(Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 2015-02-17)[Article]
The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.
The export option will allow you to export the current search results of the entered query to a file. Different
formats are available for download. To export the items, click on the button corresponding with the preferred download format.
By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.
For anonymous users the allowed maximum amount is 50 search results.
To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export.
The amount of items that can be exported at once is similarly restricted as the full export.
After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.