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

Oncogenic Function of DACT1 in Colon Cancer through the Regulation of β-catenin

The Wnt/β-catenin signaling pathway plays important roles in the progression of colon cancer. DACT1 has been identified as a modulator of Wnt signaling through its interaction with Dishevelled (Dvl), a central mediator of both the canonical and noncanonical Wnt pathways. However, the functions of DACT1 in the WNT/β-catenin signaling pathway remain unclear. Here, we present evidence that DACT1 is an important positive regulator in colon cancer through regulating the stability and sublocation of β-catenin. We have shown that DACT1 promotes cancer cell proliferation in vitro and tumor growth in vivo and enhances the migratory and invasive potential of colon cancer cells. Furthermore, the higher expression of DACT1 not only increases the nuclear and cytoplasmic fractions of β-catenin, but also increases its membrane-associated fraction. The overexpression of DACT1 leads to the increased accumulation of nonphosphorylated β-catenin in the cytoplasm and particularly in the nuclei. We have demonstrated that DACT1 interacts with GSK-3β and β-catenin. DACT1 stabilizes β-catenin via DACT1-induced effects on GSK-3β and directly interacts with β-catenin proteins. The level of phosphorylated GSK-3β at Ser9 is significantly increased following the elevated expression of DACT1. DACT1 mediates the subcellular localization of β-catenin via increasing the level of phosphorylated GSK-3β at Ser9 to inhibit the activity of GSK-3β. Taken together, our study identifies DACT1 as an important positive regulator in colon cancer and suggests a potential strategy for the therapeutic control of the β-catenin-dependent pathway

CRM1- and Ran-independent nuclear export of beta-catenin

Background: Activation of the Wnt pathway induces beta-catenin to localize inside the nucleus, where it interacts with transcription factors such as TCF/LEF-1. Regulation of the pathway occurs through a beta-catenin-degrading complex based on Axin and the tumor suppressor APC. We have previously found that beta-catenin import occurs independently of nuclear import factors but is similar to the import of the transport factors themselves do. APC, which can shuttle in and out of the nucleus, has been proposed to be responsible for reexport of beta-catenin in a CRM1-dependent manner.Results: We have studied beta-catenin export in vivo and in semipermeabilized cells. beta-catenin contains three export sequences. Export is insensitive to leptomycin B, a specific inhibitor of the CRM1-mediated pathway. It does not require nuclear RanGTP, and it can be reconstituted in the absence of additional soluble factors; this is consistent with nondirectional translocation of beta-catenin. Further observations suggest that beta-catenin subcellular distribution in vivo may depend primarily on retention through interaction with other cellular components. Finally, we show evidence that reexport is required for degradation of nuclear beta-catenin and that nuclei lack Axin, an essential component of the degradation machinery.Conclusions: beta-catenin is exported independently of the CRM1 pathway. We propose a model of free, nondirectional nuclear translocation for beta-catenin, its localization being regulated by retention in the nucleus and degradation in the cytoplasm

ARID1A depletion

Acute depletion of the ARID1A subunit of SWI/SNF complexesTHIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

Nucleo-cytoplasmic shuttling of Axin, a negative regulator of the Wnt-beta-catenin Pathway

Axin is a negative regulator of the Wnt pathway essential for down-regulation of beta-catenin. Axin has been considered so far as a cytoplasmic protein. Here we show that, although cytoplasmic at steady state, Axin shuttles in fact in and out of the nucleus; Axin accumulates in the nucleus of cells treated with leptomycin B, a specific inhibitor of the CRM1-mediated nuclear export pathway and is efficiently exported from Xenopus oocyte nuclei in a RanGTP- and CRM1-dependent manner. We have characterized the sequence requirement for export and identified two export domains, which do not contain classical nuclear export consensus sequences, and we show that Axin binds directly to the export factor CRM1 in the presence of RanGTP

Nucleosome dynamics

In the 30 years since the discovery of the nucleosome, our picture of it has come into sharp focus. The recent high-resolution structures have provided a wealth of insight into the function of the nucleosome, but they are inherently static. Our current knowledge of how nucleosomes can be reconfigured dynamically is at a much earlier stage. Here, recent advances in the understanding of chromatin structure and dynamics are highlighted. The ways in which different modes of nucleosome reconfiguration are likely to influence each other are discussed, and some of the factors likely to regulate the dynamic properties of nucleosomes are considered.</p

Nucleosome dynamics

In the 30 years since the discovery of the nucleosome, our picture of it has come into sharp focus. The recent high-resolution structures have provided a wealth of insight into the function of the nucleosome, but they are inherently static. Our current knowledge of how nucleosomes can be reconfigured dynamically is at a much earlier stage. Here, recent advances in the understanding of chromatin structure and dynamics are highlighted. The ways in which different modes of nucleosome reconfiguration are likely to influence each other are discussed, and some of the factors likely to regulate the dynamic properties of nucleosomes are considered.</p