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

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

Poly(ADP-ribose)-dependent regulation of DNA repair by the chromatin remodeling enzyme ALC1

Posttranslational modifications play key roles in regulating chromatin plasticity. Although various chromatin-remodeling enzymes have been described that respond to specific histone modifications, little is known about the role of poly[adenosine 5'-diphosphate (ADP)-ribose] in chromatin remodeling. Here, we identify a chromatin-remodeling enzyme, ALC1 (Amplified in Liver Cancer 1, also known as CHD1L), that interacts with poly(ADP-ribose) and catalyzes PARP1-stimulated nucleosome sliding. Our results define ALC1 as a DNA damage-response protein whose role in this process is sustained by its association with known DNA repair factors and its rapid poly(ADP-ribose)-dependent recruitment to DNA damage sites. Furthermore, we show that depletion or overexpression of ALC1 results in sensitivity to DNA-damaging agents. Collectively, these results provide new insights into the mechanisms by which poly(ADP-ribose) regulates DNA repair

Sialylation is essential for early development in mice

Sialic acids are widely expressed as terminal carbohydrates on glycoconjugates of eukaryotic cells. Sialylation is crucial for a variety of cellular functions, such as cell adhesion or signal recognition, and regulates the biological stability of glycoproteins. The key enzyme of sialic acid biosynthesis is the bifunctional UDP-N-acetylglucosamine-2-epimerase/N-acetylmannosamine kinase (UDP-GlcNAc 2-epimerase), which catalyzes the first two steps of sialic acid biosynthesis in the cytosol. We report that inactivation of the UDP-GlcNAc 2-epimerase by gene targeting causes early embryonic lethality in mice, thereby emphasizing the fundamental role of this bifunctional enzyme and sialylation during development. The need of UDP-GlcNAc 2-epimerase for a defined sialylation process is exemplified with the polysialylation of the neural cell adhesion molecule in embryonic stem cells

Frat Is a Phosphatidylinositol 3-Kinase/Akt-Regulated Determinant of Glycogen Synthase Kinase 3β Subcellular Localization in Pluripotent Cells

Suppressing the activity of Gsk3β is critical for maintenance of murine pluripotent stem cells. In murine embryonic stem cells (mESCs), Gsk3β is inhibited by multiple mechanisms, including its inhibitory phosphorylation on serine 9 by protein kinase B (Akt), a major effector of the canonical phosphatidylinositol 3-kinase (PI3K) pathway. A second PI3K/Akt-regulated mechanism promotes the nuclear export of Gsk3β, thereby restricting its access to nuclear substrates such as c-myc and β-catenin. Although Gsk3β shuttles between the nucleus and cytoplasm under self-renewing conditions, its localization is primarily cytoplasmic because its rate of nuclear export exceeds its rate of nuclear import. In this report, we show that Gsk3β is exported from the nucleus in a complex with Frat. Loss of PI3K/Akt activity results in dissociation of this complex and retention of Gsk3β in the nucleus. Frat continues to shuttle between the nucleus and cytoplasm under these conditions and remains predominantly in the cytoplasm. These results indicate that Frat carries Gsk3β out of the nucleus under self-renewing conditions and that PI3K regulates this by promoting its association with Frat. These findings provide new links between PI3K/Akt signaling and regulation of Gsk3β activity by Frat, an oncogene previously shown to cooperate with Myc in tumorigenesis