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

CTCF-dependent chromatin boundaries formed by asymmetric nucleosome arrays with decreased linker length

The CCCTC-binding factor (CTCF) organises the genome in 3D through DNA loops and in 1D by setting boundaries isolating different chromatin states, but these processes are not well understood. Here we focus on the relationship between CTCF binding and the decrease of the Nucleosome Repeat Length (NRL) for ∼20 adjacent nucleosomes, affecting up to 10% of the mouse genome. We found that the chromatin boundary near CTCF is created by the nucleosome-depleted region (NDR) asymmetrically located >40 nucleotides 5’-upstream from the centre of CTCF motif. The strength of CTCF binding to DNA is correlated with the decrease of NRL near CTCF and anti-correlated with the level of asymmetry of the nucleosome array. Individual chromatin remodellers have different contributions, with Snf2h having the strongest effect on the NRL decrease near CTCF and Chd4 playing a major role in the symmetry breaking. Upon differentiation of embryonic stem cells to neural progenitor cells and embryonic fibroblasts, a subset of common CTCF sites preserved in all three cell types maintains a relatively small local NRL despite genome-wide NRL increase. The sites which lost CTCF upon differentiation are characterised by nucleosome rearrangement 3’-downstream, but the boundary defined by the NDR 5’-upstream of CTCF motif remains

Ultrasound biomicroscopic imaging in intermediate uveitis

BACKGROUND—Clinical examination of the region of the eye mainly affected in patients with intermediate uveitis is difficult and often hampered by media opacities. In that perspective ultrasound biomicroscopy (UBM) promises to be a valuable additional diagnostic tool.
METHODS—UBM was performed at a sound frequency of 50 MHz on 26 eyes of 13 patients with intermediate uveitis in order to determine configuration of pars plana, peripheral retina, and vitreous. Findings of ophthalmoscopy with scleral indentation and UBM were compared.
RESULTS—In 18 of 26 eyes pathological structures such as membraneous or fluffy vitreous condensations were identified by UBM. Among these UBM revealed pathological findings which were not visible on funduscopy in nine eyes. Most importantly, vitreoretinal adhesions with traction on the retina were imaged in four eyes. However, in three eyes vitreous opacities being visible on funduscopy were not identified by UBM.
CONCLUSION—UBM seems to be a valuable diagnostic technique for the evaluation of patients with intermediate uveitis. Longitudinal studies will have to determine the relevance of UBM findings for the individual clinical course and their influence on therapeutic decisions.

 Keywords: intermediate uveitis; ultrasound biomicroscopy; vitreous opacitie