A global picture for the planar Ricker map: convergence to fixed points and identification of the stable/unstable manifolds

A quadratic Lyapunov function is demonstrated for the noninvertible planar Ricker map (x, y) → (xe^{r−x−αy}, ye^{s−y−βx}) which shows that for α,β > 0, and 0 < r, s ≤ 2 all orbits of the planar Ricker map converge to a fixed point. We establish that for 0<r, s<2, whenever a positive equilibrium exists and is locally asymptotically stable, it is globally asymptotically stable (i.e. attracts all of (0,∞)^2). Our approach bypasses and improves on methods that rely on monotonicity, which require 0 < r, s ≤ 1. We also use the Lyapunov function to identify the one-dimensional stable and unstable manifolds when the positive fixed point exists and is a hyperbolic saddle

ANO10 mutations cause ataxia and coenzyme Q(10) deficiency

Inherited ataxias are heterogeneous disorders affecting both children and adults, with over 40 different causative genes, making molecular genetic diagnosis challenging. Although recent advances in next-generation sequencing have significantly improved mutation detection, few treatments exist for patients with inherited ataxia. In two patients with adult-onset cerebellar ataxia and coenzyme Q10 (CoQ10) deficiency in muscle, whole exome sequencing revealed mutations in ANO10, which encodes anoctamin 10, a member of a family of putative calcium-activated chloride channels, and the causative gene for autosomal recessive spinocerebellar ataxia-10 (SCAR10). Both patients presented with slowly progressive ataxia and dysarthria leading to severe disability in the sixth decade. Epilepsy and learning difficulties were also present in one patient, while retinal degeneration and cataract were present in the other. The detection of mutations in ANO10 in our patients indicate that ANO10 defects cause secondary low CoQ10 and SCAR10 patients may benefit from CoQ10 supplementation

Molecular genetic analysis of podocyte genes in focal segmental glomerulosclerosis—a review

This review deals with podocyte proteins that play a significant role in the structure and function of the glomerular filter. Genetic linkage studies has identified several genes involved in the development of nephrotic syndrome and contributed to the understanding of the pathophysiology of glomerular proteinuria and/or focal segmental glomerulosclerosis. Here, we describe already well-characterized genetic diseases due to mutations in nephrin, podocin, CD2AP, alpha-actinin-4, WT1, and laminin β2 chain, as well as more recently identified genetic abnormalities in TRPC6, phospholipase C epsilon, and the proteins encoded by the mitochondrial genome. In addition, the role of the proteins which have shown to be important for the structure and functions by gene knockout studies in mice, are also discussed. Furthermore, some rare syndromes with glomerular involvement, in which molecular defects have been recently identified, are briefly described. In summary, this review updates the current knowledge of genetic causes of congenital and childhood nephrotic syndrome and provides new insights into mechanisms of glomerular dysfunction

Biomarkers in the diagnosis of lysosomal storage disorders: proteins, lipids, and inhibodies

A biomarker is an analyte indicating the presence of a biological process linked to the clinical manifestations and outcome of a particular disease. In the case of lysosomal storage disorders (LSDs), primary and secondary accumulating metabolites or proteins specifically secreted by storage cells are good candidates for biomarkers. Clinical applications of biomarkers are found in improved diagnosis, monitoring disease progression, and assessing therapeutic correction. These are illustrated by reviewing the discovery and use of biomarkers for Gaucher disease and Fabry disease. In addition, recently developed chemical tools allowing specific visualization of enzymatically active lysosomal glucocerebrosidase are described. Such probes, coined inhibodies, offer entirely new possibilities for more sophisticated molecular diagnosis, enzyme replacement therapy monitoring, and fundamental research.