Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force

Clinical practice: The care of children with Down syndrome

Down syndrome (DS) is one of the most common chromosomal abnormalities. Because of medical advances and improvements in overall medical care, the median survival of individuals with DS has increased considerably. This longer life expectancy requires giving the necessary care to the individual with DS over their total longer lifespan. DS medical guidelines are designed for the optimal care of the child in whom a diagnosis of DS has been confirmed. We present an overview of the most important issues related to children with DS based on the most relevant literature currently available

Current Treatment of Endolymphatic Sac Tumor of the Temporal Bone

An endolymphatic sac tumor (ELST) is a rare, indolent but locally aggressive tumor arising in the posterior petrous ridge. Patients present with sensorineural hearing loss and tinnitus. As the tumor progresses, patients may experience vertigo, ataxia, facial nerve paresis, pain and otorrhea. Most patients present in their 4th or 5th decade with a wide age range. Patients with von Hippel–Lindau disease have an increased likelihood of developing ELST. Histologically, ELST is a low-grade adenocarcinoma. As it progresses, it destroys bone and extends into adjacent tissues. The likelihood of regional or distant metastases is remote. The optimal treatment is resection with negative margins. Patients with positive margins, gross residual disease, or unresectable tumor are treated with radiotherapy or radiosurgery. Late recurrences are common, so long follow-up is necessary to assess efficacy. The likelihood of cure depends on tumor extent and is probably in the range of 50–75%

Fine-Tuning Roles of Endogenous Brain-Derived Neurotrophic Factor, TrkB and Sortilin in Colorectal Cancer Cell Survival

International audienceBACKGROUND: Neurotrophin receptors were initially identified in neural cells. They were recently detected in some cancers in association with invasiveness, but the function of these tyrosine kinase receptors was not previously investigated in colorectal cancer (CRC) cells. METHODS AND FINDINGS: We report herein that human CRC cell lines synthesize the neural growth factor Brain-derived neurotrophic factor (BDNF) under stress conditions (serum starvation). In parallel, CRC cells expressed high- (TrkB) and low-affinity (p75(NTR)) receptors at the plasma membrane, whereas TrkA and TrkC, two other high affinity receptors for NGF and NT-3, respectively, were undetectable. We demonstrate that BDNF induced cell proliferation and had an anti-apoptotic effect mediated through TrkB, as assessed by K252a, a Trk pharmacologic inhibitor. It suppressed both cell proliferation and survival of CRC cells that do not express TrkA nor TrkC. In parallel to the increase of BDNF secretion, sortilin, a protein acting as a neurotrophin transporter as well as a co-receptor for p75(NTR), was increased in the cytoplasm of primary and metastatic CRC cells, which suggests that sortilin could regulate neurotrophin transport in these cells. However, pro-BDNF, also detected in CRC cells, was co-expressed with p75(NTR) at the cell membrane and co-localized with sortilin. In contrast to BDNF, exogenous pro-BDNF induced CRC apoptosis, which suggests that a counterbalance mechanism is involved in the control of CRC cell survival, through sortilin as the co-receptor for p75(NTR), the high affinity receptor for pro-neurotrophins. Likewise, we show that BDNF and TrkB transcripts (and not p75(NTR)) are overexpressed in the patients' tumors by comparison with their adjacent normal tissues, notably in advanced stages of CRC. CONCLUSION: Taken together, these results highlight that BDNF and TrkB are essential for CRC cell growth and survival in vitro and in tumors. This autocrine loop could be of major importance to define new targeted therapies

MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research