The parameterization method for center manifolds

In this paper, we present a generalization of the parameterization method, introduced by Cabr\'{e}, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we find a new proof for the existence and regularity of center manifolds. However, in contrast to the classical center manifold theorem, our parameterization method will simultaneously obtain the center manifold and its conjugate center dynamical system. Furthermore, we will provide bounds on the error between approximations of the center manifold and the actual center manifold, as well as bounds for the error in the conjugate dynamical system

Energy from streaming current and potential

It is investigated how much energy can be delivered by a streaming current source. A streaming current and subsequent streaming potential originate when double layer charge is transported by hydrodynamic flow. Theory and a network model of such a source is presented and initial experimental results are given, showing a supplied power of 20 nW obtained by a pressure difference of 1 atm over a glass porous plug, using a 1-mM KCl solution. It is indicated how the rather low mechanical-to-electrical energy conversion efficiency can be increased

The parameterization method for center manifolds

In this paper, we present a generalization of the parameterization method, introduced by Cabré, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we find a new proof for the existence and regularity of center manifolds. However, in contrast to the classical center manifold theorem, our parameterization method will simultaneously obtain the center manifold and its conjugate center dynamical system. Furthermore, we will provide bounds on the error between approximations of the center manifold and the actual center manifold, as well as bounds for the error in the conjugate dynamical system

Ion Concentration Polarization for Microparticle Mesoporosity Differentiation

Microparticle porosity is normally determined in bulk manner providing an ensemble average that hinders establishing the individual role of each microparticle. On the other hand, single particle characterization implies expensive technology. We propose to use ion concentration polarization to measure differences in mesoporosity at the single particle level. Ion concentration polarization occurs at the interface between an electrolyte and a porous particle when an electric field is applied. The extent of ion concentration polarization depends, among others, on the mesopore size and density. By using a fluorescence marker, we could measure differences in concentration polarization between particles with 3 and 13 nm average mesopore diameters. A qualitative model was developed in order to understand and interpret the phenomena. We believe that this inexpensive method could be used to measure differences in mesoporous particle materials such as catalysts

Assessment of risk of ALS conferred by the GGGGCC hexanucleotide repeat expansion in C9orf72 among first-degree relatives of patients with ALS carrying the repeat expansion

Objectives: We aimed to estimate the age-related risk of ALS in first-degree relatives of patients with ALS carrying the C9orf72 repeat expansion. Methods: We included all patients with ALS carrying a C9orf72 repeat expansion in The Netherlands. Using structured questionnaires, we determined the number of first-degree relatives, their age at death due to ALS or another cause, or age at time of questionnaire. The cumulative incidence of ALS among first-degree relatives was estimated, while accounting for death from other causes. Variability in ALS risk between families was evaluated using a random effects hazards model. We used a second, distinct approach to estimate the risk of ALS and FTD in the general population, using previously published data. Results: In total, 214 of the 2,486 (9.2%) patients with ALS carried the C9orf72 repeat expansion. The mean risk of ALS at age 80 for first-degree relatives carrying the repeat expansion was 24.1%, but ranged between individual families from 16.0 to 60.6%. Using the second approach, we found the risk of ALS and FTD combined was 28.7% (95% CI 17.8%–54.3%) for carriers in the general population. Conclusions: On average, our estimated risk of ALS in the C9orf72 repeat expansion was lower compared to historical estimates. We showed, however, that the risk of ALS likely varies between families and one overall penetrance estimate may not be sufficient to describe ALS risk. This warrants a tailor-made, patient-specific approach in testing. Further studies are needed to assess the risk of FTD in the C9orf72 repeat expansion

Genotype-phenotype correlations of KIF5A stalk domain variants

The kinesin family member 5A (KIF5A) motor domain variants are typically associated with hereditary spastic paraplegia (HSP) or Charcot-Marie-Tooth 2 (CMT2), while KIF5A tail variants predispose to amyotrophic lateral sclerosis (ALS) and neonatal intractable myoclonus. Variants within the stalk domain of KIF5A are relatively rare. We describe a family of three patients with a complex HSP phenotype and a likely pathogenic KIF5A stalk variant. More family members were reported to have walking difficulties. When reviewing the literature on KIF5A stalk variants, we found 22 other cases. The phenotypes varied with most cases having (complex) HSP/CMT2 or ALS. Symptom onset varied from childhood to adulthood and common additional symptoms for HSP are involvement of the upper limbs, sensorimotor polyneuropathy, and foot deformities. We conclude that KIF5A variants lead to a broad clinical spectrum of disease. Phenotype distribution according to variants in specific domains occurs often in the motor and tail domain but are not definite. However, variants in the stalk domain are not bound to a specific phenotype

Association Between Serum Lipids and Survival in Patients With Amyotrophic Lateral Sclerosis: A Meta-analysis and Population-Based Study

Background and ObjectiveTo explore the association between lipids, polygenic profile scores (PPS) for biomarkers of lipid metabolism, markers of disease severity, and survival in patients with amyotrophic lateral sclerosis (ALS).MethodsWe meta-analyzed the current literature on the prognostic value of lipids in patients with ALS. Subsequently, we evaluated the relationship between lipid levels at diagnosis, clinical disease stage, and survival in all consecutive patients diagnosed in the Netherlands. We determined the hazard ratio (HR) of each lipid for overall survival, defined as death from any cause. A subset of patients was matched to a previous genome-wide association study; data were used to calculate PPS for biomarkers of lipid metabolism and to determine the association between observed lipid levels at diagnosis and survival.ResultsMeta-analysis of 4 studies indicated that none of the biomarkers of the lipid metabolism were statistically significantly associated with overall survival; there was, however, considerable heterogeneity between study results. Using individual patient data (N = 1,324), we found that increased high-density lipoprotein (HDL) cholesterol was associated with poorer survival (HR of 1.33 (95% CI 1.14-1.55, p 0.50).DiscussionLipids may contain valuable information about disease severity and prognosis, but their main value may be driven as a consequence of disease progression. Our results underscore that gaining further insight into lipid metabolism and longitudinal data on serum concentrations of the lipid profile could improve the monitoring of patients and potentially further disentangle ALS pathogenesis

UNC13A in amyotrophic lateral sclerosis: from genetic association to therapeutic target

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease with limited treatment options and an incompletely understood pathophysiology. Although genomewide association studies (GWAS) have advanced our understanding of the disease, the precise manner in which risk polymorphisms contribute to disease pathogenesis remains unclear. Of relevance, GWAS have shown that a polymorphism (rs12608932) in the UNC13A gene is associated with risk for both ALS and frontotemporal dementia (FTD). Homozygosity for the C-allele at rs12608932 modifies the ALS phenotype, as these patients are more likely to have bulbar-onset disease, cognitive impairment and FTD at baseline as well as shorter survival. UNC13A is expressed in neuronal tissue and is involved in maintaining synaptic active zones, by enabling the priming and docking of synaptic vesicles. In the absence of functional TDP-43, risk variants in UNC13A lead to the inclusion of a cryptic exon in UNC13A messenger RNA, subsequently leading to nonsense mediated decay, with loss of functional protein. Depletion of UNC13A leads to impaired neurotransmission. Recent discoveries have identified UNC13A as a potential target for therapy development in ALS, with a confirmatory trial with lithium carbonate in UNC13A cases now underway and future approaches with antisense oligonucleotides currently under consideration. Considering UNC13A is a potent phenotypic modifier, it may also impact clinical trial outcomes. This present review describes the path from the initial discovery of UNC13A as a risk gene in ALS to the current therapeutic options being explored and how knowledge of its distinct phenotype needs to be taken into account in future trials