Routh reduction and the class of magnetic Lagrangian systems

In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after Routh reduction of Lagrangian systems with symmetry, so-called magnetic Lagrangian systems. We use these transformations in order to show that, under suitable conditions, the reduction with respect to a (full) semi-direct product group is equivalent to the reduction with respect to an Abelian normal subgroup. The results in this paper are closely related to the more general theory of Routh reduction by stages.Comment: 23 page

Foveal avascular zone and choroidal thickness are decreased in subjects with hard drusen and without high genetic risk of developing Alzheimer’s disease

A family history (FH+) of Alzheimer’s disease (AD) and ɛ4 allele of the ApoE gene are the main genetic risk factors for developing AD, whereas ɛ4 allele plays a protective role in age-related macular degeneration. Ocular vascular changes have been reported in both pathologies. We analyzed the choroidal thickness using optical coherence tomography (OCT) and the foveal avascular zone (FAZ) using OCT-angiography and compared the results with ApoE gene expression, AD FH+, and the presence or absence of hard drusen (HD) in 184 cognitively healthy subjects. Choroidal thickness was statistically significantly different in the (FH−, ɛ4−, HD+) group compared with (i) both the (FH−, ɛ4−, HD−) and the (FH+, ɛ4+, HD+) groups in the superior and inferior points at 1500 μm, and (ii) the (FH+, ɛ4−, HD+) group in the superior point at 1500 μm. There were statistically significant differences in the superficial FAZ between the (FH+, ɛ4−, HD+) group and (i) the (FH+, ɛ4−, HD−) group and (ii) the (FH+, ɛ4+, HD−) group. In conclusion, ocular vascular changes are not yet evident in participants with a genetic risk of developing AD

Characterization of retinal drusen in subjects at high genetic risk of developing sporadic Alzheimer’s disease: An exploratory analysis

Having a family history (FH+) of Alzheimer’s disease (AD) and being a carrier of at least one ε4 allele of the ApoE gene are two of the main risk factors for the development of AD. AD and age-related macular degeneration (AMD) share one of the main risk factors, such as age, and characteristics including the presence of deposits (Aβ plaques in AD and drusen in AMD); however, the role of apolipoprotein E isoforms in both pathologies is controversial. We analyzed and characterized retinal drusen by optical coherence tomography (OCT) in subjects, classifying them by their AD FH (FH-or FH+) and their allelic characterization of ApoE ε4 (ApoE ε4-or ApoE ε4+) and considering cardiovascular risk factors (hypercholesterolemia, hypertension, and diabetes mellitus). In addition, we analyzed the choroidal thickness by OCT and the area of the foveal avascular zone with OCTA. We did not find a relationship between a family history of AD or any of the ApoE isoforms and the presence or absence of drusen. Subjects with drusen show choroidal thinning compared to patients without drusen, and thinning could trigger changes in choroidal perfusion that may give rise to the deposits that generate drusen

Non-random distribution of deleterious mutations in the DNA and protein-binding domains of IRF6 are associated with Van Der Woude syndrome

Background: The development of the face occurs during the early days of intrauterine life by the formation of facial processes from the first Pharyngeal arch. Derangement in these well-organized fusion events results in Orofacial clefts (OFC). Van der Woude syndrome (VWS) is one of the most common causes of syndromic cleft lip and/or palate accounting for 2% of all cases. Mutations in the IRF6 gene account for 70% of cases with the majority of these mutations located in the DNA-binding (exon 3, 4) or protein-binding domains (exon 7-9). The current study was designed to update the list of IRF6 variants reported for VWS by compiling all the published mutations from 2013 to date as well as including the previously unreported VWS cases from Africa and Puerto Rico.Methods: We used PubMed with the search terms; "Van der Woude syndrome," "Popliteal pterygium syndrome," "IRF6," and "Orofacial cleft" to identify eligible studies. We compiled the CADD score for all the mutations to determine the percentage of deleterious variants.Results: Twenty-one new mutations were identified from nine papers. The majority of these mutations were in exon 4. Mutations in exon 3 and 4 had CADD scores between 20 and 30 and mutations in exon 7-9 had CADD scores between 30 and 40. The presence of higher CADD scores in the protein-binding domain (exon 7-9) further confirms the crucial role played by this domain in the function of IRF6. In the new cases, we identified five IRF6 mutations, three novel missense mutations (p.Phe36Tyr, p.Lys109Thr, and p.Gln438Leu), and two previously reported nonsense mutations (p.Ser424*and p.Arg250*).Conclusion: Mutations in the protein and DNA-binding domains of IRF6 ranked among the top 0.1% and 1% most deleterious genetic mutations, respectively. Overall, these findings expand the range of VWS mutations and are important for diagnostic and counseling purposes.</p

H3K4me1 marks DNA regions hypomethylated during aging in human stem and differentiated cells

In differentiated cells, aging is associated with hypermethylation of DNA regions enriched in repressive histone post-translational modifications. However, the chromatin marks associated with changes in DNA methylation in adult stem cells during lifetime are still largely unknown. Here, DNA methylation profiling of mesenchymal stem cells (MSCs) obtained from individuals aged 2 to 92 yr identified 18,735 hypermethylated and 45,407 hypomethylated CpG sites associated with aging. As in differentiated cells, hypermethylated sequences were enriched in chromatin repressive marks. Most importantly, hypomethylated CpG sites were strongly enriched in the active chromatin mark H3K4me1 in stem and differentiated cells, suggesting this is a cell type-independent chromatin signature of DNA hypomethylation during aging. Analysis of scedasticity showed that interindividual variability of DNA methylation increased during aging in MSCs and differentiated cells, providing a new avenue for the identification of DNA methylation changes over time. DNA methylation profiling of genetically identical individuals showed that both the tendency of DNA methylation changes and scedasticity depended on nongenetic as well as genetic factors. Our results indicate that the dynamics of DNA methylation during aging depend on a complex mixture of factors that include the DNA sequence, cell type, and chromatin context involved and that, depending on the locus, the changes can be modulated by genetic and/or external factors

H3K4me1 marks DNA regions hypomethylated during aging in human stem and differentiated cells

In differentiated cells, aging is associated with hypermethylation of DNA regions enriched in repressive histone post-translational modifications. However, the chromatin marks associated with changes in DNA methylation in adult stem cells during lifetime are still largely unknown. Here, DNA methylation profiling of mesenchymal stem cells (MSCs) obtained from individuals aged 2 to 92 yr identified 18,735 hypermethylated and 45,407 hypomethylated CpG sites associated with aging. As in differentiated cells, hypermethylated sequences were enriched in chromatin repressive marks. Most importantly, hypomethylated CpG sites were strongly enriched in the active chromatin mark H3K4me1 in stem and differentiated cells, suggesting this is a cell type-independent chromatin signature of DNA hypomethylation during aging. Analysis of scedasticity showed that interindividual variability of DNA methylation increased during aging in MSCs and differentiated cells, providing a new avenue for the identification of DNA methylation changes over time. DNA methylation profiling of genetically identical individuals showed that both the tendency of DNA methylation changes and scedasticity depended on nongenetic as well as genetic factors. Our results indicate that the dynamics of DNA methylation during aging depend on a complex mixture of factors that include the DNA sequence, cell type, and chromatin context involved and that, depending on the locus, the changes can be modulated by genetic and/or external factors

Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles, Lie algebras, principal bundles, reduced systems, and constrained are included in such description. In this paper, we investigate how to derive the dynamics associated with a Lagrangian system defined on the set of admissible elements of a given Lie algebroid using Tulczyjew’s triple on Lie algebroids and constructing a Lagrangian Lie subalgebroid of a symplectic Lie algebroid, by building on the geometric formalism for mechanics on Lie algebroids developed by M. de León, J.C. Marrero and E. Martínez on “Lagrangian submanifolds and dynamics on Lie algebroids”publishe