Inverted Oscillator

The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a linear function of the quantum number $n$.Comment: 4 page

Targeted profiling of human extrachromosomal DNA by CRISPR-CATCH

Extrachromosomal DNA (ecDNA) is a common mode of oncogene amplification but is challenging to analyze. Here, we adapt CRISPR-CATCH, in vitro CRISPR-Cas9 treatment and pulsed field gel electrophoresis of agarose-entrapped genomic DNA, previously developed for bacterial chromosome segments, to isolate megabase-sized human ecDNAs. We demonstrate strong enrichment of ecDNA molecules containing EGFR, FGFR2 and MYC from human cancer cells and NRAS ecDNA from human metastatic melanoma with acquired therapeutic resistance. Targeted enrichment of ecDNA versus chromosomal DNA enabled phasing of genetic variants, identified the presence of an EGFRvIII mutation exclusively on ecDNAs and supported an excision model of ecDNA genesis in a glioblastoma model. CRISPR-CATCH followed by nanopore sequencing enabled single-molecule ecDNA methylation profiling and revealed hypomethylation of the EGFR promoter on ecDNAs. We distinguished heterogeneous ecDNA species within the same sample by size and sequence with base-pair resolution and discovered functionally specialized ecDNAs that amplify select enhancers or oncogene-coding sequences

Physcomitrella patens DCL3 Is Required for 22–24 nt siRNA Accumulation, Suppression of Retrotransposon-Derived Transcripts, and Normal Development

Endogenous 24 nt short interfering RNAs (siRNAs), derived mostly from intergenic and repetitive genomic regions, constitute a major class of endogenous small RNAs in flowering plants. Accumulation of Arabidopsis thaliana 24 nt siRNAs requires the Dicer family member DCL3, and clear homologs of DCL3 exist in both flowering and non-flowering plants. However, the absence of a conspicuous 24 nt peak in the total RNA populations of several non-flowering plants has raised the question of whether this class of siRNAs might, in contrast to the ancient 21 nt microRNAs (miRNAs) and 21–22 nt trans-acting siRNAs (tasiRNAs), be an angiosperm-specific innovation. Analysis of non-miRNA, non-tasiRNA hotspots of small RNA production within the genome of the moss Physcomitrella patens revealed multiple loci that consistently produced a mixture of 21–24 nt siRNAs with a peak at 23 nt. These Pp23SR loci were significantly enriched in transposon content, depleted in overlap with annotated genes, and typified by dense concentrations of the 5-methyl cytosine (5 mC) DNA modification. Deep sequencing of small RNAs from two independent Ppdcl3 mutants showed that the P. patens DCL3 homolog is required for the accumulation of 22–24 nt siRNAs, but not 21 nt siRNAs, at Pp23SR loci. The 21 nt component of Pp23SR-derived siRNAs was also unaffected by a mutation in the RNA-dependent RNA polymerase mutant Pprdr6. Transcriptome-wide, Ppdcl3 mutants failed to accumulate 22–24 nt small RNAs from repetitive regions while transcripts from two abundant families of long terminal repeat (LTR) retrotransposon-associated reverse transcriptases were up-regulated. Ppdcl3 mutants also displayed an acceleration of leafy gametophore production, suggesting that repetitive siRNAs may play a role in the development of P. patens. We conclude that intergenic/repeat-derived siRNAs are indeed a broadly conserved, distinct class of small regulatory RNAs within land plants

Shallow and Deep Structure of a Supradetachment Basin Based on Geological, Conventional Deep Seismic Reflection Sections and Gravity Data in the Buyuk Menderes Graben, Western Anatolia

The Buyuk Menderes Graben is a depression in the Menderes core complex of western Turkey. The region is one of the most rapidly deforming regions of continental crust in the world and has exceptionally high seismic activity. In this study, shallow and deep seismic studies were conducted at the Buyuk Menderes graben. These studies included surface geological mapping and two seismic reflection sections. Detailed modelling was performed with the seismic study. In addition to these, a moving windows power spectrum was applied to the Bouguer gravity profile data of the study area. Since no deep well is available in this area, the geological interpretation of the seismic stratigraphy is based on the correlation with the surface geology, this was combined with the major reflections and the seismic facies observed along the profiles, and, thus, four main seismic units can be distinguished in the basin fill. Structural features of the basin is driven by a complex extensional faults system, consisting of a low-angle, S-dipping Buyuk Menderes detachment and by its synthetic and antithetic splays, bordering the opposite flanks of the basin. As a result of conventional deep seismic reflection sections and gravity data, three layers were defined in the study area. The first layer occurs at a thickness of 6 km, and the second layer is between 13 and 18 km. The third layer is at similar to 33 km and may also emphasize Moho depth. The Buyuk Menderes graben has three clear reflectors which are base sediments, brittle-ductile transition, Moho and faults that show a half-graben floored by a detachment. The Moho depth is comparable with previous estimates. According to the results obtained, Bouguer gravity and seismic results are very much consistent with each other. It was observed that at the depths determined from seismic and gravity data, the distribution percentage of earthquake focal depths also rises