MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Examining the Factor Structure of the Home Mathematics Environment to Delineate Its Role in Predicting Preschool Numeracy, Mathematical Language, and Spatial Skills

A growing body of evidence suggests that the ways in which parents and preschool children interact in terms of home-based mathematics activities (i.e., the home mathematics environment; HME) is related to children’s mathematics development (e.g., primarily numeracy skills and spatial skills); however, this body of evidence is mixed with some research supporting the relation and others finding null effects. Importantly, few studies have explicitly examined the factor structure of the HME and contrasted multiple hypothesized models. To develop more precise models of how the HME supports children’s mathematics development, the structure of the HME needs to be examined and linked to mathematics performance. The purpose of this study was to extend prior work by replicating the factor structure of the HME (as one general HME factor and three specific factors of direct numeracy, indirect numeracy, and spatial) and using those factors to predict direct assessments of children’s numeracy, mathematical language, and spatial skills. It was hypothesized that the general HME factor would be related to each direct assessment, the direct numeracy factor would be related to both numeracy and mathematical language, and the spatial factor would be related to spatial skills. Using a sample of 129 preschool children (M age = 4.71 years, SD = 0.55; 46.5% female), a series of confirmatory factor analyses were conducted. Results diverged somewhat from prior work as the best fitting model was a bifactor model with a general HME factor and two specific factors (one that combined direct and indirect numeracy activities and another of spatial activities) rather than three specific factors as had previously been found. Further, structural equation modeling analyses suggested that, in contrast to expectations, only the direct + indirect numeracy factor was a significant predictor of direct child assessments when accounting for age, sex, and parental education. These findings provide evidence that a bifactor model is important in understanding the structure of the HME, but only one specific factor is related to children’s outcomes. Delineating the structure of the HME, and how specific facets of the HME relate to children’s mathematics skills, provides a strong foundation for understanding and enhancing the mechanisms that support mathematics development

Pharmacological inhibition of ULK1 kinase blocks mammalian target of rapamycin (mTOR)-dependent autophagy

Autophagy is a cell-protective and degradative process that recycles damaged and long-lived cellular components. Cancer cells are thought to take advantage of autophagy to help them to cope with the stress of tumorigenesis; thus targeting autophagy is an attractive therapeutic approach. However, there are currently no specific inhibitors of autophagy. ULK1, a serine/threonine protein kinase, is essential for the initial stages of autophagy, and here we report that two compounds, MRT67307 and MRT68921, potently inhibit ULK1 and ULK2 in vitro and block autophagy in cells. Using a drug-resistant ULK1 mutant, we show that the autophagy-inhibiting capacity of the compounds is specifically through ULK1. ULK1 inhibition results in accumulation of stalled early autophagosomal structures, indicating a role for ULK1 in the maturation of autophagosomes as well as initiation

Clearance of damaged mitochondria via mitophagy is important to the protective effect of ischemic preconditioning in kidneys

<p>Ischemic preconditioning (IPC) affords tissue protection in organs including kidneys; however, the underlying mechanism remains unclear. Here we demonstrate an important role of macroautophagy/autophagy (especially mitophagy) in the protective effect of IPC in kidneys. IPC induced autophagy in renal tubular cells in mice and suppressed subsequent renal ischemia-reperfusion injury (IRI). The protective effect of IPC was abolished by pharmacological inhibitors of autophagy and by the ablation of <i>Atg7</i> from kidney proximal tubules. Pretreatment with BECN1/Beclin1 peptide induced autophagy and protected against IRI. These results suggest the dependence of IPC protection on renal autophagy. During IPC, the mitophagy regulator PINK1 (PTEN induced putative kinase 1) was activated. Both IPC and BECN1 peptide enhanced mitolysosome formation during renal IRI in mitophagy reporter mice, suggesting that IPC may protect kidneys by activating mitophagy. We further established an in vitro model of IPC by inducing ‘chemical ischemia’ in kidney proximal tubular cells with carbonyl cyanide 3-chlorophenylhydrazone (CCCP). Brief treatment with CCCP protected against subsequent injury in these cells and the protective effect was abrogated by autophagy inhibition. In vitro IPC increased mitophagosome formation, enhanced the delivery of mitophagosomes to lysosomes, and promoted the clearance of damaged mitochondria during subsequent CCCP treatment. IPC also suppressed mitochondrial depolarization, improved ATP production, and inhibited the generation of reactive oxygen species. Knockdown of <i>Pink1</i> suppressed mitophagy and reduced the cytoprotective effect of IPC. Together, these results suggest that autophagy, especially mitophagy, plays an important role in the protective effect of IPC.</p> <p><b>Abbreviations</b>: ACTB: actin, beta; ATG: autophagy related; BNIP3: BCL2 interacting protein 3; BNIP3L/NIX: BCL2 interacting protein 3 like; BUN: blood urea nitrogen; CASP3: caspase 3; CCCP: carbonyl cyanide 3-chlorophenylhydrazone; COX4I1: cytochrome c oxidase subunit 4I1; COX8: cytochrome c oxidase subunit 8; DAPI: 4ʹ,6-diamidino-2-phenylindole; DNM1L: dynamin 1 like; EGFP: enhanced green fluorescent protein; EM: electron microscopy; ER: endoplasmic reticulum; FC: floxed control; FIS1: fission, mitochondrial 1; FUNDC1: FUN14 domain containing 1; H-E: hematoxylin-eosin; HIF1A: hypoxia inducible factor 1 subunit alpha; HSPD1: heat shock protein family D (Hsp60) member 1; IMMT/MIC60: inner membrane mitochondrial protein; IPC: ischemic preconditioning; I-R: ischemia-reperfusion; IRI: ischemia-reperfusion injury; JC-1: 5,5ʹ,6,6ʹ-tetrachloro-1,1ʹ,3,3ʹ-tetraethylbenzimidazolylcarbocyanine iodide; KO: knockout; MAP1LC3B/LC3B: microtubule associated protein 1 light chain 3 beta; mito-QC: mito-quality control; mRFP: monomeric red fluorescent protein; NAC: N-acetylcysteine; PINK1: PTEN induced putative kinase 1; PPIB: peptidylprolyl isomerase B; PRKN: parkin RBR E3 ubiquitin protein ligase; ROS: reactive oxygen species; RPTC: rat proximal tubular cells; SD: standard deviation; sIPC: simulated IPC; SQSTM1/p62: sequestosome 1; TOMM20: translocase of outer mitochondrial membrane 20; TUNEL: terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling</p

Popis suradnika u časopisu »Ekonomska i ekohistorija«, broj 9 (2013.)

<div><p>There is a growing literature concerning the role of the home math environment in children’s math development. In this study, we examined the relation between these constructs by specifically addressing three goals. The first goal was to identify the measurement structure of the home math environment through a series of confirmatory factor analyses. The second goal was to examine the role of the home math environment in predicting parent report of children’s math skills. The third goal was to test a series of potential alternative explanations for the relation between the home math environment and parent report of children’s skills, specifically the direct and indirect role of household income, parent math anxiety, and parent math ability as measured by their approximate number system performance. A final sample of 339 parents of children aged 3 through 8 drawn from Mechanical Turk answered a questionnaire online. The best fitting model of the home math environment was a bifactor model with a general factor representing the general home math environment, and three specific factors representing the direct numeracy environment, the indirect numeracy environment, and the spatial environment. When examining the association of the home math environment factors to parent report of child skills, the general home math environment factor and the spatial environment were the only significant predictors. Parents who reported doing more general math activities in the home reported having children with higher math skills, whereas parents who reported doing more spatial activities reported having children with lower math skills.</p></div

LRRK2 is a negative regulator of <em>Mycobacterium tuberculosis</em> phagosome maturation in macrophages

\ua9 2018 EMBO. Mutations in the leucine-rich repeat kinase 2 (LRRK2) are associated with Parkinson\u27s disease, chronic inflammation and mycobacterial infections. Although there is evidence supporting the idea that LRRK2 has an immune function, the cellular function of this kinase is still largely unknown. By using genetic, pharmacological and proteomics approaches, we show that LRRK2 kinase activity negatively regulates phagosome maturation via the recruitment of the Class III phosphatidylinositol-3 kinase complex and Rubicon to the phagosome in macrophages. Moreover, inhibition of LRRK2 kinase activity in mouse and human macrophages enhanced Mycobacterium tuberculosis phagosome maturation and mycobacterial control independently of autophagy. In vivo, LRRK2 deficiency in mice resulted in a significant decrease in M. tuberculosis burdens early during the infection. Collectively, our findings provide a molecular mechanism explaining genetic evidence linking LRRK2 to mycobacterial diseases and establish an LRRK2-dependent cellular pathway that controls M. tuberculosis replication by regulating phagosome maturation

Repeat Elements Organise 3D Genome Structure and Mediate Transcription in the Filamentous Fungus \u3cem\u3eEpichloë festucae\u3c/em\u3e

Structural features of genomes, including the three-dimensional arrangement of DNA in the nucleus, are increasingly seen as key contributors to the regulation of gene expression. However, studies on how genome structure and nuclear organisation influence transcription have so far been limited to a handful of model species. This narrow focus limits our ability to draw general conclusions about the ways in which three-dimensional structures are encoded, and to integrate information from three-dimensional data to address a broader gamut of biological questions. Here, we generate a complete and gapless genome sequence for the filamentous fungus, Epichloë festucae. We use Hi-C data to examine the three-dimensional organisation of the genome, and RNA-seq data to investigate how Epichloë genome structure contributes to the suite of transcriptional changes needed to maintain symbiotic relationships with the grass host. Our results reveal a genome in which very repeat-rich blocks of DNA with discrete boundaries are interspersed by gene-rich sequences that are almost repeat-free. In contrast to other species reported to date, the three-dimensional structure of the genome is anchored by these repeat blocks, which act to isolate transcription in neighbouring gene-rich regions. Genes that are differentially expressed in planta are enriched near the boundaries of these repeat-rich blocks, suggesting that their three-dimensional orientation partly encodes and regulates the symbiotic relationship formed by this organism

Defining a spinal microcircuit that gates myelinated afferent input: implications for tactile allodynia

Chronic pain presents a major unmet clinical problem. The development of more effective treatments is hindered by our limited understanding of the neuronal circuits underlying sensory perception. Here, we show that parvalbumin (PV)-expressing dorsal horn interneurons modulate the passage of sensory information conveyed by low-threshold mechanoreceptors (LTMRs) directly via presynaptic inhibition and also gate the polysynaptic relay of LTMR input to pain circuits by inhibiting lamina II excitatory interneurons whose axons project into lamina I. We show changes in the functional properties of these PV interneurons following peripheral nerve injury and that silencing these cells unmasks a circuit that allows innocuous touch inputs to activate pain circuits by increasing network activity in laminae I–IV. Such changes are likely to result in the development of tactile allodynia and could be targeted for more effective treatment of mechanical pain