Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

A critical role of RBM8a in proliferation and differentiation of embryonic neural progenitors

BACKGROUND: Nonsense mediated mRNA decay (NMD) is an RNA surveillance mechanism that controls RNA stability and ensures the speedy degradation of erroneous and unnecessary transcripts. This mechanism depends on several core factors in the exon junction complex (EJC), eIF4A3, RBM8a, Magoh, and BTZ, as well as peripheral factors to distinguish premature stop codons (PTCs) from normal stop codons in transcripts. Recently, emerging evidence has indicated that NMD factors are associated with neurodevelopmental disorders such as autism spectrum disorder (ASD) and intellectual disability (ID). However, the mechanism in which these factors control embryonic brain development is not clear. RESULT: We found that RBM8a is critical for proliferation and differentiation in cortical neural progenitor cells (NPCs). RBM8a is highly expressed in the subventricular zone (SVZ) of the early embryonic cortex, suggesting that RBM8a may play a role in regulating NPCs. RBM8a overexpression stimulates embryonic NPC proliferation and suppresses neuronal differentiation. Conversely, knockdown of RBM8a in the neocortex reduces NPC proliferation and promotes premature neuronal differentiation. Moreover, overexpression of RBM8a suppresses cell cycle exit and keeps cortical NPCs in a proliferative state. To uncover the underlying mechanisms of this phenotype, genome-wide RNAseq was used to identify potential downstream genes of RBM8a in the brain, which have been implicated in autism and neurodevelopmental disorders. Interestingly, autism and schizophrenia risk genes are highly represented in downstream transcripts of RBM8a. In addition, RBM8a regulates multiple alternative splicing genes and NMD targets that are implicated in ASD. Taken together, this data suggests a novel role of RBM8a in the regulation of neurodevelopment. CONCLUSIONS: Our studies provide some insight into causes of mental illnesses and will facilitate the development of new therapeutic strategies for neurodevelopmental illnesses. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13064-015-0045-7) contains supplementary material, which is available to authorized users

Hypoxia and reoxygenation do not upregulate adhesion molecules and natural killer cell adhesion on human endothelial cells in vitro

Objectives: Ischemia/reperfusion injury is characterized by endothelial cell activation leading to increased expression of adhesion molecules such as inter-cellular adhesion molecule (ICAM)-1, vascular cell adhesion molecule (VCAM)-1, endothelial- and platelet-selectin (E- and P-selectin), and to the subsequent recruitment of leukocytes. The aim of the present study was to investigate the respective effects of a proinflammatory cytokine (tumor necrosis factor alpha , TNF-α), hypoxia and/or reoxygenation on adhesion molecule expression and natural killer (NK) cell adhesion in an in vitro model of I/R. Methods: Human aortic endothelial cells (HAEC) were stimulated in vitro for 8h with TNF-α (1000 U/ml) and exposed to hypoxia (1% O2), reoxygenation (21% O2) or different combinations thereof. Cell surface expression of ICAM-1, VCAM-1 and E-/P-selectin on HAEC was analyzed by flow cytometry, and culture supernatants were tested for soluble adhesion molecules by ELISA. Rolling adhesion of NK cells on HAEC was determined using a rotating assay. Results: Untreated HAEC constitutively expressed ICAM-1 on their surface but neither expressed E-/P-selectin, VCAM-1, nor shedded soluble adhesion molecules. Exposure of HAEC to hypoxia or hypoxia and reoxygenation did not upregulate cell surface expression or shedding of adhesion molecules. In contrast, TNF-α significantly upregulated cell surface expression of ICAM-1, VCAM-1, and E-/P-selectin and led to the shedding of ICAM-1 and E-selectin. Combined treatment of HAEC with TNF-α, hypoxia and reoxygenation reduced E-/P-selectin surface expression and enhanced E-selectin shedding, but did not further influence ICAM-1 and VCAM-1. Soluble VCAM-1 was not detected. NK cell adhesion on HAEC increased 4-fold after TNF-α stimulation, but was not affected by hypoxia or hypoxia and reoxygenation. Conclusions: Both the expression of endothelial adhesion molecules and rolling NK cell adhesion was upregulated by TNF-α but not by hypoxia alone or hypoxia followed by reoxygenation supporting the view that anti-inflammatory treatment may reduce ischemia/reperfusion injur