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

Heart Valve Tissue Engineering: Concepts, Approaches, Progress, and Challenges

Potential applications of tissue engineering in regenerative medicine range from structural tissues to organs with complex function. This review focuses on the engineering of heart valve tissue, a goal which involves a unique combination of biological, engineering, and technological hurdles. We emphasize basic concepts, approaches and methods, progress made, and remaining challenges. To provide a framework for understanding the enabling scientific principles, we first examine the elements and features of normal heart valve functional structure, biomechanics, development, maturation, remodeling, and response to injury. Following a discussion of the fundamental principles of tissue engineering applicable to heart valves, we examine three approaches to achieving the goal of an engineered tissue heart valve: (1) cell seeding of biodegradable synthetic scaffolds, (2) cell seeding of processed tissue scaffolds, and (3) in-vivo repopulation by circulating endogenous cells of implanted substrates without prior in-vitro cell seeding. Lastly, we analyze challenges to the field and suggest future directions for both preclinical and translational (clinical) studies that will be needed to address key regulatory issues for safety and efficacy of the application of tissue engineering and regenerative approaches to heart valves. Although modest progress has been made toward the goal of a clinically useful tissue engineered heart valve, further success and ultimate human benefit will be dependent upon advances in biodegradable polymers and other scaffolds, cellular manipulation, strategies for rebuilding the extracellular matrix, and techniques to characterize and potentially non-invasively assess the speed and quality of tissue healing and remodeling

Plasmid macro-evolution: selection of deletions during adaptation in a nutrient-limited environment

Under conditions where plasmid-carriage is deleterious to the cell, evolutionary changes may be expected which result in an attenuation of the deleterious effect of the plasmid. During long-term growth in glucose-limited continuous culture, initiated with a single clone of Escherichia coli containing a derivative of the plasmid pBR322, a structural change arose in the plasmid and predominated in the plasmid-containing sector of the population. This variant possessed a 2.25 kb deletion encompassing the tetracycline resistance operon as well as a region of about 1.5 kb upstream from this operon. Competition experiments involving strains carrying the plasmid with the spontancous deletion, and strains carrying plasmids with artificially constructed deletions, revealed that deletion of this region of the plasmid, involving loss of tetracycline resistance, resulted in an increment in fitness of between 10 and 20%. From the magnitude of the growth advantage, we conclude that the attenuation of the deleterious effect of the plasmid was mainly due to a reduction in the plasmid mediated interference in the metabolism of the cell caused by a deletion of the tetracycline resistance gene.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42797/1/10709_2004_Article_BF00127247.pd

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