A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

A crucial sequence for transglutaminase type 2 extracellular trafficking in renal tubular epithelial cells lies in its N-terminal {beta}-sandwich domain

Transglutaminase type 2 (TG2) catalyzes the formation of an -( -glutamyl)-lysine isopeptide bond between adjacent peptides or proteins including those of the extracellular matrix (ECM). Elevated extracellular TG2 leads to accelerated ECM deposition and reduced clearance that underlie tissue scarring and fibrosis. The extracellular trafficking of TG2 is crucial to its role in ECM homeostasis; however, the mechanism by which TG2 escapes the cell is unknown as it has no signal leader peptide and therefore cannot be transported classically. Understanding TG2 transport may highlight novel mechanisms to interfere with the extracellular function of TG2 as isoform-specific TG2 inhibitors remain elusive. Mammalian expression vectors were constructed containing domain deletions of TG2. These were transfected into three kidney tubular epithelial cell lines, and TG2 export was assessed to identify critical domains. Point mutation was then used to highlight specific sequences within the domain required for TG2 export. The removal of -sandwich domain prevented all TG2 export. Mutations of Asp94 and Asp97 within the N-terminal -sandwich domain were identified as crucial for TG2 externalization. These form part of a previously identified fibronectin binding domain (88WTATVVDQQDCTLSLQLTT106). However, siRNA knockdown of fibronectin failed to affect TG2 export. The sequence 88WTATVVDQQDCTLSLQLTT106 within the -sandwich domain of TG2 is critical to its export in tubular epithelial cell lines. The extracellular trafficking of TG2 is independent of fibronectin

PseudoFuN: Deriving functional potentials of pseudogenes from integrative relationships with genes and microRNAs across 32 cancers

BACKGROUND: Long thought "relics" of evolution, not until recently have pseudogenes been of medical interest regarding regulation in cancer. Often, these regulatory roles are a direct by-product of their close sequence homology to protein-coding genes. Novel pseudogene-gene (PGG) functional associations can be identified through the integration of biomedical data, such as sequence homology, functional pathways, gene expression, pseudogene expression, and microRNA expression. However, not all of the information has been integrated, and almost all previous pseudogene studies relied on 1:1 pseudogene-parent gene relationships without leveraging other homologous genes/pseudogenes. RESULTS: We produce PGG families that expand beyond the current 1:1 paradigm. First, we construct expansive PGG databases by (i) CUDAlign graphics processing unit (GPU) accelerated local alignment of all pseudogenes to gene families (totaling 1.6 billion individual local alignments and >40,000 GPU hours) and (ii) BLAST-based assignment of pseudogenes to gene families. Second, we create an open-source web application (PseudoFuN [Pseudogene Functional Networks]) to search for integrative functional relationships of sequence homology, microRNA expression, gene expression, pseudogene expression, and gene ontology. We produce four "flavors" of CUDAlign-based databases (>462,000,000 PGG pairwise alignments and 133,770 PGG families) that can be queried and downloaded using PseudoFuN. These databases are consistent with previous 1:1 PGG annotation and also are much more powerful including millions of de novo PGG associations. For example, we find multiple known (e.g., miR-20a-PTEN-PTENP1) and novel (e.g., miR-375-SOX15-PPP4R1L) microRNA-gene-pseudogene associations in prostate cancer. PseudoFuN provides a "one stop shop" for identifying and visualizing thousands of potential regulatory relationships related to pseudogenes in The Cancer Genome Atlas cancers. CONCLUSIONS: Thousands of new PGG associations can be explored in the context of microRNA-gene-pseudogene co-expression and differential expression with a simple-to-use online tool by bioinformaticians and oncologists alike

Gene Co-expression Network and Copy Number Variation Analyses Identify Transcription Factors Associated With Multiple Myeloma Progression

Multiple myeloma (MM) has two clinical precursor stages of disease: monoclonal gammopathy of undetermined significance (MGUS) and smoldering multiple myeloma (SMM). However, the mechanism of progression is not well understood. Because gene co-expression network analysis is a well-known method for discovering new gene functions and regulatory relationships, we utilized this framework to conduct differential co-expression analysis to identify interesting transcription factors (TFs) in two publicly available datasets. We then used copy number variation (CNV) data from a third public dataset to validate these TFs. First, we identified co-expressed gene modules in two publicly available datasets each containing three conditions: normal, MGUS, and SMM. These modules were assessed for condition-specific gene expression, and then enrichment analysis was conducted on condition-specific modules to identify their biological function and upstream TFs. TFs were assessed for differential gene expression between normal and MM precursors, then validated with CNV analysis to identify candidate genes. Functional enrichment analysis reaffirmed known functional categories in MM pathology, the main one relating to immune function. Enrichment analysis revealed a handful of differentially expressed TFs between normal and either MGUS or SMM in gene expression and/or CNV. Overall, we identified four genes of interest (MAX, TCF4, ZNF148, and ZNF281) that aid in our understanding of MM initiation and progression

Reversible tuning of the surface state in a psuedo-binary Bi2(Te-Se)3 topological insulator

We use angle-resolved photoemission spectroscopy to study non-trivial surface state in psuedobinary Bi2Se0.6Te2.3 topological insulator. We show that unlike previously studied binaries, this is an intrinsic topological insulator with conduction bulk band residing well above the chemical potential. Our data indicates that under good vacuum condition there are no significant aging effects for more then two weeks after cleaving. We also demonstrate that shift of the Kramers point at low temperature is caused by UV assisted absorption of molecular hydrogen. Our findings pave the way for applications of these materials in devices and present an easy scheme to tune their properties.Comment: 4 pages, 4 figure

The role of matrix cracks and fibre/matrix debonding on the stress transfer between fibre and matrix in a single fibre fragmentation test

The single fibre fragmentation test is commonly used to characterise the fibre/matrix interface. During fragmentation, the stored energy is released resulting in matrix cracking and/or fibre/matrix debonding. Axisymmetric finite element models were formulated to study the impact of matrix cracks and fibre/matrix debonding on the effective stress transfer efficiency (EST) and stress transfer length (STL). At high strains, plastic deformation in the matrix dominated the stress transfer mechanism. The combination of matrix cracking and plasticity reduced the EST and increased STL. For experimental validation, three resins were formulated and the fragmentation of an unsized and uncoupled E-glass fibre examined as a function of matrix properties. Fibre failure was always accompanied by matrix cracking and debonding. With the stiff resin, debonding, transverse matrix cracking and conical crack initiation were observed. With a lower modulus and lower yield strength resin the transverse matrix crack length decreased while that of the conical crack increased. (C) 2011 Elsevier Ltd. All rights reserved

Syndecan-4 knockout leads to reduced extracellular transglutaminase-2 and protects against tubulointerstitial fibrosis

Transglutaminase type 2 (TG2) is an extracellular matrix crosslinking enzyme with a pivotal role in kidney fibrosis. The interaction of TG2 with the heparan sulfate proteoglycan syndecan-4 (Sdc4) regulates the cell surface trafficking, localization, and activity of TG2 in vitro but remains unstudied in vivo. We tested the hypothesis that Sdc4 is required for cell surface targeting of TG2 and the development of kidney fibrosis in CKD. Wild-type and Sdc4-null mice were subjected to unilateral ureteric obstruction and aristolochic acid nephropathy (AAN) as experimental models of kidney fibrosis. Analysis of renal scarring by Masson trichrome staining, kidney hydroxyproline levels, and collagen immunofluorescence demonstrated progressive fibrosis associated with increases in extracellular TG2 and TG activity in the tubulointerstitium in both models. Knockout of Sdc-4 reduced these effects and prevented AAN-induced increases in total and active TGF-b1. In wild-type mice subjected to AAN, extracellular TG2 colocalized with Sdc4 in the tubular interstitium and basement membrane, where TG2 also colocalized with heparan sulfate chains. Heparitinase I, which selectively cleaves heparan sulfate, completely abolished extracellular TG2 in normal and diseased kidney sections. In conclusion, the lack of Sdc4 heparan sulfate chains in the kidneys of Sdc4-null mice abrogates injury-induced externalization of TG2, thereby preventing profibrotic crosslinking of extracellular matrix and recruitment of large latent TGF-b1. This finding suggests that targeting the TG2- Sdc4 interaction may provide a specific interventional strategy for the treatment of CKD