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BackgroundPancreatic cancer is a complex disease with a desmoplastic stroma, extreme hypoxia, and inherent resistance to therapy. Understanding the signaling and adaptive response of such an aggressive cancer is key to making advances in therapeutic efficacy. Redox factor-1 (Ref-1), a redox signaling protein, regulates the conversion of several transcription factors (TFs), including HIF-1α, STAT3 and NFκB from an oxidized to reduced state leading to enhancement of their DNA binding. In our previously published work, knockdown of Ref-1 under normoxia resulted in altered gene expression patterns on pathways including EIF2, protein kinase A, and mTOR. In this study, single cell RNA sequencing (scRNA-seq) and proteomics were used to explore the effects of Ref-1 on metabolic pathways under hypoxia.MethodsscRNA-seq comparing pancreatic cancer cells expressing less than 20% of the Ref-1 protein was analyzed using left truncated mixture Gaussian model and validated using proteomics and qRT-PCR. The identified Ref-1’s role in mitochondrial function was confirmed using mitochondrial function assays, qRT-PCR, western blotting and NADP assay. Further, the effect of Ref-1 redox function inhibition against pancreatic cancer metabolism was assayed using 3D co-culture in vitro and xenograft studies in vivo.ResultsDistinct transcriptional variation in central metabolism, cell cycle, apoptosis, immune response, and genes downstream of a series of signaling pathways and transcriptional regulatory factors were identified in Ref-1 knockdown vs Scrambled control from the scRNA-seq data. Mitochondrial DEG subsets downregulated with Ref-1 knockdown were significantly reduced following Ref-1 redox inhibition and more dramatically in combination with Devimistat in vitro. Mitochondrial function assays demonstrated that Ref-1 knockdown and Ref-1 redox signaling inhibition decreased utilization of TCA cycle substrates and slowed the growth of pancreatic cancer co-culture spheroids. In Ref-1 knockdown cells, a higher flux rate of NADP + consuming reactions was observed suggesting the less availability of NADP + and a higher level of oxidative stress in these cells. In vivo xenograft studies demonstrated that tumor reduction was potent with Ref-1 redox inhibitor similar to Devimistat.ConclusionRef-1 redox signaling inhibition conclusively alters cancer cell metabolism by causing TCA cycle dysfunction while also reducing the pancreatic tumor growth in vitro as well as in vivo.

The authors provide a complete asymptotic expansion for a class of functions in terms of the complete Bell polynomials. In particular, they obtain known asymptotic expansions of some Keller type sequences.

We provide a mean-value theorem for a class of positive linear functionals. As an application, we improve the classical First Mean-value Theorem for Integrals and obtain other related results.

We prove that a property concerning the existence of the fixed points of the Bernstein-type operators remains valid for a large class of positive linear operators. More exactly, we prove that there is no positive linear analytic operator L : C [ 0 , 1 ] → C [ 0 , 1 ] possessing as fixed points two nonconstant monomials x i .

We provide complete asymptotic expansions for some sequences of Bernstein-type and Meyer–Konig and Zeller-type operators preserving the monomials e 0 and e j , j > 1 . In particular, this answers a conjecture related to a Voronovskaja-type theorem.

The EGLN (also called PHD) prolyl hydroxylase enzymes and their canonical targets, the HIFα subunits, represent the core of an ancient oxygen-monitoring machinery used by metazoans. In this review, we highlight recent progress in understanding the overlapping versus specific roles of EGLN enzymes and HIF isoforms and discuss how feedback loops based on recently identified noncoding RNAs introduce additional layers of complexity to the hypoxic response. Based on novel interactions identified upstream and downstream of EGLNs, an integrated network connecting oxygen-sensing functions to metabolic and signaling pathways is gradually emerging with broad therapeutic implications.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

We extend and solve an open problem concerning a Polya–Szegő type integral sequence of the form \({\sqrt[n]{\int\nolimits_{0}^{1} \prod\nolimits_{k=1}^n f(x^{k^\alpha}) \mathrm{d}x}}\), \({n\ge2}\), \({\alpha\ge 0}\).

We answer a conjecture and an open problem concerning integral sequences of the form ∫ 0 1 f ⁢ ( x ) ⁢ f ⁢ ( x 2 ) ⁢ ⋯ ⁢ f ⁢ ( x n ) ⁢ d x n , n ≥ 2 . \sqrt[n]{\int_{0}^{1}f(x)f(x^{2})\cdots f(x^{n})\,\mathrm{d}x},\quad n\geq 2.

Altered energy metabolism is a cancer hallmark as malignant cells tailor their metabolic pathways to meet their energy requirements. Glucose and glutamine are the major nutrients that fuel cellular metabolism, and the pathways utilizing these nutrients are often altered in cancer. Here, we show that the long ncRNA CCAT2, located at the 8q24 amplicon on cancer risk-associated rs6983267 SNP, regulates cancer metabolism in vitro and in vivo in an allele-specific manner by binding the Cleavage Factor I (CFIm) complex with distinct affinities for the two subunits (CFIm25 and CFIm68). The CCAT2 interaction with the CFIm complex fine-tunes the alternative splicing of Glutaminase (GLS) by selecting the poly(A) site in intron 14 of the precursor mRNA. These findings uncover a complex, allele-specific regulatory mechanism of cancer metabolism orchestrated by the two alleles of a long ncRNA., G.A.C. is The Alan M. Gewirtz Leukemia & Lymphoma Society Scholar. Work in G.A.C.’s laboratory is supported in part by the NIH/NCI grants 1UH2TR00943-01 and 1 R01 CA182905-01, the UT MD Anderson Cancer Center SPORE in Melanoma grant from NCI (P50 CA093459), Aim at Melanoma Foundation and the Miriam and Jim Mulva research funds, the Brain SPORE (2P50CA127001), the Center for Radiation Oncology Research Project, the Center for Cancer Epigenetics Pilot project, a 2014 Knowledge GAP MDACC grant, a CLL Moonshot pilot project, the UT MD Anderson Cancer Center Duncan Family Institute for Cancer Prevention and Risk Assessment, a SINF grant in colon cancer, the Laura and John Arnold Foundation, the RGK Foundation, and the Estate of C.G. Johnson, Jr. I.B.-N. was financed by a grant entitled Non-Invasive Intelligent Systems for Colorectal Cancer Diagnosis and Prognosis Based on circulating miRNAs Integrated in the Clinical Workflow – INTELCOR. S.M.G.D., A.L.B.A., and D.A. are supported by the São Paulo Research Foundation FAPESP under grants 2014/15968-3, 2014/20673-2, and 2014/17820-3, respectively. W.L. was partly supported by grants from The University of Texas MD Anderson Cancer Center Sheikh Ahmed Bin Zayed Al Nahyan Center for Pancreatic Cancer Research. J.A.B. was supported by the Cancer Center Support Grant (P30 CA016672), and the HP imaging program of the Small Animal Facility (SAIF) was supported by the Cancer Prevention and Research Institutes of Texas grant RP-101243P5. H.L. was supported by NIH/NCI grant R01CA175486, a grant (RP140462) from the Cancer Prevention and Research Institute of Texas, and the R. Lee Clark Fellow Award from The Jeanne F. Shelby Scholarship Fund. I.B.-N. was financed by a Fulbright fellowship and by a grant entitled Non-Invasive Intelligent Systems for Colorectal Cancer Diagnosis and Prognosis Based on circulating miRNAs Integrated in the Clinical Workflow – INTELCOR.

We prove that a result of Tachev concerning the optimal rate of convergence of the classical Bernstein operators remains valid for the class of discretely defined positive linear operators preserving constants.

Recently, Chang and Xu gave a probabilistic proof of a combinatorial identity which involves binomial coefficients. Duarte and Guedes de Oliveira (J Integer Seq 16, 2013) extended the result. Applying a generalization of the Leibniz rule for higher derivatives of the product of functions yields a new short proof and a generalization of the above mentioned identity.

In 1984 D.D. Stancu defined a sequence of positive linear operators generalizing the Bernstein polynomials. In this paper a Durrmeyer variant of these operators is considered. We derive some basic approximation properties and present a complete asymptotic expansion for the sequence of these operators. All coefficients are calculated in a concise form.

We prove that the classical Bernstein Voronovskaja-type theorem remains valid in general for all sequences of positive linear approximation operators.

We obtain a new recurrence formula for sequences of divided differences. In a particular case, the recurrence formula simplifies the classical Newton-Girard identities relating power sums and elementary symmetric polynomials.

Apurinic/apyrimidinic endonuclease/redox factor-1 (APE1/Ref-1) (henceforth referred to as Ref-1) is a multifunctional protein that in addition to its base excision DNA repair activity exerts redox control of multiple transcription factors, including nuclear factor κ-light chain enhancer of activated B cells (NF-κB), STAT3, activator protein-1 (AP-1), hypoxia-inducible factor-1 (HIF-1), and tumor protein 53 (p53). In recent years, Ref-1 has emerged as a promising therapeutic target in cancer, particularly in pancreatic ductal carcinoma. Although a significant amount of research has centered on Ref-1, no wide-ranging approach had been performed on the effects of Ref-1 inhibition and transcription factor activity perturbation. Starting with a broader approach, we identified a previously unsuspected effect on the nuclear factor erythroid-related factor 2 (NRF2), a critical regulator of cellular defenses against oxidative stress. Based on genetic and small molecule inhibitor-based methodologies, we demonstrated that repression of Ref-1 potently activates NRF2 and its downstream targets in a dose-dependent fashion, and that the redox, rather than the DNA repair function of Ref-1 is critical for this effect. Intriguingly, our results also indicate that this pathway does not involve reactive oxygen species. The link between Ref-1 and NRF2 appears to be present in all cells tested in vitro, noncancerous and cancerous, including patient-derived tumor samples. In particular, we focused on understanding the implications of the novel interaction between these two pathways in primary pancreatic ductal adenocarcinoma tumor cells and provide the first evidence that this mechanism has implications for overcoming the resistance against experimental drugs targeting Ref-1 activity, with clear translational implications.

MicroRNA molecules are small, single-stranded RNA molecules that function to regulate networks of genes. They play important roles in normal female reproductive tract biology, as well as in the pathogenesis and progression of epithelial ovarian cancer. DROSHA, DICER, and Argonaute proteins are components of the microRNA-regulatory machinery and mediate microRNA production and function. This review discusses aberrant expression of microRNA molecules and microRNA-regulating machinery associated with clinical features of epithelial ovarian cancer. Understanding the regulation of microRNA molecule production and function may facilitate the development of novel diagnostic and therapeutic strategies to improve the prognosis of women with epithelial ovarian cancer. Additionally, understanding microRNA molecules and microRNA-regulatory machinery associations with clinical features may influence prevention and early detection efforts.

Significance: Hypoxia is a hallmark of the tumor microenvironment and represents a major source of failure in cancer therapy. Recent Advances: Recent work has generated extensive evidence that microRNAs (miRNAs) are significant components of the adaptive response to low oxygen in tumors. Induction of specific miRNAs, collectively termed hypoxamiRs, has become an accepted feature of the hypoxic response in normal and transformed cells. Critical Issues: Overexpression of miR-210, the prototypical hypoxamiR, is detected in most solid tumors, and it has been linked to adverse prognosis in many tumor types. Several miR-210 target genes, including iron-sulfur (Fe-S) cluster scaffold protein (ISCU) and glycerol-3-phosphate dehydrogenase 1-like (GPD1L), have been correlated with prognosis in an inverse fashion to miR-210, suggesting that their down- regulation by miR-210 occurs in vivo and contributes to tumor growth. Additional miRNAs are modulated by decreased oxygen tension in a more tissue-specific fashion, adding another level of complexity over the classic hypoxia-regulated gene network. Future Directions: From a biological standpoint, hypoxamiRs are emerging modifiers of cancer cell response to the adaptive challenges of the microenvironment. From a clinical perspective, assessing the status of these miRNAs may contribute to a detailed understanding of hypoxia-induced mechanisms of resistance and/or to the fine-tuning of future hypoxia-modifying therapies. Antioxid. Redox Signal. 21, 1220–1238.

We obtain a new representation of the sum of the squared Bernstein polynomials and use it to validate a conjecture asserting that this sum is a convex function. The result is extended to some other classical approximation operators.

We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein-Durrmeyer type operators.

The classical Le Verrier algorithm for the calculation of the characteristic polynomial of a matrix has led us to a solution of an open problem concerning the Euler-Mascheroni constant @c. More exactly, we prove that there exists uniquely a sequence of rational numbers (@?"n)"n">="1 such that, for any integer q>=1, the sequence@?k=1n1k-logn-log1+@?"1n+...+@?"qn^q,is an n^-^q^-^1 order approximation of @c.

Recent data have linked hypoxia, a classic feature of the tumor microenvironment, to the function of specific microRNAs (miRNAs); however, whether hypoxia affects other types of noncoding transcripts is currently unknown. Starting from a genome-wide expression profiling, we demonstrate for the first time a functional link between oxygen deprivation and the modulation of long noncoding transcripts from ultraconserved regions, termed transcribed-ultraconserved regions (T-UCRs). Interestingly, several hypoxia-upregulated T-UCRs, henceforth named ‘hypoxia-induced noncoding ultraconserved transcripts' (HINCUTs), are also overexpressed in clinical samples from colon cancer patients. We show that these T-UCRs are predominantly nuclear and that the hypoxia-inducible factor (HIF) is at least partly responsible for the induction of several members of this group. One specific HINCUT, uc.475 (or HINCUT-1) is part of a retained intron of the host protein-coding gene, O-linked N-acetylglucosamine transferase, which is overexpressed in epithelial cancer types. Consistent with the hypothesis that T-UCRs have important function in tumor formation, HINCUT-1 supports cell proliferation specifically under hypoxic conditions and may be critical for optimal O-GlcNAcylation of proteins when oxygen tension is limiting. Our data gives a first glimpse of a novel functional hypoxic network comprising protein-coding transcripts and noncoding RNAs (ncRNAs) from the T-UCRs category.

We provide a highly convergent version of the generalized Euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form. The new approach extends and unifies many previous efforts in this direction. In addition, we answer an open problem on the asymptotic expansion of the Harmonic number sequence.

We give an affirmative answer to a conjecture of G.T. Tachev concerning the moments of the Bernstein operators.

We have devised a new method for the study of the asymptotic behavior of the iterates of positive linear operators. This technique enlarges the class of operators for which the limit of the iterates can be computed.

This short note presents a new representation of the remainder in the Bernstein approximation based on divided differences and some immediate applications. It is the only known representation of the remainder in the Bernstein approximation of arbitrary functions as a convex combination of divided differences of second order on known knots. As an application we obtain sharp inequalities for functions possessing bounded divided differences of second order and a new proof of the classical Weierstrass approximation theorem.