14 research outputs found
Generalization of “Division of Fractions with Pentagonal Cycle” Problem for Developing Teaching Materials : Proposals for Elementary, Jr. High, and High School Mathematics
The aims of this paper are generalizing the “Division of fractions with pentagonal cycle” problem and proposing this problem as a teaching material for school mathematics. “Division of fractions with pentagonal cycle” problem is a problem for students to find regularity of a sequence that can be expressed by a recursion formula of an+2 = (an+1 + 1) / an. Moreover, this number sequence is a circulating number sequence and has an interesting property of an+5 = an.
First, we explored this problem mathematically, and found that mathematical value of this problem is “circulation of the sequence derived from the original title” and “it can generalize these sequences”. We also clarified that pedagogical value of this problem is “the debate derives from various recurrence formulas and questions”. Based on the above, we proposed the “Division of fractions with pentagonal cycle” as teaching materials in elementary, junior high, and high school mathematics by using the format of teaching units (TU) or Substantial Learning Environments (SLEs) by Wittmann (1984, 2001).textapplication/pdfdepartmental bulletin pape
GRAPH COVERING AND ITS GENERALIZATION
application/pdfWe present some topics on graph covering and its generalization. We survey some results on enumeration of isomorphism classes of coverings of a graph and g-cyclic A-covers of a symmetric digraph, where $A$ is a finite group and $g¥in A$ . We also mention some related questions.departmental bulletin pape
DNA hypermethylation in arsenic-induced malignancies: a casuallink or a molecular paradigm
Arsenic is recognized as a toxicant and a poor mutagenic carcinogen. Non-occupational exposure to low or high concentrations of arsenic affects millions of people throughout the world including India. Although arsenic is a poor mutagen, it is known to cause various types of malignancies notably melanoma, oropharyngeal squamous cell carcinoma, cervical cancer, and esophageal cancer. Arsenic induced tumors show increased DNA methylation at the promoter regions of important tumor suppressor genes such as p16 and p53, suggesting an epigenetic mechanism of gene silencing in these kinds of tumors. The extent of DNA hypermethylation in such genes upon exposure to various levels of arsenic can be studied by performing simple methylation specific PCR using primers that can specifically target methylated DNA. Sequencing can also be done to validate the results of PCR. Further, the expression of p1 6 protein can be studied to confirm the results. The results obtained from the study would be helpful in early detection of DNA hypennethylation, which could be useful in predicting the risk of cancer in arsenic contaminated regions. In addition, studies on pharmacological reversal of DNA hypermethylation of tumor suppressor genes may offer therapeutic options to individuals exposed to arsenic.othe
Solution Structure of a Consensus Stem-Loop D RNA Domain that Plays Important Roles in Regulating Translation and Replication in Enteroviruses and Rhinoviruses<sup>†</sup><sup>,</sup><sup>‡</sup>
Stem-loop D from the cloverleaf RNA is a highly conserved domain within the 5‘-UTR of
enteroviruses and rhinoviruses. Interaction between the stem-loop D RNA and the viral 3C or 3CD proteins
constitutes an essential feature of a ribonucleoprotein complex that plays a critical role in regulating viral
translation and replication. Here we report the solution NMR structure of a 38-nucleotide RNA with a
sequence that encompasses the entire stem-loop D domain and corresponds to the consensus sequence
found in enteroviruses and rhinoviruses. Sequence variants corresponding to Poliovirus type 1 and
Coxsackievirus B3 have virtually the same structure, based on small differences in chemical shifts. A
substantial number (136) of 1H−13C one-bond residual dipolar coupling (RDC) values were used in the
structure determination in addition to conventional distance and torsion angle restraints. Inclusion of the
RDC restraints was essential for achieving well-defined structures, both globally and locally. The structure of the consensus stem-loop D is an elongated A-type helical stem capped by a UACG tetraloop
with a wobble UG closing base pair. Three consecutive pyrimidine base pairs (two UU and one CU pair)
are present in the middle of the helical stem, creating distinctive local structural features such as a
dramatically widened major groove. A dinucleotide bulge is located near the base of the stem. The
bulge itself is flexible and not as well defined as the other parts of the molecule, but the flanking base
pairs are intact. The peculiar spatial arrangement of the distinctive structural elements implies that they
may work synergistically to achieve optimal binding affinity and specificity toward the viral 3C or 3CD
proteins
NMR Structures of Loop B RNAs from the Stem−Loop IV Domain of the <i>Enterovirus </i>Internal Ribosome Entry Site: A Single C to U Substitution Drastically Changes the Shape and Flexibility of RNA<sup>†</sup><sup>,</sup><sup>‡</sup>
The 5‘-untranslated region of positive-strand RNA viruses harbors many cis-acting RNA
structural elements that are important for various viral processes such as replication, translation, and
packaging of new virions. Among these is loop B RNA of the stem−loop IV domain within the internal
ribosomal entry site (IRES) of enteroviruses, including Poliovirus type 1 (PV1). Studies on PV1 have
shown that specific recognition of loop B by the first KH (hnRNP K homology) domain of cellular poly(rC)-binding protein 2 (PCBP2) is essential for efficient translation of the viral mRNA. Here we report
the NMR solution structures of two representative sequence variants of enteroviral loop B RNA. The two
RNA variants differ at only one position (C vs U) within a six-nucleotide asymmetric internal loop sequence
that is the binding site for the PCBP2 KH1 domain. Surprisingly, the two RNAs are drastically different
in the overall shape and local dynamics of the bulge region. The RNA with the 5‘-AUCCCU bulge sequence
adopts an overall L shape. Its bulge nucleotides, especially the last four, are highly flexible and not very
well defined by NMR. The RNA with the 5‘-AUUCCU bulge sequence adopts an overall U shape, and
its bulge sequence exhibits only limited flexibility. A detailed analysis of the two RNA structures and
their dynamic properties, as well as available sequence data and known KH domain−RNA complex
structures, not only provides insights into how loop B RNA might be recognized by the PCBP2 KH1
domain but also suggests a possible correlation between structural flexibility and pre-existing structural
features for protein recognition
Binding Characteristics of Small Molecules That Mimic Nucleocapsid Protein-Induced Maturation of Stem-Loop 1 of HIV-1 RNA
As a retrovirus, the human immunodeficiency virus (HIV-1) packages two copies of the RNA genome as a dimer in the infectious virion. Dimerization is initiated at the dimer initiation site (DIS) which encompasses stem-loop 1 (SL1) in the 5′-UTR of the genome. Study of genomic dimerization has been facilitated by the discovery that short RNA fragments containing SL1 can dimerize spontaneously without any protein factors. On the basis of the palindromic nature of SL1, a kissing loop model has been proposed. First, a metastable kissing dimer is formed via standard Watson−Crick base pairs and then converted into a more stable extended dimer by the viral nucleocapsid protein (NCp7). This dimer maturation in vitro is believed to mimic initial steps in the RNA maturation in vivo, which is correlated with viral infectivity. We previously discovered a small molecule activator, Lys-Ala-7-amido-4-methylcoumarin (KA-AMC), which facilitates dimer maturation in vitro, and determined aspects of its structure−activity relationship. In this report, we present measurements of the binding affinity of the activators and characterization of their interactions with the SL1 RNA. Guanidinium groups and increasing positive charge on the side chain enhance affinity and activity, but features in the aromatic ring at least partially decouple affinity from activity. Although KA-AMC can bind to multiple structural motifs, the NMR study showed KA-AMC preferentially binds to unique structural motifs, such as the palindromic loop and the G-rich internal loop in the SL1 RNA. NCp7 binds to SL1 only 1 order of magnitude more tightly than the best small molecule ligand tested. This study provides guidelines for the design of superior small molecules that bind to the SL1 RNA that have the potential of being developed as an antiviral by interfering with SL1−NCp7 interaction at the packaging and/or maturation stages
Discovery of Ligands for a Novel Target, the Human Telomerase RNA, Based on Flexible-Target Virtual Screening and NMR
The human ribonucleoprotein telomerase is a validated anticancer drug target, and hTR-P2b is a part of the human telomerase RNA (hTR) essential for its activity. Interesting ligands that bind hTR-P2b were identified by iteratively using a tandem structure-based approach: docking of potential ligands from small databases to hTR-P2b via the program MORDOR, which permits flexibility in both ligand and target, with subsequent NMR screening of high-ranking compounds. A high percentage of the compounds tested experimentally were found via NMR to bind to the U-rich region of hTR-P2b; most have MW < 500 Da and are from different compound classes, and several possess a charge of 0 or +1. Of the 48 ligands identified, 24 exhibit a decided preference to bind hTR-P2b RNA rather than A-site rRNA and 10 do not bind A-site rRNA at all. Binding affinity was measured by monitoring RNA imino proton resonances for some of the compounds that showed hTR binding preference
First slices of N-HSQC NMR experiments on complexes of UN-labeled SL1-es kissing dimer and NCp7 in the 2:0, 2:1, 2:2 and 2:4 RNA strand-to-protein ratios at 15°C
<p><b>Copyright information:</b></p><p>Taken from "Nucleocapsid protein-mediated maturation of dimer initiation complex of full-length SL1 stemloop of HIV-1: sequence effects and mechanism of RNA refolding"</p><p></p><p>Nucleic Acids Research 2007;35(6):2026-2034.</p><p>Published online 6 Mar 2007</p><p>PMCID:PMC1874624.</p><p>© 2007 The Author(s)</p> Only signals from imino protons of uridines are observed in this experiment
