• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.765-780
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• 2015

We consider the problem of characterizing the palindromic sequences ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$, $c_{d-1}{\neq}0$, having the property that for any $K{\in}\mathbb{N}$ there exists a number that is a palindrome simultaneously in K different bases, with ${\langle}c_{d-1},\;c_{d-2}\;,{\cdots},\;c_0\rangle$ being its digit sequence in one of those bases. Since each number is trivially a palindrome in all bases greater than itself, we impose the restriction that only palindromes with at least two digits are taken into account. We further consider a related problem, where we count only palindromes with a fixed number of digits (that is, d). The first problem turns out not to be very hard; we show that all the palindromic sequences have the required property, even with the additional point that we can actually restrict the counted palindromes to have at least d digits. The second one is quite tougher; we show that all the palindromic sequences of length d = 3 have the required property (and the same holds for d = 2, based on some earlier results), while for larger values of d we present some arguments showing that this tendency is quite likely to change.

• Genomics & Informatics
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• v.5 no.2
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• pp.68-76
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• 2007

Due to the increasing interest in SNPs and mutational hot spots for disease traits, it is becoming more important to define and understand the relationship between SNPs and their flanking sequences. To study the effects of flanking sequences on SNPs, statistical approaches are necessary to assess bias in SNP data. In this study we mainly applied Markov chains for SNP sequences, particularly those located in intronic regions, and for analysis of in-del data. All of the pertaining sequences showed a significant tendency to generate particular SNP types. Most sequences flanking SNPs had lower complexities than average sequences, and some of them were associated with microsatellites. Moreover, many Alu repeats were found in the flanking sequences. We observed an elevated frequency of single-base-pair repeat-like sequences, mirror repeats, and palindromes in the SNP flanking sequence data. Alu repeats are hypothesized to be associated with C-to-T transition mutations or A-to-I RNA editing. In particular, the in-del data revealed an association between particular changes such as palindromes or mirror repeats. Results indicate that the mechanism of induction of in-del transitions is probably very different from that which is responsible for other SNPs. From a statistical perspective, frequent DNA lesions in some regions probably have effects on the occurrence of SNPs.

• Journal of Life Science
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• v.13 no.6
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• pp.958-969
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• 2003

The human Y chromosome is strictly paternally inherited and does not X-Y crossing over during male meiosis in most of its length. Although this region came to be known as the non-recombining region Y (NRY), it was renamed as male-specific region Y (MSY) due to abundant recombination. The MSY is a mosaic of heterochromatic sequences and three classes of euchromatic sequences: X-transposed, X-degenerated and ampliconic. The X-transposed sequences exhibit 99% identity to the X chromosomal sequences. The X-degenerate sequences are remnants of ancient autosomes from which the modem X and Y chromosomes evolved. Eight palindromes of the ampliconic comprise one-quarter of the euchromatic DNA of the male-specific region of the human Y chromosome. They contain many testis-specific genes and typically exhibit 99.97% intra-palindromic (arm-to-arm) sequence identity. The arms of these palindromes must have subsequently engaged in gene conversion, driving the pair arms to evolve it concert. Averages of approximately 600 nucleotides per newborn male have undergone Y-Y gene conversion, which has had an important role in the evolution of multi-copy testis gene families in the MSY.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.12
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• pp.4915-4920
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• 2015

Background: : Familial adenomatous polyposis (FAP) is an autosomal dominant inherited disease mainly caused by mutations of the adenomatous polyposis coli (APC) gene with almost complete penetrance. These colorectal polyps are precancerous lesions that will inevitable develop into colorectal cancer at the median age of 40-year old if total proctocolectomy is not performed. So identification of APC germline mutations has great implications for genetic counseling and management of FAP patients. In this study, we screened APC germline mutations in Chinese FAP patients, in order to find novel mutations and the APC gene germline mutation characteristics of Chinese FAP patients. Materials and Methods: The FAP patients were diagnosed by clinical manifestations, family histories, endoscope and biopsy. Then patients peripheral blood samples were collected, afterwards, genomic DNA was extracted. The mutation analysis of the APC gene was conducted by direct polymerase chain reaction (PCR) sequencing for micromutations and multiplex ligation-dependent probe amplification (MLPA) for large duplications and/or deletions. Results: We found 6 micromutations out of 14 FAP pedigrees, while there were no large duplications and/or deletions found. These germline mutations are c.5432C>T(p. Ser1811Leu), two c.3926_3930delAAAAG (p.Glu1309AspfsX4), c.3921_3924delAAAA (p.Ile1307MetfsX13), c3184_3187delCAAA(p.Gln1061AspfsX59) and c4127_4126delAT (p.Tyr1376LysfsX9), respectively, and all deletion mutations resulted in a premature stop codon. At the same time, we found c.3921_3924delAAAA and two c.3926_3930delAAAAG are located in AAAAG short tandem repeats, c3184_3187delCAAA is located in the CAAA interrupted direct repeats, and c4127_4128 del AT is located in the 5'-CCTGAACA-3', 3'-ACAAGTCC-5 palindromes (inverted repeats) of the APC gene. Furthermore, deletion mutations are mostly located at condon 1309. Conclusions: Though there were no novel mutations found as the pathogenic gene of FAP in this study, we found nucleotide sequence containing short tandem repeats and palindromes (inverted repeats), especially the 5 bp base deletion at codon 1309, are mutations in high incidence area in APC gene,.

• Genomics & Informatics
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• v.20 no.4
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• pp.43.1-43.18
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• 2022

Atropa belladonna is a valuable medicinal plant and a commercial source of tropane alkaloids, which are frequently utilized in therapeutic practice. In this study, bioinformatic methodologies were used to examine the pattern of coding sequences and the factors that might influence codon usage bias in the chloroplast genome of Atropa belladonna and other nightshade genomes. The chloroplast engineering being a promising field in modern biotechnology, the characterization of chloroplast genome is very important. The results revealed that the chloroplast genomes of Nicotiana tabacum, Solanum lycopersicum, Capsicum frutescens, Datura stramonium, Lyciumbarbarum, Solanum melongena, and Solanum tuberosum exhibited comparable codon usage patterns. In these chloroplast genomes, we observed a weak codon usage bias. According to the correspondence analysis, the genesis of the codon use bias in these chloroplast genes might be explained by natural selection, directed mutational pressure, and other factors. GC12 and GC3S were shown to have no meaningful relationship. Further research revealed that natural selection primarily shaped the codon usage in A. belladonna and other nightshade genomes for translational efficiency. The sequencing properties of these chloroplast genomes were also investigated by investing the occurrences of palindromes and inverted repeats, which would be useful for future research on medicinal plants.