Fast evaluation of derivatives of B\'{e}zier curves

New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives of rational B\'{e}zier curves of high degrees

A comprehensive view of the epigenetic landscape part I : DNA methylation, passive and active DNA demethylation pathways and histone variants

In multicellular organisms, all the cells are genetically identical but turn genes on or off at the right time to promote differentiation into specific cell types. The regulation of higher-order chromatin structure is essential for genome-wide reprogramming and for tissue-specific patterns of gene expression. The complexity of the genome is regulated by epigenetic mechanisms, which act at the level of DNA, histones, and nucleosomes. Epigenetic machinery is involved in many biological processes, including genomic imprinting, X-chromosome inactivation, heterochromatin formation, and transcriptional regulation, as well as DNA damage repair. In this review, we summarize the recent understanding of DNA methylation, cytosine derivatives, active and passive demethylation pathways as well as histone variants. DNA methylation is one of the well-characterized epigenetic signaling tools. Cytosine methylation of promoter regions usually represses transcription but methylation in the gene body may have a positive correlation with gene expression. The attachment of a methyl group to cytosine residue in the DNA sequence is catalyzed by enzymes of the DNA methyltransferase family. Recent studies have shown that the Ten-Eleven translocation family enzymes are involved in stepwise oxidation of 5-methylcytosine, creating new cytosine derivatives including 5-hydroxymethylcytosine, 5-formylcytosine, and 5-carboxylcytosine. Additionally, histone variants into nucleosomes create another strategy to regulate the structure and function of chromatin. The replacement of canonical histones with specialized histone variants regulates accessibility of DNA, and thus may affect multiple biological processes, such as replication, transcription, DNA repair, and play a role in various disorders such as cancer

A Comprehensive View of the Epigenetic Landscape Part I: DNA Methylation, Passive and Active DNA Demethylation Pathways and Histone Variants

In multicellular organisms, all the cells are genetically identical but turn genes on or off at the right time to promote differentiation into specific cell types. The regulation of higher-order chromatin structure is essential for genome-wide reprogramming and for tissue-specific patterns of gene expression. The complexity of the genome is regulated by epigenetic mechanisms, which act at the level of DNA, histones, and nucleosomes. Epigenetic machinery is involved in many biological processes, including genomic imprinting, X-chromosome inactivation, heterochromatin formation, and transcriptional regulation, as well as DNA damage repair. In this review, we summarize the recent understanding of DNA methylation, cytosine derivatives, active and passive demethylation pathways as well as histone variants. DNA methylation is one of the well-characterized epigenetic signaling tools. Cytosine methylation of promoter regions usually represses transcription but methylation in the gene body may have a positive correlation with gene expression. The attachment of a methyl group to cytosine residue in the DNA sequence is catalyzed by enzymes of the DNA methyltransferase family. Recent studies have shown that the Ten-Eleven translocation family enzymes are involved in stepwise oxidation of 5-methylcytosine, creating new cytosine derivatives including 5-hydroxymethylcytosine, 5-formylcytosine, and 5-carboxylcytosine. Additionally, histone variants into nucleosomes create another strategy to regulate the structure and function of chromatin. The replacement of canonical histones with specialized histone variants regulates accessibility of DNA, and thus may affect multiple biological processes, such as replication, transcription, DNA repair, and play a role in various disorders such as cancer