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Highlights • The results of aggregation by weighted arithmetic mean are normalization-dependent. • Weighted arithmetic mean aggregation fails to reflect preference information well. • Serious problems caused by the arithmetic mean aggregation shown on examples. • Theorems claiming the superiority of geometric mean aggregation in AHP presented. • Weighted geometric mean recommended for aggregation of local priorities in AHP. Abstract The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - and identify their strengths and weaknesses. We investigate the focus of the aggregation, the assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence. [ABSTRACT FROM AUTHOR]

Deriving accurate fuzzy priorities is very important in multi-criteria decision making with vague information. In this paper, appropriate formulas for obtaining fuzzy priorities from additive fuzzy pairwise comparison matrices are introduced. The formulas are based on the proper fuzzy extension of the formulas for obtaining priorities from additive pairwise comparison matrices proposed by Fedrizzi & Brunelli (2010, Soft Comput. 14 , 639–645) satisfying Tanino's characterization. Moreover, a new normalization condition for priorities reachable (unlike other normalization conditions formerly proposed in the literature) also for inconsistent additive pairwise comparison matrices is proposed and extended properly to additive fuzzy pairwise comparison matrices. Furthermore, a new definition of a consistent additive fuzzy pairwise comparison matrix independent of the ordering of objects in the matrix is given, and the consistency requirement is also employed directly into the formulas for obtaining fuzzy priorities. Triangular fuzzy numbers are used for the fuzzy extension in the paper, and a brief discussion on how to easily modify the formulas and the definitions presented in the paper in order to apply on intervals, trapezoidal fuzzy numbers or any other type of fuzzy numbers is provided. The theory is illustrated on numerical examples throughout the paper. [ABSTRACT FROM AUTHOR]

The transformations between multiplicatively and additively reciprocal fuzzy pairwise comparison matrices are dealt with, and formulas for obtaining multiplicative fuzzy priorities from additively reciprocal fuzzy pairwise comparison matrices are proposed in this paper. The formulas are based on the concept of constrained fuzzy arithmetic and preserve the additive reciprocity of pairwise comparisons. Further, the consistency issue is approached in the paper; the consistency check is employed directly in the formulas for obtaining multiplicative fuzzy priorities of objects both from multiplicatively and additively reciprocal fuzzy pairwise comparison matrices. Two definitions of consistency based on transitivity are employed in this paper-the traditional additive/multiplicative transitivity and the weak consistency. However, also several other transitivity conditions are discussed in this context. Finally, the proposed formulas for obtaining multiplicative fuzzy priorities from an additively reciprocal fuzzy pairwise comparison matrix and the formulas with employed consistency check are applied in an illustrative example. Triangular fuzzy numbers are used for the fuzzy extension in this paper. However, all the formulas can be modified easily to be applied on intervals, trapezoidal fuzzy numbers or any other fuzzy numbers given by $$\alpha $$ -cuts. [ABSTRACT FROM AUTHOR]

Proper formulas for obtaining the fuzzy maximal eigenvalue and the corresponding fuzzy maximal eigenvector of a fuzzy pairwise comparison matrix are proposed in this paper. First, the formulas for obtaining the fuzzy maximal eigenvalue of a fuzzy pairwise comparison matrix proposed by Csutora & Buckley (2001) and by Ishizaka (2014) are reviewed, and the flaws in their formulas regarding the violation of the reciprocity of pairwise comparisons are pointed out. New formulas for obtaining the fuzzy maximal eigenvalue preserving the reciprocity of pairwise comparisons are then proposed. After, a fuzzy extension of Saaty's Consistency Index and Consistency Ratio is introduced in order to verify an acceptable level of inconsistency of a fuzzy pairwise comparison matrix. Further, the methods for obtaining the fuzzy maximal eigenvector corresponding to the fuzzy maximal eigenvalue of a fuzzy pairwise comparison matrix proposed by Wang & Chin (2006) and by Ishizaka (2014) are reviewed. The flaws in Ishizaka's method are pointed out, and Wang & Chin's method is studied and modified in order to preserve the reciprocity of pairwise comparisons. The fuzzy maximal eigenvalues and the corresponding fuzzy maximal eigenvectors obtained by the new formulas are confronted with those obtained by methods proposed by Csutora & Buckley (2001), Wang & Chin (2006) and Ishizaka (2014), and three numerical examples are given for better illustration. [ABSTRACT FROM AUTHOR]

Cajal bodies (CBs) are important compartments containing accumulated proteins that preferentially regulate RNA-related nuclear events, including splicing. Here, we studied the nuclear distribution pattern of CBs in neurogenesis. In adult brains, coilin was present at a high density, but CB formation was absent in the nuclei of the choroid plexus of the lateral ventricles. Cells of the adult hippocampus were characterized by a crescent-like morphology of coilin protein. We additionally observed a 70 kDa splice variant of coilin in adult mouse brains, which was different to embryonic brains and mouse pluripotent embryonic stem cells (mESCs), characterized by the 80 kDa standard variant of coilin. Here, we also showed that depletion of coilin is induced during neural differentiation and HDAC1 deficiency in mESCs caused coilin accumulation inside the fibrillarin-positive region of the nucleoli. A similar distribution pattern was observed in adult brain hippocampi, characterized by lower levels of both coilin and HDAC1. In summary, we observed that neural differentiation and HDAC1 deficiency lead to coilin depletion and coilin accumulation in body-like structures inside the nucleoli. [ABSTRACT FROM AUTHOR]

In the last 30 years, several distinguished researchers have proposed and discussed different fuzzy versions of well-known Saaty's Analytic Hierarchy Process (AHP). The paper recently published by K. Zhü in the European Journal of Operational Research heavily criticizes the fuzzy approaches to AHP, claiming the fallacy of all of them. Therefore, it seems to be necessary to clarify whether the criticisms are well-founded or not. The present paper aims to rebut Zhü's claims by showing that the evidences and the reasonings in his paper are very poor and far from proving the fallacy of fuzzy AHP. [ABSTRACT FROM AUTHOR]

Abstract: Genetic and epigenetic changes in multiple myeloma (MM) correlate with the stage of the disease. Therefore, we investigated how cytostatics and gamma radiation influence MM-associated histone modifications. ChIP-PCR and ChIP-on-chip technologies were used to quantify H3K9 acetylation and H3K9 dimethylation at select loci in MM patients, lymphoblastoid ARH-77, and myeloma MOLP-8 cells. Genome-wide analysis revealed that the cytostatic, melphalan, increased H3K9 acetylation at multiple gene promoters in ARH-77 cells. Melphalan and gamma radiation also influenced histone modification of prognostically important c-myc and CCND1 genes in ARH-77 and MOLP-8 cells. Moreover, H3K9 acetylation at c-myc and CCND1 promoters was increased in individual MM patients after melphalan treatment. Western blotting revealed that these effects were accompanied by changes in c-MYC and cyclin D1 protein levels. Taken together, we showed that cytostatics significantly alter histone modification of tumor-related genes which is indispensable for understanding cancer therapies. [Copyright &y& Elsevier]

Epigenetic marks are important factors regulating the pluripotency and differentiation of human embryonic stem cells (hESCs). In this study, we analyzed H3K9 acetylation, an epigenetic mark associated with transcriptionally active chromatin, during endoderm-like differentiation of hESCs. ChIP-on-chip analysis revealed that differentiation results in a genome-wide decrease in promoter H3K9 acetylation. Among the 24,659 promoters analyzed, only 117 are likely to be involved in pluripotency, while 25 acetylated promoters are likely to be responsible for endoderm-like differentiation. In pluripotent hESCs, the chromosomes with the highest absolute levels of H3K9 acetylation are chromosomes 1, 6, 2, 17, 11, and 12 (listed in order of decreasing acetylation). Chromosomes 17, 19, 11, 20, 22, and 12 are the most prone to differentiation-related changes (both increased acetylation and deacetylation). When chromosome size (in Mb) was accounted for, the highest H3K9 acetylation levels were found on chromosome 19, 17, 6, 12, 11, and 1, and the greatest differentiation-associated decreases in H3K9 acetylation occurred on chromosomes 19, 17, 11, 12, 16, and 1. The gene density and size of individual chromosomes were strongly correlated with the levels of H3K9 acetylation. Our analyses point to chromosomes 11, 12, 17, and 19 as being critical for hESC pluripotency and endoderm-like differentiation. J. Cell. Physiol. 219: 677–687, 2009. © 2009 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]

Abstract: The nuclear arrangement of promyelocytic leukaemia nuclear bodies (PML NBs) was studied in vitro after the cell treatment by clinically used agents such as all-trans retinoic acid (RA) in human leukaemia and cytostatics or gamma radiation in multiple myeloma cells. In addition, the influence of phorbol ester (PMA) on PML NBs formation was analyzed. A reduced number of PML bodies, which led to relocation of PML NBs closer to the nuclear interior, mostly accompanied RA- and PMA-induced differentiation. Centrally located PML NBs were associated with transcriptional protein RNAP II and SC35 regions, which support importance of PML NBs in RNA processing that mostly proceeds within the nuclear interior. Conversely, the quantity of PML NBs was increased after cytostatic treatment, which caused re-distribution of PML NBs closer to the nuclear envelope. Here we showed correlations between the number of PML NBs and average Centre-to-PML distances. Moreover, a number of cells in S phase, especially during differentiation, influenced number of PML NBs. Studying the proteins involved in PML compartment, such as c-MYC, cell-type specific association of c-MYC and the PML NBs was observed in selected leukaemic cells undergoing differentiation, which was accompanied by c-MYC down-regulation. [Copyright &y& Elsevier]

It has become evident that epitranscriptome events, mediated by specific enzymes, regulate gene expression and, subsequently, cell differentiation processes. We show that methyltransferase-like proteins METTL3/METTL14 and N6-adenosine methylation (m6A) in RNAs are homogeneously distributed in embryonic hearts, and histone deacetylase (HDAC) inhibitors valproic acid and Trichostatin A (TSA) up-regulate METTL3/METTL14 proteins. The levels of METTL3 in mouse adult hearts, isolated from male and female animals, were lower in the aorta and pulmonary trunks when compared with atria, but METT14 was up-regulated in the aorta and pulmonary trunk, in comparison with ventriculi. Aging caused METTL3 down-regulation in aorta and atria in male animals. Western blot analysis in differentiated mouse embryonic stem cells (mESCs), containing 10–30 percent of cardiomyocytes, showed METTL3/METTL14 down-regulation, while the differentiation-induced increased level of METTL16 was observed in both wild type (wt) and HDAC1 depleted (dn) cells. In parallel, experimental differentiation in especially HDAC1 wild type cells was accompanied by depletion of m6A in RNA. Immunofluorescence analysis of individual cells revealed the highest density of METTL3/METTL14 in α-actinin positive cardiomyocytes when compared with the other cells in the culture undergoing differentiation. In both wt and HDAC1 dn cells, the amount of METTL16 was also up-regulated in cardiomyocytes when compared to co-cultivated cells. Together, we showed that distinct anatomical regions of the mouse adult hearts are characterized by different levels of METTL3 and METTL14 proteins, which are changed during aging. Experimental cell differentiation was also accompanied by changes in METTL-like proteins and m6A in RNA; in particular, levels and distribution patterns of METTL3/METTL14 proteins were different from the same parameters studied in the case of the METTL16 protein. [ABSTRACT FROM AUTHOR]

Cell differentiation into cardiomyocytes requires activation of differentiation-specific genes and epigenetic factors that contribute to these physiological processes. This study is focused on the in vitro differentiation of mouse embryonic stem cells (mESCs) induced into cardiomyocytes. The effects of clinically promising inhibitors of histone deacetylases (HDACi) on mESC cardiomyogenesis and on explanted embryonic hearts were also analyzed. HDAC1 depletion caused early beating of cardiomyocytes compared with those of the wild-type (wt) counterpart. Moreover, the adherence of embryonic bodies (EBs) was reduced in HDAC1 double knockout (dn) mESCs. The most important finding was differentiation-specific H4 deacetylation observed during cardiomyocyte differentiation of wt mESCs, while H4 deacetylation was weakened in HDAC1-depleted cells induced to the cardiac pathway. Analysis of the effect of HDACi showed that Trichostatin A (TSA) is a strong hyperacetylating agent, especially in wt mESCs, but only SAHA reduced the size of the beating areas in EBs that originated from HDAC1 dn mESCs. Additionally, explanted embryonic hearts (e15) responded to treatment with HDACi: all of the tested HDACi (TSA, SAHA, VPA) increased the levels of H3K9ac, H4ac, H4K20ac, and pan-acetylated lysines in embryonic hearts. This observation shows that explanted tissue can be maintained in a hyperacetylation state several hours after excision, which appears to be useful information from the view of transplantation strategy and the maintenance of gene upregulation via acetylation in tissue intended for transplantation. [ABSTRACT FROM AUTHOR]

We studied the histone signature of embryonic and adult brains to strengthen existing evidence of the importance of the histone code in mouse brain development. We analyzed the levels and distribution patterns of H3K9me1, H3K9me2, H3K9me3, and HP1β in both embryonic and adult brains. Western blotting showed that during mouse brain development, the levels of H3K9me1, H3K9me2, and HP1β exhibited almost identical trends, with the highest protein levels occurring at E15 stage. These trends differed from the relatively stable level of H3K9me3 at developmental stages E8, E13, E15, and E18. Compared with embryonic brains, adult brains were characterized by very low levels of H3K9me1/me2/me3 and HP1β. Manipulation of the embryonic epigenome through histone deacetylase inhibitor treatment did not affect the distribution patterns of the studied histone markers in embryonic ventricular ependyma. Similarly, Hdac3 depletion in adult animals had no effect on histone methylation in the adult hippocampus. Our results indicate that the distribution of HP1β in the embryonic mouse brain is related to that of H3K9me1/me2 but not to that of H3K9me3. The unique status of H3K9me3 in the brain was confirmed by its pronounced accumulation in the granular layer of the adult olfactory bulb. Moreover, among the studied proteins, H3K9me3 was the only posttranslational histone modification that was highly abundant at clusters of centromeric heterochromatin, called chromocenters. When we focused on the hippocampus, we found this region to be rich in H3K9me1 and H3K9me3, whereas H3K9me2 and HP1β were present at a very low level or even absent in the hippocampal blade. Taken together, these results revealed differences in the epigenome of the embryonic and adult mouse brain and showed that the adult hippocampus, the granular layer of the adult olfactory bulb, and the ventricular ependyma of the embryonic brain are colonized by specific epigenetic marks. [ABSTRACT FROM AUTHOR]

In this work, we have studied the structural and functional linkage between lamin A/C, nuclear actin, and organization of chromosome territories (CTs) in mammary carcinoma MCF-7 cells. Selective down-regulation of lamin A/C expression led to disruption of the lamin A/C perinuclear layer and disorganization of lamin-bound emerin complexes at the inner nuclear membrane. The silencing of lamin A/C expression resulted in a decrease in the volume and surface area of chromosome territories, especially in chromosomes with high heterochromatin content. Inhibition of actin polymerization led to relaxation of the structure of chromosome territories, and an increase in the volumes and surface areas of the chromosome territories of human chromosomes 1, 2 and 13. The results show an important role of polymeric actin in the organization of the nuclei and the chromosome territories. [ABSTRACT FROM AUTHOR]

Abstract Histone posttranslational modifications regulate diverse nuclear functions, including DNA repair. Here, we use mass spectrometry, western blotting, immunohistochemistry and advanced confocal microscopy in order to show radiation-specific changes in the histone signature. We studied wild-type mouse embryonic stem cells (mESCs) and mESCs with a depletion of histone deacetylase 1 (HDAC1), which plays a role in DNA repair. Irradiation by γ-rays increased the S139 phosphorylation of histone H2AX but reduced the level of the H3K9-R17 peptide, which contains S10 phosphorylation (H3S10ph). On an individual cellular level, H3S10ph was low in highly γH2AX-positive UV laser-induced DNA lesions, and this nuclear distribution pattern was not changed by HDAC1 depletion. Despite this fact, spontaneous γH2AX-positive DNA lesions colocalized with large H3S10ph-positive nuclear bodies that appear in the G2 phase of the cell cycle. Similarly, by FLIM-FRET analysis, we observed an interaction between H3S10ph and γH2AX in the G2 phase. However, this interaction was reduced when cells were exposed to γ-rays. A mutual link between H3S10ph and γH2AX was not observed in the G1 phase of the cell cycle. Together, our data show that despite the fact that H3S10ph is not directly involved in DNA repair, a decrease in H3S10 phosphorylation and weakened interaction between H3S10ph and γH2AX is a result of radiation-induced damage of the genome. In this case, γ-irradiation also decreased the number of cells in the G1 phase, characterized by no interaction between H3S10ph and γH2AX. Graphical abstract (A) Irradiation by γ-rays (red line) reduced H3S10ph levels. However, (B) H3S10ph was intact in the γH2AX-positive microirradiated genomic region. (C) Despite the fact that H3S10ph- and γH2AX-positive foci colocalized (interacted) in the G2 phase of the cell cycle, radiation-induced H3S10ph dephosphorylation was not directly linked to DNA repair processes, but instead (D) H3S10ph dephosphorylation was caused by a radiation-induced cell number decrease in the G1 phase. G1 phase was characterized by no interaction between H3S10ph and γH2AX (mentioned in panel C). Together, H3S10ph contributes to the function of γH2AX in DNA repair taking place in G2 phase. Image 1 Highlights • Irradiation by γ-rays increased γH2AX but reduced the level of H3S10ph. • A mutual link between H3S10ph and γH2AX was not observed in the G1 phase of the cell cycle. • An interaction between γH2AX and H3S10ph was found in the G2 phase. • H3S10ph contributes to the function of γH2AX in homologous recombination repair. [ABSTRACT FROM AUTHOR]

This review focuses on the function of heterochromatin protein HP1 in response to DNA damage. We specifically outline the regulatory mechanisms in which HP1 and its interacting partners are involved. HP1 protein subtypes (HP1α, HP1β, and HP1γ) are the main components of constitutive heterochromatin, and HP1α and HP1β in particular are responsible for heterochromatin maintenance. The recruitment of these proteins to DNA lesions is also important from the perspective of proper DNA repair mechanisms. For example, HP1α is necessary for the binding of the main DNA damage-related protein 53BP1 at DNA repair foci, which are positive not only for the HP1α protein but also for the RAD51 protein, a component of DNA repair machinery. The HP1β protein also appears in monomeric form in DNA lesions together with the evolutionarily well-conserved protein called proliferating cell nuclear antigen (PCNA). The role of HP1 in DNA lesions is also mediated via the Kap1 transcription repressor. Taken together, these results indicate that the function of HP1 after DNA injury depends strongly on the kinetics of other DNA repair-related factors and their post-translational modifications, such as the phosphorylation of Kap-1. [ABSTRACT FROM AUTHOR]

Histone variants and their epigenetic modifications determine genome function, particularly transcription. However, whether regulation of gene expression can be influenced by nuclear organization or vice versa is not completely clear. Here, we analyzed the effect of epigenetic changes induced by a histone deacetylase inhibitor (HDACi) on the nuclear radial rearrangement of select genomic regions and chromosomes. The HDACi, sodium butyrate (NaBt), induced differentiation of human adenocarcinoma HT29 cells as well as a genome-wide increase in H3K9 acetylation. Three-dimensional analysis of nuclear radial distributions revealed that this increase in H3K9 acetylation was often associated with a repositioning of select loci and chromosomes toward the nuclear center. On the other hand, many centromeres resided sites more toward the nuclear periphery, similar to sites occupied by chromosome X. In more than two-thirds of events analyzed, central nuclear positioning correlated with a high level of H3K9 acetylation, while more peripheral positioning within interphase nuclei correlated with a lower level of acetylation. This was observed for the gene-rich chromosomes 17 and 19, TP53, and CCND1 genes as well as for gene-poor chromosome 18, APC gene, regions of low transcriptional activity (anti-RIDGEs), and the relatively transcriptionally less active chromosome X. These results are consistent with a role for epigenetic histone modifications in governing the nuclear radial positioning of genomic regions during differentiation. J. Cell. Physiol. 220: 91–101, 2009. © 2009 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Recent studies have shown that histone code dictates the type and structure of chromatin. Bearing in mind the importance of A-type lamins for chromatin arrangement, we studied the effect of trichostatin A (TSA)-induced histone hyperacetylation in lamin A/C-deficient (LMNA−/−) fibroblasts. Lamin A/C deficiency caused condensation of chromosome territories and the nuclear reorganization of centromeric heterochromatin, which was accompanied by the appearance of a chain-like morphology of HP1β foci. Conversely, histone deacetylase (HDAC) inhibition induced de-condensation of chromosome territories, which compensated the effect of lamin A/C deficiency on chromosome regions. The amount of heterochromatin in the area associated with the nuclear membrane was significantly reduced in LMNA−/− cells when compared with lamin A/C-positive (LMNA+/+) fibroblasts. TSA also decreased the amount of peripheral heterochromatin, similarly as lamin A/C deficiency. In both LMNA+/+ and LMNA−/− cells, physically larger chromosomes were positioned more peripherally as compared with the smaller ones, even after TSA treatment. Our observations indicate that lamin A/C deficiency causes not only reorganization of chromatin and some chromatin-associated domains, but also has an impact on the extent of chromosome condensation. As HDAC inhibition can compensate the lamin A/C-dependent chromatin changes, the interaction between lamins and specifically modified histones may play an important role in higher-order chromatin organization, which influences transcriptional activity. [Copyright &y& Elsevier]