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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]

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]

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]