Work hardening and the study of instability is incorporated into the description of the growth of a crack in terms of the successive blocking of the plastic zone by slip barriers, such as grain boundaries, and the subsequent initiation of the slip in neighbouring grains. A simple equation is derived to determine the critical position of the crack tip in relation to the grain boundary where the plastic zone is blocked at the moment of slip transmission. The intermittent pattern of decelerating and accelerating behaviour of short cracks and the existence of non-propagating cracks is explained. Instability in crack growth is seen to occur when the rate of hardening is insufficient to compensate for the increase in crack driving force in relation to the increase in crack length. This is associated with fracture toughness. The transition point between the short and long crack régimes is seen to occur when the size of the plastic zone is of the order of the microstructural parameter.
Depressive disorders have been shown to be highly influenced by environmental pathogenic factors, some of which are believed to exert stress on human brain functioning via epigenetic modifications. Previous genome-wide methylomic studies on depression have suggested that, along with differential DNA methylation, affected co-twins of monozygotic (MZ) pairs have increased DNA methylation variability, probably in line with theories of epigenetic stochasticity. Nevertheless, the potential biological roots of this variability remain largely unexplored. The current study aimed to evaluate whether DNA methylation differences within MZ twin pairs were related to differences in their psychopathological status. Data from the Illumina Infinium HumanMethylation450 Beadchip was used to evaluate peripheral blood DNA methylation of 34 twins (17 MZ pairs). Two analytical strategies were used to identify (a) differentially methylated probes (DMPs) and (b) variably methylated probes (VMPs). Most DMPs were located in genes previously related to neuropsychiatric phenotypes. Remarkably, one of these DMPs (cg01122889) was located in the WDR26 gene, the DNA sequence of which has been implicated in major depressive disorder from genome-wide association studies. Expression of WDR26 has also been proposed as a biomarker of depression in human blood. Complementarily, VMPs were located in genes such as CACNA1C, IGF2 and the p38 MAP kinase MAPK11, showing enrichment for biological processes such as glucocorticoid signaling. These results expand on previous research to indicate that both differential methylation and differential variability have a role in the etiology and clinical manifestation of depression, and provide clues on specific genomic loci of potential interest in the epigenetics of depression.
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