The MacMahon R-matrix

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters $q$, $t^{-1}$ and $\frac{t}{q}$. We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon $R$-matrix.Comment: 39 page

The first success of glass eel production in the world: basic biology on fish reproduction advances new applied technology in aquaculture

The eel has long been esteemed as an important food fish in the world, especially in Japan, and has been used as an experimental fish for many fields of fish physiology. However, the decreases in eel resources have been a serious concern in recent years. The catches of glass eels as seedlings for aquaculture have shown a long-term decrease in both Europe and East Asia. To increase eel resources, the development of techniques for artificial induction of maturation and spawning and rearing their larvae have been eagerly desired. Recent progress of reproductive physiology of fish, especially mechanisms of oocyte maturation and ovulation in female and of spermatozoa maturation in male, facilitate to establish techniques for hormonal induction of maturation and spawning in sexually immature eels. With persistent effort to development of rearing techniques of larvae, we have first succeeded to produce glass eel. These applied techniques are may contribute to understand the basic reproductive physiology of the eel

A new type of lectin discovered in a fish, flathead (Platycephalus indicus), suggests an alternative functional role for mammalian plasma kallikrein*

A skin mucus lectin exhibiting a homodimeric structure and an S–S bond between subunits of ∼40 kDa was purified from flathead Platycephalus indicus (Scorpaeniformes). This lectin, named FHL (FlatHead Lectin), exhibited mannose-specific activity in a Ca2+-dependent manner. Although FHL showed no homology to any previously reported lectins, it did exhibit ∼20% identity to previously discovered plasma kallikreins and coagulation factor XIs of mammals and Xenopus laevis. These known proteins are serine proteases and play pivotal roles in the kinin-generating system or the blood coagulation pathway. However, alignment analysis revealed that while FHL lacked a serine protease domain, it was homologous to the heavy-chain domain of plasma kallikreins and coagulation factor XI therefore suggesting that FHL is not an enzyme but rather a novel animal lectin. On the basis of this finding, we investigated the lectin activity of human plasma kallikrein and revealed that it could indeed act as a lectin. Other genes homologous to FHL were also found in the genome databases of some fish species, but not in mammals. In contrast, plasma kallikreins and coagulation factor XI have yet to be identified in fish. The present findings suggest that these mammalian enzymes may have originally emerged as a lectin and may have evolved into molecules with protease activity after separation from common ancestors

Defending the genome from the enemy within:mechanisms of retrotransposon suppression in the mouse germline

The viability of any species requires that the genome is kept stable as it is transmitted from generation to generation by the germ cells. One of the challenges to transgenerational genome stability is the potential mutagenic activity of transposable genetic elements, particularly retrotransposons. There are many different types of retrotransposon in mammalian genomes, and these target different points in germline development to amplify and integrate into new genomic locations. Germ cells, and their pluripotent developmental precursors, have evolved a variety of genome defence mechanisms that suppress retrotransposon activity and maintain genome stability across the generations. Here, we review recent advances in understanding how retrotransposon activity is suppressed in the mammalian germline, how genes involved in germline genome defence mechanisms are regulated, and the consequences of mutating these genome defence genes for the developing germline

Nucleosomes protect DNA from DNA methylation in vivo and in vitro

Positioned nucleosomes limit the access of proteins to DNA. However, the impact of nucleosomes on DNA methylation in vitro and in vivo is poorly understood. Here, we performed a detailed analysis of nucleosome binding and nucleosomal DNA methylation by the de novo methyltransferases. We show that compared to linker DNA, nucleosomal DNA is largely devoid of CpG methylation. ATP-dependent chromatin remodelling frees nucleosomal CpG dinucleotides and renders the remodelled nucleosome a 2-fold better substrate for Dnmt3a methyltransferase compared to free DNA. These results reflect the situation in vivo, as quantification of nucleosomal DNA methylation levels in HeLa cells shows a 2-fold decrease of nucleosomal DNA methylation levels compared to linker DNA. Our findings suggest that nucleosomal positions are stably maintained in vivo and nucleosomal occupancy is a major determinant of global DNA methylation patterns in vivo