Linear Collisionless Landau Damping in Hilbert Space

The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10 (1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18, 102309 (2011)] solutions of the linear collisionless Landau damping problem is proven

Magnetic compressibility and ion-temperature-gradient-driven microinstabilities in magnetically confined plasmas

The electromagnetic theory of the strongly driven ion-temperature-gradient (ITG) instability in magnetically confined toroidal plasmas is developed. Stabilizing and destabilizing effects are identified, and a critical $\beta_{e}$ (the ratio of the electron to magnetic pressure) for stabilization of the toroidal branch of the mode is calculated for magnetic equilibria independent of the coordinate along the magnetic field. Its scaling is $\beta_{e}\sim L_{Te}/R,$ where $L_{Te}$ is the characteristic electron temperature gradient length, and $R$ the major radius of the torus. We conjecture that a fast particle population can cause a similar stabilization due to its contribution to the equilibrium pressure gradient. For sheared equilibria, the boundary of marginal stability of the electromagnetic correction to the electrostatic mode is also given. For a general magnetic equilibrium, we find a critical length (for electromagnetic stabilization) of the extent of the unfavourable curvature along the magnetic field. This is a decreasing function of the local magnetic shear

Biochemical characterization of the Chp1 chromodomain binding to the nucleosome core and its role in heterochromatin formation

Eukaryotic genomes are organized inside the cell nucleus in a structured macromolecular DNA-protein polymer named chromatin, formed by single discrete unites called Nucleosomes. The packing of the genetic information into chromatin allows the efficient regulation of several nuclear processes, such as gene expression and transcription, DNA replication, cell cycle progression, chromosome segregation and DNA damage repair. Chromatin comes in two flavors: a transcriptionally active, more loosened state, called euchromatin and a transcriptionally silent or low expressed, more compact state, called heterochromatin. The assembly of silent chromatin or heterochromatin is fundamental for the regulation of every nuclear process and it is driven in most Eukaryotes by the deposition and the read-out of the histone H3 lysine 9 methylation (H3K9me) post-translational modification (PTM). H3K9me on the nucleosome is specifically bound by chromatin readers called chromodomains (CD) and this recognition is fundamental for the downstream processes that lead to the formation of heterochromatin and shut down the expression of single genes or entire gene clusters. Despite several studies have been done on different chromodomains binding to H3K9me histone tail peptides, to date there was no structural information on how chromodomains interact with their natural binding partners, the H3K9me3 Nucleosomes. In a preliminary structural study carried out in our laboratory we solved the cryo-electron microscopy (Cryo-EM) structure of the chromodomain of the fission yeast Chp1 protein (Chp1CD) in complex with an H3K9me nucleosome. The structure showed that the Chp1CD interacts not only with the histone H3 tail but also with the histone globular domains in the Nucleosome core, primarily with histone H3. Mutations in the residues of Chp1CD that form the binding interface with the Nucleosome core (two loops in the β-sheet of the domain) caused a drop of the affinity in vitro for the H3K9me Nucleosome, which was independent from the histone H3K9me tail interaction. Cells harboring the same Chp1CD loop mutations were defective in silencing centromeric transcripts and maintain the deposition of the H3K9me mark for heterochromatin formation. This indicated that Chp1CD-nucleosome core interaction is fundamental for heterochromatin formation in fission yeast and opened up to the possibility that chromodomains could read multiple histone PTMs, on both the recruiting histone tail and on the nucleosome core. This study substantially contributes to understand how chromodomains interact with chromatin, how much the nucleosome core interaction is conserved among different CDs and how different chromodomain proteins are regulated at the same loci. Understanding how chromodomain readers recognize nucleosomes is fundamental to uncover the basics of gene silencing and heterochromatin formation