Lie nilpotency indices of symmetric elements under oriented involutions in group algebras

Let $G$ be a group and let $F$ be a field of characteristic different from 2. Denote by $(FG)^+$ the set of symmetric elements and by $\mathcal{U}^+(FG)$ the set of symmetric units, under an oriented classical involution of the group algebra $FG$. We give some lower and upper bounds on the Lie nilpotency index of $(FG)^+$ and the nilpotency class of $\mathcal{U}^+(FG)$.Comment: Some corrected typos from version v2 and problems with the bibliograph

Deciphering the 'fuzzy' interaction of FG nucleoporins and transport factors using SANS

The largely intrinsically disordered phenylalanine-glycine-rich nucleoporins (FG Nups) underline a selectivity mechanism, which enables the rapid translocation of transport factors (TFs) through the nuclear pore complexes (NPCs). Conflicting models of NPC transport have assumed that FG Nups undergo different conformational transitions upon interacting with TFs. To selectively characterize conformational changes in FG Nups induced by TFs we performed small-angle neutron scattering (SANS) with contrast matching. Conformational ensembles derived SANS data indicate an increase in the overall size of FG Nups is associated with TF interaction. Moreover, the organization of the FG motif in the interacting state is consistent with prior experimental analyses defining that FG motifs undergo conformational restriction upon interacting with TFs. These results provide structural insights into a highly dynamic interaction and illustrate how functional disorder imparts rapid and selective FG Nup / TF interactions.Comment: Minor revisions and reformattin

Evolutionarily Conserved Sequence Features Regulate the Formation of the FG Network at the Center of the Nuclear Pore Complex.

The nuclear pore complex (NPC) is the portal for bidirectional transportation of cargos between the nucleus and the cytoplasm. While most of the structural elements of the NPC, i.e. nucleoporins (Nups), are well characterized, the exact transport mechanism is still under much debate. Many of the functional Nups are rich in phenylalanine-glycine (FG) repeats and are believed to play the key role in nucleocytoplasmic transport. We present a bioinformatics study conducted on more than a thousand FG Nups across 252 species. Our results reveal the regulatory role of polar residues and specific sequences of charged residues, named 'like charge regions' (LCRs), in the formation of the FG network at the center of the NPC. Positively charged LCRs prepare the environment for negatively charged cargo complexes and regulate the size of the FG network. The low number density of charged residues in these regions prevents FG domains from forming a relaxed coil structure. Our results highlight the significant role of polar interactions in FG network formation at the center of the NPC and demonstrate that the specific localization of LCRs, FG motifs, charged, and polar residues regulate the formation of the FG network at the center of the NPC