The space of non-extendable quasimorphisms

For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov hyperbolic groups. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup.Comment: 58 pages, 1 figure. Major revision. Theorem 1.12 in v3 has been generalized to Theorem 1.2 in the current version: this new theorem treats hyperbolic mapping tori in general cases, and it serves as a leading application of our main theore

Effects of Imipramine and Lithium on the Suppression of Cell Proliferation in the Dentate Gyrus of the Hippocampus in Adrenocorticotropic Hormone-treated Rats

We examined the influence of chronic adrenocorticotropic hormone (ACTH) treatment on the number of Ki-67-positive cells in the dentate gyrus of the hippocampus in rats. ACTH treatment for 14 days decreased the number of such cells. The administration of imipramine or lithium alone for 14 days had no effect in saline-treated rats. The effect of ACTH was blocked by the administration of imipramine. Furthermore, the coadministration of imipramine and lithium for 14 days significantly increased the number of Ki-67-positive cells in both the saline and ACTH-treated rats. The coadministration of imipramine and lithium normalized the cell proliferation in the dentate gyrus of the hippocampus in rats treated with ACTH

Coarse group theoretic study on stable mixed commutator length

Let $G$ be a group and $N$ a normal subgroup of $G$. We study the large scale behavior, not the exact values themselves, of the stable mixed commutator length $scl_{G,N}$ on the mixed commutator subgroup $[G,N]$; when $N=G$, $scl_{G,N}$ equals the stable commutator length $scl_G$ on the commutator subgroup $[G,G]$. For this purpose, we regard $scl_{G,N}$ not only as a function from $[G,N]$ to $\mathbb{R}_{\geq 0}$, but as a bi-invariant metric function $d^+_{scl_{G,N}}$ from $[G,N]\times [G,N]$ to $\mathbb{R}_{\geq 0}$. Our main focus is coarse group theoretic structures of $([G,N],d^+_{scl_{G,N}})$. Our preliminary result (the absolute version) connects, via the Bavard duality, $([G,N],d^+_{scl_{G,N}})$ and the quotient vector space of the space of $G$-invariant quasimorphisms on $N$ over one of such homomorphisms. In particular, we prove that the dimension of this vector space equals the asymptotic dimension of $([G,N],d^+_{scl_{G,N}})$. Our main result is the comparative version: we connect the coarse kernel, formulated by Leitner and Vigolo, of the coarse homomorphism $\iota_{G,N}\colon ([G,N],d^+_{scl_{G,N}})\to ([G,N],d^+_{scl_{G}})$; $y\mapsto y$, and a certain quotient vector space $W(G,N)$ of the space of invariant quasimorphisms. Assume that $N=[G,G]$ and that $W(G,N)$ is finite dimensional with dimension $\ell$. Then we prove that the coarse kernel of $\iota_{G,N}$ is isomorphic to $\mathbb{Z}^{\ell}$ as a coarse group. In contrast to the absolute version, the space $W(G,N)$ is finite dimensional in many cases, including all $(G,N)$ with finitely generated $G$ and nilpotent $G/N$. As an application of our result, given a group homomorphism $\varphi\colon G\to H$ between finitely generated groups, we define an $\mathbb{R}$-linear map `inside' the groups, which is dual to the naturally defined $\mathbb{R}$-linear map from $W(H,[H,H])$ to $W(G,[G,G])$ induced by $\varphi$.Comment: 69 pages, no figure. Minor revision (v2): some symbols change

Affleck-Dine leptogenesis via multiscalar evolution in a supersymmetric seesaw model

A leptogenesis scenario in a supersymmetric standard model extended with introducing right-handed neutrinos is reconsidered. Lepton asymmetry is produced in the condensate of a right-handed sneutrino via the Affleck-Dine mechanism. The LH_u direction develops large value due to a negative effective mass induced by the right-handed sneutrino condensate through the Yukawa coupling of the right-handed neutrino, even if the minimum during the inflation is fixed at the origin. The lepton asymmetry is nonperturbatively transfered to the LH_u direction by this Yukawa coupling.Comment: 19 pages, 3 figures. Revised version for publication. The model was modified to fix some problem

Specific Recognition of Linear Ubiquitin Chains by NEMO Is Important for NF-κB Activation

Activation of nuclear factor-κB (NF-κB), a key mediator of inducible transcription in immunity, requires binding of NF-κB essential modulator (NEMO) to ubiquitinated substrates. Here, we report that the UBAN (ubiquitin binding in ABIN and NEMO) motif of NEMO selectively binds linear (head-to-tail) ubiquitin chains. Crystal structures of the UBAN motif revealed a parallel coiled-coil dimer that formed a heterotetrameric complex with two linear diubiquitin molecules. The UBAN dimer contacted all four ubiquitin moieties, and the integrity of each binding site was required for efficient NF-κB activation. Binding occurred via a surface on the proximal ubiquitin moiety and the canonical Ile44 surface on the distal one, thereby providing specificity for linear chain recognition. Residues of NEMO involved in binding linear ubiquitin chains are required for NF-κB activation by TNF-α and other agonists, providing an explanation for the detrimental effect of NEMO mutations in patients suffering from X-linked ectodermal dysplasia and immunodeficiency

Structural Basis of the Autophagy-Related LC3/Atg13 LIR Complex: Recognition and Interaction Mechanism

SummaryAutophagy is a bulk degradation pathway that removes cytosolic materials to maintain cellular homeostasis. The autophagy-related gene 13 (Atg13) and microtubule associate protein 1 light chain 3 (LC3) proteins are required for autophagosome formation. We demonstrate that each of the human LC3 isoforms (LC3A, LC3B, and LC3C) interacts with Atg13 via the LC3 interacting region (LIR) of Atg13. Using X-ray crystallography, we solved the macromolecular structures of LC3A and LC3C, along with the complex structures of the LC3 isoforms with the Atg13 LIR. Together, our structural and binding analyses reveal that the side-chain of Lys49 of LC3 acts as a gatekeeper to regulate binding of the LIR. We verified this observation by mutation of Lys49 in LC3A, which significantly reduces LC3A positive puncta formation in cultured cells. Our results suggest that specific affinity of the LC3 isoforms to the Atg13 LIR is required for proper autophagosome formation