Orientation in operator algebras

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

Prime factors

We use Voiculescu’s free probability theory to prove the existence of prime factors, hence answering a longstanding problem in the theory of von Neumann algebras.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

β-Catenin Can Be Transported into the Nucleus in a Ran-unassisted Manner

The nuclear accumulation of β-catenin plays an important role in the Wingless/Wnt signaling pathway. This study describes an examination of the nuclear import of β-catenin in living mammalian cells and in vitro semi-intact cells. When injected into the cell cytoplasm, β-catenin rapidly migrated into the nucleus in a temperature-dependent and wheat germ agglutinin–sensitive manner. In the cell-free import assay, β-catenin rapidly migrates into the nucleus without the exogenous addition of cytosol, Ran, or ATP/GTP. Cytoplasmic injection of mutant Ran defective in its GTP hydrolysis did not prevent β-catenin import. Studies using tsBN2, a temperature-sensitive mutant cell line that possesses a point mutation in the RCC1 gene, showed that the import of β-catenin is insensitive to nuclear Ran-GTP depletion. These results show that β-catenin possesses the ability to constitutively translocate through the nuclear pores in a manner similar to importin β in a Ran-unassisted manner. We further showed that β-catenin also rapidly exits the nucleus in homokaryons, suggesting that the regulation of nuclear levels of β-catenin involves both nuclear import and export of this molecule.

Nuclear Import of Sterol Regulatory Element–binding Protein-2, a Basic Helix-Loop-Helix–Leucine Zipper (bHLH-Zip)–containing Transcription Factor, Occurs through the Direct Interaction of Importin β with HLH-Zip

The sterol regulatory element–binding protein-2 (SREBP-2) is produced as a large precursor molecule attached to the endoplasmic reticulum membrane. In response to the sterol depletion, the N-terminal segment of the precursor, which contains a basic helix-loop-helix–leucine zipper domain, is released by two sequential cleavages and is translocated to the nucleus, where it activates the transcription of target genes. The data herein show that released SREBP-2 uses a distinct nuclear transport pathway, which is mediated by importin β. The mature form of SREBP-2 is actively transported into the nucleus when injected into the cell cytoplasm. SREBP-2 binds directly to importin β in the absence of importin α. Ran-GTP but not Ran-GDP causes the dissociation of the SREBP-2–importin β complex. G19VRan-GTP inhibits the nuclear import of SREBP-2 in living cells. In the permeabilized cell in vitro transport system, nuclear import of SREBP-2 is reconstituted only by importin β in conjunction with Ran and its interacting protein p10/NTF2. We further demonstrate that the helix-loop-helix–leucine zipper motif of SREBP-2 contains a novel type of nuclear localization signal, which binds directly to importin β.

Transforming Growth Factor-β Induces Nuclear Import of Smad3 in an Importin-β1 and Ran-dependent Manner

Smad proteins are cytoplasmic signaling effectors of transforming growth factor-β (TGF-β) family cytokines and regulate gene transcription in the nucleus. Receptor-activated Smads (R-Smads) become phosphorylated by the TGF-β type I receptor. Rapid and precise transport of R-Smads to the nucleus is of crucial importance for signal transduction. By focusing on the R-Smad Smad3 we demonstrate that 1) only activated Smad3 efficiently enters the nucleus of permeabilized cells in an energy- and cytosol-dependent manner. 2) Smad3, via its N-terminal domain, interacts specifically with importin-β1 and only after activation by receptor. In contrast, the unique insert of exon3 in the N-terminal domain of Smad2 prevents its association with importin-β1. 3) Nuclear import of Smad3 in vivo requires the action of the Ran GTPase, which mediates release of Smad3 from the complex with importin-β1. 4) Importin-β1, Ran, and p10/NTF2 are sufficient to mediate import of activated Smad3. The data describe a pathway whereby Smad3 phosphorylation by the TGF-β receptor leads to enhanced interaction with importin-β1 and Ran-dependent import and release into the nucleus. The import mechanism of Smad3 shows distinct features from that of the related Smad2 and the structural basis for this difference maps to the divergent sequences of their N-terminal domains.

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Circadian-Regulated Transcription of the psbD Light-Responsive Promoter in Wheat Chloroplasts1

The level of mRNAs derived from the plastid-encoded psbD light-responsive promoter (LRP) is controlled by a circadian clock(s) in wheat (Triticum aestivum). The circadian oscillations in the psbD LRP mRNA level persisted for at least three cycles in continuous light and for one cycle in continuous dark, with maxima in subjective morning and minima in subjective early night. In vitro transcription in chloroplast extracts revealed that the circadian cycles in the psbD LRP mRNA level were dominantly attributed to the circadian-regulated transcription of the psbD LRP. The effects of various mutations introduced into the promoter region on the psbD LRP activity in vitro suggest the existence of two positive elements located between −54 and −36, which generally enhance the transcription activity, and an anomalous core promoter structure lacking the functional “−35” element, which plays a crucial role in the circadian fluctuation and light dependency of psbD LRP transcription activity.

Targeted disruption of gp130, a common signal transducer for the interleukin 6 family of cytokines, leads to myocardial and hematological disorders.

gp130 is a ubiquitously expressed signal-transducing receptor component shared by interleukin 6, interleukin 11, leukemia inhibitory factor, oncostatin M, ciliary neurotrophic factor, and cardiotrophin 1. To investigate physiological roles of gp130 and to examine pathological consequences of a lack of gp130, mice deficient for gp130 have been prepared. Embryos homozygous for the gp130 mutation progressively die between 12.5 days postcoitum and term. On 16.5 days postcoitum and later, they show hypoplastic ventricular myocardium without septal and trabecular defect. The subcellular ultrastructures in gp130-/- cardiomyocytes appear normal. The mutant embryos have greatly reduced numbers of pluripotential and committed hematopoietic progenitors in the liver and differentiated lineages such as T cells in the thymus. Some gp130-/- embryos show anemia due to impaired development of erythroid lineage cells. These results indicate that gp130 plays a crucial role in myocardial development and hematopoiesis during embryogenesis.

Different cellular backgrounds confer a marked advantage to either mutant or wild-type mitochondrial genomes.

After the introduction of mitochondria with a mixture of mutant and wild-type mitochondrial DNA (mtDNA) into a human rho degree cell line (143B.206), Yoneda et al. [Yoneda, M., Chomyn, A., Martinuzzi, A., Hurko, O. & Attardi, G. (1992) Proc. Natl. Acad. Sci. USA 89, 11164-11168] observed a shift in the proportion of the two mitochondrial genotypes in a number of cybrid clones. In every case where a shift was observed, there was an increase in the proportion of mutant mtDNA. By using the same cell line (143B.206 rho degree), we also generated cybrids that were either stable in their mitochondrial genotype or showed an increase in the proportion of mutant mtDNA. However, temporal analysis of the same mutant mtDNA type in another rho degree cell line revealed a quite distinct outcome. Those clones that showed a change shifted toward higher levels of wild-type rather than mutant mtDNA. These results indicate that the nuclear genetic background of the recipient (rho degree) cell can influence the segregation of mutant and wild-type mitochondrial genomes in cell cybrids.