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.

Nuclear hourglass technique: An approach that detects electrically open nuclear pores in Xenopus laevis oocyte

Nuclear pore complexes (NPCs) mediate both active transport and passive diffusion across the nuclear envelope (NE). Determination of NE electrical conductance, however, has been confounded by the lack of an appropriate technical approach. The nuclear patch clamp technique is restricted to preparations with electrically closed NPCs, and microelectrode techniques fail to resolve the extremely low input resistance of large oocyte nuclei. To address the problem, we have developed an approach for measuring the NE electrical conductance of Xenopus laevis oocyte nuclei. The method uses a tapered glass tube, which narrows in its middle part to 2/3 of the diameter of the nucleus. The isolated nucleus is sucked into the narrow part of the capillary by gentle fluid movement, while the resulting change in electrical resistance is monitored. NE electrical conductance was unexpectedly large (7.9 ± 0.34 S/cm2). Evaluation of NPC density by atomic force microscopy showed that this conductance corresponded to 3.7 × 106 NPCs. In contrast to earlier conclusions drawn from nuclear patch clamp experiments, NPCs were in an electrically “open” state with a mean single NPC electrical conductance of 1.7 ± 0.07 nS. Enabling or blocking of active NPC transport (accomplished by the addition of cytosolic extracts or gp62-directed antibodies) revealed this large NPC conductance to be independent of the activation state of the transport machinery located in the center of NPCs. We conclude that peripheral channels, which are presumed to reside in the NPC subunits, establish a high ionic permeability that is virtually independent of the active protein transport mechanism.

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.

Isolation and Contraction of the Stress Fiber

Stress fibers were isolated from cultured human foreskin fibroblasts and bovine endothelial cells, and their contraction was demonstrated in vitro. Cells in culture dishes were first treated with a low-ionic-strength extraction solution and then further extracted using detergents. With gentle washes by pipetting, the nucleus and the apical part of cells were removed. The material on the culture dish was scraped, and the freed material was forced through a hypodermic needle and fractionated by sucrose gradient centrifugation. Isolated, free-floating stress fibers stained brightly with fluorescently labeled phalloidin. When stained with anti-α-actinin or anti-myosin, isolated stress fibers showed banded staining patterns. By electron microscopy, they consisted of bundles of microfilaments, and electron-dense areas were associated with them in a semiperiodic manner. By negative staining, isolated stress fibers often exhibited gentle twisting of microfilament bundles. Focal adhesion–associated proteins were also detected in the isolated stress fiber by both immunocytochemical and biochemical means. In the presence of Mg-ATP, isolated stress fibers shortened, on the average, to 23% of the initial length. The maximum velocity of shortening was several micrometers per second. Polystyrene beads on shortening isolated stress fibers rotated, indicating spiral contraction of stress fibers. Myosin regulatory light chain phosphorylation was detected in contracting stress fibers, and a myosin light chain kinase inhibitor, KT5926, inhibited isolated stress fiber contraction. Our study demonstrates that stress fibers can be isolated with no apparent loss of morphological features and that they are truly contractile organelle.

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.

The cranium of Parapithecus grangeri, an Egyptian Oligocene anthropoidean primate

A nearly complete skull of Parapithecus grangeri from the early Oligocene of Egypt is described. The specimen is relatively undistorted and is undoubtedly the most complete higher primate skull yet found in the African Oligocene, which also makes it the most complete Oligocene primate cranium worldwide. Belonging in superfamily Parapithecoidea, a group regarded by some as the sister group to all other Anthropoidea, this skull reveals important information about the radiation of stem anthropoideans. This cranium is about 15% larger than size estimates based on a fragmentary cranium of its contemporary and close relative Apidium phiomense. It is about the same size as that of the gray gentle lemur, Hapalemur griseus, or of platyrrhines such as the owl monkey, Aotus trivirgatus, or the titi monkey, Callicebus torquatus. Comparatively small orbits and size differences in jaws and teeth show it was both diurnal and dimorphic. This is the only specimen of the species that shows (from sockets) that there were four small upper incisors. Several mandibular specimens of the species establish that there were no permanent lower incisors and that the symphysis was fused. Like other early anthropoideans this species possessed a lower encephalization quotient and less-developed orbital frontality than later anthropoideans. There is full postorbital closure and fusion of the metopic suture, and the ectotympanic forms a rim to the auditory aperture. A probable frontal/alisphenoid contact is a potentially derived resemblance to Catarrhini. A proposed separate genus for the species P. grangeri is not sustained.

Genetic interactions affecting touch sensitivity in Caenorhabditis elegans.

At least 13 genes (mec-1, mec-2, mec-4-10, mec-12, mec-14, mec-15, and mec-18) are needed for the response to gentle touch by 6 touch receptor neurons in the nematode Caenorhabditis elegans. Several, otherwise recessive alleles of some of these genes act as dominant enhancer mutations of temperature-sensitive alleles of mec-4, mec-5, mec-6, mec-12, and mec-15. Screens for additional dominant enhancers of mec-4 and mec-5 yielded mutations in previously known genes. In addition, some mec-7 alleles showed allele-specific, dominant suppression of the mec-15 touch-insensitive (Mec) phenotype. The dominant enhancement and suppression exhibited by these mutations suggest that the products of several touch genes interact. These results are consistent with a model, supported by the known sequences of these genes, that almost all of the touch function genes contribute to the mechanosensory apparatus.