Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure

Cu2Se and Cu Nanocrystals as Local Sources of Copper in Thermally Activated in Situ Cation Exchange

Among the different synthesis approaches to colloidal nanocrystals, a recently developed toolkit is represented by cation exchange reactions, where the use of template nanocrystals gives access to materials that would be hardly attainable via direct synthesis. Besides, postsynthetic treatments, such as thermally activated solid-state reactions, represent a further flourishing route to promote finely controlled cation exchange. Here, we report that, upon in situ heating in a transmission electron microscope, Cu2Se or Cu nanocrystals deposited on an amorphous solid substrate undergo partial loss of Cu atoms, which are then engaged in local cation exchange reactions with Cu “acceptor” phases represented by rod- and wire-shaped CdSe nanocrystals. This thermal treatment slowly transforms the initial CdSe nanocrystals into Cu2−xSe nanocrystals, through the complete sublimation of Cd and the partial sublimation of Se atoms. Both Cu “donor” and “acceptor” particles were not always in direct contact with each other; hence, the gradual transfer of Cu species from Cu2Se or metallic Cu to CdSe nanocrystals was mediated by the substrate and depended on the distance between the donor and acceptor nanostructures. Differently from what happens in the comparably faster cation exchange reactions performed in liquid solution, this study shows that slow cation exchange reactions can be performed at the solid state and helps to shed light on the intermediate steps involved in such reactions

In vitro evaluation of a novel bioreactor based on an integral oxygenator and a spirally wound nonwoven polyester matrix for hepatocyte culture as small aggregates

BACKGROUND/AIMS: The development of custom-made bioreactors for use as a bioartificial liver (BAL) is considered to be one of the last challenges on the road to successful temporary extracorporeal liver support therapy. We devised a novel bioreactor (patent pending) which allows individual perfusion of high density cultured hepatocytes with low diffusional gradients, thereby more closely resembling the conditions in the intact liver lobuli. METHODS: The bioreactor consists of a spirally wound nonwoven polyester matrix, i.e. a sheet-shaped, three-dimensional framework for hepatocyte immobilization and aggregation, and of integrated hydrophobic hollow-fiber membranes for decentralized oxygen supply and CO2 removal. Medium (plasma in vivo) was perfused through the extrafiber space and therefore in direct hepatocyte contact. Various parameters were assessed over a period of 4 days including galactose elimination, urea synthesis, lidocaine elimination, lactate/pyruvate ratios, amino acid metabolism, pH, the last day being reserved exclusively for determination of protein secretion. RESULTS: Microscopic examination of the hepatocytes revealed cytoarchitectural characteristics as found in vivo. The biochemical performance of the bioreactor remained stable over the investigated period. The urea synthesizing capacity of hepatocytes in the bioreactor was twice that of hepatocytes in monolayer cultures. Flow sensitive magnetic resonance imaging (MRI) revealed that the bioreactor construction ensured medium flow through all parts of the device irrespective of its size. CONCLUSIONS: The novel bioreactor showed encouraging efficiency. The device is easy to manufacture with scale-up to the liver mass required for possible short-term support of patients in hepatic failur

Avidity in antibody effector functions and biotherapeutic drug design

Antibody function is dependent on avidity - the accumulated strength of multiple affinity interactions between the antibody, antigen, cell surface receptors and other antibodies. In this Review, Oostindie et al. discuss the role of avidity in eliciting antibody functional responses and review the current engineering strategies for manipulating avidity interactions in antibody-based therapies.Antibodies are the cardinal effector molecules of the immune system and are being leveraged with enormous success as biotherapeutic drugs. A key part of the adaptive immune response is the production of an epitope-diverse, polyclonal antibody mixture that is capable of neutralizing invading pathogens or disease-causing molecules through binding interference and by mediating humoral and cellular effector functions. Avidity - the accumulated binding strength derived from the affinities of multiple individual non-covalent interactions - is fundamental to virtually all aspects of antibody biology, including antibody-antigen binding, clonal selection and effector functions. The manipulation of antibody avidity has since emerged as an important design principle for enhancing or engineering novel properties in antibody biotherapeutics. In this Review, we describe the multiple levels of avidity interactions that trigger the overall efficacy and control of functional responses in both natural antibody biology and their therapeutic applications. Within this framework, we comprehensively review therapeutic antibody mechanisms of action, with particular emphasis on engineered optimizations and platforms. Overall, we describe how affinity and avidity tuning of engineered antibody formats are enabling a new wave of differentiated antibody drugs with tailored properties and novel functions, promising improved treatment options for a wide variety of diseases.Transplantation and autoimmunit

Atomic structure of T1 precipitates in Al-Li-Cu alloys revisited with HAADF-STEM imaging and small-angle X-ray scattering

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