Pauli equation and the method of supersymmetric factorization

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.Comment: 18 pages, Late

Invariant vector fields and the prolongation method for supersymmetric quantum systems

The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method. Generators of supersymmetries are then introduced so that we get Lie superalgebras of symmetries and supersymmetries. This approach does not require the introduction of Grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry. The Jaynes-Cummings model and supersymmetric generalizations are then studied. We show how it is closely related to the preceding models. Lie algebras of symmetries and supersymmetries are also obtained.Comment: 37 pages, 7 table

Supersymmetric Homogeneous Quantum Cosmologies Coupled to a Scalar Field

Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a scalar field is extended to a general treatment of homogeneous quantum cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX, describing a virtual wormhole fluctuation, an additional explicit solution is given and identified with the `no-boundary state'.Comment: 23 PAGE

Pentaquark baryons in SU(3) quark model

We study the SU(3) group structure of pentaquark baryons which are made of four quarks and one antiquark. The pentaquark baryons form {1}, {8}, {10}, {10}-bar, {27}, and {35} multiplets in SU(3) quark model. First, the flavor wave functions of all the pentaquark baryons are constructed in SU(3) quark model and then the flavor SU(3) symmetry relations for the interactions of the pentaquarks with three-quark baryons and pentaquark baryons are obtained.Comment: REVTeX, 36 pages, 8 figures, references added, section for mass sum rules is added, to appear in Phys. Rev.

A nuclear factor 1 binding site mediates the transcriptional activation of a type I collagen promoter by transforming growth factor-beta

Transforming growth factor-beta (TGF-beta) increases the steady-state RNA levels of several fibroblast extracellular matrix proteins. Using DNA transfection, we show that TGF-beta stimulates the activity of the mouse alpha 2(l) collagen promoter 5- to 10-fold in mouse NIH 3T3 and rat osteosarcoma cells. Deletion analysis indicates that a segment of this promoter between -350 and -300, overlapping a nuclear factor 1 (NF1) binding site, is needed for TGF-beta stimulation. A 3 bp substitution mutation abolishing NF1 binding to this site inhibits TGF-beta activation. Insertion of this NF1 binding site 5' to the SV40 early promoter makes the promoter TGF-beta inducible, but the 3 bp substitution does not. Similarly, when the NF1 binding site at the replication origin of adenovirus 2 and 5 is inserted 5' to the SV40 promoter, the promoter responds to TGF-beta. Therefore an NF1 binding site mediates the transcriptional activation of the mouse alpha 2(l) collagen promoter by TGF-beta

S.6.1 β-catenin is a central mediator in SSc

Background. β-catenin is the central integrator of canonical Wnt signalling. Since recent evidence suggests a central role of Wnts in fibrosis, we examined the β-catenin/Wnt pathway in SSc and focused on the role of β-catenin in fibroblast activation. Methods. We performed qPCR for several Wnt ligands and axin-2 to examine Wnt expression in SSc skin. We further studied protein levels of Wnt-1, -4, -10b and β-catenin by IHC. To establish the effects of β-catenin/Wnt signalling on collagen release, we created mice with fibroblast-specific stabilization of β-catenin (dEx3 β-catenin (wt/fl) × Col1a2; Cre-ER) as well as mice carrying fibroblast-specific deletion of β-catenin [Ctnnb1(fl/fl) × Col1a2; Cre-ER]. Summary of the results. We could demonstrate mRNA overexpression of Wnt-1, -2, -9a, -9b, -10a, -10b and -16 in SSc skin. Wnt-1, -4 and -10b consistently showed strong expression in SSc skin when compared with healthy skin. On protein level, however, Wnt-4 was indistinguishable between SSc patients and healthy controls, whereas Wnt-1 and Wnt-10b protein levels were increased in SSc skin. The overexpression of Wnt-1 and Wnt-10b resulted in a prominent nuclear accumulation of β-catenin in fibroblasts. Finally, increased mRNA levels of the target gene axin-2 confirmed the activation of canonical Wnt signalling. In dEx3 β-catenin (wt/ex) mice, we addressed the consequences of enhanced Wnt signalling and increased accumulation of β-catenin in SSc. We selectively targeted β-catenin in fibroblasts. Cre-activated dEx3 β-catenin (wt/fl) × Col1a2; Cre-ER mice showed massive and spontaneous dermal thickening even 2 weeks after Cre activation. Eight weeks after Cre-activation, skin thickening cumulated at 102.6% (P < 0.001). In line with the dermal thickening, hydroxyproline content and myofibroblast counts showed strong increases. To test the therapeutic potential of targeting β-catenin/Wnt signaling, we created Ctnnb1(fl/fl) x Col1a2;Cre-ER mice to specifically delete β-catenin in fibroblasts. After Cre activation and β-catenin deletion in fibroblasts, mice were challenged with bleomycin subcutaneously for 4 weeks. We found that Cre-activated Ctnnb1(fl/fl) × Col1a2; Cre-ER mice were protected from bleomycin-induced dermal with a reduction of skin thickening by 71% (P < 0.05). Conclusions. We demonstrated a prominent activation of canonical Wnt signalling in SSc with nuclear accumulation of β-catenin in fibroblasts and activation of the target gene axin-2. Our results showed that fibroblast-specific stabilization of β-catenin resulted in enhanced collagen release, whereas deletion of β-catenin potently reduced collagen production. Together, our findings highlight a key role of β-catenin in fibroblast activation and fibrosis. Thus, β-catenin may be promising molecular target for anti-fibrotic therapie

The dimerization domain of SOX9 is required for transcription activation of a chondrocyte-specific chromatin DNA template

Mutations in SOX9, a gene essential for chondrocyte differentiation cause the human disease campomelic dysplasia (CD). To understand how SOX9 activates transcription, we characterized the DNA binding and cell-free transcription ability of wild-type SOX9 and a dimerization domain SOX9 mutant. Whereas formation of monomeric mutant SOX9–DNA complex increased linearly with increasing SOX9 concentrations, formation of a wild-type SOX9–DNA dimeric complex increased more slowly suggesting a more sigmoidal-type progression. Stability of SOX9–DNA complexes, however, was unaffected by the dimerization mutation. Both wild-type and mutant SOX9 activated transcription of a naked Col2a1 DNA template. However, after nucleosomal assembly, only wild-type and not the mutant was able to remodel chromatin and activate transcription of this template. Using a cell line, in which the Col2a1 vector was stably integrated, no differences were seen in the interactions of wild-type and mutant SOX9 with the chromatin of the Col2a1 vector using ChIP. However, the mutant was unable to activate transcription in agreement with in vitro results. We hypothesize that the SOX9 dimerization domain is necessary to remodel the Col2a1 chromatin in order to allow transcription to take place. These results further clarify the mechanism that accounts for CD in patients harboring SOX9 dimerization domain mutations

Role of PACAP and VIP Signalling in Regulation of Chondrogenesis and Osteogenesis

Pituitary adenylate cyclase activating polypeptide (PACAP) and vasoactive intestinal peptide (VIP) are multifunctional proteins that can regulate diverse physiological processes. These are also regarded as neurotrophic and anti-inflammatory substances in the CNS, and PACAP is reported to prevent harmful effects of oxidative stress. In the last decade more and more data accumulated on the similar function of PACAP in various tissues, but its cartilage- and bone-related presence and functions have not been widely investigated yet. In this summary we plan to verify the presence and function of PACAP and VIP signalling tool kit during cartilage differentiation and bone formation. We give evidence about the protective function of PACAP in cartilage regeneration with oxidative or mechanically stress and also with the modulation of PACAP signalling in vitro in osteogenic cells. Our observations imply the therapeutic perspective that PACAP might be applicable as a natural agent exerting protecting effect during joint inflammation and/or may promote cartilage regeneration during degenerative diseases of articular cartilage