The Friedrichs-Model with fermion-boson couplings II

In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by applying standard methods of representation of bound and resonant states.Comment: 13 page

Kinetics of recruitment and allosteric activation of ARHGEF25 isoforms by the heterotrimeric G-protein Gαq

Rho GTPases are master regulators of the eukaryotic cytoskeleton. The activation of Rho GTPases is governed by Rho guanine nucleotide exchange factors (GEFs). Three RhoGEF isoforms are produced by the gene ARHGEF25; p63RhoGEF580, GEFT and a recently discovered longer isoform of 619 amino acids (p63RhoGEF619). The subcellular distribution of p63RhoGEF580 and p63RhoGEF619 is strikingly different in unstimulated cells, p63RhoGEF580 is located at the plasma membrane and p63RhoGEF619 is confined to the cytoplasm. Interestingly, we find that both P63RhoGEF580 and p63RhoGEF619 activate RhoGTPases to a similar extent after stimulation of Gαq coupled GPCRs. Furthermore, we show that p63RhoGEF619 relocates to the plasma membrane upon activation of Gαq coupled GPCRs, resembling the well-known activation mechanism of RhoGEFs activated by Gα12/13. Synthetic recruitment of p63RhoGEF619 to the plasma membrane increases RhoGEF activity towards RhoA, but full activation requires allosteric activation via Gαq. Together, these findings reveal a dual role for Gαq in RhoGEF activation, as it both recruits and allosterically activates cytosolic ARHGEF25 isoforms

The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

The balance between Gα_i-Cdc42/Rac and Gα_12/13-RhoA pathways determines endothelial barrier regulation by sphingosine-1-phosphate

The bioactive sphingosine-1-phosphatephosphate (S1P) is present in plasma, bound to carrier proteins, and involved in many physiological processes, including angiogenesis, inflammatory responses, and vascular stabilization. S1P can bind to several G-protein-coupled receptors (GPCRs) activating a number of different signaling networks. At present, the dynamics and relative importance of signaling events activated immediately downstream of GPCR activation are unclear. To examine these, we used a set of fluorescence resonance energy transfer-based biosensors for different RhoGTPases (Rac1, RhoA/B/C, and Cdc42) as well as for heterotrimeric G-proteins in a series of live-cell imaging experiments in primary human endothelial cells. These experiments were accompanied by biochemical GTPase activity assays and transendothelial resistance measurements. We show that S1P promotes cell spreading and endothelial barrier function through S1PR1-Gαi-Rac1 and S1PR1-Gαi-Cdc42 pathways. In parallel, a S1PR2-Gα12/13-RhoA pathway is activated that can induce cell contraction and loss of barrier function, but only if Gαi-mediated signaling is suppressed. Our results suggest that Gαq activity is not involved in S1P-mediated regulation of barrier integrity. Moreover, we show that early activation of RhoA by S1P inactivates Rac1 but not Cdc42, and vice versa. Together, our data show that the rapid S1P-induced increase in endothelial integrity is mediated by a S1PR1-Gαi-Cdc42 pathwa

Економіко-правове забезпечення формування та реалізації соціальної політики держави, регіону, міста

У статті визначено потребу послідовного правового забезпечення формування та реалізації соціальної політики в багаторівневій системі управління. Обґрунтовано зміст та особливості соціальної політики залежно від рівня управління. Сформульовано пропозиції з удосконалення соціальної політики держави та її регіонів, виконано їх правову регламентацію

Classical and quantum integrability in 3D systems

In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the second, we discuss a three dimensional system without spatial symmetry which admits separation of variables if we use ellipsoidal coordinates. In both cases, and as a condition for integrability, certain conditions arise in the integrals of motion. Finally, we study integrability in the three dimensional sphere and a particular case associated with the Kepler problem in $S^3$.Comment: plenary talk on the Conference QTS-5, July 2007, Valladolid, Spai

Some Secrets of Fluorescent Proteins: Distinct Bleaching in Various Mounting Fluids and Photoactivation of cyan fluorescent proteins at YFP-Excitation

Background
The use of spectrally distinct variants of green fluorescent protein (GFP) such as cyan or yellow mutants (CFP and YFP, respectively) is very common in all different fields of life sciences, e.g. for marking specific proteins or cells or to determine protein interactions. In the latter case, the quantum physical phenomenon of fluorescence resonance energy transfer (FRET) is exploited by specific microscopy techniques to visualize proximity of proteins.

Methodology/Principal Findings
When we applied a commonly used FRET microscopy technique - the increase in donor (CFP)-fluorescence after bleaching of acceptor fluorophores (YFP), we obtained good signals in live cells, but very weak signals for the same samples after fixation and mounting in commercial microscopy mounting fluids. This observation could be traced back to much faster bleaching of CFP in these mounting media. Strikingly, the opposite effect of the mounting fluid was observed for YFP and also for other proteins such as Cerulean, TFP or Venus. The changes in photostability of CFP and YFP were not caused by the fixation but directly dependent on the mounting fluid. Furthermore we made the interesting observation that the CFP-fluorescence intensity increases by about 10 - 15% after illumination at the YFP-excitation wavelength – a phenomenon, which was also observed for Cerulean. This photoactivation of cyan fluorescent proteins at the YFP-excitation can cause false-positive signals in the FRET-microscopy technique that is based on bleaching of a yellow FRET acceptor.

Conclusions/Significance
Our results show that photostability of fluorescent proteins differs significantly for various media and that CFP bleaches significantly faster in commercial mounting fluids, while the opposite is observed for YFP and some other proteins. Moreover, we show that the FRET microscopy technique that is based on bleaching of the YFP is prone to artifacts due to photoactivation of cyan fluorescent proteins under these conditions

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equation--and therefore for scattering theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur

On two superintegrable nonlinear oscillators in N dimensions

We consider the classical superintegrable Hamiltonian system given by $H=T+U={p^2}/{2(1+\lambda q^2)}+{{\omega}^2 q^2}/{2(1+\lambda q^2)}$, where U is known to be the "intrinsic" oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term T and parametrized by {\lambda}. We show that H is Stackel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for H. Furthermore, we analyze in terms of {\lambda} the three different underlying manifolds whose geodesic motion is provided by T. As a consequence, we find that H comprises three different nonlinear physical models that, by constructing their radial effective potentials, are shown to be two different nonlinear oscillators and an infinite barrier potential. The quantization of these two oscillators and its connection with spherical confinement models is briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60 years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics, quantization and related topics" hold in Valladolid (Spain), 14-16th july 201