Dispersion approach to real and virtual Compton scattering

In recent years, new precision experiments have become possible withthe high luminosity accelerator facilities at MAMIand JLab, supplyingphysicists with precision data sets for different hadronic reactions inthe intermediate energy region, such as pion photo- andelectroproduction and real and virtual Compton scattering.By means of the low energy theorem (LET), the global properties of thenucleon (its mass, charge, and magnetic moment) can be separated fromthe effects of the internal structure of the nucleon, which areeffectively described by polarizabilities. Thepolarizabilities quantify the deformation of the charge andmagnetization densities inside the nucleon in an applied quasistaticelectromagnetic field. The present work is dedicated to develop atool for theextraction of the polarizabilities from these precise Compton data withminimum model dependence, making use of the detailed knowledge of pionphotoproduction by means of dispersion relations (DR). Due to thepresence of t-channel poles, the dispersion integrals for two ofthe six Compton amplitudes diverge. Therefore, we have suggested to subtract the s-channel dispersion integrals at zero photon energy($nu=0$). The subtraction functions at $nu=0$ are calculated through DRin the momentum transfer t at fixed $nu=0$, subtracted at t=0. For this calculation, we use the information about the t-channel process, $gammagammatopipito Nbar{N}$. In this way, four of thepolarizabilities can be predicted using the unsubtracted DR in the $s$-channel. The other two, $alpha-beta$ and $gamma_pi$, are free parameters in ourformalism and can be obtained from a fit to the Compton data.We present the results for unpolarized and polarized RCS observables,%in the kinematics of the most recent experiments, and indicate anenhanced sensitivity to the nucleon polarizabilities in theenergy range between pion production threshold and the $Delta(1232)$-resonance.newlineindentFurthermore,we extend the DR formalism to virtual Compton scattering (radiativeelectron scattering off the nucleon), in which the concept of thepolarizabilities is generalized to the case of avirtual initial photon by introducing six generalizedpolarizabilities (GPs). Our formalism provides predictions for the fourspin GPs, while the two scalar GPs $alpha(Q^2)$ and $beta(Q^2)$ have to befitted to the experimental data at each value of $Q^2$.We show that at energies betweenpion threshold and the $Delta(1232)$-resonance position, thesensitivity to the GPs can be increased significantly, as compared tolow energies, where the LEX is applicable. Our DR formalism can be used for analysing VCS experiments over a widerange of energy and virtuality $Q^2$, which allows one to extract theGPs from VCS data in different kinematics with a minimum of model dependence.

Oligomerisation, localisation and interaction of the sensor histidine kinases DcuS and CitA in Escherichia coli

The two-component system DcuSR of Escherichia coli regulates gene expression of anaerobic fumarate respiration and aerobic C4-dicarboxylate uptake. C4-dicarboxylates and citrate are perceived by the periplasmic domain of the membrane-integral sensor histidine kinase DcuS. The signal is transduced across the membrane by phosphorylation of DcuS and of the response regulator DcuR, resulting in activation of DcuR and transcription of the target genes.rnIn this work, the oligomerisation of full-length DcuS was studied in vivo and in vitro. DcuS was genetically fused to derivatives of the green fluorescent protein (GFP), enabling fluorescence resonance energy transfer (FRET) measurements to detect protein-protein interactions in vivo. FRET measurements were also performed with purified His6-DcuS after labelling with fluorescent dyes and reconstitution into liposomes to study oligomerisation of DcuS in vitro. In vitro and in vivo fluorescence resonance energy transfer showed the presence of oligomeric DcuS in the membrane, which was independent of the presence of effector. Chemical crosslinking experiments allowed clear-cut evaluation of the oligomeric state of DcuS. The results showed that detergent-solubilised His6-DcuS was mainly monomeric and demonstrated the presence of tetrameric DcuS in proteoliposomes and in bacterial membranes.rnThe sensor histidine kinase CitA is part of the two-component system CitAB of E. coli, which is structurally related to DcuSR. CitAB regulates gene expression of citrate fermentation in response to external citrate. The sensor kinases DcuS and CitA were fused with an enhanced variant of the yellow fluorescent protein (YFP) and expressed in E. coli under the control of an arabinose-inducible promoter. The subcellular localisation of DcuS-YFP and CitA-YFP within the cell membrane was studied by means of confocal laser fluorescence microscopy. Both fusion proteins were found to accumulate at the cell poles. The polar accumulation was slightly increased in the presence of the stimulus fumarate or citrate, respectively, but independent of the expression level of the fusion proteins. Cell fractionation demonstrated that polar accumulation was not related to inclusion bodies formation. The degree of polar localisation of DcuS-YFP was similar to that of the well-characterised methyl-accepting chemotaxis proteins (MCPs), but independent of their presence. To enable further investigations on the function of the polar localisation of DcuS under physiological conditions, the sensor kinase was genetically fused to the flavin-based fluorescent protein Bs2 which shows fluorescence under aerobic and anaerobic conditions. The resulting dcuS-bs2 gene fusion was inserted into the chromosome of various E. coli strains.rnFurthermore, a protein-protein interaction between the related sensor histidine kinases DcuS and CitA, regulating common metabolic pathways, was detected via expression studies under anaerobic conditions in the presence of citrate and by in vivo FRET measurements.