Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors.

We report on the first experimental demonstration of higher-order Laguerre-Gauss (LG(p)(ℓ)) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LG(p)(ℓ) modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG(0)(0) Gaussian beam into an LG(3)(3) mode with a purity of 98%. The ratio between the power of the LG(0)(0) mode of our laser and the power of the LG(3)(3) transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG(0)(0), we inferred that the conversion efficiency specific to the LG(3)(3) mode was 49%. We illuminated a Michelson interferometer with the LG(3)(3) beam and achieved a visibility of 97%.

A state observer for the Virgo inverted pendulum.

We report an application of Kalman filtering to the inverted pendulum (IP) of the Virgo gravitational wave interferometer. Using subspace method system identification techniques, we calculated a linear mechanical model of Virgo IP from experimental transfer functions. We then developed a Kalman filter, based on the obtained state space representation, that estimates from open loop time domain data, the state variables of the system. This allows the observation (and eventually control) of every resonance mode of the IP mechanical structure independently.

Metal binding sites of H(+)-ATPase from chloroplast and Bacillus PS3 studied by EPR and pulsed EPR spectroscopy of bound manganese(II).

The metal binding sites of isolated F1 ATPase from spinach chloroplasts (CF1) and from the thermophilic bacterium Bacillus PS3 (TF1) have been studied by EPR and pulsed EPR spectroscopy using Mn(II) as a paramagnetic probe. After dialysis in the presence of EDTA, purified CF1 retains 0.14 +/- 0.07 Mg(II) and approximately 0.75 +/- 0.25 ADP. TF1 retains 0.31 +/- 0.03 Mg(II) and 0.08 +/- 0.01 nucleotide (ADP + ATP) after the same treatment. Supplementing known quantities of Mn(II) to metal-depleted CF1 allowed a spectroscopic characterization of the bound Mn(II) cations, for which the EPR spectra at X- and Q-band are reported. The zero field splitting parameters of Mn(II) are derived from the simulation of the EPR signal recorded at Q-band for a sample supplemented with 0.3 Mn/CF1. The values, magnitude of D approximately 200 x 10(-4) cm-1 and magnitude of E approximately 40 x 10(-4) cm-1 suggest that the Mn(II) binds to CF1 in a slightly distorted environment. The ESEEM spectra of complexes of Mn(II) with CF1 were also recorded for different Mn/CF1 ratios. For a complex with 0.8 Mn/CF1, the ESEEM spectrum shows two frequencies at 3.7 and 8.6 MHz that are attributed to the magnetic coupling with 31P with a hyperfine coupling constant of magnitude of A approximately 5.3 MHz, reflecting the interaction with a phosphate group from the endogenous ADP molecule. This demonstrates close proximity of the strong affinity metal site M1 and the endogenous ADP binding site N1, and binding of the ADP beta-phosphate to the divalent metal cation. For Mn(II) complexes with higher Mn/CF1 ratios, new frequency components below approximately 5 MHz are resolved in the spectra in addition to the peaks from 31P. From a comparison of the CF1 spectra and their magnetic field dependence across the Mn(II) EPR line shape with those of Mn(II) complexes with imidazole, glycine, poly-L-lysine, and nucleotide ligands, it is concluded that additional metal binding sites are filled at higher Mn contents and that these involve 14N donors. It is suggested that the most probable set of ligands of the divalent metal(s) for these additional metal sites in CF1 includes a lysine residue, in line with a previous proposal [Houseman, A. L. P., Morgan, L., LoBrutto, R., & Frasch, W. D. (1994) Biochemistry 33, 4910-4917]. Similar experiments for a Mn(II) complex with TF1 (0.4 Mn/TF1) showed no interaction with 31P; instead modulations are detected in the ESEEM below approximately 5 MHz that are attributed to a 14N ligand. This is tentatively attributed to the deprotonated amine of Lys-162 from a beta subunit, on the basis of the structural data available for the mitochondrial F1 complex. Addition of the substrate ATP to this Mn.TF1 complex leads to the formation of a ternary Mn.TF1.ATP complex with coordination of the Mn(II) by a phosphate group from the ATP as judged from the ESEEM results (magnitude of A(31P) approximately 4.5 MHz). An increase in the hyperfine coupling constant of 31P of the phosphate bound to Mn(II) to magnitude of A(31P) approximately 5.1 MHz is observed after incubation of the ternary complex at room temperature. This is interpreted as a significant rearrangement of the coordination sphere of the Mn(II) in the M1 site of the Mn.TF1.ATP complex and may reflect conformational changes of catalytic significance that occur in the nucleotide binding site during unisite hydrolysis of ATP to ADP by this complex.

Binding sites for Mg(II) in H(+)-ATPase from Bacillus PS3 and in the alpha 3 beta 3 gamma subcomplex studied by one-dimensional ESEEM and two-dimensional HYSCORE spectroscopy of oxovanadium(IV) complexes: a possible role for beta-His-324.

The binding sites for Mg2+ in wild type F1 ATPase (TF1) and in the alpha 3 beta 3 gamma subcomplex from the thermophilic bacterium Bacillus PS3 have been studied by EPR and by ESEEM and HYSCORE spectroscopy of complexes with the oxovanadium cation VO2+. Complexes of metal-depleted TF1 and substoichiometric amounts of VO2+ display low-temperature EPR signals with spectral parameters g parallel = 1.947 and g perpendicular = 1.980, and hyperfine couplings with 51V, A parallel = 169 x 10(-4) cm-1 and A perpendicular = 61 x 10(-4) cm-1, that are indicative of a binding site for VO2+ with nitrogen ligands from the protein. This binding site is probably identical with the metal binding site with strong affinity M1 that has been characterized using Mn2+ in a previous study [Buy, C., Girault, G., & Zimmermann, J. L. (1996) Biochemistry 35, 9880-9891]. The three-pulse ESEEM spectrum of the VO2+ complex with TF1 shows a frequency pattern with spectral properties that are evidence for two nitrogen ligands to the VO2+ with hyperfine couplings A1 = 4.75 MHz and A2 = 6.5 MHz and nuclear quadrupole parameters e2Qq1 = 2.8-3.2 MHz and e2Qq2 = 2.0-2.3 MHz. The ligands are identified as a lysine terminal amine and a histidine imidazole, which are proposed as Lys-164 and His-324 from a beta subunit. The HYSCORE data obtained for the VO.TF1 complex show correlations within each pair of the ESEEM nu dq peaks from the 14N nuclei, confirming the interpretation of the one-dimensional spectra. Evidence for the formation of a ternary complex by addition of VO2+ and ATP to metal-depleted TF1 is shown in the EPR and ESEEM spectra and in the contour plots of the HYSCORE data. Two pairs of correlation patterns are resolved in addition to the peaks from the two 14N ligands, which are interpreted as hyperfine couplings with 31P beta and 31P gamma of the ATP that binds the VO2+ cation. The assignment of the two hyperfine couplings to the specific phosphates, A(31P beta) = 15.5 MHz and A(31P gamma) = 8.7 MHz, in the VO.TF1.ATP complex is proposed by comparison with those measured for VO2+ in solution with ATP at pH 6.3 and 2.3. These results are discussed in light of the previous data with the analogous Mn.TF1 complex, and a model is proposed in which the native Mg2+ in the M1 site is coordinated by the side chain of beta-Lys-164 and is in close proximity to a histidine residue (probably beta-His-324) that may have a critical role. Additional coordination by two phosphates from ATP (probably the beta- and gamma-phosphates) is observed in the ternary complex VO.TF1.ATP. ESEEM and HYSCORE data are also obtained for the analogous complexes VO. alpha 3 beta 3 gamma and VO. alpha 3 beta 3 gamma .ATP that show very similar properties in terms of coordination of the divalent metal cation, except for the lysine ligand that is found to be lost in the ternary complex with ATP. It is suggested that this observation may reflect changes in the metal and nucleotide active sites that are associated with the absence of the delta and epsilon subunits in the subcomplex.