Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.Comment: REVTeX, 18 pages, no figure

Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Whether one starts form the analytic S-matrix definition or the requirement of gauge parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value s of energy squared. The complex number s does not define the mass and width separately and this definition does not lead to interfering Breit-Wigner if two or more resonances are involved. To accomplish both we invoke the decaying particle aspect of a resonance and associate to each pole a space of relativistic Gamow kets which transform irreducibly under causal Poincare transformations. A Gamow state has an exponential time evolution and one can choose of the many possible width parameters, that parameter as the width of the relativistic resonance which equals the inverse lifetime. This uniquely defines the mass and width parameters for a relativistic resonance. Two or more poles in the same partial wave are given by the sum of Breit-Wigners in the scattering amplitude and by a superposition of Gamow vectors with each Gamow vector corresponding to one Breit-Wigner. In addition to the sum of Breit-Wigners the scattering amplitude contains a background amplitude representing direct production of the final state (contact terms).This contact amplitude is associated to a background vector which is a continuous superposition of Lippmann-Schwinger states. Omitting this continuum gives the Weisskopf-Wigner approximation.Comment: 22 pages, REVTe

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

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

A Bayesian method for inferring quantitative information from FRET data

<p>Abstract</p> <p>Background</p> <p>Understanding biological networks requires identifying their elementary protein interactions and establishing the timing and strength of those interactions. Fluorescence microscopy and Förster resonance energy transfer (FRET) have the potential to reveal such information because they allow molecular interactions to be monitored in living cells, but it is unclear how best to analyze FRET data. Existing techniques differ in assumptions, manipulations of data and the quantities they derive. To address this variation, we have developed a versatile Bayesian analysis based on clear assumptions and systematic statistics.</p> <p>Results</p> <p>Our algorithm infers values of the FRET efficiency and dissociation constant, <it>K_d</it>, between a pair of fluorescently tagged proteins. It gives a posterior probability distribution for these parameters, conveying more extensive information than single-value estimates can. The width and shape of the distribution reflects the reliability of the estimate and we used simulated data to determine how measurement noise, data quantity and fluorophore concentrations affect the inference. We are able to show why varying concentrations of donors and acceptors is necessary for estimating <it>K_d</it>. We further demonstrate that the inference improves if additional knowledge is available, for example of the FRET efficiency, which could be obtained from separate fluorescence lifetime measurements.</p> <p>Conclusions</p> <p>We present a general, systematic approach for extracting quantitative information on molecular interactions from FRET data. Our method yields both an estimate of the dissociation constant and the uncertainty associated with that estimate. The information produced by our algorithm can help design optimal experiments and is fundamental for developing mathematical models of biochemical networks.</p

Expression of Tas1 Taste Receptors in Mammalian Spermatozoa: Functional Role of Tas1r1 in Regulating Basal Ca2+ and cAMP Concentrations in Spermatozoa

Background: During their transit through the female genital tract, sperm have to recognize and discriminate numerous chemical compounds. However, our current knowledge of the molecular identity of appropriate chemosensory receptor proteins in sperm is still rudimentary. Considering that members of the Tas1r family of taste receptors are able to discriminate between a broad diversity of hydrophilic chemosensory substances, the expression of taste receptors in mammalian spermatozoa was examined. Methodology/Principal Findings: The present manuscript documents that Tas1r1 and Tas1r3, which form the functional receptor for monosodium glutamate (umami) in taste buds on the tongue, are expressed in murine and human spermatozoa, where their localization is restricted to distinct segments of the flagellum and the acrosomal cap of the sperm head. Employing a Tas1r1-deficient mCherry reporter mouse strain, we found that Tas1r1 gene deletion resulted in spermatogenic abnormalities. In addition, a significant increase in spontaneous acrosomal reaction was observed in Tas1r1 null mutant sperm whereas acrosomal secretion triggered by isolated zona pellucida or the Ca2+ ionophore A23187 was not different from wild-type spermatozoa. Remarkably, cytosolic Ca2+ levels in freshly isolated Tas1r1-deficient sperm were significantly higher compared to wild-type cells. Moreover, a significantly higher basal cAMP concentration was detected in freshly isolated Tas1r1-deficient epididymal spermatozoa, whereas upon inhibition of phosphodiesterase or sperm capacitation, the amount of cAMP was not different between both genotypes. Conclusions/Significance: Since Ca2+ and cAMP control fundamental processes during the sequential process of fertilization, we propose that the identified taste receptors and coupled signaling cascades keep sperm in a chronically quiescent state until they arrive in the vicinity of the egg - either by constitutive receptor activity and/or by tonic receptor activation by gradients of diverse chemical compounds in different compartments of the female reproductive tract

Glycolipid migration from the apical to the equatorial subdomains of the sperm head plasma membrane precedes the acrosome reaction. Evidence for a primary capacitation event in boar spermatozoa

In order to extend the static information of immunolabelling sulphogalactolipids in fixed boar spermatozoa, a fluorescent sulphogalactolipid analogue, galactose(3-sulphate)-b1-1¢[( N-lissamine rhodaminyl)-12-aminododecanoyl]-sphingosine, was incorporated into plasma membranes of living spermatozoa and its lateral distribution over the sperm head was studied. The fluorescent lipid was enriched in the apical ridge subdomain of freshly ejaculated sperm cells. After sperm binding to the zona pellucida the lipid redistributed to the equatorial segment of the sperm surface. A similar shift occurred during capacitation in vitro with 2 mM CaCl2 or with 4% (w/v)bovine serum albumin. The desulphated derivative galactose-b1-1¢[(N-lissamine rhodaminyl)-12-aminododecanoyl]- sphingosine was also incorporated into the plasma membrane of freshly ejaculated sperm cells and clearly stained the apical ridge subdomain and the (pre)-equatorial subdomains of the sperm heads. The desulphogalactolipid analogue showed a slightly faster migration to the equatorial segment of the sperm plasma membrane than did its sulphated counterpart. The measured fluorescence intensity distributions correlated linearly with the spatial probe distribution, which was checked by fluorescence lifetime imaging microscopy. The observed migration of the incorporated glycolipids precedes the acrosome reaction and is one of the underlying molecular events likely to be important in the process of sperm capacitation. The results of this study suggest that lipid phase segregation is an important driving force for the organization of the sperm head plasma membrane into subdomains

Microspectroscopic imaging of nodulation factor-binding sites on living Vicia sativa roots using a novel bioactive fluorescent nodulation factor.

A novel bioactive fluorescent nodulation (Nod) factor, NodRlv-IV(BODIPY FL-C16), has been synthesized by attaching a BODIPY FL-C16 acyl chain to the primary amino group of chitotetraose deacetylated at the nonreducing terminus by recombinant NodB. The binding of the fluorescent Nod factor to root systems of Vicia sativa was investigated with fluorescence spectral imaging microscopy (FSPIM) and fluorescence ratio imaging microscopy (FRIM). Spatially resolved fluorescence spectra of living and labeled Vicia sativa root systems were measured by FSPIM. Strong autofluorescence, inherent to many plant systems when excited at 488 nm, was corrected for by utilizing the difference in fluorescence emission spectra of the autofluorescence and NodRlv-IV(BODIPY FL-C16). A methodology is presented to break down the in situ fluorescence emission spectra into spatially resolved autofluorescence and BODIPY FL fluorescence spectra. Furthermore, an FRIM method was developed for correcting autofluorescence in fluorescence micrographs for this system. After autofluorescence correction it was shown that NodRlv-IV(BODIPY FL-C16) was concentrated in the root hairs, but was also bound to other parts of the root surface