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

Deformation Quantization of Bosonic Strings

Deformation quantization of bosonic strings is considered. We show that the light-cone gauge is the most convenient classical description to perform the quantization of bosonic strings in the deformation quantization formalism. Similar to the field theory case, the oscillator variables greatly facilitates the analysis. The mass spectrum, propagators and the Virasoro algebra are finally described within this deformation quantization scheme.Comment: 33+1 pages, harvmac file, no figure

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

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

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

Imaging fluorescence lifetime modulation of a ruthenium-based dye in living cells: the potential for oxygen sensing

Fluorescence lifetime measurements of long excited-state lifetime, oxygen-quenched ruthenium dyes are emerging as methods for intracellular oxygen sensing. Fluorescence lifetime imaging microscopy (FLIM) studies in cells have been reported previously. Many current FLIM systems use high repetition rate (∼107 Hz) lasers optimized for nanosecond lifetime measurements, making measurement of long, microsecond lifetime fluorophores difficult. Here, we present an experimental approach for obtaining a large temporal dynamic range in a FLIM system by using a low repetition rate (101 Hz), high output, nitrogen pumped dye laser and a wide-field, intensified CCD camera for image detection. We explore the feasibility of the approach by imaging the oxygen-sensitive dye tris(2,2′-bipyridyl)dichloro-ruthenium(II) hexahydrate (RTDP) in solution and in living cells. We demonstrate the ability of the system to resolve 60% variations in RTDP fluorescence lifetime upon oxygen cycling in solution. Furthermore, the FLIM system was able to resolve an increase in RTDP fluorescence lifetime in cultured human epithelial cells under diminished oxygen conditions. The technique may be useful in developing methods for quantifying intracellular oxygen concentrations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48916/2/d31406.pd

A mTurquoise-Based cAMP Sensor for Both FLIM and Ratiometric Read-Out Has Improved Dynamic Range

FRET-based sensors for cyclic Adenosine Mono Phosphate (cAMP) have revolutionized the way in which this important intracellular messenger is studied. The currently prevailing sensors consist of the cAMP-binding protein Epac1, sandwiched between suitable donor- and acceptor fluorescent proteins (FPs). Through a conformational change in Epac1, alterations in cellular cAMP levels lead to a change in FRET that is most commonly detected by either Fluorescence Lifetime Imaging (FLIM) or by Sensitized Emission (SE), e.g., by simple ratio-imaging. We recently reported a range of different Epac-based cAMP sensors with high dynamic range and signal-to-noise ratio. We showed that constructs with cyan FP as donor are optimal for readout by SE, whereas other constructs with green FP donors appeared much more suited for FLIM detection. In this study, we present a new cAMP sensor, termed TEpacVV, which employs mTurquoise as donor. Spectrally very similar to CFP, mTurquoise has about doubled quantum efficiency and unlike CFP, its fluorescence decay is strictly single-exponential. We show that TEpacVV appears optimal for detection both by FLIM and SE, that it has outstanding FRET span and signal-to-noise ratio, and improved photostability. Hence, TEpacVV should become the cAMP sensor of choice for new experiments, both for FLIM and ratiometric detection

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