Fluorescence resonance energy transfer and f luorescence polarization anisotropy are used to investigate single molecules of the enzyme staphylococcal nuclease. Intramolecular f luorescence resonance energy transfer and f luorescence polarization anisotropy measurements of f luorescently labeled staphylococcal nuclease molecules reveal distinct patterns of f luctuations that may be attributed to protein conformational dynamics on the millisecond time scale. Intermolecular f luorescence resonance energy transfer measurements provide information about the dynamic interactions of staphylococcal nuclease with single substrate molecules. The experimental methods demonstrated here should prove generally useful in studies of protein folding and enzyme catalysis at single-molecule resolution.Single-molecule spectroscopy can provide information about complex biological molecules and systems that is difficult to obtain from ensemble measurements (1-6). For example, one can observe the time trajectories of single molecules in biochemical reactions that cannot be synchronized in ensemble experiments. In a population of molecules heterogeneous in a particular property, single-molecule spectroscopy can also resolve and quantitatively compare distinct subpopulations that would be indistinguishable at the ensemble level.Fluorescence resonance energy transfer (FRET) measurements between single pairs of acceptor and donor fluorophores can yield information about structural relationships and distance fluctuations between regions of a single biomolecule or between components of an interacting system of biomolecules (7-10). In addition, the rotational dynamics of a single fluorophore can be probed by monitoring fluctuations in fluorescence polarization (11)(12)(13)(14). Here we develop the techniques of single-pair FRET (spFRET) and singlemolecule fluorescence polarization anisotropy (smFPA) and show how they can be used to observe the conformational fluctuations and catalytic reactions of enzymes at singlemolecule resolution.Staphylococcal nuclease (SNase) is a 19 kDa Ca 2ϩ -dependent enzyme that catalyzes the hydrolysis of DNA and RNA into mono-and dinucleotides (15). Its catalytic mechanism, thermodynamic stability, and folding pathway have been studied extensively at the ensemble level (16-21). To probe the conformational dynamics of SNase and its interactions with substrate at single-molecule resolution, three experimental methods were used. First, intramolecular spFRET was measured between donor and acceptor fluorophores attached to single SNase proteins. Second, single-molecule fluorescence polarization anisotropy measurements were performed by using SNase labeled singly with one type of fluorophore. Third, intermolecular spFRET was measured between donor-labeled SNase and acceptor-labeled DNA substrate.Using intramolecular spFRET measurements on single SNase protein molecules, we observe interesting dynamics including gradual fluctuations in the FRET efficiencies. A combination of smFPA measurements, simulations, and...

In this paper, we present the design, implementation, and application of several families of fast multiplierless approximations of the discrete cosine transform (DCT) with the lifting scheme called the binDCT. These binDCT families are derived from Chen's and Loeffler's plane rotation-based factorizations of the DCT matrix, respectively, and the design approach can also be applied to a DCT of arbitrary size. Two design approaches are presented. In the first method, an optimization program is defined, and the multiplierless transform is obtained by approximating its solution with dyadic values. In the second method, a general lifting-based scaled DCT structure is obtained, and the analytical values of all lifting parameters are derived, enabling dyadic approximations with different accuracies. Therefore, the binDCT can be tuned to cover the gap between the Walsh-Hadamard transform and the DCT. The corresponding two-dimensional (2-D) binDCT allows a 16-bit implementation, enables lossless compression, and maintains satisfactory compatibility with the floating-point DCT. The performance of the binDCT in JPEG, H.263+, and lossless compression is also demonstrated.

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