Confocal laser scanning microscopy (CLSM) is commonly used to observe molecules of biological relevance in their native environment, the live cell, and study their spatial distribution and interactions nondestructively. CLSM can be easily extended to measure the lifetime of the excited state, the concentration and the diffusion properties of fluorescently labeled molecules, using fluorescence lifetime imaging microscopy (FLIM) and fluorescence correlation spectroscopy (FCS), respectively, in order to provide information about the local environment and the kinetics of molecular interaction in live cells. However, these parameters cannot be measured simultaneously using conventional CLSM due to damaging effects that are associated with strong illumination, including phototoxicity, photobleaching, and saturation of the fluorescence signal. To overcome these limitations, we have developed a new camera consisting of 1024 single-photon avalanche diodes that is optimized for multifocal microscopy, FLIM and FCS. We show proof-of-principle measurements of fluorescence intensity distribution and lifetime of the enhanced green fluorescent protein expressed in live cells and measurement of quantum dot diffusion in solution by FCS using the same detector.

We present the Hanle EIT resonances obtained from the various segments of the Gaussian laser beam cross-section, selected by moving the small aperture (placed in front of the detector) radially along the laser beam. Significant differences in the Hanle lineshapes are observed depending on whether the central or outer parts of the Gaussian laser beam are detected. The line narrowing and two counter-sign peaks occur at outer, less intense parts of the beam. The theoretical model suggests that the EIT lineshapes in the laser wings are result of the interference of the laser light and coherently prepared atoms coming from the central part of the beam. By blocking the central part of the laser beam in front of the detector, narrower, and for high laser intensities, even more contrasted Hanle resonances are obtained.

It is well known that Akhmediev breathers of the nonlinear cubic Schrödinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds linearly to form the peak height of the final breather. Using this new peak-height formula, we show that at any given periodicity, there exist a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higherorder breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrödinger equation.

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Functional fluorescence microscopy imaging (fFMI), a timeresolved (21 μs/frame) confocal fluorescence microscopy imaging technique without scanning, is developed for quantitative characterization of fast reaction-transport processes in solution and in live cells. The method is based on massively parallel fluorescence correlation spectroscopy (FCS). Simultaneous excitation of fluorescent molecules in multiple spots in the focal plane is achieved using a diffractive optical element (DOE). Fluorescence from the DOE-generated 1024 illuminated spots is detected in a confocal arrangement by a matching matrix detector comprising 32 × 32 single-photon avalanche photodiodes (SPADs). Software for data acquisition and fast auto-and cross-correlation analysis by parallel signal processing using a graphic processing unit (GPU) allows temporal autocorrelation across all pixels in the image frame in 4 s and crosscorrelation between firstand second-order neighbor pixels in 45 s. We present here this quantitative, time-resolved imaging method with single-molecule sensitivity and demonstrate its usefulness for mapping in live cell location-specific differences in the concentration and translational diffusion of molecules in different subcellular compartments. In particular, we show that molecules without a specific biological function, e.g., the enhanced green fluorescent protein (eGFP), exhibit uniform diffusion. In contrast, molecules that perform specialized biological functions and bind specifically to their molecular targets show location-specific differences in their concentration and diffusion, exemplified here for two transcription factor molecules, the glucocorticoid receptor (GR) before and after nuclear translocation and the Sex combs reduced (Scr) transcription factor in the salivary gland of Drosophila ex vivo.

We present analytical and numerical doubleperiodic solutions of the one-dimensional nonlinear Schrödinger equation and its extended versions in the form of Talbot carpets. The breathers and rogue waves of different orders are obtained using numerical simulations, starting from the initial conditions calculated by the Darboux transformation. To suppress undesirable aspects of modulation instability leading to homoclinic chaos, Fourier mode pruning procedures are invented to preserve and maintain the twofold periodicity of carpets. The novelty of this paper is analytical Talbot carpets for Hirota-quintic equation and ability to obtain them dynamically by controlling the growth of the Fourier modes. In addition, the new period-matching procedure is also described for periodic rogue waves that can be utilized to produce Talbot carpets without

Hox genes encode transcription factors that control the formation of body structures, segment-specifically along the anterior-posterior axis of metazoans. Hox transcription factors bind nuclear DNA pervasively and regulate a plethora of target genes, deploying various molecular mechanisms that depend on the developmental and cellular context. To analyze quantitatively the dynamics of their DNA-binding behavior we have used confocal laser scanning microscopy (CLSM), single-point fluorescence correlation spectroscopy (FCS), fluorescence cross-correlation spectroscopy (FCCS) and bimolecular fluorescence complementation (BiFC). We show that the Hox transcription factor Sex combs reduced (Scr) forms dimers that strongly associate with its specific fork head binding site (fkh250) in live salivary gland cell nuclei. In contrast, dimers of a constitutively inactive, phospho-mimicking variant of Scr show weak, non-specific DNA-binding. Our studies reveal that nuclear dynamics of Scr is complex, exhibiting a changing landscape of interactions that is difficult to characterize by probing one point at a time. Therefore, we also provide mechanistic evidence using massively parallel FCS (mpFCS). We found that Scr dimers are predominantly formed on the DNA and are equally abundant at the chromosomes and an introduced multimeric fkh250 binding-site, indicating different mobilities, presumably reflecting transient binding with different affinities on the DNA. Our proof-of-principle results emphasize the advantages of mpFCS for quantitative characterization of fast dynamic processes in live cells.

Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations, such as the Hirota equation, are indicated.