Signal, noise and resolution in linear and nonlinear structured-illumination microscopy.

Structured-illumination microscopy allows widefield fluorescence imaging with resolution beyond the classical diffraction limit. Its linear form extends resolution by a factor of two, and its nonlinear form by an in-principle infinite factor, the effective resolution in practice being determined by noise. In this paper, we analyse the noise properties and achievable resolution of linear and nonlinear 1D and 2D patterned SIM from a frequency-space perspective. We develop an analytical theory for a general case of linear or nonlinear fluorescent imaging, and verify the analytical calculations with numerical simulation for a special case where nonlinearity is produced by photoswitching of fluorescent labels. We compare the performance of two alternative implementations, using either two-dimensional (2D) illumination patterns or sequentially rotated one-dimensional (ID) patterns. We show that 1D patterns are advantageous in the linear case, and that in the nonlinear case 2D patterns provide a slight signal-to-noise advantage under idealised conditions, but perform worse than 1D patterns in the presence of nonswitchable fluorescent background. LAY DESCRIPTION: Structured-illumination microscopy (SIM) is a high-resolution light microscopy technique that allows imaging of fluorescence at a resolution about twice the classical diffraction limit. There are various ways that the illumination can be structured, but it is not obvious how the choice of illumination pattern affects the final image quality, especially in view of the noise. We present a detailed performance analysis considering two illumination techniques: sequential illumination with line-gratings that are shifted and rotated during image acquisition and two-dimensional (2D) illumination structures requiring only shift operations. Our analysis is based on analytical theory, supported by simulations of images considering noise. We also extend our analysis to a nonlinear variant of SIM, with which enhanced resolution can be achieved, limited only by noise. This includes nonlinear SIM based on the light-induced switching of the fluorescent molecules between a bright and a dark state. We find sequential illumination with line-gratings to be advantageous in ordinary (linear) SIM, whereas 2D patterns provides a slight signal-to-noise advantage under idealised conditions in nonlinear SIM if there is no nonswitching background.

Seamless stitching of tile scan microscope images.

For diagnostic purposes, optical imaging techniques need to obtain high-resolution images of extended biological specimens in reasonable time. The field of view of an objective lens, however, is often smaller than the sample size. To image the whole sample, laser scanning microscopes acquire tile scans that are stitched into larger mosaics. The appearance of such image mosaics is affected by visible edge artefacts that arise from various optical aberrations which manifest in grey level jumps across tile boundaries. In this contribution, a technique for stitching tiles into a seamless mosaic is presented. The stitching algorithm operates by equilibrating neighbouring edges and forcing the brightness at corners to a common value. The corrected image mosaics appear to be free from stitching artefacts and are, therefore, suited for further image analysis procedures. The contribution presents a novel method to seamlessly stitch tiles captured by a laser scanning microscope into a large mosaic. The motivation for the work is the failure of currently existing methods for stitching nonlinear, multimodal images captured by our microscopic setups. Our method eliminates the visible edge artefacts that appear between neighbouring tiles by taking into account the overall illumination differences among tiles in such mosaics. The algorithm first corrects the nonuniform brightness that exists within each of the tiles. It then compensates for grey level differences across tile boundaries by equilibrating neighbouring edges and forcing the brightness at the corners to a common value. After these artefacts have been removed further image analysis procedures can be applied on the microscopic images. Even though the solution presented here is tailored for the aforementioned specific case, it could be easily adapted to other contexts where image tiles are assembled into mosaics such as in astronomical or satellite photos.

Structured illumination fluorescence microscopy with distorted excitations using a filtered blind-SIM algorithm.

Structured illumination microscopy (SIM) is a powerful technique for obtaining super-resolved fluorescence maps of samples, but it is very sensitive to aberrations or misalignments affecting the excitation patterns. Here, we present a reconstruction algorithm that is able to process SIM data even if the illuminations are strongly distorted. The approach is an extension of the recent blind-SIM technique, which reconstructs simultaneously the sample and the excitation patterns without a priori information on the latter. Our algorithm was checked on synthetic and experimental data using distorted and nondistorted illuminations. The reconstructions were similar to that obtained by up-to-date SIM methods when the illuminations were periodic and remained artifact-free when the illuminations were strongly distorted.

Silencing of EphA3 through a cis interaction with ephrinA5.

EphAs and ephrinAs are expressed in multiple areas of the developing brain in overlapping countergradients, notably in the retina and tectum. Here they are involved in targeting retinal axons to their correct topographic position in the tectum. We have used truncated versions of EphA3, single-amino acid point mutants of ephrinA5 and fluorescence resonance energy transfer technology to uncover a cis interaction between EphA3 and ephrinA5 that is independent of the established ligand-binding domain of EphA3. This cis interaction abolishes the induction of tyrosine phosphorylation of EphA3 and results in a loss of sensitivity of retinal axons to ephrinAs in trans. Our data suggest that formation of this complex transforms the uniform expression of EphAs in the nasal part of the retina into a gradient of functional EphAs and has a key role in controlling retinotectal mapping.

Double-pass Fourier transform imaging spectroscopy.

Fourier-Transform Imaging Spectroscopy (FTIS) has recently become a widely used tool for spectral imaging of biological fluorescent samples. Here we report on a novel double-pass FTIS system, that is capable of obtaining an excitation as well as an emission spectrum of the fluorescent sample with only a single sweep of the interferometer. This is achieved by modifying an existing FTIS system, placing the excitation source before the interferometer so as to spectrally modulate the excitation as well as the detection. An analysis of the acquired signal allows for the reconstruction of the excitation as well as the emission spectrum of each fluorophore assuming an independence of the two spectra for each fluorophore. Due to the patterned excitation generated by the Sagnac interferometer a substantial degree of optically sectioning is achieved at excitation wavelengths. Further analysis of the acquired data also enables the generation of optically sectioned emission images. A theoretical analysis and experimental data based on fluorescent beads are presented.

Ensemble and single particle photophysical properties (two-photon excitation, anisotropy, FRET, lifetime, spectral conversion) of commercial quantum dots in solution and in live cells.

In this work, we characterized streptavidin-conjugated quantum dots (QDs) manufactured by Quantum Dot Corporation. We present data on: (1) two-photon excitation; (2) fluorescence lifetimes; (3) ensemble and single QD emission anisotropy; (4) QDs as donors for Forster resonance energy transfer (FRET); and (5) spectral conversion of QDs exposed to high-intensity illumination. We also demonstrate the utility of QDs for (1) imaging the binding and uptake of biotinylated transferrin on living cells, and (2) resolving by fluorescence lifetime imaging microscopy (FLIM) signals originating from QDs from those of spatially and spectrally overlapping visible fluorescent proteins (VFPs).

Imaging molecular interactions in cells by dynamic and static fluorescence anisotropy (rFLIM and emFRET).

We report the implementation and exploitation of fluorescence polarization measurements, in the form of anisotropy fluorescence lifetime imaging microscopy (rFLIM) and energy migration Förster resonance energy transfer (emFRET) modalities, for wide-field, confocal laser-scanning microscopy and flow cytometry of cells. These methods permit the assessment of rotational motion, association and proximity of cellular proteins in vivo. They are particularly applicable to probes generated by fusions of visible fluorescence proteins, as exemplified by studies of the erbB receptor tyrosine kinases involved in growth-factor-mediated signal transduction.

Axial tomographic confocal fluorescence microscopy.

By physical rotation of the sample, axial tomography enables the acquisition of otherwise inaccessible spatial information from an object. In combination with confocal microscopy, the method can fundamentally improve the effective three-dimensional (3D) resolution. In this report we present a novel method for high resolution reconstruction of confocal axial tomographic data. The method automatically determines the relative angles of rotation, aligns the data from different rotational views and reconstructs a single high resolution 3D dataset. The reconstruction makes use of a known point spread function and is based on an unconstrained maximum likelihood deconvolution performed simultaneously from multiple (in our case three) angular views. It was applied to simulated as well as to experimental confocal datasets. The gain in resolution was quantified and the effect of choice of overrelaxation factors on the speed of convergence was investigated. A clearly improved 3D resolution was obtained by axial tomography together with reconstruction as compared with reconstruction of confocal data from only a single angular view.

A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images.

A programmable array microscope (PAM) incorporates a spatial light modulator (SLM) placed in the primary image plane of a widefield microscope, where it is used to define patterns of illumination and/or detection. We describe the characteristics of a special type of PAM collecting two images simultaneously. The conjugate image (Ic) is formed by light originating from the object plane and returning along the optical path of the illumination light. The non-conjugate image (Inc) receives light from only those regions of the SLM that are not used for illuminating the sample. The dual-signal PAM provides much more time-efficient excitation than the confocal laser scanning microscope (CLSM) and greater utilization of the available emission light. It has superior noise characteristics in comparison to single-sided instruments. The axial responses of the system under a variety of conditions were measured and the behaviour of the novel Inc image characterized. As in systems in which only Ic images are collected (Nipkow-disc microscopes, and previously characterized PAMs), the axial response to thin fluorescent films showed a sharpening of the axial response as the unit cell of the repetitive patterns decreased in size. The dual-signal PAM can be adapted to a wide range of data analysis and collection strategies. We investigated systematically the effects of patterns and unit cell dimensions on the axial response. Sufficiently sparse patterns lead to an Ic image formed by the superposition of the many parallel beams, each of which is equivalent to the single scanning spot of a CLSM. The sectioning capabilities of the system, as given by its axial responses, were similar for a given scan pattern and for processed pseudorandom sequence (PRS) scans with the same size of the unit cell. For the PRS scans, optical sectioning was achieved by a subtraction of an Inc image or, alternatively, a scaled widefield image from the Ic image. Based on the comparative noise levels of the two methods, the non-conjugate subtraction was significantly superior. A point spread function for Ic and Inc was simulated and properties of the optical transfer functions (OTFs) were compared. Simulations of the OTF in non-conjugate imaging did not suffer from the missing cone problem, enabling a high quality deconvolution of the non-conjugate side alone. We also investigated the properties of images obtained by subjecting the Ic and Inc data to a combined maximum likelihood deconvolution.

Spatially modulated illumination microscopy: online visualization of intensity distribution and prediction of nanometer precision of axial distance measurements by computer simulations.

During the last years, measurements considerably beyond the conventional "Abbe-Limit" of optical resolution in far field light microscopy were realized by several light microscopical approaches. Point spread function (PSF) engineering, spectral precision distance microscopy (SPDM), and related methods were used to demonstrate the feasibility of such measurements. SPDM allows the measurement of position and multiple distances between point-like fluorescent objects of different spectral signatures far below the optical resolution criterion as defined by the full width at half maximum of the PSF. Here, we report a software method to obtain online visualization of light distribution in the lateral and axial direction of any object detected in a spatially modulated illumination (SMI) microscope. This strongly facilitates routine application of SMI microscopy. The software was developed using Microsoft Visual C++ running on Windows NT. Furthermore, some aspects of the theoretical limits of the SPDM method were studied by virtual microscopy. For the case of SMI microscopy the precision of axial distance measurements was studied, taking into account photon statistics and image analysis procedures. The results indicate that even under low fluorescence intensity conditions typical for biological structure research, precise distance measurements in the nanometer range can be determined, and that axial distances in the order of 40 nm are detectable with such precision.

Reconstruction of axial tomographic high resolution data from confocal fluorescence microscopy: a method for improving 3D FISH images.

Fluorescent confocal laser scanning microscopy allows an improved imaging of microscopic objects in three dimensions. However, the resolution along the axial direction is three times worse than the resolution in lateral directions. A method to overcome this axial limitation is tilting the object under the microscope, in a way that the direction of the optical axis points into different directions relative to the sample. A new technique for a simultaneous reconstruction from a number of such axial tomographic confocal data sets was developed and used for high resolution reconstruction of 3D-data both from experimental and virtual microscopic data sets. The reconstructed images have a highly improved 3D resolution, which is comparable to the lateral resolution of a single deconvolved data set. Axial tomographic imaging in combination with simultaneous data reconstruction also opens the possibility for a more precise quantification of 3D data. The color images of this publication can be accessed from http://www.esacp.org/acp/2000/20-1/heintzmann.++ +htm. At this web address an interactive 3D viewer is additionally provided for browsing the 3D data. This java applet displays three orthogonal slices of the data set which are dynamically updated by user mouse clicks or keystrokes.

Chromosome territories, interchromatin domain compartment, and nuclear matrix: an integrated view of the functional nuclear architecture.

Advances in the specific fluorescent labeling of chromatin in fixed and living human cells in combination with three-dimensional (3D) and 4D (space plus time) fluorescence microscopy and image analysis have opened the way for detailed studies of the dynamic, higher-order architecture of chromatin in the human cell nucleus and its potential role in gene regulation. Several features of this architecture are now well established: 1. Chromosomes occupy distinct territories in the cell nucleus with preferred nuclear locations, although there is no evidence of a rigid suprachromosomal order. 2. Chromosome territories (CTs) in turn contain distinct chromosome arm domains and smaller chromatin foci or domains with diameters of some 300 to 800 nm and a DNA content in the order of 1 Mbp. 3. Gene-dense, early-replicating and gene-poor, middle-to-late-replicating chromatin domains exhibit different higher-order nuclear patterns that persist through all stages of interphase. In mitotic chromosomes early replicating chromatin domains give rise to Giemsa light bands, whereas middle-to-late-replicating domains form Giemsa dark bands and C-bands. In an attempt to integrate these experimental data into a unified view of the functional nuclear architecture, we present a model of a modular and dynamic chromosome territory (CT) organization. We propose that basically three nuclear compartments exist, an "open" higher-order chromatin compartment with chromatin domains containing active genes, a "closed" chromatin compartment comprising inactive genes, and an interchromatin domain (ICD) compartment (Cremer et al., 1993; Zirbel et al., 1993) that contains macromolecular complexes for transcription, splicing, DNA replication, and repair. Genes in "open," but not in "closed" higher-order chromatin compartments have access to transcription and splicing complexes located in the ICD compartment. Chromatin domains that build the "open" chromatin compartment are organized in a way that allows the direct contact of genes and nascent RNA to transcription and splicing complexes, respectively, preformed in the ICD compartment. In contrast, chromatin domains that belong to the "closed" compartment are topologically arranged and compacted in a way that precludes the accessibility of genes to transcription complexes. We argue that the content of the ICD compartment is highly enriched in DNA depleted biochemical matrix preparations. The ICD compartment may be considered as the structural and functional equivalent of the in vivo nuclear matrix. A matrix in this functional sense is compatible with but does not necessitate the concept of a 3D nuclear skeleton existing of long, extensively arborized filaments. In the absence of unequivocal evidence for such a structural matrix in the nucleus of living cells we keep an agnostic attitude about its existence and possible properties in maintaining the higher-order nuclear architecture. Quantitative modeling of the 3D and 4D human genome architecture in situ shows that such an assumption is not necessary to explain presently known aspects of the higher-order nuclear architecture. We expect that the interplay of quantitative modeling and experimental tests will result in a better understanding of the compartmentalized nuclear architecture and its functional consequences.