Super-resolution in confocal scanning microscopy: generalized inversion formulae

It was shown in previous papers that the resolution of a confocal scanning microscope can be significantly improved by measuring, for each scanning position, the full diffraction image and by inverting these data to recover the value of the object at the confocal point. In the present work, the authors generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use of the data samples recorded at other scanning positions. This leads them to a family of generalized inversion formulae, either exact or approximate. Some previously known formulae are re-derived here as special cases in a particularly simple way.

Super-resolution in confocal scanning microscopy: II :The incoherent case

For pt.I see ibid. vol.3, p.195 (1987). The authors have shown that the resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data. These analyses were restricted to the case of coherent illumination. They investigate, along similar lines, the incoherent case, which applies to fluorescence microscopy. They investigate the one-dimensional and two-dimensional square-pupil problems and they prove, by means of numerical computations of the singular value spectrum and of the impulse response function, that for a signal-to-noise ratio of, say 10%, it is possible to obtain an improvement of approximately 60% in resolution with respect to the conventional incoherent light confocal microscope. This represents a working bandwidth of 3.5 times the Rayleigh limit.

How to beat the Rayleigh limit?

The problem of achieving super-resolution, i.e. resolution beyond the classical Rayleigh distance of half a wavelength, is a real challenge in several imaging problems. The development of computer-assisted instruments and the possibility of inverting the recorded data has clearly modified the traditional concept of resolving power of an instrument. We show that, in the framework of inverse problem theory, the achievable resolution limit arises no longer from a universal rule but instead from a practical limitation due to noise amplification in the data inversion process. We analyze under what circumstances super-resolution can be achieved and we show how to assess the actual resolution limits in a given experiment, as a function of the noise level and of the available a priori knowledge about the object function. We emphasize the importance of the a priori knowledge of its effective support and we show that significant super-resolution can be achieved for "subwavelength sources", i.e. objects which are smaller than the probing wavelength.

New data inversion formulae in confocal scanning microscopy

Whereas the resolving power of an ordinary optical microscope is determined by the classical Rayleigh distance, significant super-resolution, i.e. resolution improvement beyond that Rayleigh limit, has been achieved by confocal scanning light microscopy. Furthermore is has been shown that the resolution of a confocal scanning microscope can still be significantly enhanced by measuring, for each scanning position, the full diffraction image by means of an array of detectors and by inverting these data to recover the value of the object at the focus. We discuss the associated inverse problem and show how to generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use also of the diffraction images recorded at other scanning positions. This leads us to a whole family of generalized inversion formulae, which contains as special cases some previously known formulae. We also show how these exact inversion formulae can be implemented in practice.

Structures of P-glycoprotein reveal its conformational flexibility and an epitope on the nucleotide-binding domain

P-glycoprotein (P-gp) is one of the best-known mediators of drug efflux-based multidrug resistance in many cancers. This validated therapeutic target is a prototypic, plasma membrane resident ATPBinding Cassette transporter that pumps xenobiotic compounds out of cells. The large, polyspecific drug-binding pocket of P-gp recognizes a variety of structurally unrelated compounds. The transport of these drugs across the membrane is coincident with changes in the size and shape of this pocket during the course of the transport cycle. Here, we present the crystal structures of three inward-facing conformations of mouse P-gp derived from two different crystal forms. One structure has a nanobody bound to the C-terminal side of the first nucleotide-binding domain. This nanobody strongly inhibits the ATP hydrolysis activity of mouse Pgp by hindering the formation of a dimeric complex between the ATP-binding domains, which is essential for nucleotide hydrolysis. Together, these inward-facing conformational snapshots of P-gp demonstrate a range of flexibility exhibited by this transporter, which is likely an essential feature for the binding and transport of large, diverse substrates. The nanobody-bound structure also reveals a unique epitope on P-gp.

Solution structure of the N-terminal transactivation domain of ERM modified by SUMO-1.

ERM is a member of the PEA3 group of the Ets transcription factor family that plays important roles in development and tumorigenesis. The PEA3s share an N-terminal transactivation domain (TADn) whose activity is inhibited by small ubiquitin-like modifier (SUMO). However, the consequences of sumoylation and its underlying molecular mechanism remain unclear. The domain structure of ERM TADn alone or modified by SUMO-1 was analyzed using small-angle X-ray scattering (SAXS). Low resolution shapes determined ab initio from the scattering data indicated an elongated shape and an unstructured conformation of TADn in solution. Covalent attachment of SUMO-1 does not perturb the structure of TADn as indicated by the linear arrangement of the SUMO moiety with respect to TADn. Thus, ERM belongs to the growing family of proteins that contain intrinsically unstructured regions. The flexible nature of TADn may be instrumental for ERM recognition and binding to diverse molecular partners.