Phase Retrieval with Application to Optical Imaging

This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art in this area, identify challenges, and suggest vision and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large, with applications in a variety of fields ranging from biology and chemistry to physics and engineering

Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval

Coherent diffraction imaging (CDI) allows the retrieval of the structure of an isolated object, such as a macromolecule, from its diffraction pattern. CDI requires the fulfilment of two conditions: the imaging radiation must be coherent and the object must be isolated. We discuss that it is possible to directly retrieve the molecular structure from its diffraction pattern which was acquired neither with coherent radiation nor from an individual molecule, provided the molecule exhibits periodicity in one direction, as in the case of fiber diffraction. We demonstrate that by applying iterative phase retrieval methods to a fiber diffraction pattern, the repeating unit, that is, the molecule structure, can directly be reconstructed without any prior modeling. As an example, we recover the structure of the DNA double helix in three-dimensions from its two-dimensional X-ray fiber diffraction pattern, Photograph 51, acquired in the famous experiment by Raymond Gosling and Rosalind Franklin, at a resolution of 3.4 Angstrom

Holography and Coherent Diffraction with Low-Energy Electrons: A Route towards Structural Biology at the Single Molecule Level

The current state of the art in structural biology is led by NMR, X-ray crystallography and TEM investigations. These powerful tools however all rely on averaging over a large ensemble of molecules. Here, we present an alternative concept aiming at structural analysis at the single molecule level. We show that by combining electron holography and coherent diffraction imaging estimations concerning the phase of the scattered wave become needless as the phase information is extracted from the data directly and unambiguously. Performed with low-energy electrons the resolution of this lens-less microscope is just limited by the De Broglie wavelength of the electron wave and the numerical aperture, given by detector geometry. In imaging freestanding graphene, a resolution of 2 Angstrom has been achieved revealing the 660.000 unit cells of the graphene sheet from one data set at once. Applied to individual biomolecules the method allows for non-destructive imaging and imports the potential to distinguish between different conformations of proteins with atomic resolution.Comment: 17 pages, 10 figures; Ultramicroscopy 201

Structural biology: a century-long journey into an unseen world

© Institute of Materials, Minerals and Mining 2015.When the first atomic structures of salt crystals were determined by the Braggs in 1912–1913, the analytical power of X-ray crystallography was immediately evident. Within a few decades the technique was being applied to the more complex molecules of chemistry and biology and is rightly regarded as the foundation stone of structural biology, a field that emerged in the 1950s when X-ray diffraction analysis revealed the atomic architecture of DNA and protein molecules. Since then the toolbox of structural biology has been augmented by other physical techniques, including nuclear magnetic resonance spectroscopy, electron microscopy, and solution scattering of X-rays and neutrons. Together these have transformed our understanding of the molecular basis of life. Here I review the major and most recent developments in structural biology that have brought us to the threshold of a landscape of astonishing molecular complexity

Solving Virus Structures from XFEL Diffraction Patterns of Random Particle Orientations Using Angular Correlations of Intensities

The world\u27s first x-ray free electron laser (XFEL), the Linac Coherent Light Source (LCLS) at the Stanford Linear Accelerator Center (SLAC) is now creating X-ray pulses not only of unprecendented brilliance; (a billion times brighter than the most powerful previous sources [8]) but also of ex- tremely short duration. Amongst the promised capabilities of this fourth- generation x-ray sources is the ability to record diffraction patterns from individual bio-molecules. The very first XFEL \u27\u27diffract and destroy\u27\u27 exper- iments are being performed on relatively large objects such as viruses. To quote from Caspar and Klug[2], \u27\u27there are only a limited number of efficient designs possible for biological container which can be constructed from a large number of identical protein molecules-the two basic designs are helical tubes and icosahedral shells . Viruses have regular shapes since their protein coats are formed by the self assembly of identical protein subunits which are coded by their genetic material. Here we develop a test based on the angular correlations of measured diffraction data to determine if the scattering is of an icosahedral particle. For a positive correlation test; an efficient algorithm can combine diffraction data from multiple shots of particles frozen in completely random orientations to generate a full 3-D image of the icosahedral particle. With this method it is expected to be possible to increase the concentration of particles in a solution beyond that of a single particle per snapshot thus allowing the possibility to get more signals from particles in the solvant. We sucessfully apply this method [3] to reconstruct 3-D images of satellite tobacco necrosis virus (STNV) whose atomic coordinates are given in Protein Data Bank entry 2BUK and of paramecium bursarium chlorella viruses (PBCV) from experimental data deposited at cxidb.org Most of prior structural studies involve scattering by ensembles of biomolecules or viruses, often in the form of crystals. However the state of biomolecules or viruses could be altered by the crystallization process. The understanding of bio-functioning of those ultrasmall quantities could be greatly enhanced if the structural studies were performed on individual uncrystallized particles. Fiber diffraction played a pioneering role for solving the structure of syn- thetic polypeptides [4], structure of deoxyribonucleic acid (DNA) [5] and the structure of helical viruses [6] to name only three of the most important. In a typical fiber diffarction experiment identical particles are all aligned along the fiber axis which give rise to layer lines. In this work we have shown that fiber diffraction can be obtained from a single particle diffraction volume reconstructed from completely randomly oriented helical structures, thus ob- viating the need of single axis alignment done experimentally such as forming lasers, laser- or flow-alignment

3D Reconstruction of Proteins and Viruses from Angular Correlations of the Scattered Intensities

There is a remarkable shortage of the detailed knowledge of membrane proteins at atomic resolution despite the fact that they are the targets of many of today\u27s drugs. The reason is that membrane proteins tend to have large hydrophobic surfaces which ensure their correct positioning in a membrane. However, this seems to make crystallization difficult, and this makes traditional methods of structure determination by X-ray crystallography difficult. In this thesis, we take advantage of this very fact to suggest an alternative method for structure determination by X-ray scattering of the projected structures of membrane proteins in their natural environments. Although in such environments the proteins are not perfectly aligned as in a crystal, we find that the algorithm suggested by Kurta and Pedrini appears to promise structure determination, perhaps down to atomic resolution. We also suggest and develop how the method may be extended to obtain general (non-symmetric) 3D structures by exploiting the curved nature of Ewald spheres at lower energy. The extension of the 2D idea into 3D is straightforward, since a curved Ewald sphere also consists of a set of rings (one expects the different rings have different q_z components). We can get the intensities in 3D reciprocal space as that is exactly what we need for 3D structure recovery via a phasing program. Of course, the construction of intensity data on a uniform grid in 3D reciprocal space (required by a typical phasing program) requires a girdding program. The registry between the I_m(q)\u27s on different q\u27s can be found as before if one knows B_m(q_1,q_2) from the experiment, as can be found from a set of diffraction patterns of the same energy. Of course, varying the energy then gives us the 3D reciprocal space for a range of q_z\u27s, just what we need for getting info about the 3D structure. In the second part of this thesis, we have reconstructed icosahedral images of the Coliphage PR772 and Rice Dwarf (RDV) viruses from the angular correlations of experimental data. We calculate the correlations using the standard method that Hanbury, Brown and Twiss developed in astronomy. The pattern of dominant icosahedral angular momentum quantum numbers that results is a strong indication of the icosahedral nature of the capsid. Having first determined by objective means that the structure of the capsid has icosahedral symmetry, we then recover a dodecahedral diffraction volume from which we correctly reconstruct an icosahedral structure using our phasing algorithm. We quantify the quality of the reconstructed image using the Fourier shell correlation curve of two independent datasets. For PR772, the FSC curve stays above 0.5 throughout the range of experimental data, which suggests that the resolution is still determined by the limitations of the experimental data rather than by the reconstruction method. For RDV, the resolution is around 200A. We also calculated an R_spllit quantity that compares two randomly split diffraction patterns for PR772 and RDV data and, as expected, they remained low. In a nutshell, three most important things to come out of this work are: 1-We recover the 2D structure of an individual membrane proteins up to atomic resolution using our suggested 2D phasing algorithm. 2-We develop an idea for producing 3D images using 2D diffraction patterns by combining multi-wavelength data from a soft X-ray fluctuation scattering experiment on membrane proteins partially oriented in a membrane, for the first time. 3- We also determine the the three-dimensional structure of PR772 and RDV viruses from experimental data, using our new 3D method