Ultraschnelle kohärente Abbildung von Nanopartikeln mit Hilfe von Röntgen- Laser Strahlung

Abstract Zusammenfassung Publications Introduction Currently used imaging techniques Towards a new method Free-electron lasers Serial coherent diffractive imaging Sorting diffraction patterns The orientation problem Motivation and outline Part I Background 1 The theory of coherent X-ray diffractive imaging 1.1 Lensless imaging: the phase problem 1.1.1 Phase retrieval 1.1.2 Iterative phase retrieval algorithms 1.2 The orientation problem 1.3 Resolution and the number of required diffraction snapshots 2 Digital image analysis and pattern recognition 2.1 Classification 2.2 Feature extraction 2.2.1 Intensity variations 2.2.2 Rotation symmetry 2.2.3 "Eigenpatterns" 2.3 Supervised classification 2.3.1 Partitioning the feature space 2.3.2 Random forest classifier Part II Results 3 Geodesic orientation recovery 3.1 Establishing and interpreting similarities among diffraction patterns 43 3.2 Identifying in-plane and out-of-plane rotations and combining them to span the orientation space 3.3 gipral - an orientation recovery algorithm in ten steps 3.4 Computational complexity 3.5 Generalization to symmetric objects 4 On-line analysis 4.1 On-line hit rate estimation 4.2 On- line size estimation 4.3 On-line feedback on sample concentration 4.4 CASS - a framework for on-line analysis 5 Application 5.1 nanorice - an ellipsoidal iron oxide nanoparticle 5.1.1 Data acquisition 5.1.2 Classification results 5.1.3 Orientation recovery results 5.1.4 Phase retrieval 5.1.5 Data inhomogeneity 5.1.6 Using a simple geometric consideration as a control 5.2 Preliminary application to virus diffraction data 5.2.1 Samples 5.2.2 Results - aerosol injection 5.2.3 Results - liquid jet injection x Table of Contents 6 Discussion 6.1 Comparison to other orientation recovery approaches 6.2 Towards the imaging of biological samples 6.3 Room for improvements / outlook 6.3.1 Technical improvements 6.3.2 direct measurement and manipulation of orientations 6.4 Conclusions Appendix A Existing approaches to the orientation problem A.1 Correlation A.2 Common arc A.3 Bayesian methods A.4 Diffusion map / graph theory Appendix B Implementation B.1 Hardware optimization B.2 Parallelization B.2.1 Shared memory parallelization B.2.2 Distributed memory parallellization B.3 Class hierarchies Appendix C Mathematical Tools C.1 Rodrigues Frank parametrization C.2 Object symmetries in Rodrigues-Frank space C.3 extending geodesics C.4 Projections and mirror symmetry C.5 Orthogonalizing in-plane and out-of-plane rotations C.6 Discontinued: neighborhood preserving embedding Appendix D Publications Acknowledgments Index ReferencesCoherent diffractive imaging with X-ray free-electron lasers (X-FEL) promises high-resolution structure determination of single microscopic particles without the need for crystallization. The diffraction signal of small samples can be very weak, a difficulty that can not be countered by merely increasing the number of photons because the sample would be damaged by a high absorbed radiation dose. Traditional X-ray crystallography avoids this problem by bringing many sample particles into a periodic arrangement, which amplifies the individual signals while distributing the absorbed dose. Depending on the sample, however, crystallization can be very difficult or even impossible. This thesis presents algorithms for a new imaging approach using X-FEL radiation that works with single, non-crystalline sample particles. X-FELs can deliver X-rays with a peak brilliance many orders of magnitude higher than conventional X-ray sources, compensating for their weak interaction cross sections. At the same time, FELs can produce ultra-short pulses down to a few femtoseconds. In this way it is possible to perform ultra-fast imaging, essentially “freezing” the atomic positions in time and terminating the imaging process before the sample is destroyed by the absorbed radiation. This thesis primarily focuses on the three-dimensional reconstruction of single (and not necessarily crystalline) particles using coherent diffractive imaging at X-FELs: in order to extract three-dimensional information from scattering data, two-dimensional diffraction patterns from many different viewing angles must be combined. Therefore, the diffraction signal of many identical sample copies in random orientations is measured. The main result of this work is a globally optimal algorithm that can recover the sample orientations solely based on the diffraction signal, enabling three-dimensional imaging for arbitrary samples. The problem of finding three-dimensional orientations is reduced to one-dimensional sub-problems by arranging diffraction patterns in geodesic similarity sequences. Relations between the one-dimensional sub- problems are established by identifying rotations about the X-ray axis and one-dimensional solutions are combined into a three-dimensional orientation recovery. The global optimization approach ensures that information is extracted from the whole diffraction dataset, not only individual diffraction patterns. Therefore this method can cope with diffraction data sets consisting of individual diffraction patterns with weak signals. The geodesic approach can handle datasets from inhomogeneous samples as well as samples with symmetries. A successful application to experimental X-FEL data is shown, resulting in the first three-dimensional reconstruction of a nanoparticle using X-FEL coherent diffractive imaging.Kohärente Abbildung mit Röntgenlasern (X-ray free-electron lasers, X-FEL) ermöglicht die Strukturbestimmung von einzelnen mikroskopischen Teilchen mit hoher Auflösung, ohne dass ihre Kristallisation notwendig ist. Das gestreute Signal von kleinen Proben kann jedoch sehr schwach sein. Diese Schwierigkeit kann nicht einfach durch mehr einfallende Photonen umgangen werden, da die Probe bei der Absorption einer hohen Strahlendosis Schaden nimmt. Herkömmliche Kristallographie vermeidet dieses Problem durch das periodische Anordnen vieler Probenteilchen, wodurch das Signal verstärkt und die Strahlendosis verteilt wird. Je nach Probe kann die Kristallisation jedoch sehr aufwändig oder gar unmöglich sein. Diese Arbeit behandelt Algorithmen für ein neues bildgebendes Verfahren mit X-FEL Strahlung, das ohne Kristallisation auskommt. Mit X-FELs können Röntgenstrahlen mit sehr viel höherer Spitzenbrillanz erzeugt werden als mit herkömmlichen Röntgenquellen; somit können die schwachen Wechselwirkungsquerschnitte von Röntgenphotonen mit Materie kompensiert werden. Gleichzeitig können diese Röntgenstrahlen sehr kurz gepulst werden, bis hin zu wenigen Femtosekunden. Dadurch kann eine Bildgebung erreicht werden, die so schnell ist, dass die Atompositionen zeitlich „eingefroren“ werden und ein Abbild der Probe erzeugt wird, bevor diese durch die absorbierte Strahlung zerstört wird. Das Hauptaugenmerk dieser Arbeit liegt auf der dreidimensionalen Rekonstruktion: Um dreidimensionale Information aus Streudaten zu gewinnen ist es erforderlich viele zweidimensionale Streubilder aus verschiedenen Blickwinkeln zusammenzufassen. Dazu werden Streubilder von vielen identischen Kopien der Probe sequentiell gesammelt, wobei jede Probenkopie eine zufällige Orientierung hat. Das wichtigste Ergebnis dieser Arbeit ist ein global optimaler Algorithmus, der die Orientierungen allein mit Hilfe der Streubilder rekonstruiert, wodurch eine dreidimensionale Bildgebung für beliebige Proben möglich wird. Dazu wird das Problem dreidimensionale Orientierungen zu rekonstruieren in eindimensionale Teilprobleme unterteilt, indem Streubilder aufgrund ihrer Ähnlichkeit in geodätische Bildfolgen angeordnet werden. Die eindimensionalen Teilprobleme werden dann miteinander in Bezug gebracht, indem gemeinsame Drehungen um die Röntgenachse identifiziert werden. Somit können eindimensionale Lösungen in eine dreidimensionale Rekonstruktion der Orientierungen kombiniert werden. Die globale Optimierung stellt dabei sicher, dass die Information des gesamten Datensatz genutzt wird, anstatt nur einzelne Streubilder zu berücksichtigen. Aus diesem Grund kann diese Methode auch bei Datensätzen eingesetzt werden, bei denen einzelne Streubilder nur ein schwaches Signal erhalten. Die auf Geodäten beruhende Methode kann sowohl Datensätze von inhomogenen Proben bewältigen, als auch mit Objektsymmetrien umgehen. In dieser Arbeit wird eine erfolgreiche Anwendung auf experimentelle X-FEL Daten gezeigt, die die erste dreidimensionalen Rekonstruktion eines Nanopartikels mit Hilfe von kohärenten Abbildungen mit X-FELs ermöglichte

Indications of Radiation Damage in Ferredoxin Microcrystals using High-Intensity X-FEL Beams

Proteins that contain metal cofactors are expected to be highly radiation sensitive since the degree of X-ray absorption correlates with the presence of high-atomic-number elements and X-ray energy. To explore the effects of local damage in serial femtosecond crystallography (SFX), Clostridium ferredoxin was used as a model system. The protein contains two [4Fe-4S] clusters that serve as sensitive probes for radiation-induced electronic and structural changes. High-dose room-temperature SFX datasets were collected at the Linac Coherent Light Source of ferredoxin microcrystals. Difference electron density maps calculated from high-dose SFX and synchrotron data show peaks at the iron positions of the clusters, indicative of decrease of atomic scattering factors due to ionization. The electron density of the two [4Fe-4S] clusters differs in the FEL data, but not in the synchrotron data. Since the clusters differ in their detailed architecture, this observation is suggestive of an influence of the molecular bonding and geometry on the atomic displacement dynamics following initial photoionization. The experiments are complemented by plasma code calculations

Diffraction data of core-shell nanoparticles from an X-ray free electron laser

X-ray free-electron lasers provide novel opportunities to conduct single particle analysis on nanoscale particles. Coherent diffractive imaging experiments were performed at the Linac Coherent Light Source (LCLS), SLAC National Laboratory, exposing single inorganic core-shell nanoparticles to femtosecond hard-X-ray pulses. Each facetted nanoparticle consisted of a crystalline gold core and a differently shaped palladium shell. Scattered intensities were observed up to about 7 nm resolution. Analysis of the scattering patterns revealed the size distribution of the samples, which is consistent with that obtained from direct real-space imaging by electron microscopy. Scattering patterns resulting from single particles were selected and compiled into a dataset which can be valuable for algorithm developments in single particle scattering research

Free-electron laser data for multiple-particle fluctuation scattering analysis.

Fluctuation X-ray scattering (FXS) is an emerging experimental technique in which solution scattering data are collected using X-ray exposures below rotational diffusion times, resulting in angularly anisotropic X-ray snapshots that provide several orders of magnitude more information than traditional solution scattering data. Such experiments can be performed using the ultrashort X-ray pulses provided by a free-electron laser source, allowing one to collect a large number of diffraction patterns in a relatively short time. Here, we describe a test data set for FXS, obtained at the Linac Coherent Light Source, consisting of close to 100 000 multi-particle diffraction patterns originating from approximately 50 to 200 Paramecium Bursaria Chlorella virus particles per snapshot. In addition to the raw data, a selection of high-quality pre-processed diffraction patterns and a reference SAXS profile are provided

Free-electron laser data for multiple-particle fluctuation scattering analysis.

Fluctuation X-ray scattering (FXS) is an emerging experimental technique in which solution scattering data are collected using X-ray exposures below rotational diffusion times, resulting in angularly anisotropic X-ray snapshots that provide several orders of magnitude more information than traditional solution scattering data. Such experiments can be performed using the ultrashort X-ray pulses provided by a free-electron laser source, allowing one to collect a large number of diffraction patterns in a relatively short time. Here, we describe a test data set for FXS, obtained at the Linac Coherent Light Source, consisting of close to 100 000 multi-particle diffraction patterns originating from approximately 50 to 200 Paramecium Bursaria Chlorella virus particles per snapshot. In addition to the raw data, a selection of high-quality pre-processed diffraction patterns and a reference SAXS profile are provided

x-Ray Free-Electron Lasers

Free-electron lasers (FELs) operating in the soft and hard x-ray wavelength range deliver unprecedented peak and average brilliance, opening new scientific opportunities in many disciplines. A striking advance compared to third-generation synchrotron-based light sources is the duration of the photon pulse: a few to some hundred femtoseconds with peak powers in the gigawatt range are delivered routinely today. Probing femtosecond-scale dynamics in atomic and molecular reactions using, for instance, a combination of x-ray and optical pulses are now possible. Single-shot diffraction imaging of biological objects and molecules allows to produce movies of femtosecond-scale reactions. This chapter describes the basic physics of high-gain self-amplified spontaneous emission FELs, discusses technological challenges and solutions, provides an overview on present operating x-ray FELs, and gives examples for medical applications

Anomalous signal from S atoms in protein crystallographic data from an X-ray free-electron laser

X-ray free-electron lasers (FELs) enable crystallographic data collection using extremely bright femtosecond pulses from microscopic crystals beyond the limitations of conventional radiation damage. This diffraction-before-destruction approach requires a new crystal for each FEL shot and, since the crystals cannot be rotated during the X-ray pulse, data collection requires averaging over many different crystals and a Monte Carlo integration of the diffraction intensities, making the accurate determination of structure factors challenging. To investigate whether sufficient accuracy can be attained for the measurement of anomalous signal, a large data set was collected from lysozyme microcrystals at the newly established `multi-purpose spectroscopy/imaging instrument' of the SPring-8 Ångstrom Compact Free-Electron Laser (SACLA) at RIKEN Harima. Anomalous difference density maps calculated from these data demonstrate that serial femtosecond crystallography using a free-electron laser is sufficiently accurate to measure even the very weak anomalous signal of naturally occurring S atoms in a protein at a photon energy of 7.3 keV

Structure of a photosynthetic reaction centre determined by serial femtosecond crystallography

Serial femtosecond crystallography is an X-ray free-electron-laser-based method with considerable potential to have an impact on challenging problems in structural biology. Here we present X-ray diffraction data recorded from microcrystals of the Blastochloris viridis photosynthetic reaction centre to 2.8 angstrom resolution and determine its serial femtosecond crystallography structure to 3.5 angstrom resolution. Although every microcrystal is exposed to a dose of 33MGy, no signs of X-ray-induced radiation damage are visible in this integral membrane protein structure

Radiation damage in protein serial femtosecond crystallography using an x-ray free-electron laser

X−ray free−electron lasers deliver intense femtosecond pulses that promise to yield high resolution diffraction data of nanocrystals before the destruction of the sample by radiation damage. Diffraction intensities of lysozyme nanocrystals collected at the Linac Coherent Light Source using 2 keV photons were used for structure determination by molecular replacement and analyzed for radiation damage as a function of pulse length and fluence. Signatures of radiation damage are observed for pulses as short as 70 fs. Parametric scaling used in conventional crystallography does not account for the observed effect