X-ray free electron lasers are used in measuring diffraction patterns from nanocrystals in the 'diffract-before-destroy' mode by outrunning radiation damage. The finite-sized nanocrystals provide an opportunity to recover intensity between Bragg spots by removing the modulating function that depends on crystal shape, i.e. the transform of the crystal shape. This shape-transform dividing-out scheme for solving the phase problem has been tested using simulated examples with cubic crystals. It provides a phasing method which does not require atomic resolution data, chemical modification to the sample, or modelling based on the protein databases. It is common to find multiple structural units (e.g. molecules, in symmetry-related positions) within a single unit cell, therefore incomplete unit cells (e.g. one additional molecule) can be observed at surface layers of crystals. In this work, the effects of such incomplete unit cells on the 'dividing-out' phasing algorithm are investigated using 2D crystals within the projection approximation. It is found that the incomplete unit cells do not hinder the recovery of the scattering pattern from a single unit cell (after dividing out the shape transforms from data merged from many nanocrystals of different sizes), assuming that certain unit-cell types are preferred. The results also suggest that the dynamic range of the data is a critical issue to be resolved in order to apply the shape transform method practically.
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.
Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a well-characterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 μm diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 Ångström were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.
(XFEL) allows it to outrun radiation damage in coherent diffractive imaging since elastic scattering terminates before photoelectron cascades commences. This “diffract-before-destroy” feature of XFEL opened up new opportunities for biological macromolecule imaging and structure studies by breaking the limit to spatial resolution imposed by the maximum dose that is allowed before radiation damage. However, data collection in serial femto-second crystallography (SFX) using XFEL is affected by a bunch of stochastic factors, which pose great challenges to the data analysis in SFX. These stochastic factors include crystal size, shape, random orientation, X-ray photon flux, position and energy spectrum. Monte-Carlo integration proves effective and successful in extracting the structure factors by merging all diffraction patterns given that the data set is sufficiently large to average out all stochastic factors. However, this approach typically requires hundreds of thousands of patterns collected from experiments. This dissertation explores both experimental and algorithmic methods to eliminate or reduce the effect of stochastic factors in data acquisition and analysis. Coherent convergent X-ray beam diffraction (CCB) is discussed for possibilities of obtaining single-shot angular-integrated rocking curves. It is also shown the interference between Bragg disks helps ab-initio phasing. Two-color diffraction scheme is proposed for time-resolved studies and general data collection strategies are discussed based on error metrics. A new auto-indexing algorithm for sparse patterns is developed and demonstrated for both simulated and experimental data. Statistics show that indexing rate is increased by 3 times for I3C data set collected from beam time LJ69 at Linac coherent light source (LCLS). Finally, dynamical inversion from electron diffraction is explored as an alternative approach for structure determination.
This dissertation begins by proposing a new flexible policy iteration (FPI) framework. To improve sample efficiency, FPI can utilize either on-policy or off-policy learning strategy, can learn from either online or offline data, and can even adopt exiting knowledge of an external critic. Approximate convergence to Bellman optimal solutions are guaranteed under mild conditions. Simulation studies validated that FPI was data efficient compared to several established RL methods. Furthermore, a simplified version of FPI was implemented to learn from offline data, and then the learned policy was successfully tested for tuning the control parameters online on a human subject.
Next, the dissertation discusses RL control with information transfer (RL-IT), or knowledge-guided RL (KG-RL), which is motivated to benefit from transferring knowledge acquired from one subject to another. To explore its feasibility, knowledge was extracted from data measurements of able-bodied (AB) subjects, and transferred to guide Q-learning control for an amputee in OpenSim simulations. This result again demonstrated that data and time efficiency were improved using previous knowledge.
While the present study is new and promising, there are still many open questions to be addressed in future research. To account for human adaption, the learning control objective function may be designed to incorporate human-prosthesis performance feedback such as symmetry, user comfort level and satisfaction, and user energy consumption. To make the RL based control parameter tuning practical in real life, it should be further developed and tested in different use environments, such as from level ground walking to stair ascending or descending, and from walking to running.
Photosynthesis, a process catalysed by plants, algae and cyanobacteria converts sunlight to energy thus sustaining all higher life on Earth. Two large membrane protein complexes, photosystem I and II (PSI and PSII), act in series to catalyse the light-driven reactions in photosynthesis. PSII catalyses the light-driven water splitting process, which maintains the Earth’s oxygenic atmosphere. In this process, the oxygen-evolving complex (OEC) of PSII cycles through five states, S0 to S4, in which four electrons are sequentially extracted from the OEC in four light-driven charge-separation events. Here we describe time resolved experiments on PSII nano/microcrystals from Thermosynechococcus elongatus performed with the recently developed technique of serial femtosecond crystallography. Structures have been determined from PSII in the dark S1 state and after double laser excitation (putative S3 state) at 5 and 5.5 Å resolution, respectively. The results provide evidence that PSII undergoes significant conformational changes at the electron acceptor side and at the Mn4CaO5 core of the OEC. These include an elongation of the metal cluster, accompanied by changes in the protein environment, which could allow for binding of the second substrate water molecule between the more distant protruding Mn (referred to as the ‘dangler’ Mn) and the Mn3CaOx cubane in the S2 to S3 transition, as predicted by spectroscopic and computational studies. This work shows the great potential for time-resolved serial femtosecond crystallography for investigation of catalytic processes in biomolecules.
The Smoothened receptor (SMO) belongs to the Class Frizzled of the G protein-coupled receptor (GPCR) superfamily, constituting a key component of the Hedgehog signalling pathway. Here we report the crystal structure of the multi-domain human SMO, bound and stabilized by a designed tool ligand TC114, using an X-ray free-electron laser source at 2.9 Å. The structure reveals a precise arrangement of three distinct domains: a seven-transmembrane helices domain (TMD), a hinge domain (HD) and an intact extracellular cysteine-rich domain (CRD). This architecture enables allosteric interactions between the domains that are important for ligand recognition and receptor activation. By combining the structural data, molecular dynamics simulation, and hydrogen-deuterium-exchange analysis, we demonstrate that transmembrane helix VI, extracellular loop 3 and the HD play a central role in transmitting the signal employing a unique GPCR activation mechanism, distinct from other multi-domain GPCRs.
