Effects of self-seeding and crystal post-selection on the quality of Monte Carlo-integrated SFX data.

Serial femtosecond crystallography (SFX) is an emerging method for data collection at free-electron lasers (FELs) in which single diffraction snapshots are taken from a large number of crystals. The partial intensities collected in this way are then combined in a scheme called Monte Carlo integration, which provides the full diffraction intensities. However, apart from having to perform this merging, the Monte Carlo integration must also average out all variations in crystal quality, crystal size, X-ray beam properties and other factors, necessitating data collection from thousands of crystals. Because the pulses provided by FELs running in the typical self-amplified spontaneous emission (SASE) mode of operation have very irregular, spiky spectra that vary strongly from pulse to pulse, it has been suggested that this is an important source of variation contributing to inaccuracies in the intensities, and that, by using monochromatic pulses produced through a process called self-seeding, fewer images might be needed for Monte Carlo integration to converge, resulting in more accurate data. This paper reports the results of two experiments performed at the Linac Coherent Light Source in which data collected in both SASE and self-seeded mode were compared. Importantly, no improvement attributable to the use of self-seeding was detected. In addition, other possible sources of variation that affect SFX data quality were investigated, such as crystal-to-crystal variations reflected in the unit-cell parameters; however, these factors were found to have no influence on data quality either. Possibly, there is another source of variation as yet undetected that affects SFX data quality much more than any of the factors investigated here.

Parameter inversion of a polydisperse system in small-angle scattering.

A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.

Dynamical Accuracy of Water Models on Supercooling.

Molecular dynamics (MD) simulations are commonly used to explore the structural and dynamical properties of supercooled bulk water in the so-called "no man's land" (NML) (150-227 K), where crystallization occurs almost instantaneously. This approach has provided significant insight into experimentally inaccessible phenomena. In this paper, we compare the dynamics of simulations using one-, three-, and four-body water models to experimentally measured quasielastic neutron scattering spectra. We show that the agreement between simulated and experimental data becomes substantially worse with a decrease in temperature toward the deeply supercooled regime. It was found that it is mainly the nature of the local dynamics that is poorly reproduced, as opposed to the macroscopic properties such as the diffusion coefficient. This strongly implies that the molecular mechanism describing the water dynamics is poorly captured in the MD models, and simulated structural and dynamical properties of supercooled water in NML must be interpreted with care.

Three-centre hydrogen bonds in triphenyl-phosphine oxide-hydro-quinone (1/1).

The title cocrystal, C(18)H(15)OP·C(6)H(6)O(2), belongs to a series of mol-ecular systems based on triphenyl-phosphine P-oxide. The O atom of the oxide group acts as an acceptor for hydrogen bonds from OH groups of two hydro-quinone mol-ecules which lie on inversion centres [O⋯O = 2.7451 (17) and 2.681 (2) Å]. The crystal structure is stabilized by weak C-H⋯O hydrogen bonds, forming a C(2) (1)(8) chain which runs parallel to the [100] direction.

Structural studies of P-type ATPase-ligand complexes using an X-ray free-electron laser.

Membrane proteins are key players in biological systems, mediating signalling events and the specific transport of e.g. ions and metabolites. Consequently, membrane proteins are targeted by a large number of currently approved drugs. Understanding their functions and molecular mechanisms is greatly dependent on structural information, not least on complexes with functionally or medically important ligands. Structure determination, however, is hampered by the difficulty of obtaining well diffracting, macroscopic crystals. Here, the feasibility of X-ray free-electron-laser-based serial femtosecond crystallography (SFX) for the structure determination of membrane protein-ligand complexes using microcrystals of various native-source and recombinant P-type ATPase complexes is demonstrated. The data reveal the binding sites of a variety of ligands, including lipids and inhibitors such as the hallmark P-type ATPase inhibitor orthovanadate. By analyzing the resolution dependence of ligand densities and overall model qualities, SFX data quality metrics as well as suitable refinement procedures are discussed. Even at relatively low resolution and multiplicity, the identification of ligands can be demonstrated. This makes SFX a useful tool for ligand screening and thus for unravelling the molecular mechanisms of biologically active proteins.

Conformational analysis by solid-state NMR and its application to restrained structure determination from powder diffraction data.

Solid-state NMR is used to dramatically improve the efficiency and reliability of molecular crystal structure determination from X-ray powder diffraction data.

A maximum-likelihood method for global-optimization-based structure determination from powder diffraction data.

A maximum-likelihood algorithm has been incorporated into a crystal structure determination from a powder diffraction data framework that uses an integrated-intensity-based global optimization technique. The algorithm is appropriate when the structural model being optimized is not a complete description of the crystal structure under study.

A hybrid Monte Carlo method for crystal structure determination from powder diffraction data.

A hybrid Monte Carlo algorithm for crystal structure determination from powder diffraction data is presented. The algorithm combines the key components of molecular dynamics and Monte Carlo simulations to achieve efficient sampling of phase space, allowing the crystal structure of capsaicin to be determined from powder diffraction data more effectively than by a simulated-annealing approach. The implementation of the algorithm, the choice of the simulation parameters and the performance of the algorithm are discussed.

Diffusion-equation method for crystallographic figure of merits.

Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem. 93, 3339-3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data.