Phase Problem In Crystallography Research Articles

AI can solve the crystallographic phase problem

A neural network identifies molecular crystal structures with just a fraction of the data that other methods need.

PhAI: A deep-learning approach to solve the crystallographic phase problem.

X-ray crystallography provides a distinctive view on the three-dimensional structure of crystals. To reconstruct the electron density map, the complex structure factors [Formula: see text] of a sufficiently large number of diffracted reflections must be known. In a conventional experiment, only the amplitudes [Formula: see text] are obtained, and the phases ϕ are lost. This is the crystallographic phase problem. In this work, we show that a neural network, trained on millions of artificial structure data, can solve the phase problem at a resolution of only 2 angstroms, using only 10 to 20% of the data needed for direct methods. The network works in common space groups and for modest unit-cell dimensions and suggests that neural networks could be used to solve the phase problem in the general case for weakly scattering crystals.

A deep learning solution for crystallographic structure determination

The general de novo solution of the crystallographic phase problem is difficult and only possible under certain conditions. This paper develops an initial pathway to a deep learning neural network approach for the phase problem in protein crystallography, based on a synthetic dataset of small fragments derived from a large well curated subset of solved structures in the Protein Data Bank (PDB). In particular, electron-density estimates of simple artificial systems are produced directly from corresponding Patterson maps using a convolutional neural network architecture as a proof of concept.

Inter-Bragg crystallographic phase retrieval from shape transforms, stacking faults and substitutional disorder

One of the brilliant ideas of John Spence when he saw the first diffraction patterns from the Linac Coherent Light Source was that one could solve the crystallographic phase problem by utilising the intensities between Bragg peaks. Because these intensities are due to the Fourier transform of the shape of the crystal, the approach came to be known as “shape-transform phasing.”Shape-transform phasing was developed over the next ten years and formed the basis for many other interesting ideas and pursuits. Here we describe the current best implementation of the original idea using a lattice occupancy formalism and show that certain types of crystal defects can also be modelled via this approach, allowing the molecular structure to be recovered from the additional information offered by the inter-Bragg intensities from these crystal defects.

Accelerating crystal structure determination with iterative AlphaFold prediction.

Experimental structure determination can be accelerated with artificial intelligence (AI)-based structure-prediction methods such as AlphaFold. Here, an automatic procedure requiring only sequence information and crystallographic data is presented that uses AlphaFold predictions to produce an electron-density map and a structural model. Iterating through cycles of structure prediction is a key element of this procedure: a predicted model rebuilt in one cycle is used as a template for prediction in the next cycle. This procedure was applied to X-ray data for 215 structures released by the Protein Data Bank in a recent six-month period. In 87% of cases our procedure yielded a model with at least 50% of Cα atoms matching those in the deposited models within 2 Å. Predictions from the iterative template-guided prediction procedure were more accurate than those obtained without templates. It is concluded that AlphaFold predictions obtained based on sequence information alone are usually accurate enough to solve the crystallographic phase problem with molecular replacement, and a general strategy for macromolecular structure determination that includes AI-based prediction both as a starting point and as a method of model optimization is suggested.

Fragment-Based Ab Initio Phasing of Peptidic Nanocrystals by MicroED.

Electron diffraction (MicroED/3DED) can render the three-dimensional atomic structures of molecules from previously unamenable samples. The approach has been particularly transformative for peptidic structures, where MicroED has revealed novel structures of naturally occurring peptides, synthetic protein fragments, and peptide-based natural products. Despite its transformative potential, MicroED is beholden to the crystallographic phase problem, which challenges its de novo determination of structures. ARCIMBOLDO, an automated, fragment-based approach to structure determination, eliminates the need for atomic resolution, instead enforcing stereochemical constraints through libraries of small model fragments, and discerning congruent motifs in solution space to ensure validation. This approach expands the reach of MicroED to presently inaccessible peptide structures including fragments of human amyloids, and yeast and mammalian prions. For electron diffraction, fragment-based phasing portends a more general phasing solution with limited model bias for a wider set of chemical structures.

Solving the crystallographic phase problem using dynamical scattering in electron diffraction

Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can only be retrieved from such data if the atoms can be resolved as sharply peaked objects. Here a method is presented by which the fact that multiple scattering encodes structure factor phases in the diffracted intensities is being used for solving the crystallographic phase problem. The retrieval of both amplitudes and phases of electron structure factors from diffraction patterns recorded with varying angle of incidence will be demonstrated. No assumption about the scattering potential itself is being made. In particular, the resolution in the diffraction data does not need to be sufficient to resolve atoms, making this method potentially interesting for electron crystallography of 2-dimensional protein crystals and other beam-sensitive complex structures.

A phase retrieval algorithm for triply periodic minimal surface like structures.

A method to solve the crystallographic phase problem of materials with triply periodic minimal surface like structures, such as lyotropic liquid crystal bicontinuous cubic phases, is reported. In triply periodic minimal surface like structures, the difference between the maximum and minimum electron densities tends to be the smallest for the true phase combination among the possible combinations [Oka (2022). Acta Cryst. A78, 430-436]. Using this feature, a new iterative phase retrieval algorithm for structure determination was developed. The algorithm modifies electron densities outside the upper and lower thresholds in the iterative Fourier transformation process with fixed amplitudes for the structure factors, and efficiently searches for the structure with the smallest difference between the maximum and minimum electron densities. The proper structure was determined by this algorithm for all tested data for lyotropic liquid crystal bicontinuous cubic phases and mesoporous silicas. Although some cases required constraints such as the volume fraction for structure determination, more than half could be determined without any constraints, including space groups.

Data-driven approach for the solution of the phase problem in crystallography: first insights

Data-driven approach for the solution of the phase problem in crystallography: first insights

Data-driven approach for the solution of the phase problem in crystallography: first insights

Data-driven approach for the solution of the phase problem in crystallography: first insights

Editorial

Editorial

Michael Mark Woolfson. 9 January 1927—23 December 2019

Michael Woolfson contributed enormously to the theory and practice of X-ray crystallography for almost 60 years. He extended the theory of ‘direct methods’, which provided a general solution of the crystallographic phase problem from the measured diffraction data alone, and provided tools to exploit this theory. Software developed in his laboratory, such as the computer package MULTAN, was responsible for about half of the structures determined around the world in the 1970s and 1980s. His parallel work on the origin of the Solar System renewed interest in the Capture theory, and he contributed numerous stimulating ideas to the general study of the origin and dynamical evolution of the Solar System. Michael was a great educator and mentor for both undergraduates and young researchers, and many of these went on to make significant scientific contributions.

Crystallographic molecular replacement using an in silico-generated search model of SARS-CoV-2 ORF8.

The majority of crystal structures are determined by the method of molecular replacement (MR). The range of application of MR is limited mainly by the need for an accurate search model. In most cases, pre‐existing experimentally determined structures are used as search models. In favorable cases, ab initio predicted structures have yielded search models adequate for MR. The ORF8 protein of SARS‐CoV‐2 represents a challenging case for MR using an ab initio prediction because ORF8 has an all β‐sheet fold and few orthologs. We previously determined experimentally the structure of ORF8 using the single anomalous dispersion (SAD) phasing method, having been unable to find an MR solution to the crystallographic phase problem. Following a report of an accurate prediction of the ORF8 structure, we assessed whether the predicted model would have succeeded as an MR search model. A phase problem solution was found, and the resulting structure was refined, yielding structural parameters equivalent to the original experimental solution.

Crystal Structure: Reciprocal Space Methods for Carry out the Structure Solution from Powder Data

It is a relatively easy task to the solution of the so-called phase problem in crystallography, by applying ab initio phasing methods for the efficiency of structure solution from single-crystal data. Their effective application to powder x-ray diffraction data is still a real challenge unless the size of the structure is moderate. The percentage of principal success hinges on a number of factors; included are the quality of the experimental pattern, the success of the pattern-decomposition programs, the quality of the extracted structure-factor from the experimental pattern via the Le Bail or Pawley methods, the normalization of structure-factor process, the experimental resolution and the straightforward of the phasing process. This paper aims at providing an overall overview of the reciprocal space RS methods (ab initio phasing methods of crystal structure) as well as the direct methods, Patterson function and maximum entropy methods. This paper will also describe the factors affecting phasing by reciprocal space methods and the limitation of reciprocal space methods. Those are available for carry out the structure solution, in order to provide a clear theoretical account, experimental practice and computing approaches regarding and describe an outline of the solution process of phase problem by powder X-ray diffraction, leads to the best structure solution using practical examples.

Experimental phasing with vanadium and application to nucleotide-binding membrane proteins.

The structure determination of soluble and membrane proteins can be hindered by the crystallographic phase problem, especially in the absence of a suitable homologous structure. Experimental phasing is the method of choice for novel structures; however, it often requires heavy-atom derivatization, which can bedifficult and time-consuming. Here, a novel and rapid method to obtain experimental phases for protein structure determination by vanadium phasing is reported. Vanadate is a transition-state mimic of phosphoryl-transfer reactions and it has the advantage of binding specifically to the active site of numerous enzymes catalyzing this reaction. The applicability of vanadium phasing has been validated by determining the structures of three different protein-vanadium complexes, two of which are integral membrane proteins: the rabbit sarcoplasmic reticulum Ca2+-ATPase, the antibacterial peptide ATP-binding cassette transporter McjD from Escherichia coli and the soluble enzyme RNAse A from Bos taurus. Vanadium phasing was successful even at low resolution and despite severe anisotropy in the data. This method is principally applicable to a large number of proteins, representing six of the seven Enzyme Commission classes. It relies exclusively on the specific chemistry of the protein and it does not require any modifications, making it a very powerful addition to the phasing toolkit. In addition to the phasing power of this technique, the protein-vanadium complexes also provide detailed insights into the reaction mechanisms of the studied proteins.

Optimal data-driven parameterization of coiled coils

α-Helical coiled coils (CCs) represent an important, highly regular protein folding motif. To date, many thousands of CC structures have been determined experimentally. Their geometry is usually modelled by theoretical equations introduced by F. Crick that involve a predefined set of parameters. Here we have addressed the problem of efficient CC parameterization from scratch by performing a statistical evaluation of all available CC structures. The procedure is based on the principal component analysis and yields a minimal set of independent parameters that provide for the reconstruction of the complete CC structure at a required precision. The approach is successfully validated on a set of canonical parallel CC dimers. Its applications include all cases where an efficient sampling of the CC geometry is important, such as for solving the phase problem in crystallography.

Solving the crystal structure of human calcium-free S100Z: the siege and conquer of one of the last S100 family strongholds.

The X-ray structure of human apo-S100Z has been solved and compared with that of the zebrafish calcium-bound S100Z, which is the closest in sequence. Human apo-S100A12, which shows only 43% sequence identity to human S100Z, has been used as template model to solve the crystallographic phase problem. Although a significant buried surface area between the two physiological dimers is present in the asymmetric unit of human apo-S100Z, the protein does not form the superhelical arrangement in the crystal as observed for the zebrafish calcium-bound S100Z and human calcium-bound S100A4. These findings further demonstrate that calcium plays a fundamental role in triggering quaternary structure formation in several S100s. Solving the X-ray structure of human apo-S100Z by standard molecular replacement procedures turned out to be a challenge and required trying different models and different software tools among which only one was successful. The model that allowed structure solution was that with one of the lowest sequence identity with the target protein among the S100 family in the apo state. Based on the previously solved zebrafish holo-S100Z, a putative human holo-S100Z structure has been then calculated through homology modeling; the differences between the experimental human apo and calculated holo structure have been compared to those existing for other members of the family.

Acknowledging Errors: Advanced Molecular Replacement with Phaser.

Molecular replacement is a method for solving the crystallographic phase problem using an atomic model for the target structure. State-of-the-art methods have moved the field significantly from when it was first envisaged as a method for solving cases of high homology and completeness between a model and target structure. Improvements brought about by application of maximum likelihood statistics mean that various errors in the model and pathologies in the data can be accounted for, so that cases hitherto thought to be intractable are standardly solvable. As a result, molecular replacement phasing now accounts for the lion's share of structures deposited in the Protein Data Bank. However, there will always be cases at the fringes of solvability. I discuss here the approaches that will help tackle challenging molecular replacement cases.

Rosetta Structure Prediction as a Tool for Solving Difficult Molecular Replacement Problems.

Molecular replacement (MR), a method for solving the crystallographic phase problem using phases derived from a model of the target structure, has proven extremely valuable, accounting for the vast majority of structures solved by X-ray crystallography. However, when the resolution of data is low, or the starting model is very dissimilar to the target protein, solving structures via molecular replacement may be very challenging. In recent years, protein structure prediction methodology has emerged as a powerful tool in model building and model refinement for difficult molecular replacement problems. This chapter describes some of the tools available in Rosetta for model building and model refinement specifically geared toward difficult molecular replacement cases.

Recovering low spatial frequencies in wavefront sensing based on intensity measurements

AbstractThe transport of intensity equation (TIE) offers a convenient method to retrieve the phase of a wave function from maps of the irradiance (images) recorded at different planes along the optic axis of an optical system. However, being a second-order partial differential equation, even for noise-free data a unique solution of the TIE requires boundary conditions to be specified which are generally not accessible experimentally, jeopardizing retrieval of the low-frequency information in particular. Here we introduce an iterative algorithm which forgoes the need for explicit boundary conditions and combines the well-known reciprocal space solution of the TIE with the charge-flipping algorithm that has originally been developed to solve the crystallographic phase problem in X-ray diffraction. Application of this algorithm to experimental data and comparison with conventionally used algorithms demonstrates an improved retrieval of the low spatial frequencies of the phase.