Ab initio solution of macromolecular crystal structures without direct methods.

The majority of macromolecular crystal structures are determined using the method of molecular replacement, in which known related structures are rotated and translated to provide an initial atomic model for the new structure. A theoretical understanding of the signal-to-noise ratio in likelihood-based molecular replacement searches has been developed to account for the influence of model quality and completeness, as well as the resolution of the diffraction data. Here we show that, contrary to current belief, molecular replacement need not be restricted to the use of models comprising a substantial fraction of the unknown structure. Instead, likelihood-based methods allow a continuum of applications depending predictably on the quality of the model and the resolution of the data. Unexpectedly, our understanding of the signal-to-noise ratio in molecular replacement leads to the finding that, with data to sufficiently high resolution, fragments as small as single atoms of elements usually found in proteins can yield ab initio solutions of macromolecular structures, including some that elude traditional direct methods.

A fragmentation and reassembly method for ab initio phasing.

Ab initio phasing with de novo models has become a viable approach for structural solution from protein crystallographic diffraction data. This approach takes advantage of the known protein sequence information, predicts de novo models and uses them for structure determination by molecular replacement. However, even the current state-of-the-art de novo modelling method has a limit as to the accuracy of the model predicted, which is sometimes insufficient to be used as a template for successful molecular replacement. A fragment-assembly phasing method has been developed that starts from an ensemble of low-accuracy de novo models, disassembles them into fragments, places them independently in the crystallographic unit cell by molecular replacement and then reassembles them into a whole structure that can provide sufficient phase information to enable complete structure determination by automated model building. Tests on ten protein targets showed that the method could solve structures for eight of these targets, although the predicted de novo models cannot be used as templates for successful molecular replacement since the best model for each target is on average more than 4.0 Šaway from the native structure. The method has extended the applicability of the ab initio phasing by de novo models approach. The method can be used to solve structures when the best de novo models are still of low accuracy.

Macromolecular phasing using diffraction from multiple crystal forms.

A phasing algorithm for macromolecular crystallography is proposed that utilizes diffraction data from multiple crystal forms - crystals of the same molecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the molecular envelope and positional relationships between the molecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing.

Crystal structure of the Rab-binding domain of Rab11 family-interacting protein 2.

The small GTPases Rab11, Rab14 and Rab25 regulate membrane trafficking through the recruitment of Rab11 family-interacting proteins (FIPs) to endocytic compartments. FIPs are multi-domain effector proteins that have a highly conserved Rab-binding domain (RBD) at their C-termini. Several structures of complexes of Rab11 with RBDs have previously been determined, including those of Rab11-FIP2 and Rab11-FIP3. In addition, the structures of the Rab14-FIP1 and Rab25-FIP2 complexes have been determined. All of the RBD structures contain a central parallel coiled coil in the RBD that binds to the switch 1 and switch 2 regions of the Rab. Here, the crystal structure of the uncomplexed RBD of FIP2 is presented at 2.3 Šresolution. The structure reveals antiparallel α-helices that associate through polar interactions. These include a remarkable stack of arginine residues within a four-helix bundle in the crystal lattice.

Improving the convergence rate of a hybrid input-output phasing algorithm by varying the reflection data weight.

In an iterative projection algorithm proposed for ab initio phasing, the error metrics typically exhibit little improvement until a sharp decrease takes place as the iteration converges to the correct high-resolution structure. Related to that is the small convergence probability for certain structures. As a remedy, a variable weighting scheme on the diffraction data is proposed. It focuses on phasing low- and medium-resolution data first. The weighting shifts to incorporate more high-resolution reflections when the iteration proceeds. It is found that the precipitous drop in error metrics is replaced by a less dramatic drop at an earlier stage of the iteration. It seems that once a good configuration is formed at medium resolution, convergence towards the correct high-resolution structure is almost guaranteed. The original problem of phasing all diffraction data at once is reduced to a much more manageable one due to the dramatically smaller number of reflections involved. As a result, the success rate is significantly enhanced and the speed of convergence is raised. This is illustrated by applying the new algorithm to several structures, some of which are very difficult to solve without data weighting.

The phase problem for two-dimensional crystals. II. Simulations.

Phasing of diffraction data from two-dimensional crystals using only minimal molecular envelope information is investigated by simulation. Two-dimensional crystals are an attractive target for studying membrane proteins using X-ray free-electron lasers, particularly for dynamic studies at room temperature. Simulations using an iterative projection algorithm show that phasing is feasible with fairly minimal molecular envelope information, supporting recent uniqueness results for this problem [Arnal & Millane (2017). Acta Cryst. A73, 438-448]. The effects of noise and likely requirements for structure determination using X-ray free-electron laser sources are investigated.

The phase problem for two-dimensional crystals. I. Theory.

Properties of the phase problem for two-dimensional crystals are examined. This problem is relevant to protein structure determination using diffraction from two-dimensional crystals that has been proposed using new X-ray free-electron laser sources. The problem is shown to be better determined than for conventional three-dimensional crystallography, but there are still a large number of solutions in the absence of additional a priori information. Molecular envelope information reduces the size of the solution set, and for an envelope that deviates sufficiently from the unit cell a unique solution is possible. The effects of various molecular surface features and incomplete data on uniqueness and prospects for ab initio phasing are assessed. Simulations of phase retrieval for two-dimensional crystal data are described in the second paper in this series.

Approaches to ab initio molecular replacement of α-helical transmembrane proteins.

α-Helical transmembrane proteins are a ubiquitous and important class of proteins, but present difficulties for crystallographic structure solution. Here, the effectiveness of the AMPLE molecular replacement pipeline in solving α-helical transmembrane-protein structures is assessed using a small library of eight ideal helices, as well as search models derived from ab initio models generated both with and without evolutionary contact information. The ideal helices prove to be surprisingly effective at solving higher resolution structures, but ab initio-derived search models are able to solve structures that could not be solved with the ideal helices. The addition of evolutionary contact information results in a marked improvement in the modelling and makes additional solutions possible.

Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm.

An iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationship of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.

Mask-based approach to phasing of single-particle diffraction data.

A Monte Carlo-type approach for low- and medium-resolution phasing of single-particle diffraction data is suggested. Firstly, the single-particle phase problem is substituted with the phase problem for an imaginary crystal. A unit cell of this crystal contains a single isolated particle surrounded by a large volume of bulk solvent. The developed phasing procedure then generates a large number of connected and finite molecular masks, calculates their Fourier coefficients, selects the sets with magnitudes that are highly correlated with the experimental values and finally aligns the selected phase sets and calculates the averaged phase values. A test with the known structure of monomeric photosystem II resulted in phases that have 97% correlation with the exact phases in the full 25 Å resolution shell (1054 structure factors) and correlations of 99, 94, 81 and 79% for the resolution shells ∞-60, 60-40, 40-30 and 30-25 Å, respectively. The same procedure may be used for crystallographic ab initio phasing.

Direct-methods structure determination of a trypanosome RNA-editing substrate fragment with translational pseudosymmetry.

Using direct methods starting from random phases, the crystal structure of a 32-base-pair RNA (675 non-H RNA atoms in the asymmetric unit) was determined using only the native diffraction data (resolution limit 1.05 Å) and the computer program SIR2014. The almost three helical turns of the RNA in the asymmetric unit introduced partial or imperfect translational pseudosymmetry (TPS) that modulated the intensities when averaged by the l Miller indices but still escaped automated detection. Almost six times as many random phase sets had to be tested on average to reach a correct structure compared with a similar-sized RNA hairpin (27 nucleotides, 580 non-H RNA atoms) without TPS. More sensitive methods are needed for the automated detection of partial TPS.

Ab initio phasing by molecular averaging in real space with new criteria: application to structure determination of a betanodavirus.

Molecular averaging, including noncrystallographic symmetry (NCS) averaging, is a powerful method for ab initio phase determination and phase improvement. Applications of the cross-crystal averaging (CCA) method have been shown to be effective for phase improvement after initial phasing by molecular replacement, isomorphous replacement, anomalous dispersion or combinations of these methods. Here, a two-step process for phase determination in the X-ray structural analysis of a new coat protein from a betanodavirus, Grouper nervous necrosis virus, is described in detail. The first step is ab initio structure determination of the T = 3 icosahedral virus-like particle using NCS averaging (NCSA). The second step involves structure determination of the protrusion domain of the viral molecule using cross-crystal averaging. In this method, molecular averaging and solvent flattening constrain the electron density in real space. To quantify these constraints, a new, simple and general indicator, free fraction (ff), is introduced, where ff is defined as the ratio of the volume of the electron density that is freely changed to the total volume of the crystal unit cell. This indicator is useful and effective to evaluate the strengths of both NCSA and CCA. Under the condition that a mask (envelope) covers the target molecule well, an ff value of less than 0.1, as a new rule of thumb, gives sufficient phasing power for the successful construction of new structures.

Uniqueness of the macromolecular crystallographic phase problem.

Uniqueness of the phase problem in macromolecular crystallography, and its relationship to the case of single particle imaging, is considered. The crystallographic problem is characterized by a constraint ratio that depends only on the size and symmetry of the molecule and the unit cell. The results are used to evaluate the effect of various real-space constraints. The case of an unknown molecular envelope is considered in detail. The results indicate the quite wide circumstances under which ab initio phasing should be possible.

Macromolecular ab initio phasing enforcing secondary and tertiary structure.

Ab initio phasing of macromolecular structures, from the native intensities alone with no experimental phase information or previous particular structural knowledge, has been the object of a long quest, limited by two main barriers: structure size and resolution of the data. Current approaches to extend the scope of ab initio phasing include use of the Patterson function, density modification and data extrapolation. The authors' approach relies on the combination of locating model fragments such as polyalanine α-helices with the program PHASER and density modification with the program SHELXE. Given the difficulties in discriminating correct small substructures, many putative groups of fragments have to be tested in parallel; thus calculations are performed in a grid or supercomputer. The method has been named after the Italian painter Arcimboldo, who used to compose portraits out of fruit and vegetables. With ARCIMBOLDO, most collections of fragments remain a 'still-life', but some are correct enough for density modification and main-chain tracing to reveal the protein's true portrait. Beyond α-helices, other fragments can be exploited in an analogous way: libraries of helices with modelled side chains, ß-strands, predictable fragments such as DNA-binding folds or fragments selected from distant homologues up to libraries of small local folds that are used to enforce nonspecific tertiary structure; thus restoring the ab initio nature of the method. Using these methods, a number of unknown macromolecules with a few thousand atoms and resolutions around 2 Šhave been solved. In the 2014 release, use of the program has been simplified. The software mediates the use of massive computing to automate the grid access required in difficult cases but may also run on a single multicore workstation (http://chango.ibmb.csic.es/ARCIMBOLDO_LITE) to solve straightforward cases.

Direct phasing of protein crystals with high solvent content.

An iterative transform method is proposed for solving the phase problem in protein crystallography. In each iteration, a weighted average electron-density map is constructed to define an estimated protein mask. Solvent flattening is then imposed through the hybrid input-output algorithm [Fienup (1982). Appl. Opt. 21, 2758-2769]. Starting from random initial phases, after thousands of iterations the mask evolves into the correct shape and the phases converge to the correct values with an average error of 30-40° for high-resolution data for several protein crystals with high solvent content. With the use of non-crystallographic symmetry, the method could potentially be extended to phase protein crystals with less than 50% solvent fraction. The new phasing algorithm can supplement and enhance the traditional refinement tools.