Surprises and pitfalls arising from (pseudo)symmetry

Group Theory on Quasisymmetry and Protected Near Degeneracy

In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to symmetry breaking, its application to determining the magnitude of energy splitting resulting from symmetry lowering is limited. Here, we propose a theory on quasisymmetry and near degeneracy, thereby expanding the applicability of group theory to address questions regarding large-or-small energy splitting. Defined within the degenerate subspace of an unperturbed Hamiltonian, quasisymmetries form an enlarged symmetry group eliminating the first-order splitting. This framework ensures that the magnitude of splitting arises as a second-order effect of symmetry-lowering perturbations, such as external fields and spin-orbit coupling. We systematically tabulate the quasisymmetry groups within 32 crystallographic point groups and find all the possible unitary quasisymmetry group structures regarding double degeneracy. Applying our theory to the realistic material AgLa, we predict a "quasi-Dirac semimetal" phase characterized by two tiny-gap band anticrossings.

Continuous Invariant-Based Maps of the Cambridge Structural Database

The Cambridge Structural Database (CSD) played a key role in the recently established crystal isometry principle (CRISP). The CRISP says that any real periodic crystal is uniquely determined as a rigid structure by the geometry of its atomic centers without atomic types. Ignoring atomic types allows us to study all periodic crystals in a common space whose continuous nature is justified by the continuity of real-valued coordinates of atoms. Our previous work introduced structural descriptors pointwise distance distributions (PDD) that are invariant under isometry defined as a composition of translations, rotations, and reflections. The PDD invariants distinguished all nonduplicate periodic crystals in the CSD. This paper presents the first continuous maps of the CSD and its important subsets in invariant coordinates that have analytic formulas and physical interpretations. Any existing periodic crystal has a uniquely defined location on these geographic-style maps. Any newly discovered periodic crystals will appear on the same maps without disturbing the past materials.

The importance of definitions in crystallography

This paper was motivated by the articles `Same or different - that is the question' in CrystEngComm (July 2020) and `Change to the definition of a crystal' in the IUCr Newsletter (June 2021). Experimental approaches to crystal comparisons require rigorously defined classifications in crystallography and beyond. Since crystal structures are determined in a rigid form, their strongest equivalence in practice is rigid motion, which is a composition of translations and rotations in 3D space. Conventional representations based on reduced cells and standardizations theoretically distinguish all periodic crystals. However, all cell-based representations are inherently discontinuous under almost any atomic displacement that can arbitrarily scale up a reduced cell. Hence, comparison of millions of known structures in materials databases requires continuous distance metrics.

Carotenoid cleavage enzymes evolved convergently to generate the visual chromophore

The retinal light response in animals originates from the photoisomerization of an opsin-coupled 11-cis-retinaldehyde chromophore. This visual chromophore is enzymatically produced through the action of carotenoid cleavage dioxygenases. Vertebrates require two carotenoid cleavage dioxygenases, β-carotene oxygenase 1 and retinal pigment epithelium 65 (RPE65), to form 11-cis-retinaldehyde from carotenoid substrates, whereas invertebrates such as insects use a single enzyme known as Neither Inactivation Nor Afterpotential B (NinaB). RPE65 and NinaB couple trans-cis isomerization with hydrolysis and oxygenation, respectively, but the mechanistic relationship of their isomerase activities remains unknown. Here we report the structure of NinaB, revealing details of its active site architecture and mode of membrane binding. Structure-guided mutagenesis studies identify a residue cluster deep within the NinaB substrate-binding cleft that controls its isomerization activity. Our data demonstrate that isomerization activity is mediated by distinct active site regions in NinaB and RPE65-an evolutionary convergence that deepens our understanding of visual system diversity.

Elucidating the Polymorphism of Xanthone: A Crystallization and Characterization Study

The aim of this work is to shed light on the polymorphism of xanthones, a class of oxygenated molecules well known for their bioactivity, including antioxidant, anticancer, and anti-inflammatory effects. Understanding the polymorphism of xanthones can enable the design of novel solid products for pharmaceutical, nutraceutical, and agrochemical applications. Prior to this work, two entries accounting for different space groups were deposited for 9-xanthone in the Cambridge Structure Database (CSD): an orthorhombic P212121 and a monoclinic P21 structure solved at room and low temperatures, respectively. However, the very high similarity between these two structures and the lack of clear differences in their physical properties (e.g., thermal behavior) suggested the possibility of the existence of only one crystal structure. In fact, the differences shown in the literature data might be related to the chosen operating parameters, as well as the instrumental resolution of the single-crystal X-ray diffraction experiments. In the work presented here, the ambiguity in the polymorphism of xanthone is investigated using thermal analysis, powder and synchrotron single-crystal XRD, and optical microscopy. Additionally, a workflow for the correct identification of twinned crystal structures, which can be applied to other polymorphic systems, is presented. Such workflow combines the collection of a large data set of high-resolution diffraction patterns using synchrotron radiation with the use of principal component analysis, a dimensionality reduction technique, for a quick and effective identification of phase transitions happening during the data collection. Crystallization experiments were designed to promote the formation of different crystal structures of xanthone that were recrystallized based on past literature and beyond.

Continuous chiral distances for two-dimensional lattices

Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two-dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic-style coordinates. The four non-oblique Bravais classes of two-dimensional lattices form low-dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real-valued distances satisfying metric axioms. This article analyzes these and newer G-chiral distances for millions of two-dimensional lattices that are extracted from thousands of available two-dimensional materials and real crystal structures in the Cambridge Structural Database.

Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

Mechanism of selective recognition of Lys48-linked polyubiquitin by macrocyclic peptide inhibitors of proteasomal degradation

Post-translational modification of proteins with polyubiquitin chains is a critical cellular signaling mechanism in eukaryotes with implications in various cellular states and processes. Unregulated ubiquitin-mediated protein degradation can be detrimental to cellular homeostasis, causing numerous diseases including cancers. Recently, macrocyclic peptides were developed that selectively target long Lysine-48-linked polyubiquitin chains (tetra-ubiquitin) to inhibit ubiquitin-proteasome system, leading to attenuation of tumor growth in vivo. However, structural determinants of the chain length and linkage selectivity by these cyclic peptides remained unclear. Here, we uncover the mechanism underlying cyclic peptide's affinity and binding selectivity by combining X-ray crystallography, solution NMR, and biochemical studies. We found that the peptide engages three consecutive ubiquitins that form a ring around the peptide and determined requirements for preferential selection of a specific trimer moiety in longer polyubiquitin chains. The structural insights gained from this work will guide the development of next-generation cyclic peptides with enhanced anti-cancer activity.

Geographic style maps for two-dimensional lattices

This paper develops geographic style maps containing two-dimensional lattices in all known periodic crystals parameterized by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of two-dimensional lattices is a square with identified edges or a punctured sphere. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualize hundreds of thousands of lattices of real crystal structures from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.

Structures of Streptococcus pyogenes Class A sortase in complex with substrate and product mimics provide key details of target recognition

The cell wall is a critical extracellular barrier for bacteria and many other organisms. In bacteria, this structural layer consists of peptidoglycan, which maintains cell shape and structural integrity and provides a scaffold for displaying various protein factors. To attach proteins to the cell wall, Gram-positive bacteria utilize sortase enzymes, which are cysteine transpeptidases that recognize and cleave a specific sorting signal, followed by ligation of the sorting signal–containing protein to the peptidoglycan precursor lipid II (LII). This mechanism is the subject of considerable interest as a target for therapeutic intervention and as a tool for protein engineering, where sortases have enabled sortase-mediated ligation or sortagging strategies. Despite these uses, there remains an incomplete understanding of the stereochemistry of substrate recognition and ligation product formation. Here, we solved the first structures of sortase A from Streptococcus pyogenes bound to two substrate sequences, LPATA and LPATS. In addition, we synthesized a mimetic of the product of sortase-mediated ligation involving LII (LPAT-LII) and solved the complex structure in two ligand conformations. These structures were further used as the basis for molecular dynamics simulations to probe sortase A-ligand dynamics and to construct a model of the acyl–enzyme intermediate, thus providing a structural view of multiple key states in the catalytic mechanism. Overall, this structural information provides new insights into the recognition of the sortase substrate motif and LII ligation partner and will support the continued development of sortases for protein engineering applications.

Variations on a theme: crystal forms of the amino-acid transporter MhsT

An unusual case of protein–substrate complexes that were obtained under similar conditions but contain different packing arrangements is reported. The crystals exhibit a combination of various crystal imperfections (pseudosymmetry, twinning and translational non­crystallographic symmetry), masking the true crystal symmetry and challenging data processing and structure determination.

The bacterial amino-acid transporter MhsT from the SLC6A family has been crystallized in complex with different substrates in order to understand the determinants of the substrate specificity of the transporter. Surprisingly, crystals of the different MhsT–substrate complexes showed interrelated but different crystal-packing arrangements. Space-group assignment and structure determination of these different crystal forms present challenging combinations of pseudosymmetry, twinning and translational non­crystallographic symmetry.

Resolving alternative structure determinations of indapamide using 13C solid-state NMR

The conflict between alternative crystal structures in the Cambridge Structural Database for the diuretic drug indapamide hemihydrate (IND) has been resolved with the aid of ¹³C solid-state NMR. IND is seen to contain multiple distinct molecules in the asymmetric unit (Z' = 4) rather than exhibiting disorder in the orientation of sulfonamide groups. The NMR crystallographic approach is a more effective tool for distinguishing between alternative structures than naïve judgements of quality based on crystallographic refinement agreement factors.

Frequency distribution of space groups in soluble and membrane proteins and their complexes

The space-group frequency distributions for two types of proteins and their complexes are explored. Based on the incremental availability of data in the Protein Data Bank, an analytical assessment shows a preferential distribution of three space groups, i.e. P212121 > P1211 > C121, in soluble and membrane proteins as well as in their complexes. In membrane proteins, the order of the three space groups is P212121 > C121 > P1211. The distribution of these space groups also shows the same pattern whether a protein crystallizes with a monomer or an oligomer in the asymmetric unit. The results also indicate that the sizes of the two entities in the structures of soluble proteins crystallized as complexes do not influence the frequency distribution of space groups. In general, it can be concluded that the space-group frequency distribution is homogenous across different types of proteins and their complexes.

The tetrameric structure of the novel haloalkane dehalogenase DpaA from Paraglaciecola agarilytica NO2

Haloalkane dehalogenases (EC 3.8.1.5) are microbial enzymes that catalyse the hydrolytic conversion of halogenated compounds, resulting in a halide ion, a proton and an alcohol. These enzymes are used in industrial biocatalysis, bioremediation and biosensing of environmental pollutants or for molecular tagging in cell biology. The novel haloalkane dehalogenase DpaA described here was isolated from the psychrophilic and halophilic bacterium Paraglaciecola agarilytica NO2, which was found in marine sediment collected from the East Sea near Korea. Gel-filtration experiments and size-exclusion chromatography provided information about the dimeric composition of the enzyme in solution. The DpaA enzyme was crystallized using the sitting-drop vapour-diffusion method, yielding rod-like crystals that diffracted X-rays to 2.0 Å resolution. Diffraction data analysis revealed a case of merohedral twinning, and subsequent structure modelling and refinement resulted in a tetrameric model of DpaA, highlighting an uncommon multimeric nature for a protein belonging to haloalkane dehalogenase subfamily I.

Detection of translational noncrystallographic symmetry in Patterson functions

Detection of translational noncrystallographic symmetry (TNCS) can be critical for success in crystallographic phasing, particularly when molecular-replacement models are poor or anomalous phasing information is weak. If the correct TNCS is detected then expected intensity factors for each reflection can be refined, so that the maximum-likelihood functions underlying molecular replacement and single-wavelength anomalous dispersion use appropriate structure-factor normalization and variance terms. Here, an analysis of a curated database of protein structures from the Protein Data Bank to investigate how TNCS manifests in the Patterson function is described. These studies informed an algorithm for the detection of TNCS, which includes a method for detecting the number of vectors involved in any commensurate modulation (the TNCS order). The algorithm generates a ranked list of possible TNCS associations in the asymmetric unit for exploration during structure solution.

Structure of 3-mercaptopropionic acid dioxygenase with a substrate analog reveals bidentate substrate binding at the iron center

Thiol dioxygenases are a subset of nonheme iron oxygenases that catalyze the formation of sulfinic acids from sulfhydryl-containing substrates and dioxygen. Among this class, cysteine dioxygenases (CDOs) and 3-mercaptopropionic acid dioxygenases (3MDOs) are the best characterized, and the mode of substrate binding for CDOs is well understood. However, the manner in which 3-mercaptopropionic acid (3MPA) coordinates to the nonheme iron site in 3MDO remains a matter of debate. A model for bidentate 3MPA coordination at the 3MDO Fe-site has been proposed on the basis of computational docking, whereas steady-state kinetics and EPR spectroscopic measurements suggest a thiolate-only coordination of the substrate. To address this gap in knowledge, we determined the structure of Azobacter vinelandii 3MDO (Av3MDO) in complex with the substrate analog and competitive inhibitor, 3-hydroxypropionic acid (3HPA). The structure together with DFT computational modeling demonstrates that 3HPA and 3MPA associate with iron as chelate complexes with the substrate-carboxylate group forming an additional interaction with Arg168 and the thiol bound at the same position as in CDO. A chloride ligand was bound to iron in the coordination site assigned as the O2-binding site. Supporting HYSCORE spectroscopic experiments were performed on the (3MPA/NO)-bound Av3MDO iron nitrosyl (S = 3/2) site. In combination with spectroscopic simulations and optimized DFT models, this work provides an experimentally verified model of the Av3MDO enzyme-substrate complex, effectively resolving a debate in the literature regarding the preferred substrate-binding denticity. These results elegantly explain the observed 3MDO substrate specificity, but leave unanswered questions regarding the mechanism of substrate-gated reactivity with dioxygen.

Optimizing the refinement of merohedrally twinned P61 HIV-1 protease-inhibitor cocrystal structures

Twinning is a crystal-growth anomaly in which protein monomers exist in different orientations but are related in a specific way, causing diffraction reflections to overlap. Twinning imposes additional symmetry on the data, often leading to the assignment of a higher symmetry space group. Specifically, in merohedral twinning, reflections from each monomer overlap and require a twin law to model unique structural data from overlapping reflections. Neglecting twinning in the crystallographic analysis of quasi-rotationally symmetric homo-oligomeric protein structures can mask the degree of structural non-identity between monomers. In particular, any deviations from perfect symmetry will be lost if higher than appropriate symmetry is applied during crystallographic analysis. Such cases warrant choosing between the highest symmetry space group possible or determining whether the monomers have distinguishable structural asymmetries and thus require a lower symmetry space group and a twin law. Using hexagonal cocrystals of HIV-1 protease, a C2-symmetric homodimer whose symmetry is broken by bound ligand, it is shown that both assigning a lower symmetry space group and applying a twin law during refinement are critical to achieving a structural model that more accurately fits the electron density. By re-analyzing three recently published HIV-1 protease structures, improvements in nearly every crystallographic metric are demonstrated. Most importantly, a procedure is demonstrated where the inhibitor can be reliably modeled in a single orientation. This protocol may be applicable to many other homo-oligomers in the PDB.

Structural basis of binding of homodimers of the nuclear receptor NR4A2 to selective Nur-responsive DNA elements

Proteins of nuclear receptor subfamily 4 group A (NR4A), including NR4A1/NGFI-B, NR4A2/Nurr1, and NR4A3/NOR-1, are nuclear transcription factors that play important roles in metabolism, apoptosis, and proliferation. NR4A proteins recognize DNA response elements as monomers or dimers to regulate the transcription of a variety of genes involved in multiple biological processes. In this study, we determined two crystal structures of the NR4A2 DNA-binding domain (NR4A2-DBD) bound to two Nur-responsive elements: an inverted repeat and an everted repeat at 2.6-2.8 Å resolution. The structures revealed that two NR4A2-DBD molecules bind independently to the everted repeat, whereas two other NR4A2-DBD molecules form a novel dimer interface on the inverted repeat. Moreover, substitution of the interfacial residue valine 298 to lysine as well as mutation of DNA bases involved in the interactions abolished the dimerization. Overall, our structural, biochemical, and bioinformatics analyses provide a molecular basis for the binding of the NR4A2 protein dimers to NurREs and advance our understanding of the dimerization specificity of nuclear receptors.

Resolving indexing ambiguities in X-ray free-electron laser diffraction patterns

Processing X-ray free-electron laser (XFEL) diffraction images poses challenges, as an XFEL pulse is powerful enough to destroy or damage the diffracting volume and thereby yields only one diffraction image per volume. Moreover, the crystal is stationary during the femtosecond pulse, so reflections are generally only partially recorded. Therefore, each XFEL diffraction image must be scaled individually and, ideally, corrected for partiality prior to merging. An additional complication may arise owing to indexing ambiguities when the symmetry of the Bravais lattice is higher than that of the space group, or when the unit-cell dimensions are similar to each other. Here, an automated method is presented that diagnoses these indexing ambiguities based on the Brehm-Diederichs algorithm [Brehm & Diederichs (2014), Acta Cryst. D70, 101-109] and produces a consistent indexing choice for the large majority of diffraction images. This method was applied to an XFEL diffraction data set measured from crystals of the neuronal SNARE-complexin-1-synaptotagmin-1 complex. After correcting the indexing ambiguities, substantial improvements were observed in the merging statistics and the atomic model refinement R values. This method should be a useful addition to the arsenal of tools for the processing of XFEL diffraction data sets.

Crystal structure of (2E,4Z)-dimethyl 4-((phenylamino)methylene)pent-2-enedioate, C14H15N1O4

C14H15N1O4, triclinic, P1̄, a = 8.2018(4) Å, b = 11.5512(5) Å, c = 14.4121(7) Å, α = 79.242(2)°, β = 78.647(3)°, γ = 85.496(3)°, V = 1313.93(11) Å3, Z = 2, R gt(F) = 0.0548, wR ref(F 2) = 0.1805, T = 296(2) K.

Pathological macromolecular crystallographic data affected by twinning, partial-disorder and exhibiting multiple lattices for testing of data processing and refinement tools

Twinning is a crystal growth anomaly, which has posed a challenge in macromolecular crystallography (MX) since the earliest days. Many approaches have been used to treat twinned data in order to extract structural information. However, in most cases it is usually simpler to rescreen for new crystallization conditions that yield an untwinned crystal form or, if possible, collect data from non-twinned parts of the crystal. Here, we report 11 structures of engineered variants of the E. coli enzyme N-acetyl-neuraminic lyase which, despite twinning and incommensurate modulation, have been successfully indexed, solved and deposited. These structures span a resolution range of 1.45-2.30 Å, which is unusually high for datasets presenting such lattice disorders in MX and therefore these data provide an excellent test set for improving and challenging MX data processing programs.

Refining the macromolecular model - achieving the best agreement with the data from X-ray diffraction experiment

Refinement of macromolecular X-ray crystal structures involves using complex software with hundreds of different settings. The complexity of underlying concepts and the sheer amount sof instructions may make it difficult for less experienced crystallographers to achieve optimal results in their refinements. This tutorial review offers guidelines for choosing the best settings for the reciprocal-space refinement of macromolecular models and provides practical tips for manual model correction. To help aspiring crystallographers navigate the process, some of the most practically important concepts of protein structure refinement are described. Among the topics covered are the use and purpose of R-free, geometrical restraints, restraints on atomic displacement parameters (ADPs), refinement weights, various parametrizations of ADPs (full anisotropic refinement and TLS), and omit maps. We also give practical tips for manual model correction in Coot, modelling of side-chains with poor or missing density, and ligand identification, fitting, and refinement.

Perfect merohedral twinning combined with noncrystallographic symmetry potentially causes the failure of molecular replacement with low-homology search models for the flavin-dependent halogenase HalX from Xanthomonas campestris

Flavin-dependent halogenases can be used as biocatalysts because they regioselectively halogenate their substrates under mild reaction conditions. New halogenases with novel substrate specificities will add to the toolbox of enzymes available to organic chemists. HalX, the product of the xcc-b100_4193 gene, is a putative flavin-dependent halogenase from Xanthomonas campestris. The enzyme was recombinantly expressed and crystallized in order to aid in identifying its hitherto unknown substrate. Native data collected to a resolution of 2.5 Å showed indications of merohedral twinning in a hexagonal lattice. Attempts to solve the phase problem by molecular replacement failed. Here, a detailed analysis of the suspected twinning is presented. It is most likely that the crystals are trigonal (point group 3) and exhibit perfect hemihedral twinning so that they appear to be hexagonal (point group 6). As there are several molecules in the asymmetric unit, noncrystallographic symmetry may complicate twinning analysis and structure determination.

Against Method: Table 1-Cui Bono?

The almost universally required "Table 1," summarizing data-collection and data-processing statistics, has in its present form outlived its usefulness in almost all publications of biomolecular crystal structure reports. Information contained in "Table 1" is insufficient to evaluate or repeat the experiment; is redundant with information extractable from deposited diffraction data; and includes data items whose meaning is under increased scrutiny in the crystallographic community. Direct and consistent extraction and analysis of data quality metrics from preferably unmerged intensity data with graphical presentation of reciprocal space features, including impact on map and model features, should replace "Table 1."

Identifying and Overcoming Crystal Pathologies: Disorder and Twinning

Macromolecular crystals are prone to a number of pathologies that result from aberrant molecular packing. Two common pathologies encountered in macromolecular crystals are rigid-body disorder and twinning. When a crystal displays one of these pathologies, its diffraction pattern is altered in a way that generally complicates structure determination. The severity of the underlying abnormalities varies from case to case, and sometimes the resulting alterations to the diffraction pattern are immediately obvious, while at other times they may go entirely unnoticed. Structure determination from a crystal that suffers from disorder or twinning may or may not be possible, depending on the specific nature of the pathology, and on how the data are handled. This chapter provides an introduction to these pathologies, with an emphasis on providing guidelines for identifying and overcoming them when they pose a threat to successful structure determination.

Controlling miRNA-like off-target effects of an siRNA with nucleobase modifications

SiRNAs can cause unintended gene silencing due to miRNA-like effects because of the similarity in function of an siRNA guide strand and a miRNA. Here we evaluate the effect on miRNA-like off targeting of introducing the adenosine derivative 7-EAA and triazoles prepared from 7-EAA at different positions in an siRNA guide strand. We find that a sterically demanding triazole placed in the RNA duplex major groove at position six of the guide strand dramatically reduces miRNA-like off targeting potency. A high-resolution structure of an RNA duplex bearing a novel, major-groove localized triazole is reported, which suggests that modified triazoles could be disrupting the hAgo2-guide-target RNA ternary complex. Five different triazole modifications were tested at the guide strand 6-position for effects on on-target and miRNA-like off target knockdown potency. A 7-EAA triazole bearing a benzylamine substituent displayed on-target knockdown activity as potent as the native siRNA, while having an IC₅₀ against a miRNA-like off target >100-fold higher. Melting temperature studies revealed no obvious correlation between potency in knockdown assays and a modification's effect on duplex stability. These results, along with known structures of hAgo2-guide-target ternary complexes, are used to rationalize the effect of 7-EAA triazoles on miRNA-like off target effects.

Datasets, processing and refinement details for Mtb-AnPRT: inhibitor structures with various space groups

There are twenty-five published structures of Mycobacterium tuberculosis anthranilate phosphoribosyltransferase (Mtb-AnPRT) that use the same crystallization protocol. The structures include protein complexed with natural and alternative substrates, protein:inhibitor complexes, and variants with mutations of substrate-binding residues. Amongst these are varying space groups (i.e. P2₁, C2, P2₁2₁2, P2₁2₁2₁). This article outlines experimental details for 3 additional Mtb-AnPRT:inhibitor structures. For one protein:inhibitor complex, two datasets are presented – one generated by crystallization of protein in the presence of the inhibitor and another where a protein crystal was soaked with the inhibitor. Automatic and manual processing of these datasets indicated the same space group for both datasets and thus indicate that the space group differences between structures of Mtb-AnPRT:ligand complexes are not related to the method used to introduce the ligand.

Data on crystal organization in the structure of the Fab fragment from the NIST reference antibody, RM 8671

The reported data describe the crystallization, crystal packing, structure determination and twinning of the unliganded Fab (antigen-binding fragment) from the NISTmAb (standard reference material 8671). The raw atomic coordinates are available as Protein Data Bank structure 5K8A and biological aspects are described in the article, (Karageorgos et al., 2017) [1]. Crystal data show that the packing is unique, and show the basis for the crystal's twinned growth. Twinning is a common and often serious problem in protein structure determination by x-ray crystallography [2]. In the present case the twinning is due to a small deviation (about 0.3 nm) from 4-fold symmetry in the primary intermolecular interface. The deviation produces pseudosymmetry, generating slightly different conformations of the protein, and alternating strong and weak forms of key packing interfaces throughout the lattice.

Exceptionally tight membrane-binding may explain the key role of the synaptotagmin-7 C2A domain in asynchronous neurotransmitter release

Synaptotagmins (Syts) act as Ca²⁺ sensors in neurotransmitter release by virtue of Ca²⁺-binding to their two C₂ domains, but their mechanisms of action remain unclear. Puzzlingly, Ca²⁺-binding to the C₂B domain appears to dominate Syt1 function in synchronous release, whereas Ca²⁺-binding to the C₂A domain mediates Syt7 function in asynchronous release. Here we show that crystal structures of the Syt7 C₂A domain and C₂AB region, and analyses of intrinsic Ca²⁺-binding to the Syt7 C2 domains using isothermal titration calorimetry, did not reveal major differences that could explain functional differentiation between Syt7 and Syt1. However, using liposome titrations under Ca²⁺ saturating conditions, we show that the Syt7 C₂A domain has a very high membrane affinity and dominates phospholipid binding to Syt7 in the presence or absence of l-α-phosphatidylinositol 4,5-diphosphate (PIP₂). For Syt1, the two Ca²⁺-saturated C₂ domains have similar affinities for membranes lacking PIP₂, but the C₂B domain dominates binding to PIP₂-containing membranes. Mutagenesis revealed that the dramatic differences in membrane affinity between the Syt1 and Syt7 C₂A domains arise in part from apparently conservative residue substitutions, showing how striking biochemical and functional differences can result from the cumulative effects of subtle residue substitutions. Viewed together, our results suggest that membrane affinity may be a key determinant of the functions of Syt C₂ domains in neurotransmitter release.

Probing the structural basis of oxygen binding in a cofactor-independent dioxygenase

The enzyme DpgC is included in the small family of cofactor-independent dioxygenases. The chemistry of DpgC is uncommon as the protein binds and utilizes dioxygen without the aid of a metal or organic cofactor. Previous structural and biochemical studies identified the substrate-binding mode and the components of the active site that are important in the catalytic mechanism. In addition, the results delineated a putative binding pocket and migration pathway for the co-substrate dioxygen. Here, structural biology is utilized, along with site-directed mutagenesis, to probe the assigned dioxygen-binding pocket. The key residues implicated in dioxygen trafficking were studied to probe the process of binding, activation and chemistry. The results support the proposed chemistry and provide insight into the general mechanism of dioxygen binding and activation.

Structure-Activity Relationship for Sulfonamide Inhibition of Helicobacter pylori α-Carbonic Anhydrase

α-Carbonic anhydrase of Helicobacter pylori (HpαCA) plays an important role in the acclimation of this oncobacterium to the acidic pH of the stomach. Sulfonamide inhibitors of HpαCA possess anti-H. pylori activity. The crystal structures of complexes of HpαCA with a family of acetazolamide-related sulfonamides have been determined. Analysis of the structures revealed that the mode of sulfonamide binding correlates well with their inhibitory activities. In addition, comparisons with the corresponding inhibitor complexes of human carbonic anhydrase II (HCAII) indicated that HpαCA possesses an additional, alternative binding site for sulfonamides that is not present in HCAII. Furthermore, the hydrophobic pocket in HCAII that stabilizes the apolar moiety of sulfonamide inhibitors is replaced with a more open, hydrophilic pocket in HpαCA. Thus, our analysis identified major structural features can be exploited in the design of selective and more potent inhibitors of HpαCA that may lead to novel antimicrobials.

Quadruple space-group ambiguity owing to rotational and translational noncrystallographic symmetry in human liver fructose-1,6-bisphosphatase

Fructose-1,6-bisphosphatase (FBPase) is a key regulator of gluconeogenesis and a potential drug target for type 2 diabetes. FBPase is a homotetramer of 222 symmetry with a major and a minor dimer interface. The dimers connected via the minor interface can rotate with respect to each other, leading to the inactive T-state and active R-state conformations of FBPase. Here, the first crystal structure of human liver FBPase in the R-state conformation is presented, determined at a resolution of 2.2 Å in a tetragonal setting that exhibits an unusual arrangement of noncrystallographic symmetry (NCS) elements. Self-Patterson function analysis and various intensity statistics revealed the presence of pseudo-translation and the absence of twinning. The space group is P41212, but structure determination was also possible in space groups P43212, P4122 and P4322. All solutions have the same arrangement of three C2-symmetric dimers spaced by 1/3 along an NCS axis parallel to the c axis located at (1/4, 1/4, z), which is therefore invisible in a self-rotation function analysis. The solutions in the four space groups are related to one another and emulate a body-centred lattice. If all NCS elements were crystallographic, the space group would be I4122 with a c axis three times shorter and a single FBPase subunit in the asymmetric unit. I4122 is a minimal, non-isomorphic supergroup of the four primitive tetragonal space groups, explaining the space-group ambiguity for this crystal.

Manipulation of an existing crystal form unexpectedly results in interwoven packing networks with pseudo-translational symmetry

Nonribosomal peptide synthetases (NRPSs) are multimodular enzymes that synthesize a myriad of diverse molecules. Tailoring domains have been co-opted into NRPSs to introduce further variety into nonribosomal peptide products. Linear gramicidin synthetase contains a unique formylation-tailoring domain in its initiation module (F-A-PCP). The structure of the F-A di-domain has previously been determined in a crystal form which had large solvent channels and no density for the minor Asub subdomain. An attempt was made to take advantage of this packing by removing the Asub subdomain from the construct (F-AΔsub) in order to produce a crystal that could accommodate the PCP domain. In the resulting crystal the original packing network was still present, but a second network with the same packing and almost no contact with the original network took the place of the solvent channels and changed the space group of the crystal.

Twinned CsLn2F7 compounds (Ln=Nd, Gd, Tb, Er, Yb): the role of a highly symmetrical cation lattice with an arrangement analogous to the Laves phase MgZn2

The occurrence of twinning can often be related to higher symmetrical structures. Fluorides are frequently twinned due to their close relation to high symmetry structures like fluoride, tysonite or pyrochlores. The series of compounds CsLn2F7 is no exception. We refined the structures of the twinned compounds with Ln=Nd, Gd, Tb, Er, Yb in space group P1121/b. An analysis of the pseudosymmetry of the resulting structures shows a highly symmetrical cation partial structure with a cation distribution similar to the one in the hexagonal Laves phase MgZn2. Several other compounds ALn2F7, which have been described in the literature, show a similar cation array. The diversity of different space groups which have been reported for ALn2F7 compounds can be better understood using group-subgroup relationships assuming the hypothetical structure of the cation array with space group P63/mmc as aristotype. Furthermore, the twinning is easily understood on the basis of the lost symmetry operations in the symmetry reduction from point group 6/mmm, e.g. to 2/m in the case of the CsLn2F7 compounds.

Molecular architecture of the human sperm IZUMO1 and egg JUNO fertilization complex

Fertilization is an essential biological process in sexual reproduction and comprises a series of molecular interactions between the sperm and egg. The fusion of the haploid spermatozoon and oocyte is the culminating event in mammalian fertilization, enabling the creation of a new, genetically distinct diploid organism. The merger of two gametes is achieved through a two-step mechanism in which the sperm protein IZUMO1 on the equatorial segment of the acrosome-reacted sperm recognizes its receptor, JUNO, on the egg surface. This recognition is followed by the fusion of the two plasma membranes. IZUMO1 and JUNO proteins are indispensable for fertilization, as constitutive knockdown of either protein results in mice that are healthy but infertile. Despite their central importance in reproductive medicine, the molecular architectures of these proteins and the details of their functional roles in fertilization are not known. Here we present the crystal structures of human IZUMO1 and JUNO in unbound and bound conformations. The human IZUMO1 structure exhibits a distinct boomerang shape and provides structural insights into the IZUMO family of proteins. Human IZUMO1 forms a high-affinity complex with JUNO and undergoes a major conformational change within its N-terminal domain upon binding to the egg-surface receptor. Our results provide insights into the molecular basis of sperm-egg recognition, cross-species fertilization, and the barrier to polyspermy, thereby promising benefits for the rational development of non-hormonal contraceptives and fertility treatments for humans and other mammals.

Structure of the Dcp2-Dcp1 mRNA-decapping complex in the activated conformation

The removal of the mRNA 5' cap (decapping) by Dcp2 shuts down translation and commits mRNA to full degradation. Dcp2 activity is enhanced by activator proteins such as Dcp1 and Edc1. However, owing to conformational flexibility, the active conformation of Dcp2 and the mechanism of decapping activation have remained unknown. Here, we report a 1.6-Å-resolution crystal structure of the Schizosaccharomyces pombe Dcp2-Dcp1 heterodimer in an unprecedented conformation that is tied together by an intrinsically disordered peptide from Edc1. In this ternary complex, an unforeseen rotation of the Dcp2 catalytic domain allows residues from both Dcp2 and Dcp1 to cooperate in RNA binding, thus explaining decapping activation by increased substrate affinity. The architecture of the Dcp2-Dcp1-Edc1 complex provides a rationale for the conservation of a sequence motif in Edc1 that is also present in unrelated decapping activators, thus indicating that the presently described mechanism of decapping activation is evolutionarily conserved.

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.

Atomic resolution structure of a chimeric DNA-RNA Z-type duplex in complex with Ba(2+) ions: a case of complicated multi-domain twinning

The self-complementary dCrGdCrGdCrG hexanucleotide, in which not only the pyrimidine/purine bases but also the ribo/deoxy sugars alternate along the sequence, was crystallized in the presence of barium cations in the form of a left-handed Z-type duplex. The asymmetric unit of the P21 crystal with a pseudohexagonal lattice contains four chimeric duplexes and 16 partial Ba(2+) sites. The chimeric (DNA-RNA)2 duplexes have novel patterns of hydration and exhibit a high degree of discrete conformational disorder of their sugar-phosphate backbones, which can at least partly be correlated with the fractional occupancies of the barium ions. The crystals of the DNA-RNA chimeric duplex in complex with Ba(2+) ions and also with Sr(2+) ions exhibit complicated twinning, which in combination with structural pseudosymmetry made structure determination difficult. The structure could be successfully solved by molecular replacement in space groups P1 and P21 but not in orthorhombic or higher symmetry and, after scrupulous twinning and packing analysis, was refined in space group P21 to an R and Rfree of 11.36 and 16.91%, respectively, using data extending to 1.09 Å resolution. With the crystal structure having monoclinic symmetry, the sixfold crystal twinning is a combination of threefold and twofold rotations. The paper describes the practical aspects of dealing with cases of complicated twinning and pseudosymmetry, and compares the available software tools for the refinement and analysis of such cases.

Two different centered monoclinic crystals of the E. coli outer-membrane protein OmpF originate from the same building block

Macromolecule crystal formation can be divided in two major steps: 1. the formation of a nucleus and 2. the growth of this nucleus into a full mature crystal. The latter is well described and understood, while the former remains elusive due to the difficulty to study it and is described by nucleation theories. Here we report the structure of the Escherichia coli outer membrane porin OmpF in two centered monoclinic space groups. Strikingly, the two crystals originate from the same building block, made of two trimers of OmpF interacting via their rough side. The different crystallization conditions trigger the formation of distinct arrangement of these building blocks, leading to the formation of translational non-crystallographic symmetry (tNCS) in one case, made possible by the loose lateral packing mediated by detergents. In light of nucleation theories, these results allow us to speculate that these two crystals originate from nuclei made of either clusters of building blocks, or already forming columns that later associate laterally using detergents as glue.

Molecular pharmacodynamics of emixustat in protection against retinal degeneration

Emixustat is a visual cycle modulator that has entered clinical trials as a treatment for age-related macular degeneration (AMD). This molecule has been proposed to inhibit the visual cycle isomerase RPE65, thereby slowing regeneration of 11-cis-retinal and reducing production of retinaldehyde condensation byproducts that may be involved in AMD pathology. Previously, we reported that all-trans-retinal (atRAL) is directly cytotoxic and that certain primary amine compounds that transiently sequester atRAL via Schiff base formation ameliorate retinal degeneration. Here, we have shown that emixustat stereoselectively inhibits RPE65 by direct active site binding. However, we detected the presence of emixustat-atRAL Schiff base conjugates, indicating that emixustat also acts as a retinal scavenger, which may contribute to its therapeutic effects. Using agents that lack either RPE65 inhibitory activity or the capacity to sequester atRAL, we assessed the relative importance of these 2 modes of action in protection against retinal phototoxicity in mice. The atRAL sequestrant QEA-B-001-NH2 conferred protection against phototoxicity without inhibiting RPE65, whereas an emixustat derivative incapable of atRAL sequestration was minimally protective, despite direct inhibition of RPE65. These data indicate that atRAL sequestration is an essential mechanism underlying the protective effects of emixustat and related compounds against retinal phototoxicity. Moreover, atRAL sequestration should be considered in the design of next-generation visual cycle modulators.

Catalytic mechanism of a retinoid isomerase essential for vertebrate vision

Visual function in vertebrates is dependent on the membrane-bound retinoid isomerase RPE65, an essential component of the retinoid cycle pathway that regenerates 11-cis-retinal for rod and cone opsins. The mechanism by which RPE65 catalyzes stereoselective retinoid isomerization has remained elusive because of uncertainty about how retinoids bind to its active site. Here we present crystal structures of RPE65 in complex with retinoid-mimetic compounds, one of which is in clinical trials for the treatment of age-related macular degeneration. The structures reveal the active site retinoid-binding cavity located near the membrane-interacting surface of the enzyme as well as an Fe-bound palmitate ligand positioned in an adjacent pocket. With the geometry of the RPE65-substrate complex clarified, we delineate a mechanism of catalysis that reconciles the extensive biochemical and structural research on this enzyme. These data provide molecular foundations for understanding a key process in vision and pharmacological inhibition of RPE65 with small molecules.

Structural Basis for the Inhibition of Helicobacter pylori α-Carbonic Anhydrase by Sulfonamides

Periplasmic α-carbonic anhydrase of Helicobacter pylori (HpαCA), an oncogenic bacterium in the human stomach, is essential for its acclimation to low pH. It catalyses the conversion of carbon dioxide to bicarbonate using Zn(II) as the cofactor. In H. pylori, Neisseria spp., Brucella suis and Streptococcus pneumoniae this enzyme is the target for sulfonamide antibacterial agents. We present structural analysis correlated with inhibition data, on the complexes of HpαCA with two pharmacological inhibitors of human carbonic anhydrases, acetazolamide and methazolamide. This analysis reveals that two sulfonamide oxygen atoms of the inhibitors are positioned proximal to the putative location of the oxygens of the CO₂ substrate in the Michaelis complex, whilst the zinc-coordinating sulfonamide nitrogen occupies the position of the catalytic water molecule. The structures are consistent with acetazolamide acting as site-directed, nanomolar inhibitors of the enzyme by mimicking its reaction transition state. Additionally, inhibitor binding provides insights into the channel for substrate entry and product exit. This analysis has implications for the structure-based design of inhibitors of bacterial carbonic anhydrases.

The solvent component of macromolecular crystals

The mother liquor from which a biomolecular crystal is grown will contain water, buffer molecules, native ligands and cofactors, crystallization precipitants and additives, various metal ions, and often small-molecule ligands or inhibitors. On average, about half the volume of a biomolecular crystal consists of this mother liquor, whose components form the disordered bulk solvent. Its scattering contributions can be exploited in initial phasing and must be included in crystal structure refinement as a bulk-solvent model. Concomitantly, distinct electron density originating from ordered solvent components must be correctly identified and represented as part of the atomic crystal structure model. Herein, are reviewed (i) probabilistic bulk-solvent content estimates, (ii) the use of bulk-solvent density modification in phase improvement, (iii) bulk-solvent models and refinement of bulk-solvent contributions and (iv) modelling and validation of ordered solvent constituents. A brief summary is provided of current tools for bulk-solvent analysis and refinement, as well as of modelling, refinement and analysis of ordered solvent components, including small-molecule ligands.

ANS complex of St John's wort PR-10 protein with 28 copies in the asymmetric unit: a fiendish combination of pseudosymmetry with tetartohedral twinning

Hyp-1, a pathogenesis-related class 10 (PR-10) protein from St John's wort (Hypericum perforatum), was crystallized in complex with the fluorescent probe 8-anilino-1-naphthalene sulfonate (ANS). The highly pseudosymmetric crystal has 28 unique protein molecules arranged in columns with sevenfold translational noncrystallographic symmetry (tNCS) along c and modulated X-ray diffraction with intensity crests at l = 7n and l = 7n ± 3. The translational NCS is combined with pseudotetragonal rotational NCS. The crystal was a perfect tetartohedral twin, although detection of twinning was severely hindered by the pseudosymmetry. The structure determined at 2.4 Å resolution reveals that the Hyp-1 molecules (packed as β-sheet dimers) have three novel ligand-binding sites (two internal and one in a surface pocket), which was confirmed by solution studies. In addition to 60 Hyp-1-docked ligands, there are 29 interstitial ANS molecules distributed in a pattern that violates the arrangement of the protein molecules and is likely to be the generator of the structural modulation. In particular, whenever the stacked Hyp-1 molecules are found closer together there is an ANS molecule bridging them.

On the validation of crystallographic symmetry and the quality of structures

In 2008, Zwart and colleagues observed that the fraction of the structures deposited in the PDB alleged to have "pseudosymmetry" or "special noncrystallographic symmetry" (NCS) was about 6%, and that this percentage was rising annually. A few years later, Poon and colleagues found that 2% of all the crystal structures in the PDB belonged to higher symmetry space groups than those assigned to them. Here, I report an analysis of the X-ray diffraction data deposited for this class of structures, which shows that most of the "pseudosymmetry" and "special NCS" that has been reported is in fact true crystallographic symmetry (CS). This distinction is important because the credibility of crystal structures depends heavily on quality control statistics such as Rfree that are unreliable when they are computed incorrectly, which they often are when CS is misidentified as "special NCS" or "pseudosymmetry". When mistakes of this kind are made, artificially low values of Rfree can give unjustified confidence in the accuracy of the reported structures.

Continuous mutual improvement of macromolecular structure models in the PDB and of X-ray crystallographic software: the dual role of deposited experimental data

Accurate crystal structures of macromolecules are of high importance in the biological and biomedical fields. Models of crystal structures in the Protein Data Bank (PDB) are in general of very high quality as deposited. However, methods for obtaining the best model of a macromolecular structure from a given set of experimental X-ray data continue to progress at a rapid pace, making it possible to improve most PDB entries after their deposition by re-analyzing the original deposited data with more recent software. This possibility represents a very significant departure from the situation that prevailed when the PDB was created, when it was envisioned as a cumulative repository of static contents. A radical paradigm shift for the PDB is therefore proposed, away from the static archive model towards a much more dynamic body of continuously improving results in symbiosis with continuously improving methods and software. These simultaneous improvements in methods and final results are made possible by the current deposition of processed crystallographic data (structure-factor amplitudes) and will be supported further by the deposition of raw data (diffraction images). It is argued that it is both desirable and feasible to carry out small-scale and large-scale efforts to make this paradigm shift a reality. Small-scale efforts would focus on optimizing structures that are of interest to specific investigators. Large-scale efforts would undertake a systematic re-optimization of all of the structures in the PDB, or alternatively the redetermination of groups of structures that are either related to or focused on specific questions. All of the resulting structures should be made generally available, along with the precursor entries, with various views of the structures being made available depending on the types of questions that users are interested in answering.

Click modification of RNA at adenosine: structure and reactivity of 7-ethynyl- and 7-triazolyl-8-aza-7-deazaadenosine in RNA

Ribonucleoside analogues bearing terminal alkynes, including 7-ethynyl-8-aza-7-deazaadenosine (7-EAA), are useful for RNA modification applications. However, although alkyne- and triazole-bearing ribonucleosides are in widespread use, very little information is available on the impact of these modifications on RNA structure. By solving crystal structures for RNA duplexes containing these analogues, we show that, like adenosine, 7-EAA and a triazole derived from 7-EAA base pair with uridine and are well-accommodated within an A-form helix. We show that copper-catalyzed azide/alkyne cycloaddition (CuAAC) reactions with 7-EAA are sensitive to the RNA secondary structure context, with single-stranded sites reacting faster than duplex sites. 7-EAA and its triazole products are recognized in RNA template strands as adenosine by avian myoblastosis virus reverse transcriptase. In addition, 7-EAA in RNA is a substrate for an active site mutant of the RNA editing adenosine deaminase, ADAR2. These studies extend our understanding of the impact of these novel nucleobase analogues and set the stage for their use in probing RNA structure and metabolism.

Purification, crystallization and room-temperature X-ray diffraction of inositol dehydrogenase LcIDH2 from Lactobacillus casei BL23

Lactobacillus casei BL23 contains two genes, iolG1 and iolG2, homologous with inositol dehydrogenase encoding genes from many bacteria. Inositol dehydrogenase catalyzes the oxidation of inositol with concomitant reduction of NAD+. The protein encoded by iolG2, LcIDH2, has been purified to homogeneity, crystallized and cryoprotected for diffraction at 77 K. The crystals had a high mosaicity and poor processing statistics. Subsequent diffraction measurements were performed without cryoprotectant at room temperature. These crystals were radiation-resistant and a full diffraction data set was collected at room temperature to 1.6 Å resolution.

Ten years of probabilistic estimates of biocrystal solvent content: new insights via nonparametric kernel density estimate

The probabilistic estimate of the solvent content (Matthews probability) was first introduced in 2003. Given that the Matthews probability is based on prior information, revisiting the empirical foundation of this widely used solvent-content estimate is appropriate. The parameter set for the original Matthews probability distribution function employed in MATTPROB has been updated after ten years of rapid PDB growth. A new nonparametric kernel density estimator has been implemented to calculate the Matthews probabilities directly from empirical solvent-content data, thus avoiding the need to revise the multiple parameters of the original binned empirical fit function. The influence and dependency of other possible parameters determining the solvent content of protein crystals have been examined. Detailed analysis showed that resolution is the primary and dominating model parameter correlated with solvent content. Modifications of protein specific density for low molecular weight have no practical effect, and there is no correlation with oligomerization state. A weak, and in practice irrelevant, dependency on symmetry and molecular weight is present, but cannot be satisfactorily explained by simple linear or categorical models. The Bayesian argument that the observed resolution represents only a lower limit for the true diffraction potential of the crystal is maintained. The new kernel density estimator is implemented as the primary option in the MATTPROB web application at http://www.ruppweb.org/mattprob/.