Bulk-solvent Model Research Articles

Accounting for nonuniformity of bulk-solvent: A mosaic model.

A flat mask-based model is almost universally used in macromolecular crystallography to account for disordered (bulk) solvent. This model assumes any voxel of the crystal unit cell that is not occupied by the atomic model is occupied by the solvent. The properties of this solvent are assumed to be exactly the same across the whole volume of the unit cell. While this is a reasonable approximation in practice, there are a number of scenarios where this model becomes suboptimal. In this work, we enumerate several of these scenarios and describe a new generalized approach to modeling the bulk-solvent which we refer to as mosaic bulk-solvent model. The mosaic bulk-solvent model allows nonuniform features of the solvent in the crystal to be accounted for in a computationally efficient way. It is implemented in the computational crystallography toolbox and the Phenix software.

Universal parameters of bulk-solvent masks.

The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Å for the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox (CCTBX) and in Phenix as the default choice.

Better bulk-solvent models can improve model-to-data fit

Better bulk-solvent models can improve model-to-data fit

Polder maps: improving OMIT maps by excluding bulk solvent.

The crystallographic maps that are routinely used during the structure-solution workflow are almost always model-biased because model information is used for their calculation. As these maps are also used to validate the atomic models that result from model building and refinement, this constitutes an immediate problem: anything added to the model will manifest itself in the map and thus hinder the validation. OMIT maps are a common tool to verify the presence of atoms in the model. The simplest way to compute an OMIT map is to exclude the atoms in question from the structure, update the corresponding structure factors and compute a residual map. It is then expected that if these atoms are present in the crystal structure, the electron density for the omitted atoms will be seen as positive features in this map. This, however, is complicated by the flat bulk-solvent model which is almost universally used in modern crystallographic refinement programs. This model postulates constant electron density at any voxel of the unit-cell volume that is not occupied by the atomic model. Consequently, if the density arising from the omitted atoms is weak then the bulk-solvent model may obscure it further. A possible solution to this problem is to prevent bulk solvent from entering the selected OMIT regions, which may improve the interpretative power of residual maps. This approach is called a polder (OMIT) map. Polder OMIT maps can be particularly useful for displaying weak densities of ligands, solvent molecules, side chains, alternative conformations and residues both in terminal regions and in loops. The tools described in this manuscript have been implemented and are available in PHENIX.

New bulk-solvent model improves model-to-data fit and facilitates map interpretation

New bulk-solvent model improves model-to-data fit and facilitates map interpretation

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.

Bulk-solvent and overall scaling revisited: faster calculations, improved results.

A fast and robust method for determining the parameters for a flat (mask-based) bulk-solvent model and overall scaling in macromolecular crystallographic structure refinement and other related calculations is described. This method uses analytical expressions for the determination of optimal values for various scale factors. The new approach was tested using nearly all entries in the PDB for which experimental structure factors are available. In general, the resulting R factors are improved compared with previously implemented approaches. In addition, the new procedure is two orders of magnitude faster, which has a significant impact on the overall runtime of refinement and other applications. An alternative function is also proposed for scaling the bulk-solvent model and it is shown that it outperforms the conventional exponential function. Similarly, alternative methods are presented for anisotropic scaling and their performance is analyzed. All methods are implemented in the Computational Crystallography Toolbox (cctbx) and are used in PHENIX programs.

On the application of structure-specific bulk-solvent models

It is often discussed, mainly in connection with the rather high macromolecular R factors, that the treatment of bulk solvent in macromolecular refinement may lack the detail needed for modelling the solvent environment of molecules as complex as proteins and nucleic acids. This line of thought directly leads to the hypothesis that improvements in the modelling of the bulk solvent may substantially improve the agreement between the experimental data and the crystallographic models. Here, part of this hypothesis is being tested through the construction, via molecular-dynamics simulations, of a highly detailed, physics-based, structure-specific and crystallographic data-agnostic model of the bulk solvent of a known crystal structure. The water-distribution map obtained from the simulation is converted (after imposing space-group symmetry) to a constant (but scalable) partial structure factor which is then added in a re-refinement of the crystal structure. Compared with the simple Babinet-based correction, a reduction of the totally cross-validated free R value by 0.3% is observed. The implications and possible interpretations of these results are discussed.

A smooth and differentiable bulk-solvent model for macromolecular diffraction.

Inclusion of low-resolution data in macromolecular crystallography requires a model for the bulk solvent. Previous methods have used a binary mask to accomplish this, which has proven to be very effective, but the mask is discontinuous at the solute-solvent boundary (i.e. the mask value jumps from zero to one) and is not differentiable with respect to atomic parameters. Here, two algorithms are introduced for computing bulk-solvent models using either a polynomial switch or a smoothly thresholded product of Gaussians, and both models are shown to be efficient and differentiable with respect to atomic coordinates. These alternative bulk-solvent models offer algorithmic improvements, while showing similar agreement of the model with the observed amplitudes relative to the binary model as monitored using R, R(free) and differences between experimental and model phases. As with the standard solvent models, the alternative models improve the agreement primarily with lower resolution (>6 A) data versus no bulk solvent. The models are easily implemented into crystallographic software packages and can be used as a general method for bulk-solvent correction in macromolecular crystallography.

Theoretical Study on the Redox Cycle of Bovine Glutathione Peroxidase GPx1: pKa Calculations, Docking, and Molecular Dynamics Simulations.

Three approaches of computational chemistry [quantum mechanics (QM) calculations, docking, and molecular dynamics (MD) simulations] were used to investigate the redox cycle of bovine erythrocyte glutathione peroxidase from class 1 (GPx1, EC 1.11.1.9). The pKa calculations for two redox states of the active-site selenocysteine of GPx1 (selenol, Sec45-SeH, and selenenic acid, Sec45-SeOH) were estimated using a bulk solvent model (B3LYP-IEFPCM and B3LYP-CPCM-COSMO-RS). The calculated pKa values of Sec45-SeH and Sec45-SeOH were corrected via a simple linear fit to a training set of organoselenium compounds, which consisted of aliphatic selenols and aromatic selenenic acids with available experimental pKa values. Based on docking calculations, binding sites for both molecules of the cofactor glutathione (GSH) are described. MD simulations on the dimer of GPx1 have been performed for all chemical states of the redox cycle: without GSH and with one or two molecules of GSH bound at the active site. Conformational analyses of MD trajectories indicate high mobility of the Arg177 and His79 residues. These residues can approach the vicinity of Sec45 and take part in the catalytic mechanism. On the basis of the calculated data, new atomistic details for a generally accepted mechanism of GPx1 are proposed.

Mechanism of nitric oxide induced deamination of cytosine

A five-step mechanism is proposed for the NO -induced deamination of cytosine. It has been investigated using DFT calculations, including both explicit water molecules and a bulk solvent model to mimic an aqueous environment. According to this mechanism, cytosine first undergoes tautomerization with the assistance of a water molecule from the bulk. A NO(+) cation produced by the autooxidation of NO is subsequently added to the exocyclic imino group of the cytosine imine tautomer. The resulting adduct is able to undergo a tautomerization step with the participation of a water molecule to produce a cytosine in which a -N(2)OH group is attached to carbon C4. Protonation of the oxygen of the latter gives a water molecule which dissociates instantaneously, leading to a pyrimidinic diazonium cation. This constitutes the rate-determining step of the mechanism with an activation free energy of 92.6 kJ mol(-1). The last step, which is highly exergonic, represents the driving force of the reaction. It is the substitution of the -N(2)(+) terminal group by a water molecule which simultaneously allows the transfer of one of the two hydrogens to the bulk. Thus, the two products of the reaction consist of a nitrogen molecule and the enol tautomer of uracil in equilibrium with the keto form.

Version 1.2 of the Crystallography and NMR system

Version 1.2 of the software system, termed Crystallography and NMR system (CNS), for crystallographic and NMR structure determination has been released. Since its first release, the goals of CNS have been (i) to create a flexible computational framework for exploration of new approaches to structure determination, (ii) to provide tools for structure solution of difficult or large structures, (iii) to develop models for analyzing structural and dynamical properties of macromolecules and (iv) to integrate all sources of information into all stages of the structure determination process. Version 1.2 includes an improved model for the treatment of disordered solvent for crystallographic refinement that employs a combined grid search and least-squares optimization of the bulk solvent model parameters. The method is more robust than previous implementations, especially at lower resolution, generally resulting in lower R values. Other advances include the ability to apply thermal factor sharpening to electron density maps. Consistent with the modular design of CNS, these additions and changes were implemented in the high-level computing language of CNS.

A robust bulk-solvent correction and anisotropic scaling procedure.

A reliable method for the determination of bulk-solvent model parameters and an overall anisotropic scale factor is of increasing importance as structure determination becomes more automated. Current protocols require the manual inspection of refinement results in order to detect errors in the calculation of these parameters. Here, a robust method for determining bulk-solvent and anisotropic scaling parameters in macromolecular refinement is described. The implementation of a maximum-likelihood target function for determining the same parameters is also discussed. The formulas and corresponding derivatives of the likelihood function with respect to the solvent parameters and the components of anisotropic scale matrix are presented. These algorithms are implemented in the CCTBX bulk-solvent correction and scaling module.

Refinement of severely incomplete structures with maximum likelihood inBUSTER–TNT

BUSTER-TNT is a maximum-likelihood macromolecular refinement package. BUSTER assembles the structural model, scales observed and calculated structure-factor amplitudes and computes the model likelihood, whilst TNT handles the stereochemistry and NCS restraints/constraints and shifts the atomic coordinates, B factors and occupancies. In real space, in addition to the traditional atomic and bulk-solvent models, BUSTER models the parts of the structure for which an atomic model is not yet available ('missing structure') as low-resolution probability distributions for the random positions of the missing atoms. In reciprocal space, the BUSTER structure-factor distribution in the complex plane is a two-dimensional Gaussian centred around the structure factor calculated from the atomic, bulk-solvent and missing-structure models. The errors associated with these three structural components are added to compute the overall spread of the Gaussian. When the atomic model is very incomplete, modelling of the missing structure and the consistency of the BUSTER statistical model help structure building and completion because (i) the accuracy of the overall scale factors is increased, (ii) the bias affecting atomic model refinement is reduced by accounting for some of the scattering from the missing structure, (iii) the addition of a spatial definition to the source of incompleteness improves on traditional Luzzati and sigmaA-based error models and (iv) the program can perform selective density modification in the regions of unbuilt structure alone.

Crystal structure of hypothetical protein PH0642 from Pyrococcus horikoshii at 1.6A resolution.

Crystal structure of hypothetical protein PH0642 from Pyrococcus horikoshii at 1.6A resolution.

The Structure of the AXH Domain of Spinocerebellar Ataxin-1

Spinocerebellar ataxia type 1 is a late-onset neurodegenerative disease caused by the expansion of a CAG triplet repeat in the SCA1 gene. This results in the lengthening of a polyglutamine tract in the gene product ataxin-1. This produces a toxic gain of function that results in specific neuronal death. A region in ataxin-1, the AXH domain, exhibits significant sequence similarity to the transcription factor HBP1. This region of the protein has been implicated in RNA binding and self-association. We have determined the crystal structure of the AXH domain of ataxin-1. The AXH domain is dimeric and contains an OB-fold, a structural motif found in many oligonucleotide-binding proteins, supporting its proposed role in RNA binding. By structure comparison with other proteins that contain an OB-fold, a putative RNA-binding site has been identified. We also identified a cluster of charged surface residues that are well conserved among AXH domains. These residues may constitute a second ligand-binding surface, suggesting that all AXH domains interact with a common yet unidentified partner.

Monomeric Structure of the Human EphB2 Sterile α Motif Domain

The sterile alpha motif (SAM) domain is a protein module found in many diverse signaling proteins. SAM domains in some systems have been shown to self-associate. Previous crystal structures of an EphA4-SAM domain dimer (Stapleton, D., Balan, I., Pawson, T., and Sicheri, F. (1999) Nat. Struct. Biol. 6, 44-49) and a possible EphB2-SAM oligomer (Thanos, C. D., Goodwill, K. E., and Bowie, J. U. (1999) Science 283, 833-836) both revealed large interfaces comprising an exchange of N-terminal peptide arms. Within the arm, a conserved hydrophobic residue (Tyr-8 in the EphB2-SAM structure or Phe-910 in the EphA4-SAM structure) is anchored into a hydrophobic cleft on a neighboring molecule. Here we have solved a new crystal form of the human EphB2-SAM domain that has the same overall SAM domain fold yet has no substantial intermolecular contacts. In the new structure, the N-terminal peptide arm of the EphB2-SAM domain protrudes out from the core of the molecule, leaving both the arm (including Tyr-8) and the hydrophobic cleft solvent-exposed. To verify that Tyr-8 is solvent-exposed in solution, we made a Tyr-8 to Ala-8 mutation and found that the EphB2-SAM domain structure and stability were only slightly altered. These results suggest that Tyr-8 is not part of the hydrophobic core of the EphB2-SAM domain and is conserved for functional reasons. Cystallographic evidence suggests a possible role for the N-terminal arm in oligomerization. In the absence of a direct demonstration of biological relevance, however, the functional role of the N-terminal arm remains an open question.

Assessment of bulk solvent models by cross-validation

Assessment of bulk solvent models by cross-validation