Macromolecular Crystal Structures Research Articles

Modelling prior distributions of atoms for macromolecular refinement and completion

Until modelling is complete, macromolecular structures are refined in the absence of a model for some of the atoms in the crystal. Techniques for defining positional probability distributions of atoms, and using them to model the missing part of a macromolecular crystal structure and the bulk solvent, are described. The starting information may consist of either a tentative structural model for the missing atoms or an electron-density map. During structure completion and refinement, the use of probability distributions enables the retention of low-resolution phase information while avoiding premature commitment to uncertain higher resolution features. Homographic exponential modelling is proposed as a flexible, compact and robust parametrization that proves to be superior to a traditional Fourier expansion in approximating a model protein envelope. The homographic exponential model also has potential applications to ab initio phasing of Fourier amplitudes associated with macromolecular envelopes.

Current Methods and Optimization Algorithms for the Refinement of X-Ray Crystal Structures

Optimization algorithms and other techniques used for the crystallographic refinement of both small molecule and macromolecular X-ray crystal structures are reviewed in this work. Emphasis is made on the advantages and disadvantages of every method in its application to the refinement process of different problems, as well as on their actual implementation in current program packages. A description of the most basic (first-level) algorithms based on physical grounds, such as maximum-likelihood, least-squares, molecular dynamics, maximum-entropy, Fourier and graphical methods, and holographic methods, is followed by a second-level approach, including Newton methods, simulated annealing, and gradient methods, among others, and finally by a third-level study which includes matrix decompositions and iterative methods for the solution of the resulting linear systems of equations. In addition, by descending to the most basic mathematical and physical level, connections with other disciplines that use almost the same tools are easily made, showing not only the interdisciplinarity of crystallography but also the flow of information between different sciences.

Messages from ultrahigh resolution crystal structures

The ever growing availability of macromolecular crystal structures determined at atomic resolution has now reached a critical size, making it possible to obtain statistically unbiased data on both protein stereochemistry and the validity of the parameters used in their refinement. Besides the determination of the precise geometry of proteins and their active sites, high resolution structures have made it possible to check the application of normal mode calculations, to calculate charge density distributions and to analyze hydration shells around protein molecules. Even if only a few structures involve protein complexes, either with ligands or prosthetic groups, the information obtained in these cases is of great interest for obtaining the physical parameters of these interactions.

On the use of strong Patterson function signals in many-body molecular replacement.

The symmetry elements detected by the self-rotation and the Patterson functions, associated to strong correlations between the positions of the molecules in the asymmetric unit, are used to reduce the effective number of independent bodies to be located by the molecular replacement method. A distinction is made between 'frustrated' crystallographic symmetries, i.e. those that are almost crystallographic ones, and 'standard' non-crystallographic symmetries, which are taken into account by specific techniques. These have been successfully applied to many-body macromolecular crystal structures, with important savings in time and computational effort.

32] Patterson correlation searches and refinement

Publisher Summary This chapter discusses the Patterson correlation searches and refinement. The Patterson searches or molecular replacement has proved to be an effective means of solving macromolecular crystal structures using the knowledge of similar structures. A model is obtained by sequence similarity searches using the database of known crystal and solution nuclear magnetic resonance (NMR) structures. This search model is first rotated and then translated in the unit cell of the target crystal to obtain a maximum fit between observed- and calculated-diffraction data. If the correct orientation and position are found, the model can serve as a starting point for model rebuilding and refinement. The chapter focuses on the Patterson searches of crystal structures, with particular emphasis on multidomain macromolecular complexes and independent molecules related by noncrystallographic symmetry. The chapter discusses the algorithms that are based on the Patterson correlation coefficient, that is, the direct rotation function, the Patterson correlation refinement, and the Patterson correlation translation search. The chapter compares the performance of the direct rotation function with that of other most commonly used functions. The chapter discusses the radius of convergence of the Patterson correlation refinement and demonstrates its effect on the subsequent translation search. The effective uses of partial model information at the rotation, translation, and refinement stages are discussed in the chapter. A general strategy for applying these computational tools to difficult molecular replacement cases is also discussed in the chapter.

23] Bayesian statistical viewpoint on structure determination: Basic concepts and examples

This chapter discusses the Bayesian statistical viewpoint for the determination of macromolecular crystal structures. Its application to ab initio phasing at typical macromolecular resolutions requires in addition the incorporation of stereochemical information into structure factor statistics. The concepts and methods of Bayesian statistics are designed to enable the numerical representation (via probabilities) and the bookkeeping of various states of incomplete knowledge about a system, especially of the transition from an initial (or prior) state of knowledge toward subsequent (or posterior) states as new information acquired through observations is incorporated by means of Bayes' theorem. The concepts and methods of the Bayesian statistics provide a natural framework for a unified approach combining a statistical scheme for describing in a quantitatively correct fashion the ambiguities present at each stage of a structure determination, encompassing all current methods, together with a general exploratory mechanism for resolving these ambiguities by systematically forming and evaluating multiple hypotheses about the missing information.

Diffraction data deposition

A formal discussion of the archival journal requirements for data deposition was held at the International Seminar-cum-School on Macromolecular Crystallographic Data at Calcutta, India in November 1995.The current policy of the International Union of Crystallography (IUCr) is that on publication of a crystal structure determination of a macromolecule the atomic parameters used or represented in the publication must be deposited in the Brookhaven Protein Data Bank. The deposition of structure amplitudes is recommended but not obligatory. The policy provides crystallographers with the option to delay the release of atomic parameters for one year and of structure amplitudes for up to four years from the date of publication. Participants strongly supported this policy and felt it should be strictly applied by the journals.Recent developments in X-ray crystallographic experimental and refinement techniques and the huge expansion in computing power and networking, however, necessitate the review of deposition arrangements.It was noted that the new validation procedures are much more effective but require the experimental structure amplitudes as well as the atomic parameters. In addition, the technical arrangements for deposition, analysis and validation of macromolecular crystal structures are now much easier.We consider it vital for macromolecular crystallographers to respond to these developments in their deposition practices. We recommend, therefore, that publication of macromolecular crystal structures should be accompanied by deposition of atomic parameters and also structure amplitudes. Amongst the many reasons identified for this practice, the following two are critical.(1) Rigorous validation of the structure determination results can only be carried out using both atomic parameters and experimental structure amplitudes. It is important that journals ensure referees have sufficient information to prevent incorrect structures being published.(2) Archiving of these data will ensure that they are not lost. There were numerous reports at this meeting of data being lost. This probably reflects a widespread problem in the crystallographic community.

The direct rotation function: Patterson correlation search applied to molecular replacement.

Most rotation functions try to achieve maximal correlation between two Patterson functions by systematically rotating one and computing the overlap with the other. In contrast, the direct rotation function rotates a search model relative to the crystal unit cell and evaluates the linear correlation coefficient (Patterson correlation, PC) between squared normalized structure-factor amplitudes of the observed and calculated diffraction data. Structure factors are calculated from the rotated search model in a P1 unit cell identical to that of the target crystal. PC makes use of all self-Patterson vectors of the search model. A comparison of the direct rotation function, a real-space rotation function, and a fast rotation function suggests that the direct rotation function provides a considerable enhancement of the signal-to-noise ratio compared to other two. Combined with PC refinement, the direct rotation function was successful in solving multidomain macromolecular crystal structures.

Hydrogen bonding motifs of protein side chains: descriptions of binding of arginine and amide groups.

The modes of hydrogen bonding of arginine, asparagine, and glutamine side chains and of urea have been examined in small-molecule crystal structures in the Cambridge Structural Database and in crystal structures of protein-nucleic acid and protein-protein complexes. Analysis of the hydrogen bonding patterns of each by graph-set theory shows three patterns of rings (R) with one or two hydrogen bond acceptors and two donors and with eight, nine, or six atoms in the ring, designated R2(2)(8), R2(2)(9), and R1(2)(6). These three patterns are found for arginine-like groups and for urea, whereas only the first two patterns R2(2)(8) and R2(2)(9) are found for asparagine- and glutamine-like groups. In each case, the entire system is planar within 0.7 A or less. On the other hand, in macromolecular crystal structures, the hydrogen bonding patterns in protein-nucleic acid complexes between the nucleic acid base and the protein are all R2(2)(9), whereas hydrogen bonding between Watson-Crick-like pairs of nucleic acid bases is R2(2)(8). These two hydrogen bonding arrangements [R2(2)(9)] and R2(2)(8)] are predetermined by the nature of the groups available for hydrogen bonding. The third motif identified, R1(2)(6), involves hydrogen bonds that are less linear than in the other two motifs and is found in proteins.

Protein Hydration Observed by X-ray Diffraction: Solvation Properties of Penicillopepsin and Neuraminidase Crystal Structures

Solvation in macromolecular crystal structures was studied by analyzing X-ray diffraction data of two proteins, penicillopepsin and neuraminidase. The quality of several solvent models was assessed by complete cross-validation in order to prevent overfitting the diffraction data. Radial solvent distribution functions were computed from electron density maps using phases obtained from multiple isomorphous replacement and from the protein's atomic model combined with the best solvent model. Distribution functions were computed around hydrophilic and hydrophobic groups on the protein's surface. Averaging of the distribution functions was performed in order to reduce the influence of noise. The first solvation shell is characterized by a peak in the average distribution functions. At 1·8 Å resolution, polar groups show a sharp peak while non-polar groups show a broad one. The distinction between hydrophobic and hydrophilic solvation sites is lost when using lower resolution (2·8 Å) diffraction data. Higher-order solvation shells are not observed in the average distribution functions. We hope that site-specific radial distribution functions obtained from high-quality diffraction data will produce a picture of macromolecular solvation consistent with available experimental data and computational results.

Comparison of real space and reciprocal space criteria to assess the accuracy of macromolecular crystal structures

Comparison of real space and reciprocal space criteria to assess the accuracy of macromolecular crystal structures

Entropy maximization constrained by solvent flatness: a new method for macromolecular phase extension and map improvement.

A practical generally applicable procedure for exponential modeling to maximum likelihood of macromolecular data sets constrained by a moderately large basis set of reliable phases and a molecular envelope is described, based on the computer program MICE [Bricogne & Gilmore (1990). Acta Cryst. A46, 284-297]. Procedures were first tested with simulated data sets. Exact and randomly perturbed amplitudes and phases were generated, together with a known envelope for solvent-free protein and for protein in an electron-dense crystal mother liquor typical of many real protein crystals. These experiments established useful guidelines and values for various parameters. Tests with basis sets chosen from the largest amplitudes indicate that exponential models with considerable correct extrapolated phase and amplitude information can be constructed from as few as 16% of the total number of reflections, with mean phase errors of about 30 degrees, at resolution limits of either 5 or 3 A. When the shape of the solvent channels in macromolecular crystals is known, it offers an important additional source of information. MICE was, therefore, adapted to average the density outside the molecular boundary defined by an input envelope. This flattening process imposes a uniform density distribution in solvent-filled channels as an additional constraint on the exponential model and is analogous to the treatment of solvent in conventional solvent flattening. Experimental data for cytidine deaminase, a structure recently solved by making extensive use of conventional solvent flattening, provides an example of the performance of maximum-entropy methods in a real situation and a compelling comparison of this method to standard procedures. Exponential models of the electron density constrained by the most reliable phases obtained by multiple isomorphous replacement with anomalous scattering (MIRAS) (figure of merit > 0.7, representing 34% of the total number of reflections) and by the envelope give rise to centroid electron-density maps which are quantitatively superior by numerous statistical criteria to conventionally solvent-flattened density. Similarity of these maps to the 2F(obs) - F(calc) map calculated with phases obtained after crystallographic refinement of the model implies that maximum-entropy extrapolation provides better phases for the remaining 66% of the reflections than the original centroid MIRAS distributions. Importantly, the solvent-flattened electron density, although it did permit interpretation of the map which was not readily accomplished with the MIRAS map, contains substantial errors. It is proposed that errors of this sort may account for previously noted deficiencies of the solvent-flattening method [Fenderson, Herriott & Adman (1990). J. Appl. Cryst. 23, 115-131] and for the occasional tendency of incorrect interpretations to be 'locked in' by crystallographic refinement [Brändén & Jones (1990). Nature (London), 343, 687-689, and references cited therein]. Solvent flattening with combined maximization of entropy and likelihood represents a phase-refinement path independent of atomic models, using the experimental amplitudes and the most reliable phases. It should, therefore, become a valuable and generally useful procedure in macromolecular crystal structure determination.

Model bias in macromolecular crystal structures

Reduction of model bias in macromolecular crystallography through various omit-map techniques has been investigated. The two cases studied were the p21 protein complexed with GDP at 2.25 Å resolution and the AN02 Fab fragment of an anti-dinitrophenyl-spin-label murine monoclonal antibody complexed with its hapten at 2.9 Å resolution. In the former case, the correct model was compared to a partially incorrect model consisting of an exchanged pair of β strands along with rearrangement of the connecting loops whereas, in the latter case, the correct placement of an active-site tryptophan side chain was compared to an incorrect rotamer conformation. Partial structures were created by omission of spherical regions around the incorrect region. Omit maps without refinement of the partial structure showed a large degree of model bias. Model bias could be reduced significantly by refinement of the partial structure. Simulated-annealing refinement of the partial structure showed the best results, followed by conjugate-gradient minimization with or without prior randomization of the partial structure. To avoid compensation for missing atoms during simulated-annealing refinement of the partial structure, a suitable `boundary' region was restrained to the starting coordinates. Model bias removal by iterative density modification was not successful in that it reduced density for both the correct and incorrect conformations.

Isomorphous replacement with optimized anomalous scattering applied to protein crystallography

Isomorphous replacement is an essential technique for the de novo solution of macromolecular crystal structures. The use of the anomalous-dispersion effect of the heavy atom in the derivative leads to the acronyms SIRAS or MIRAS (single or multiple isomorphous replacement with anomalous scattering) as the term for the phase determination method. Synchrotron radiation is tuneable over a wavelength range encompassing the absorption edges of the typically used derivative atoms such as Hg, Au and Pt. Hence, it is possible to optimize the anomalous-scattering signal of such atoms by appropriate choice of a wavelength between -0.8 and 1.1 A,. This paper reports a comparison of this method (which we call SIROAS; O for optimized) and SIRAS on related mercury derivatives of glutamate dehydrogenase. The anomalous-scattering signal is enhanced in the SIROAS experiment and this results in an increase of the phasing power of the derivative data.

Station on the SR beam of the VEPP-3 storage ring for the study of macromolecular crystal structure (abstract)

The station designed to speed up the collection of integral intensity data from protein and virus crystals is constructed on the SR beam of the VEPP-3 storage ring. A flat triangular Si crystal cut at 8° relative to the (111) plane is used to monochromatize the radiation. The monochromator is placed on the automatic goniometer which allows us to obtain the necessary energy of radiation, to make the adjusting turns and displacements, and to bend the crystal in order to achieve focusing in the horizontal plane. All the mechanical drive units are supplied with position sensors based on multiturn potentiometers. A conventional Arndt-Wonacott rotation camera is used to collect structure information. The station also includes an optical bench which can turn about the axis coinciding with that of the monochromator, and a set of slits to cut the background and to form the beam. The ionization camera serves to adjust the monochromator and to monitor the beam.

Multiwavelength anomalous diffraction as a direct phasing vehicle in macromolecular crystallography.

The possibility for definitive phase determination from diffraction measurements made at multiple wavelengths from crystals that contain anomalous scatterers has long been recognized (Okaya and Pepinsky, 1956). This potential is easy to appreciate since multiwavelength anomalous diffraction (MAD) experiments can be thought of as in situ multiple isomorphous replacements (MIR) arising from the variations in scattering factors that accompany changes of wavelengths. These variations, known as anomalous scattering, result from the resonance that occurs between the oscillations of atomic orbitals and x-ray-induced electronic vibrations. With synchrotron radiation such experiments are now quite feasible, and with recently developed methods for analyzing MAD measurements, accurate phases can be obtained for macromolecular crystal structures. Anomalous scattering centers appropriate for MAD experiments can be introduced as for conventional heavy atom derivatives or they may occur naturally in metalloproteins. In addition, selenomethionyl proteins produced biologically are suitable for MAD phasing. Since a single crystalline species (and often a single crystal) suffices for MAD analysis of such molecules, the MAD method serves as a vehicle for direct structure determination.

MEDIT: an interactive graphics editor for molecular envelopes

MEDIT is a computer program for the interactive editing or ab initio construction of molecular envelopes on the Evans & Sutherland PS300 graphics display. It has been designed as a tool for molecular replacement and electron density modification methods used in the determination of macromolecular crystal structures.

An efficient general-purpose least-squares refinement program for macromolecular structures

A package of programs has been developed for efficient restrained least-squares refinement of macromolecular crystal structures. The package has been designed to be as flexible and general purpose as possible. The process of refinement is divided into basic units and an independent computer program handles each task. Each functional unit communicates with other programs in the package by way of files of well defined format. To modify or replace any program, the user need only understand the function of that particular element. Stereochemical restraints are defined in a general way that can be applied to proteins, nucleic acids, prosthetic groups, solvent atoms and so on. Guide values for bond lengths and bond angles are specified in a straightforward direct manner. Designated groups of atoms can be held constant or constrained to behave as a rigid body during refinement. In order to make the package as efficient as possible, the fast Fourier transform algorithm is used for all the crystallographic transformations. To highlight potential errors in the refined structure the user can list those atoms that have the worst bond lengths and angles, or have the largest positional, temperature-factor or occupancy gradients. It is also possible to check that protein and solvent atoms do not sterically clash with symmetry-related neighbors. Applications of the program package to a bacteriochlorophyll-containing protein, thermolysin-inhibitor complexes and mutants of bacteriophage T4 lysozyme are described.

Crystallographic R Factor Refinement by Molecular Dynamics

Molecular dynamics was used to refine macromolecular structures by incorporating the difference between the observed crystallographic structure factor amplitude and that calculated from an assumed atomic model into the total energy of the system. The method has a radius of convergence that is larger than that of conventional restrained least-squares refinement. Test cases showed that the need for manual corrections during refinement of macromolecular crystal structures is reduced. In crambin, the dynamics calculation moved residues that were misplaced by more than 3 angstroms into the correct positions without human intervention.

Anisotropic thermal-parameter refinement of the DNA dodecamer CGCGAATTCGCG by the segmented rigid-body method

A structure-factor least-squares refinement of the deoxyoligonucleotide (CGCGAATTCGCG)2 has been conducted using a model with constraints and restraints on the positional parameters and a segmented rigid-body representation for the anisotropic temperature factors. The macromolecule was divided into subgroups each of which was treated as a rigid body in terms of both positional and thermal parameters. For each subgroup, the thermal parameters determined were elements of translation, libration and correlation (TLS) tensors. This segmented rigidbody model of thermal motion has not previously been applied to the refinement of a macromolecular crystal structure. The anisotropic thermal-parameter refinement has significantly reduced the classical R factor as judged by the Hamilton test. The resulting difference Fourier map has a considerably lower noise level allowing fifteen additional low-occupancy water positions to be identified. In addition, analysis of the anisotropic thermal parameters has revealed new information about the local mobility of the groups in the oligonucleotide. Thus, the method of segmented rigid-body anisotropic temperature-factor refinement appears to be uniquely suited to macromolecules, especially nucleic acids, where high-resolution data are usually unavailable.