Showing papers in "Acta Crystallographica Section D-biological Crystallography in 2006"

Scaling and assessment of data quality

Abstract: The various physical factors affecting measured diffraction intensities are discussed, as are the scaling models which may be used to put the data on a consistent scale. After scaling, the intensities can be analysed to set the real resolution of the data set, to detect bad regions (e.g. bad images), to analyse radiation damage and to assess the overall quality of the data set. The significance of any anomalous signal may be assessed by probability and correlation analysis. The algorithms used by the CCP4 scaling program SCALA are described. A requirement for the scaling and merging of intensities is knowledge of the Laue group and point-group symmetries: the possible symmetry of the diffraction pattern may be determined from scores such as correlation coefficients between observations which might be symmetry-related. These scoring functions are implemented in a new program POINTLESS.

HKL-3000: the integration of data reduction and structure solution--from diffraction images to an initial model in minutes.

Abstract: A new approach that integrates data collection, data reduction, phasing and model building significantly accelerates the process of structure determination and on average minimizes the number of data sets and synchrotron time required for structure solution. Initial testing of the HKL-3000 system (the beta version was named HKL-2000_ph) with more than 140 novel structure determinations has proven its high value for MAD/SAD experiments. The heuristics for choosing the best computational strategy at different data resolution limits of phasing signal and crystal diffraction are being optimized. The typical end result is an interpretable electron-density map with a partially built structure and, in some cases, an almost complete refined model. The current development is oriented towards very fast structure solution in order to provide feedback during the diffraction experiment. Work is also proceeding towards improving the quality of phasing calculation and model building.

The Buccaneer software for automated model building. 1. Tracing protein chains.

Abstract: A new technique for the automated tracing of protein chains in experimental electron-density maps is described. The technique relies on the repeated application of an oriented electron-density likelihood target function to identify likely Cα positions. This function is applied both in the location of a few promising `seed' positions in the map and to grow those initial Cα positions into extended chain fragments. Techniques for assembling the chain fragments into an initial chain trace are discussed.

Optimal description of a protein structure in terms of multiple groups undergoing TLS motion.

Abstract: A single protein crystal structure contains information about dynamic properties of the protein as well as providing a static view of one three-dimensional conformation. This additional information is to be found in the distribution of observed electron density about the mean position of each atom. It is general practice to account for this by refining a separate atomic displacement parameter (ADP) for each atomic center. However, these same displacements are often described well by simpler models based on TLS (translation/libration/screw) rigid-body motion of large groups of atoms, for example interdomain hinge motion. A procedure, TLSMD, has been developed that analyzes the distribution of ADPs in a previously refined protein crystal structure in order to generate optimal multi-group TLS descriptions of the constituent protein chains. TLSMD is applicable to crystal structures at any resolution. The models generated by TLSMD analysis can significantly improve the standard crystallographic residuals R and Rfree and can reveal intrinsic dynamic properties of the protein.

A time- and cost-efficient system for high-level protein production in mammalian cells.

Abstract: Most proteins for structural biology studies are produced by high-level expression in Escherichia coli. However, pro­kary­otic based expression systems fail to generate correctly folded functional forms of many proteins and hence a variety of eukaryotic based expression systems have been developed. Of these, yeast and baculovirus-infected insect cells currently represent the expression systems of choice for structural biologists. Here, protocols for a simple, fast and affordable method for transient protein expression in mammalian cells are reported. The results demonstrate that it combines several features necessary for the production of suitable samples for structural biology, in particular protein crystallography, namely high protein yield, straightforward purification, selenomethionine incorporation and control of N-linked glycosylation. The system is suitable for use in conventional laboratories or can be implemented in a medium- or high-throughput pipeline.

Small revisions to predicted distances around metal sites in proteins

Abstract: A new analysis has been made of distances around metal sites in protein structures in the Protein Data Bank determined with resolution ≤1.25 A and equivalent distances have been extracted from the Cambridge Structural Database. They are for the metals Na, Mg, K, Ca, Mn, Fe, Co, Cu, Zn and the donor atoms O of water, O of Asp and Glu, O of the main-chain carbonyl group, N of His and S of Cys. Some revisions are recommended to the tables of `target distances' previously given [Harding (2001), Acta Cryst. D57, 401–411; Harding (2002), Acta Cryst. D58, 872–874]. As well as small changes in many distances and a large improvement for Mg—Ocarboxylate, the table includes an indication of how reliable each prediction may be. Special attention was given to carboxylate interactions. When the carboxylate group is monodentate, the M—Ocarboxylate distance is well defined, but for bidentate carboxylate groups a wide range of distances is allowable; when the metal is Co, Cu or Zn the M—O1 and M—O2 distances are clearly inversely correlated; for the more purely electrostatic interactions involving Na, K and Ca there is a wider scatter of distances and little correlation.

Entropy and surface engineering in protein crystallization.

Abstract: Protein crystallization remains a key limiting step in the characterization of the atomic structures of proteins and their complexes by X-ray diffraction methods. Current data indicate that standard screening procedures applied to soluble well folded prokaryotic proteins yield X-ray diffraction crystals with an ∼20% success rate and for eukaryotic proteins this figure may be significantly lower. Protein crystallization is predominantly dependent on entropic effects and the driving force appears to be the release of ordered water from the sites of crystal contacts. This is countered by the entropic cost of ordering of protein molecules and by the loss of conformational freedom of side chains involved in the crystal contacts. Mutational surface engineering designed to create patches with low conformational entropy and thereby conducive to formation of crystal contacts promises to be an effective tool allowing direct enhancement of the success rate of macromolecular crystallization.

Recombinant protein expression and solubility screening in Escherichia coli: a comparative study

Abstract: Producing soluble proteins in Escherichia coli is still a major bottleneck for structural proteomics. Therefore, screening for soluble expression on a small scale is an attractive way of identifying constructs that are likely to be amenable to structural analysis. A variety of expression-screening methods have been developed within the Structural Proteomics In Europe (SPINE) consortium and to assist the further refinement of such approaches, eight laboratories participating in the network have benchmarked their protocols. For this study, the solubility profiles of a common set of 96 His6-tagged proteins were assessed by expression screening in E. coli. The level of soluble expression for each target was scored according to estimated protein yield. By reference to a subset of the proteins, it is demonstrated that the small-scale result can provide a useful indicator of the amount of soluble protein likely to be produced on a large scale (i.e. sufficient for structural studies). In general, there was agreement between the different groups as to which targets were not soluble and which were the most soluble. However, for a large number of the targets there were wide discrepancies in the results reported from the different screening methods, which is correlated with variations in the procedures and the range of parameters explored. Given finite resources, it appears that the question of how to most effectively explore `expression space' is similar to several other multi-parameter problems faced by crystallographers, such as crystallization.

Cryocooling and radiation damage in macromolecular crystallography

Abstract: Advances in cryocrystallographic techniques for macromolecular crystallography have been intimately intertwined with efforts to reduce the deleterious effects of X-ray damage inflicted during the collection of diffraction data. A brief overview of cryomethods and their rationale is given. This is followed by a summary of our current limited understanding of radiation damage in cryocooled crystals, investigations aimed at minimizing its effects and finally some developments which actually utilize it both for phasing and to extend structural knowledge.

Co-expression of protein complexes in prokaryotic and eukaryotic hosts: experimental procedures, database tracking and case studies

Abstract: Structure determination and functional characterization of macromolecular complexes requires the purification of the different subunits in large quantities and their assembly into a functional entity. Although isolation and structure determination of endogenous complexes has been reported, much progress has to be made to make this technology easily accessible. Co-expression of subunits within hosts such as Escherichia coli and insect cells has become more and more amenable, even at the level of high-throughput projects. As part of SPINE (Structural Proteomics In Europe), several laboratories have investigated the use co-expression techniques for their projects, trying to extend from the common binary expression to the more complicated multi-expression systems. A new system for multi-expression in E. coli and a database system dedicated to handle co-expression data are described. Results are also reported from various case studies investigating different methods for performing co-expression in E. coli and insect cells.

NORMA: a tool for flexible fitting of high-resolution protein structures into low-resolution electron-microscopy-derived density maps

Abstract: This paper describes a freely available software suite that allows the modelling of large conformational changes of high-resolution three-dimensional protein structures under the constraint of a low-resolution electron-density map. Typical applications are the interpretation of electron-microscopy data using atomic scale X-ray structural models. The software package provided should enable the interested user to perform flexible fitting on new cases without encountering major technical difficulties. The NORMA software suite including three fully executable reference cases and extensive user instructions are available at http://www.elnemo.org/NORMA/.

High-resolution structure of human D-glyceraldehyde-3-phosphate dehydrogenase.

Abstract: GAPDH (d-glyceraldehyde-3-phosphate dehydrogenase) is a multifunctional protein that is a target for the design of antitrypanosomatid and anti-apoptosis drugs. Here, the first high-resolution (1.75 A) structure of a human GAPDH is reported. The structure shows that the intersubunit selectivity cleft that has been leveraged in the design of antitrypanosomatid compounds is closed in human GAPDH. Modeling of an anti-trypanosomatid GAPDH inhibitor in the human GAPDH active site provides insights into the basis for the observed selectivity of this class of inhibitor. Moreover, the high-resolution data reveal a new feature of the cleft: water-mediated intersubunit hydrogen bonds that assist closure of the cleft in the human enzyme. The structure is used in a computational ligand-docking study of the small-molecule compound CGP-3466, which inhibits apoptosis by preventing nuclear accumulation of GAPDH. Plausible binding sites are identified in the adenosine pocket of the NAD+-binding site and in a hydrophobic channel located in the center of the tetramer near the intersection of the three molecular twofold axes. The structure is also used to build a qualitative model of the complex between GAPDH and the E3 ubiquitin ligase Siah1. The model suggests that the convex surface near GAPDH Lys227 interacts with a large shallow groove of the Siah1 dimer. These results are discussed in the context of the recently discovered NO–S-nitrosylation–GAPDH–Siah1 apoptosis cascade.

Eukaryotic expression: developments for structural proteomics.

Abstract: The production of sufficient quantities of protein is an essential prelude to a structure determination, but for many viral and human proteins this cannot be achieved using prokaryotic expression systems. Groups in the Structural Proteomics In Europe (SPINE) consortium have developed and implemented high-throughput (HTP) methodologies for cloning, expression screening and protein production in eukaryotic systems. Studies focused on three systems: yeast (Pichia pastoris and Saccharomyces cerevisiae), baculovirus-infected insect cells and transient expression in mammalian cells. Suitable vectors for HTP cloning are described and results from their use in expression screening and protein-production pipelines are reported. Strategies for co-expression, selenomethionine labelling (in all three eukaryotic systems) and control of glycosylation (for secreted proteins in mammalian cells) are assessed.

Structure of Plasmodium falciparum dihydroorotate dehydrogenase with a bound inhibitor.

Abstract: Membrane-associated dihydroorotate dehydrogenase (DHODH) is an antimalarial therapeutic target without an effective inhibitor. Studies on human DHODH (HsDHODH) led to a structural mechanistic model in which respiratory quinones bind in a tunnel formed by the highly variable N-­terminus that leads to the flavin mononucleotide-binding site. The therapeutic agents leflunomide (Arava) and brequinar sodium inhibit HsDHODH by binding in this tunnel. Plasmodium falciparum DHODH (PfDHODH) and HsDHODH have markedly different sensitivities to the two drugs. To understand the structural basis of this differential sensitivity and begin a structure-based drug-design cycle for PfDHODH inhibitors, the three-dimensional structure (2.4 A, R = 20.1%) of PfDHODH bound to the active metabolite of leflunomide was determined by X-ray crystallography. Comparison of the structures of HsDHODH and PfDHODH reveals a completely different binding mode for the same inhibitor in these two catalytically identical enzymes and explains the previously observed species-specific preferential binding. Because no effective inhibitors have been described for PfDHODH, this structure provides critical insight for the design of potential antimalarials.

Automated ligand fitting by core-fragment fitting and extension into density

Abstract: A procedure for fitting of ligands to electron-density maps by first fitting a core fragment of the ligand to density and then extending the remainder of the ligand into density is presented The approach was tested by fitting 9327 ligands over a wide range of resolutions (most are in the range 08–­48 A) from the Protein Data Bank (PDB) into (Fo − Fc)exp(iφc) difference density calculated using entries from the PDB without these ligands The procedure was able to place 58% of these 9327 ligands within 2 A (rmsd) of the coordinates of the atoms in the original PDB entry for that ligand The success of the fitting procedure was relatively insensitive to the size of the ligand in the range 10–100 non-H atoms and was only moderately sensitive to resolution, with the percentage of ligands placed near the coordinates of the original PDB entry for fits in the range 58–73% over all resolution ranges tested

Automation of sample mounting for macromolecular crystallography.

Abstract: A standard sample holder and vial for cryocooled macromolecular crystals has been defined for use with robotic sample changers. This SPINE standard sample holder is a modified version, with added features and specifications, of sample holders in common use. In particular, the SPINE standard meets the precision required for automatic sample exchange and includes a cap that is identified by a two-dimensional datamatrix code as well as an optional vial. At the ESRF, the sample holder standard is in use with the EMBL/ESRF/BM14 robotic sample changer (SC3) which is installed on eight beamlines. The SC3 can hold up to 50 crystals stored in five baskets. A datamatrix reader in the SC3 ensures safe management of the sample flow and facilitates fully automatic screening and characterization of samples. Tools for handling and transporting 50 samples in a dry shipping dewar have been developed. In addition to the SC3, the SPINE sample holder is currently compatible with a number of other robotic sample changers.

Mapping the active site of Escherichia coli malonyl-CoA-acyl carrier protein transacylase (FabD) by protein crystallography.

Abstract: Malonyl-CoA–acyl carrier protein transacylase (FabD; EC 2.3.1.39) is a key enzyme in the fatty-acid biosynthesis pathway of bacteria, catalyzing the transfer of a malonyl moiety from malonyl-CoA to holo acyl carrier protein (ACP), generating malonyl-ACP and free CoASH. Malonyl-ACP, which is the product of this reaction, is the key building block for de novo fatty-acid biosynthesis. Various binary complex structures of the Escherichia coli enzyme are presented, including that of the natural substrate malonyl-CoA, indicating the functional role of the highly conserved amino acids Gln11, Ser92, Arg117 and His201 and the stabilizing function of the preformed oxyanion hole during the enzymatic reaction. Based on the presented structural data, a possible new catalytic enzyme mechanism is discussed. The data obtained could be used in aiding the process of rational inhibitor design.

A quantitative approach to data-collection strategies

Abstract: Statistical descriptors of the X-ray diffraction data set for a macromolecular crystal can be modelled using the information present in the initial diffraction images. Quantitative relationships between the crystal quality, beam apertures, oscillation width, resolution limit, redundancy and the data statistics are presented. They are analysed in terms of the radiation-dose requirements based on modelling in program the BEST. The influence of radiation damage on the data statistics is discussed.

Introduction and validation of an invariom database for amino-acid, peptide and protein molecules.

Abstract: A database of invarioms for structural refinement of amino-acid, oligopeptide and protein molecules is presented. The spherical scattering factors of the independent atom or promolecule model are replaced by `individual' aspherical scattering factors that take into account the chemical environment of a bonded atom. All amino acids were analysed in terms of their invariom fragments. In order to generate 73 database entries that cover this class of compounds, 37 model compounds were geometry-optimized and theoretical structure factors were calculated. Multipole refinements were then performed on these theoretical structure factors to yield the invariom database. Validation of this database on an extensive number of experimental small-molecule crystal structures of varying quality and resolution shows that invariom modelling improves various figures of merit. Differences in figures of merit between invariom and promolecule models give insight into the importance of disorder for future protein-invariom refinements. The suitability of structural data for application of invarioms can be predicted by Cruickshank's diffraction-component precision index [Cruickshank (1999), Acta Cryst. D55, 583–601].

Hydrophobin HFBII in detail : ultrahigh-resolution structure at 0.75 Å

Abstract: Hydrophobins are small proteins secreted by filamentous fungi that have a unique ability to spontaneously form amphiphilic layers. Hydrophobins have only recently been structurally characterized through the first crystal structure determination of a protein of this class, Trichoderma reesei hydrophobin HFBII [Hakanpaa, Paananen et al. (2004), J. Biol. Chem. 279, 534–539]. The resolution of the HFBII structure has now been extended to an ultrahigh resolution of 0.75 A. The structure was refined conventionally and multipole refinement has been initiated. The ultrahigh-resolution structure is analyzed here in detail and comparison is made to the previous atomic resolution structure of the same protein as well as to other ultrahigh-resolution structures found in the Protein Data Bank.

Quantifying X-ray radiation damage in protein crystals at cryogenic temperatures.

Abstract: The dependence of radiation damage to protein crystals at cryogenic temperatures upon the X-ray absorption cross-section of the crystal has been examined. Lysozyme crystals containing varying heavy-atom concentrations were irradiated and diffraction patterns were recorded as a function of the total number of incident photons. An experimental protocol and a coefficient of sensitivity to absorbed dose, proportional to the change in relative isotropic B factor, are defined that together yield a sensitive and robust measure of damage. Radiation damage per incident photon increases linearly with the absorption coefficient of the crystal, but damage per absorbed photon is the same for all heavy-atom concentrations. Similar damage per absorbed photon is observed for crystals of three proteins with different molecular sizes and solvent contents.

Considerations for the refinement of low-resolution crystal structures

Abstract: It is often assumed that crystal structures have to be obtained at sufficiently high resolution in order to perform macromolecular refinement. In several recent structures, the threshold of what is considered `acceptable' has been pushed to lower diffraction resolutions. Here, considerations and modifications to standard refinement protocols are described that were used to solve and refine a particular set of low-resolution structures for the ATPase p97/VCP. It was found that reasonable Rfree values and good geometry can be achieved upon refinement that includes experimental phase information along with judicious use of restraints at diffraction limits as low as 4.7 A. At this resolution, the topology and the backbone-chain trace are mostly defined, some side-chain positions can be unambiguously assigned and ligands within known binding sites can be identified. Furthermore, large conformational changes can be discerned when structures in different states are available, information that is not easily obtainable by other means.

Structures of the Dsk2 UBL and UBA domains and their complex

Abstract: The yeast proteins Dsk2 and Rad23 belong to a family of proteins that contain an N-terminal ubiquitin-like domain (UBL) and a C-terminal ubiquitin-associated domain (UBA). Both Dsk2 and Rad23 function as adaptors to target ubiquitin-labelled proteins to the proteasome through recognition of polyubiquitin (four or more K48-linked ubiquitins) by their UBA domains and to the yeast proteasomal subunit Rpn1 by their UBL domains. The crystal structures of the Dsk2 UBL domain, the Dsk2 UBA domain and the Dsk2 UBA–UBL complex are reported. In the crystal, the Dsk2 UBA domains associate through electrostatic interactions to form ninefold helical ribbons that leave the ubiquitin-binding surface exposed. The UBA–UBL complex explains the reduced affinity of the UBA domain for UBL compared with ubiquitin and has implications for the regulation of Dsk2 adaptor function during ubiquitin-mediated proteasomal targeting. A model is discussed in which two or more Dsk2 UBA molecules may selectively bind to K48-linked polyubiquitin.

Automated ligand placement and refinement with a combined force field and shape potential.

Abstract: An automated computational procedure for fitting a ligand into its electron density with the use of the MMFF94 force field and a Gaussian shape description has been developed. It employs a series of adiabatic optimizations of gradually increasing shape potential. Starting from a set of energy-relaxed ligand conformations, the final results are structures realistically strained to fit the crystallographic data.

Structure of human ferritin L chain.

Abstract: Ferritin is the major iron-storage protein present in all cells. It generally contains 24 subunits, with different ratios of heavy chain (H) to light chain (L), in the shape of a hollow sphere hosting up to 4500 ferric Fe atoms inside. H-rich ferritins catalyse the oxidation of iron(II), while L-rich ferritins promote the nucleation and storage of iron(III). Several X-­ray structures have been determined, including those of L-­chain ferritins from horse spleen (HoSF), recombinant L-­chain ferritins from horse (HoLF), mouse (MoLF) and bullfrog (BfLF) as well as recombinant human H-chain ferritin (HuHF). Here, structures have been determined of two crystal forms of recombinant human L-chain ferritin (HuLF) obtained from native and perdeuterated proteins. The structures show a cluster of acidic residues at the ferrihydrite nucleation site and at the iron channel along the threefold axis. An ordered Cd2+ structure is observed within the iron channel, offering further insight into the route and mechanism of iron transport into the capsid. The loop between helices D and E, which is disordered in many other L-­chain structures, is clearly visible in these two structures. The crystals generated from perdeuterated HuLF will be used for neutron diffraction studies.

The impact of protein characterization in structural proteomics.

Abstract: Protein characterization plays a role in two key aspects of structural proteomics. The first is the quality assessment of the produced protein preparations. Obtaining well diffracting crystals is one of the major bottlenecks in the structure-determination pipeline. Often, this is caused by the poor quality of the protein preparation used for crystallization trials. Hence, it is essential to perform an extensive quality assessment of the protein preparations prior to crystallization and to use the results in the evaluation of the process. Here, a protein-production and crystallization strategy is proposed with threshold values for protein purity (95%) and monodispersity (85%) below which a further optimization of the protein-production process is strongly recommended. The second aspect is the determination of protein characteristics such as domains, oligomeric state, post-translational modifications and protein–protein and protein–ligand interactions. In this paper, applications and new developments of protein-characterization methods using MS, fluorescence spectroscopy, static light scattering, analytical ultracentrifugation and small-angle X-ray scattering within the EC Structural Proteomics in Europe contract are described. Examples of the application of the various methods are given.

Rapid and simple protein-stability screens : application to membrane proteins

Abstract: Approximately 30% of the human genome, and likewise for other genomes, encodes membrane proteins. Also, the majority of known human pharmaceutical targets are membrane proteins. As a consequence, the future success of structure-based drug-design efforts will rely heavily on membrane-protein structural information. While a number of techniques are available to determine the structure of membrane proteins, crystallographic methods (either using two-dimensional or three-dimensional crystals) have been the most productive. Nonetheless, membrane-protein structure determination using crystallographic methods has encountered at least three serious bottlenecks: protein production, purification and crystallization. While a number of crystallization strategies for membrane proteins are available today, they all must ensure that the membrane protein of interest is thermodynamically stable for crystallization to be feasible. Thermodynamic stability is so fundamental to protein crystallization that it is often overlooked experimentally. Here, simple and effective protocols for determining the relative stabilities of membrane proteins using commercially available instruments and reagents are demonstrated. The results demonstrate suitability for the rapid screening of conditions that maximize protein stability using minimal amounts of reagents and protein.

LAFIRE : software for automating the refinement process of protein-structure analysis

Abstract: Manual intervention is usually required in the multiple rounds of refinement of protein crystal structures, including linking and/or extending the fragments of the initial model and rebuilding (fitting) ill-matched residues using computer-graphics software. Such manual modification is both time-consuming and requires a great deal of expertise in crystallography. Consequently, the refinement process becomes the bottleneck for high-throughput structure analysis. A program, Local correlation coefficient-based Automatic FItting for REfinement (LAFIRE), has been developed to achieve manual intervention-free refinement. This program was designed to perform the entire process of protein structural refinement automatically using the refinement programs CNS1.1 (CNS v.1.1) or REFMAC5. The automatic process begins from an initial model, which can be approximate, fragmentary or even only main-chain, and refines it to the final model including water molecules, controlled by monitoring the Rfree factor. More than 30 structures have now been refined successfully in a fully or semi-automatic manner within a few hours or days using LAFIRE.

Some aspects of quantitative analysis and correction of radiation damage

Abstract: Radiation damage is the major source of systematic error in macromolecular data collected at third-generation synchrotron beamlines. In this paper, a simple way of analysing data for radiation damage is proposed and shown to give results that are easy to interpret. Results of correction of radiation damage obtained with an exponential decay function as implemented in XSCALE (from the XDS package) are shown, and aspects of the mathematical treatment of radiation damage, as well as experimental requirements for the correction and utilization of radiation damage are discussed. Furthermore, a method for quantifying the coverage and evenness of sampling of rotation range is proposed.

Crystallization to obtain protein–ligand complexes for structure-aided drug design

Abstract: The use of X-ray crystallography to derive three-dimensional structures for structure-aided drug design (SADD) is a common activity in drug discovery today. In this process, the structures of inhibitors or other ligands of interest complexed with their macromolecular target are solved and the structural information is used iteratively to design new molecules. The ability to form cocrystal complexes between a target protein and a ligand is essential to this process and therefore is of considerable interest to anyone practicing in this field. In the course of obtaining the necessary ligand-protein crystals, even with crystallization conditions well established for a protein of interest, obtaining co-structures with inhibitors either through cocrystallization or soaking is too often not successful. There are numerous potential reasons for this lack of success and this article outlines a number of possible factors that may be involved and discusses considerations that should be taken into account when designing successful experiments to obtain iterative costructures.