Gérard Bricogne

[27] Maximum-likelihood heavy-atom parameter refinement for multiple isomorphous replacement and multiwavelength anomalous diffraction methods

Publisher Summary This chapter discusses the maximum-likelihood heavy-atom parameter refinement for multiple isomorphous replacement (MIR) and multiwavelength anomalous diffraction (MAD). The chapter describes its extension to probability distributions incorporating anomalous diffraction effects, as well as measurement error and nonisomorphism. Integrating these distributions in a whole complex plane leads to likelihood functions that can be used for heavy-atom detection and refinement and for producing phase-probability distributions. The current implementation of this formalism in the computer program statistical heavy-atom refinement and phasing (SHARP) is also described in the chapter. Likelihood functions can be used for the final phasing and calculation of Hendrickson–Lattman coefficients. Numerical tests have been performed for three types of common refinements—namely, single isomorphous replacement, multiple isomorphous replacement with anomalous scattering (MIRAS), and MAD—and the results are summarized in the chapter. A key feature of SHARP is its ability to refine lack-of-isomorphism parameters along with all the others.

Tryptophanyl-tRNA synthetase crystal structure reveals an unexpected homology to tyrosyl-tRNA synthetase

BACKGROUNDnTryptophanyl-tRNA synthetase (TrpRS) catalyzes activation of tryptophan by ATP and transfer to tRNA(Trp), ensuring translation of the genetic code for tryptophan. Interest focuses on mechanisms for specific recognition of both amino acid and tRNA substrates.nnnRESULTSnMaximum-entropy methods enabled us to solve the TrpRS structure. Its three parts, a canonical dinucleotide-binding fold, a dimer interface, and a helical domain, have enough structural homology to tyrosyl-tRNA synthetase (TyrRS) that the two enzymes can be described as conformational isomers. Structure-based sequence alignment shows statistically significant genetic homology. Structural elements interacting with the activated amino acid, tryptophanyl-5AMP, are almost exactly as seen in the TyrRS:tyrosyl-5AMP complex. Unexpectedly, side chains that recognize indole are also highly conserved, and require reorientation of a specificity-determining helix containing a conserved aspartate to assure selection of tryptophan versus tyrosine. The carboxy terminus, which is disordered and therefore not seen in TyrRS, forms part of the dimer interface in TrpRS.nnnCONCLUSIONSnFor the first time, the Bayesian statistical paradigm of entropy maximization and likelihood scoring has played a critical role in an X-ray structure solution. Sequence relatedness of structurally superimposable residues throughout TrpRS and TyrRS implies that they diverged more recently than most aminoacyl-tRNA synthetases. Subtle, tertiary structure changes are crucial for specific recognition of the two different amino acids. The conformational isomerism suggests that movement of the KMSKS loop, known to occur in the TyrRS transition state for amino acid activation, may provide a basis for conformational coupling during catalysis.

Structure of tomato bushy stunt virus IV: The virus particle at 2·9resolution

The structure of tomato bushy stunt virus has been determined crystallographically to 2·9resolution. Details are presented of both the molecular structure and the methods by which it has been solved. The icosahedrally symmetric viral shell is composed of 180 protein subunits ( M r 43,000), with three similar but distinct modes of subunit bonding. This capacity for alternative packing is due to localized flexibility in the folded polypeptide (hinges between domains) and to multiple conformations for surface side-chains. The polypeptide backbone has an essentially invariant fold within a compact domain. A mechanism for correct positioning of the different modes of subunit interaction is evident from the structure of the TBSV particle. Thirty-five residues of the polypeptide chain fold in an ordered way on 60 of the 180 subunits, forming an internal framework. Interaction of folded domains with this framework permits accuracy of long-range geometry (correct curvature and closure) to be determined by unambiguous switching between alternative local contact angles. RNA packs tightly into the particle interior. Protein-RNA interactions occur through parts of the subunit that are flexibly linked to the well-ordered domains of the shell. This variable interaction imposes minimum restrictions on the folding of the RNA chain.

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

Publisher Summary 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.

Crystal structure of a fungal elicitor secreted by Phytophthora cryptogea, a member of a novel class of plant necrotic proteins.

BACKGROUNDnElicitins form a novel class of plant necrotic proteins which are secreted by Phytophthora and Pythium fungi, parasites of many economically important crops. These proteins induce leaf necrosis in infected plants and elicit an incompatible hypersensitive-like reaction, leading to the development of a systemic acquired resistance against a range of fungal and bacterial plant pathogens. No crystal structures of this class of protein are available. The crystal structure determination of beta-cryptogein (CRY), secreted by Phytophthora cryptogea, was undertaken to identify structural features important for the necrotic activity of elicitins.nnnRESULTSnThe structure of CRY was determined using the multiwavelength anomalous diffraction technique and refined to 2.2 A resolution. The overall structure has a novel fold consisting of six alpha helices and a beak-like motif, whose sequence is highly conserved within the family, composed of an antiparallel two-stranded beta sheet and an omega loop. This motif is assumed to be a major recognition site for a putative receptor and/or ligand. Two other distinct binding sites seem to be correlated to the level of necrotic activity of elicitins.nnnCONCLUSIONSnThe determination of the crystal structure of a member of the elicitin family may make it possible to separate the activity that causes leaf necrosis from that inducing systemic acquired resistance to pathogens, making it feasible to engineer a non-toxic elicitin that only elicits plant defences. Such studies should aid the development of non-toxic agricultural pest control.

The 1.2 A crystal structure of hirustasin reveals the intrinsic flexibility of a family of highly disulphide-bridged inhibitors.

BACKGROUNDnLeech-derived inhibitors have a prominent role in the development of new antithrombotic drugs, because some of them are able to block the blood coagulation cascade. Hirustasin, a serine protease inhibitor from the leech Hirudo medicinalis, binds specifically to tissue kallikrein and possesses structural similarity with antistasin, a potent factor Xa inhibitor from Haementeria officinalis. Although the 2.4 A structure of the hirustasin-kallikrein complex is known, classical methods such as molecular replacement were not successful in solving the structure of free hirustasin.nnnRESULTSnAb initio real/reciprocal space iteration has been used to solve the structure of free hirustasin using either 1.4 A room temperature data or 1.2 A low temperature diffraction data. The structure was also solved independently from a single pseudo-symmetric gold derivative using maximum likelihood methods. A comparison of the free and complexed structures reveals that binding to kallikrein causes a hinge-bending motion between the two hirustasin subdomains. This movement is accompanied by the isomerisation of a cis proline to the trans conformation and a movement of the P3, P4 and P5 residues so that they can interact with the cognate protease.nnnCONCLUSIONSnThe inhibitors from this protein family are fairly flexible despite being highly cross-linked by disulphide bridges. This intrinsic flexibility is necessary to adopt a conformation that is recognised by the protease and to achieve an optimal fit, such observations illustrate the pitfalls of designing inhibitors based on static lock-and-key models. This work illustrates the potential of new methods of structure solution that require less or even no prior phase information.

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.

Triiodide derivatization and combinatorial counter-ion replacement: two methods for enhancing phasing signal using laboratory Cu Kα X-ray equipment

A series of experiments performed at Cu Kalpha wavelength on in-house X-ray equipment are presented which investigate two possibilities for enhancing the experimental phasing signal by means of (i) triiodide/iodide soaks using KI/I(2) and (ii) combinations of counter-ions introduced using the short cryosoak method. Triiodide-derivative crystal structures for five test proteins have been refined and reveal that iodine can bind as polyiodide and single iodide ions through hydrophobic and hydrogen-bonding interactions both at the molecular surface and in intramolecular and intermolecular cavities. In three cases, the structures could be automatically determined with autoSHARP using in-house SAD and SIRAS data. The investigation of combinatorial counter-ion replacement using multiple salts with Na(+) and Cs(+) as cations and I(-) and Cl(-) as anions reveals that, for the case of hen egg-white lysozyme, significant improvement in phasing signal is obtained by the combined use of salts compared with SIRAS methods using native and single short-soak derivative data sets.

Applications of single-wavelength anomalous dispersion at high and atomic resolution.

Two examples of the application of single-wavelength anomalous dispersion (SAD) in macromolecular structure determination are described, both using the statistical phasing program SHARP. For the holmium-substituted calcium-binding protein psoriasin (22.7u2005kDa), a set of accurate phases has been obtained to a resolution of 1.05u2005A without recourse to an atomic model of the molecule. The accuracy of the phases resulted in an electron-density map of a quality comparable to σA-weighted 2mFo − DFc maps derived from the final model refined with SHELX97. Comparison of the refined and SAD electron-density maps showed significant discrepancies resulting from the iterative refinement in reciprocal space. Additionally, it is shown that the structure of psoriasin can be determined from native data extending to 2.0u2005A alone by exploiting the minute anomalous signal from a bound zinc ion.

Applications of the maximum entropy method to powder diffraction and electron crystallography

A new multisolution phasing method based on entropy maximization and likelihood ranking, proposed for the specific purpose of increasing the accuracy and sensitivity of probabilistic phase indications compared with conventional direct methods, has been implemented and applied to a wide variety of problems. The latter comprise the determination of small crystal structures from X-ray diffraction data obtained from single crystals or from powders, and from electron diffraction data, both with and without partial phase information obtained by image processing of electron micrographs; the ranking of phase sets for a small protein; and the improvement of poor quality phases for a larger protein at medium resolution under constraint of solvent flatness. The main components of the method are (1) a tree-directed search through a space of trial phase sets; (2) the saddlepoint method for calculating joint probabilities of structure factors, using entropy maximization; (3) likelihood-based scores to rank trial phase sets and prune the search tree; (4) a statistical analysis of the scores for automatically selecting reliable phase indications. Their use is illustrated here on structure determinations from powder X-ray diffraction data and from electron diffraction data.