Shake-and-Bake applications using simulated reference-beam data for crambin.

The Shake-and-Bake method, as implemented in the computer program SnB, has been applied to simulated reference-beam data for the small protein crambin at several resolutions in the range 1.5-3.0 A. Sets of triplet invariants were generated having simulated mean triplet-phase errors from 0 to 60 degrees. Provided that these errors were no larger than 40 degrees, it was possible (at all resolutions tested) to find trial sets of individual Bragg phases with mean errors of 40-45 degrees. At 1.5 A, this could be achieved using only a single reference-beam data set. Peak picking provided useful phase constraints even at the lowest resolution tested. These results suggest that direct methods may be useful in conjunction with reference-beam data at resolutions lower than 1.2 A.

Optimizing DREAR and SnB parameters for determining Se-atom substructures.

The determination of the anomalous scattering substructure is the first essential step in any successful macromolecular structure determination using the multiwavelength anomalous diffraction (MAD) technique. The diffE method of calculating difference Es in conjunction with SnB has had considerable success in determining large Se-atom substructures. An investigation of the parameters used in both the data-reduction and error-analysis routines (DREAR) as well as the SnB phasing process itself was undertaken to optimize these parameters for more efficient use of the procedure. Two sets of selenomethionyl S-adenosylhomocysteine hydrolase MAD data were used as test data. The elimination of all erroneously large differences prior to phasing was found to be critical and the best results were obtained from accurate highly redundant intensity measurements. The high-resolution data collected in the typical MAD experiment are sufficient, but the inclusion of low-resolution data below 20 A improved the success rate considerably. Although the best results have been obtained from single-wavelength peak anomalous diffraction data alone, independent SnB analysis of data measured at other wavelengths can provide confirmation for questionable sites.

Ill-conditioned Shake-and-Bake: the trap of the false minimum.

The alternation of phase refinement with the imposition of real-space constraints is the essence of the Shake-and-Bake procedure. Typically, these constraints prevent trial structures from falling into local minima. Nevertheless, P1 structures appear to migrate to false minima with significant frequency. These false minima are characterized by the presence of a large 'uranium' peak on the corresponding Fourier map. Fortunately, they can be recognized and avoided by considering the values of the minimal function both before and after the application of constraints. However, it appears that finding solutions for large P1 structures is likely also to require parameter-shift conditions different from those that have been found to work well in other space groups. In fact, these conditions often yield an unusually high percentage of solutions.

P1 Shake-and-Bake: can success be guaranteed?

The multi-trial direct-methods procedure known as Shake-and-Bake has been applied to three small proteins (alpha-1 peptide, vancomycin and lysozyme) that crystallize in space group P1. Phase refinement was accomplished through parameter-shift optimization using both the cosine and exponential forms of the minimal function. By extending error-free data to sufficiently high resolution, 100% convergence of trial structures to solution could be achieved in all three cases by using the exponential minimal function and a shift angle in the range 130-150 degrees. These results suggest optimum parameters for other P1 structures and emphasize the importance of collecting data to the highest possible resolution.

Exponential Shake-and-Bake: theoretical basis and applications.

The simple cosine function used in the formulation of the traditional minimal principle and the related Shake-and-Bake algorithm is here replaced by a function of exponential type and its expected value and variance are derived. These lead to the corresponding exponential minimal principle and its associated Exponential Shake-and-Bake algorithm. Recent applications of the exponential function to several protein structures within the Shake-and-Bake framework suggest that this function leads, in general, to significant improvements in the success rate (percentage of trial structures yielding solution) of the Shake-and-Bake procedure. However, only in space group P1 is it presently possible to assign optimal values a priori for the exponential-function parameters.

Optimizing Shake-and-Bake for proteins.

Shake-and-Bake is a direct-methods procedure which has provided ab initio solutions for protein structures containing as many as 1000 independent non-H atoms. This algorithm extends the range of conventional direct methods by repetitively, unconditionally and automatically alternating reciprocal-space phase refinement with filtering in real space to impose constraints. The application of SnB to protein-sized molecules is significantly affected by the choice made for certain critical parameters, including the number of peaks used for density modification, the choice of phase-refinement method and the number of refinement cycles. The effects of parameter variation have been studied for six protein structures, all of which are solvable by Shake-and-Bake using data at 1.1 A or higher resolution. Solvability in the resolution range 1.2-1.4 A appears to be enhanced by the presence of heavier atoms (S, Cl). Furthermore, it appears that in this range the ratio of refinement cycles and triplet phase invariants to atoms in the structure must be increased. Large structures lacking atoms of any element heavier than oxygen also require non-traditional parameter values.

Structure of rabbit liver fructose 1,6-bisphosphatase at 2.3 A resolution.

The three-dimensional structure of the R form of rabbit liver fructose 1,6-bisphosphatase (Fru-1,6-Pase; E.C. 3.1.3.11) has been determined by a combination of heavy-atom and molecular-replacement methods. A model, which includes 2394 protein atoms and 86 water molecules, has been refined at 2.3 A resolution to a crystallographic R factor of 0.177. The root-mean-square deviations of bond distances and angles from standard geometry are 0.012 A and 1.7 degrees, respectively. This structural result, in conjunction with recently redetermined amino-acid sequence data, unequivocally establishes that the rabbit liver enzyme is not an aberrant bisphosphatase as once believed, but is indeed homologous to other Fru-1,6-Pases. The root-mean-square deviation of the Calpha atoms in the rabbit liver structure from the homologous atoms in the pig kidney structure complexed with the product, fructose 6-phosphate, is 0.7 A. Fru-1,6-Pases are homotetramers, and the rabbit liver protein crystallizes in space group I222 with one monomer in the asymmetric unit. The structure contains a single endogenous Mg2+ ion coordinated by Glu97, Asp118, Asp121 and Glu280 at the site designated metal site 1 in pig kidney Fru-1,6-Pase R-form complexes. In addition, two sulfate ions, which are found at the positions normally occupied by the 6-phosphate group of the substrate, as well as the phosphate of the allosteric inhibitor AMP appear to provide stability. Met177, which has hydrophobic contacts with the adenine moiety of AMP in pig kidney T-form complexes, is replaced by glycine. Binding of a non-hydrolyzable substrate analog, beta-methyl-fructose 1,6-bisphosphate, at the catalytic site is also examined.

The Shake-and-Bake structure determination of triclinic lysozyme.

The crystal structure of triclinic lysozyme, comprised of 1,001 non-H protein atoms and approximately 200 bound water molecules, has been determined ab initio (using native data alone) by the "Shake-and-Bake" method by using the computer program SnB. This is the largest structure determined so far by the SnB program. Initial experiments, using default SnB parameters derived from studies of smaller molecules, were unsuccessful. In fact, such experiments produced electron density maps dominated by a single large peak. This problem was overcome by considering the choice of protocol used during the parameter-shift phase refinement. When each phase was subjected to a single shift of +/-157.5 degrees during each SnB cycle, an unusually high percentage of random trials (approximately 22%) yielded correct solutions within 750 cycles. This success rate is higher than that typically observed, even for much smaller structures.

The 1.1 A resolution crystal structure of [Tyr15]EpI, a novel alpha-conotoxin from Conus episcopatus, solved by direct methods.

Conotoxins are valuable probes of receptors and ion channels because of their small size and highly selective activity. alpha-Conotoxin EpI, a 16-residue peptide from the mollusk-hunting Conus episcopatus, has the amino acid sequence GCCSDPRCNMNNPDY(SO3H)C-NH2 and appears to be an extremely potent and selective inhibitor of the alpha3beta2 and alpha3beta4 neuronal subtypes of the nicotinic acetylcholine receptor (nAChR). The desulfated form of EpI ([Tyr15]EpI) has a potency and selectivity for the nAChR receptor similar to those of EpI. Here we describe the crystal structure of [Tyr15]EpI solved at a resolution of 1.1 A using SnB. The asymmetric unit has a total of 284 non-hydrogen atoms, making this one of the largest structures solved de novo by direct methods. The [Tyr15]EpI structure brings to six the number of alpha-conotoxin structures that have been determined to date. Four of these, [Tyr15]EpI, PnIA, PnIB, and MII, have an alpha4/7 cysteine framework and are selective for the neuronal subtype of the nAChR. The structure of [Tyr15]EpI has the same backbone fold as the other alpha4/7-conotoxin structures, supporting the notion that this conotoxin cysteine framework and spacing give rise to a conserved fold. The surface charge distribution of [Tyr15]EpI is similar to that of PnIA and PnIB but is likely to be different from that of MII, suggesting that [Tyr15]EpI and MII may have different binding modes for the same receptor subtype.

A ligand-mediated dimerization mode for vancomycin.

BACKGROUND: Vancomycin and related glycopeptide antibiotics exert their antimicrobial effect by binding to carboxy-terminal peptide targets in the bacterial cell wall and preventing the biosynthesis of peptidoglycan. Bacteria can resist the action of these agents by replacing the peptide targets with depsipeptides. Rational efforts to design new agents effective against resistant bacteria require a thorough understanding of the structural determinants of peptide recognition by vancomycin. RESULTS: The crystal structure of vancomycin in complex with N-acetyl-D-alanine has been determined at atomic resolution. Two different oligomeric interactions are seen in the structure: back-to-back dimers, as previously described for the vancomycin-acetate complex, and novel face-to-face dimers, mediated largely by the bound ligands. Models of longer, naturally occurring peptide ligands may be built by extension of N-acetyl-D-alanine. These larger ligands can form an extensive array of polar and nonpolar interactions with two vancomycin monomers in the face-to-face configuration. CONCLUSIONS: A new dimeric form of vancomycin has been found in which two monomers are related in a face-to-face configuration, and bound ligands comprise a large portion of the dimer interface. The relative importance of face-to-face and back-to-back dimers to the antimicrobial activity of vancomycin remains to be established, but face-to-face interactions appear to explain how increased antimicrobial activity may arise in covalent vancomycin dimers.

X-ray crystallographic analysis of the hydration of A- and B-form DNA at atomic resolution.

We have determined single crystal structures of an A-DNA decamer and a B-DNA dodecamer at 0.83 and 0.95 A, respectively. The resolution of the former is the highest reported thus far for any right-handed nucleic acid duplex and the quality of the diffraction data allowed determination of the structure with direct methods. The structures reveal unprecedented details of DNA fine structure and hydration; in particular, we have reexamined the overall hydration of A- and B-form DNA, the distribution of water around phosphate groups, and features of the water structure that may underlie the B to A transition.

Incorporating tangent refinement in the Shake-and-Bake formalism.

Shake-and-Bake is a direct-methods procedure in which phase refinement and Fourier refinement are alternated repetitively, unconditionally and automatically. The traditional Shake-and-Bake approach invoked a parameter-shift routine to perform phase refinement in an effort to reduce the value of minimal function. In this paper, parameter shift is replaced with the tangent formula as a means of phase refinement. This study shows that the tangent formula is more efficient than parameter shift for small structures when the number of refinement cycles and number of applications of the tangent formula per Shake-and-Bake cycle are chosen very carefully. For larger structures, including the 400 non-H-atom crambin structure, the two methods generally perform with similar efficiency. However, only parameter shift has successfully produced recognizable solutions for the difficult 317 non-H-atom structure gramicidin A.

X-ray crystal structure of cytotoxic oxidized cholesterols: 7-ketocholesterol and 25-hydroxycholesterol.

The cytotoxic cholesterol derivative, 7-ketocholesterol, crystallizes in a monoclinic unit cell, space group P2(1) with a = 11.405 A, b = 6.288 A, c = 35.393 A and beta = 92.75 degrees (Z = 4). Its room temperature crystal structure was solved by direct methods, i.e., the minimal principle via the Shake-and-Bake (SnB) algorithm. In contrast to the continuous chain pattern found for the cholesterol monohydrate structure, hydrogen bonding in the 7-ketocholesterol structure is localized to specific sites via one water molecule that forms linkages between two O3 hydroxyl groups and one keto oxygen. The final weighted R factor for 4562 reflections was 0.144. The 25-hydroxycholesterol also crystallizes in a monoclinic unit cell (P2(1)), with a = 10.840 A, b = 14.533 A, c = 16.093 A and beta = 95.91 degrees (Z = 4). The low temperature structure was solved by DIRDIF. In this instance, molecular packing is anti-parallel in layers stabilized by hydrogen bonding networks via both hydroxyl functions, differing both from cholesterol monohydrate and the 7-ketocholesterol. The final weighted R-factor for 6566 reflections was 0.034. Functional differences of the oxysterols therefore, may be expressed by observed variations in the molecular packing and geometry.

Fructose-1,6-bisphosphatase. Primary structure of the rabbit liver enzyme. 'Intermediate' variability of an oligomeric protein.

The primary structure of rabbit liver fructose-1,6-bisphosphatase was determined by peptide analysis of digests with different proteases. The results establish the primary structure, complete data bank entries, and show that this enzyme variant is indeed homologous with other liver fructose-1,6-bisphosphatases. Residue differences with the enzymes from other mammals are 9-15%, with those from plants and yeasts about 50%, and with those from characterized prokaryotes up to 70%, showing an enzyme variability intermediate between those of 'variable' and 'constant' oligomeric dehydrogenases. Structural relationships, conformations and catalytic mechanisms are consistent within the family of fructose-1,6-bisphosphatases, and the rabbit protein is a typical rather than an aberrant form of the enzyme.

Crambin: a direct solution for a 400-atom structure.

The crystal structure of crambin, a 46-residue protein containing the equivalent of approximately 400 fully occupied non-H-atom positions, was originally solved at 1.5 A by exploiting the anomalous scattering of its six S atoms at a single wavelength far removed from the absorption edge of sulfur. The crambin structure has now been resolved without the use of any anomalous-dispersion measurements. The technique employed was an ab initio 'shake-and-bake' method, consisting of a phase-refinement procedure based on the minimal function alternated with Fourier refinement. This method has successfully yielded solutions for a smaller molecule (28 atoms) using 1.2 A data, and a crambin solution was obtained at 1.1 A.

The refined three-dimensional structure of 3 alpha,20 beta-hydroxysteroid dehydrogenase and possible roles of the residues conserved in short-chain dehydrogenases.

BACKGROUND: Bacterial 3 alpha,20 beta-hydroxysteroid dehydrogenase reversibly oxidizes the 3 alpha and 20 beta hydroxyl groups of steroids derived from androstanes and pregnanes. It was the first short-chain dehydrogenase to be studied by X-ray crystallography. The previous description of the structure of this enzyme, at 2.6 A resolution, did not permit unambiguous assignment of several important groups. We have further refined the structure of the complex of the enzyme with its cofactor, nicotinamide adenine dinucleotide (NAD), and solvent molecules, at the same resolution. RESULTS: The asymmetric unit of the crystal contains four monomers, each with 253 amino acid residues, 38 water molecules, and 176 cofactor atoms belonging to four NAD molecules--one for each subunit. The positioning of the cofactor molecule has been modified from our previous model and is deeper in the catalytic cavity as observed for other members of both the long-chain and short-chain dehydrogenase families. The nicotinamide-ribose end of the cofactor has several possible conformations or is dynamically disordered. CONCLUSIONS: The catalytic site contains residues Tyr152 and Lys156. These two amino acids are strictly conserved in the short-chain dehydrogenase superfamily. Modeling studies with a cortisone molecule in the catalytic site suggest that the Tyr152, Lys156 and Ser139 side chains promote electrophilic attack on the (C20-O) carbonyl oxygen atom, thus enabling the carbon atom to accept a hydride from the reduced cofactor.

Structure solution by minimal-function phase refinement and Fourier filtering. I. Theoretical basis.

Eliminating the N atomic position vectors rj, j = 1, 2, ..., N, from the system of equations defining the normalized structure factors EH yields a system of identities that the EH's must satisfy, provided that the set of EH's is sufficiently large. Clearly, for fixed N and specified space group, this system of identities depends only on the set [H], consisting of n reciprocal-lattice vectors H, and is independent of the crystal structure, which is assumed for simplicity to consist of N identical atoms per unit cell. However, for a fixed crystal structure, the magnitudes magnitude of /EH/ are uniquely determined so that a system of identities is obtained among the corresponding phases psi H alone, which depends on the presumed known magnitudes magnitude of /EH/ and which must of necessity be satisfied. The known conditional probability distributions of triplets and quartets, given the values of certain magnitudes magnitude of /E/, lead to a function R(psi) of phases, uniquely determined by magnitudes magnitude of /E/ and having the property that RT < 1/2 < RR, where RT is the value of R(psi) when the phases are equal to their true values, no matter what the choice of origin and enantiomorph, and RR is the value of R(psi) when the phases are chosen at random. The following conjecture is therefore plausible: the global minimum of R(psi), where the phases are constrained to satisfy all identities among them that are known to exist, is attained when the phases are equal to their true values and is thus equal to RT.(ABSTRACT TRUNCATED AT 250 WORDS)

Structure solution by minimal-function phase refinement and Fourier filtering. II. Implementation and applications.

The minimal function, R(psi), has been used to provide the basis for a new computer-intensive direct-methods procedure that shows potential for providing fully automatic routine solutions for structures in the 200-400 atom range. This procedure, which has been called shake-and-bake, is an iterative process in which real-space filtering is alternated with phase refinement using a technique that reduces the value of R(psi). It has been successfully tested using experimental data for a dozen known structures ranging in size from 25 to 317 atoms and crystallizing in a variety of space groups. The details of this procedure, the parameters used and the results of these applications are described.

On the application of the minimal principle to solve unknown structures.

The Shake-and-Bake method of structure determination is a new direct methods phasing algorithm based on a minimum-variance, phase invariant residual, which is referred to as the minimal principle. Previously, the algorithm had been applied only to known structures. This algorithm has now been applied to two previously unknown structures that contain 105 and 110 non-hydrogen atoms, respectively. This report focuses on (i) algorithmic and parametric optimizations of Shake-and-Bake and (ii) the determination of two previously unknown structures. Traditional tangent formula phasing techniques were unable to unravel these two new structures.

Application of the minimal principle to peptide structures.

A new direct-methods procedure has been devised which consists of phase refinement via the minimal function, R(phi), alternated with Fourier summation and real space filtering. All phases are initially assigned values by computing structure factors for a randomly positioned set of atoms. These phases are then refined by using a parameter shift method to minimize R(phi). The refined phases are Fourier transformed, and a specified number of the largest peaks in the electron-density function are found and used as a new trial structure. The probability of a trial structure converging to a solution appears to depend on structural complexity and a number of refinement parameters. This procedure shows potential for providing fully automatic routine solutions for structures in the 200-400 atom range.