On the number of different dynamics in Boolean networks with deterministic update schedules.

Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction diagraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics.

FIP: a highly automated beamline for multiwavelength anomalous diffraction experiments.

FIP is a French Collaborating Research Group (CRG) beamline at the European Synchrotron Radiation Facility (ESRF) dedicated exclusively to crystallography of biological macromolecules, with a special emphasis on multiwavelength anomalous diffraction data collection in the 0.7-1.81 A wavelength range. The optics, consisting of long cylindrical grazing-angle mirrors associated with a cryocooled double-crystal monochromator, delivers an optimal beam in the corresponding energy range. The high level of automation, which includes automated crystal centring, automated data-collection management and data processing, makes the use of this beamline very easy. This is illustrated by the large number of challenging structures that have been solved since 1999.

The iota-carrageenase of Alteromonas fortis. A beta-helix fold-containing enzyme for the degradation of a highly polyanionic polysaccharide.

Carrageenans are gel-forming hydrocolloids extracted from the cell walls of marine red algae. They consist of d-galactose residues bound by alternate alpha(1-->3) and beta(1-->4) linkages and substituted by one (kappa-carrageenan), two (iota-carrageenan), or three (lambda-carrageenan) sulfate-ester groups per disaccharide repeating unit. Both the kappa- and iota-carrageenan chains adopt ordered conformations leading to the formation of highly ordered aggregates of double-stranded helices. Several kappa-carrageenases and iota-carrageenases have been cloned from marine bacteria. Kappa-carrageenases belong to family 16 of the glycoside hydrolases, which essentially encompasses polysaccharidases specialized in the hydrolysis of the neutral polysaccharides such as agarose, laminarin, lichenan, and xyloglucan. In contrast, iota-carrageenases constitute a novel glycoside hydrolase structural family. We report here the crystal structure of Alteromonas fortis iota-carrageenase at 1.6 A resolution. The enzyme folds into a right-handed parallel beta-helix of 10 complete turns with two additional C-terminal domains. Glu(245), Asp(247), or Glu(310), in the cleft of the enzyme, are proposed as candidate catalytic residues. The protein contains one sodium and one chloride binding site and three calcium binding sites shown to be involved in stabilizing the enzyme structure.

Anomalous X-ray diffraction with soft X-ray synchrotron radiation.

Anomalous diffraction with soft X-ray synchrotron radiation opens new possibilities in protein crystallography and materials science. Low-Z elements like silicon, phosphorus, sulfur and chlorine become accessible as new labels in structural studies. Some of the heavy elements like uranium exhibit an unusually strong dispersion at their M(V) absorption edge (lambdaMV = 3.497 A, E(MV) = 3545 eV) and so does thorium. Two different test experiments are reported here showing the feasibility of anomalous X-ray diffraction at long wavelengths with a protein containing uranium and with a salt containing chlorine atoms. With 110 electrons the anomalous scattering amplitude of uranium exceeds by a factor of 4 the resonance scattering of other strong anomalous scatterers like that of the lanthanides at their L(III) edge. The resulting exceptional phasing power of uranium is most attractive in protein crystallography using the multi-wavelength anomalous diffraction (MAD) method. The anomalous dispersion of an uranium derivative of asparaginyl-tRNA synthetase (hexagonal unit cell; a = 123.4 A, c = 124.4 A) has been measured for the first time at 4 wavelengths near the M(V) edge using the beamline ID1 of ESRF (Grenoble, France). The present set up allowed to measure only 30% of the possible reflections at a resolution of 4 A, mainly because of the low sensitivity of the CCD detector. In the second experiment, the dispersion of the intensity of 5 X-ray diffraction peaks from pentakismethylammonium undecachlorodibismuthate (PMACB, orthorhombic unit cell; a = 13.003 A, b = 14.038 A, c = 15.450 A) has been measured at 30 wavelengths near the K absorption edge of chlorine (lambdaK = 4.397 A, EK= 2819.6 eV). All reflections within the resolution range from 6.4 A to 3.4 A expected in the 20 degree scan were observed. The chemical state varies between different chlorine atoms of PMACB, and so does the dispersion of different Bragg peaks near the K-edge of chlorine. The results reflect the performance of the beamline ID1 of ESRF at wavelengths beyond 3 A at the end of 1998. A gain by a factor 100 for diffraction experiments with 4.4 A photons was achieved in Autumn 1999 when two focusing mirrors had been added to the X-ray optics. Further progress is expected from area detectors more sensitive to soft X-rays. Both CCD detectors and image plates would provide a gain of two orders of measured intensity. Image plates would have the additional advantage that they can be bent cylindrically and thus cover a larger solid angle in reciprocal space. In many cases, samples need to be cooled: closed and open systems are presented. A comparison with the state of art of soft X-ray diffraction, as it had been reached at HASYLAB (Hamburg, Germany), and as it is developing at the Brookhaven National Laboratory (USA), is given.

"Open" structures of MurD: domain movements and structural similarities with folylpolyglutamate synthetase.

UDP-N-acetylmuramoyl-l-alanine:d-glutamate (MurD) ligase catalyses the addition of d-glutamate to the nucleotide precursor UDP-N-acetylmuramoyl-l-alanine (UMA). The crystal structures of Escherichia coli in the substrate-free form and MurD complexed with UMA have been determined at 2.4 A and 1.88 A resolution, respectively. The MurD structure comprises three domains each of a topology reminiscent of nucleotide-binding folds. In the two structures the C-terminal domain undergoes a large rigid-body rotation away from the N-terminal and central domains. These two "open" structures were compared with the four published "closed" structures of MurD. In addition the comparison reveals which regions are affected by the binding of UMA, ATP and d-Glu. Also we compare and discuss two structurally characterized enzymes which belong to the same ligase superfamily: MurD and folylpolyglutamate synthetase (FGS). The analysis allows the identification of key residues involved in the reaction mechanism of FGS. The determination of the two "open" conformation structures represents a new step towards the complete elucidation of the enzymatic mechanism of the MurD ligase.

Feasibility and review of anomalous X-ray diffraction at long wavelengths in materials research and protein crystallography.

The feasibility and a review of progress in the long-wavelengths anomalous dispersion technique is given in the context of the development of beamline ID1 of the ESRF for such studies. First experiments on this beamline and their analyses are described. The first study reports on the use of uranium which exhibits an unusually strong anomalous dispersion at its M(V) absorption edge (lambda(M(V)) = 3.5 A). The anomalous scattering amplitude of uranium with 110 anomalous electrons exceeds the resonance scattering of other strong anomalous scatterers like that of the rare earth ions by a factor of four. The resulting exceptional phasing power of uranium is most attractive in protein crystallography using the MAD method. The anomalous dispersion of a uranium derivative of asparaginyl-tRNA synthetase (hexagonal, a = 124.4 A, c = 123.4 A) has been measured at three wavelengths near the M(V) edge using beamline ID1 of the ESRF. The present set-up allowed the measurement of 10% of the possible reflections at a resolution of 8 A. This is mainly due to the low sensitivity of the CCD camera. The second study, involving DAFS experiments at wavelengths near the K-absorption edge of chlorine (lambda(K) = 4.4 A), reports the use of salt crystals which give rise to much stronger intensities of diffraction peaks than those of protein crystals. In the case of a crystal of pentamethylammonium undecachlorodibismuthate (PMACB, orthorhombic, a = 13.00 A, b = 14.038 A, c = 15.45 A), all reflections within the resolution range from 6.4 A to 3.5 A and the total scan width of 24 degrees were collected. The crystalline structure of PMACB implies two chemically distinct states of the Cl atom. Consequently, different dispersions near the K-edge of chlorine are expected. The dispersion of the intensity of five Bragg peaks of the PMACB crystal has been measured at 30 wavelengths. The relative success of these preliminary experiments with X-rays of long wavelength shows that the measurement of anomalous X-ray diffraction at wavelengths beyond 3 A is feasible. Starting from the experience gained in these experiments, an increased efficiency of the instrument ID1 by two to three orders of magnitude will be achieved in this wavelength range. A comparison with different techniques of anomalous diffraction which rely on the use of argon/ethane-filled multiwire chambers and image plates as detectors for wavelengths near the K-edge of sulfur and phosphorus is also given.

Determination of the MurD mechanism through crystallographic analysis of enzyme complexes.

UDP -N- acetylmuramoyl- L -alanine: D -glutamate (MurD) ligase catalyses the addition of d -glutamate to the nucleotide precursor UDP -N- acetylmuramoyl- L -alanine (UMA). The crystal structures of three complexes of Escherichia coli MurD with a variety of substrates and products have been determined to high resolution. These include (1) the quaternary complex of MurD, the substrate UMA, the product ADP, and Mg2+, (2) the quaternary complex of MurD, the substrate UMA, the product ADP, and Mn2+, and (3) the binary complex of MurD with the product UDP - N- acetylmuramoyl- L -alanine- D -glutamate (UMAG). The reaction mechanism supported by these structures proceeds by the phosphorylation of the C-terminal carboxylate group of UMA by the gamma-phosphate group of ATP to form an acyl-phosphate intermediate, followed by the nucleophilic attack by the amino group of D-glutamate to produce UMAG. A key feature in the reaction intermediate is the presence of two magnesium ions bridging negatively charged groups.

Large-scale preparation, purification, and crystallization of UDP-N-acetylmuramoyl-L-alanine: D-glutamate ligase from Escherichia coli.

The UDP-N-acetylmuramoyl-L-alanine:D-glutamate ligase from Escherichia coli, an enzyme involved in the biosynthesis of the bacterial peptidoglycan monomer unit, was overproduced and purified to homogeneity on a large scale, yielding 4 mg of protein per liter of bacterial culture. Crystals of the complex with the substrate UDP-MurNAc-L-Ala were grown by the hanging drop method using ammonium sulfate as the precipitant. They are tetragonal with cell dimensions a = b = 65.5 A and c = 134.59 A, space group P4(1) or P4(3), and contain one monomer of 46,842 Da in the asymmetric unit. In order to use the multiple-wavelength anomalous diffraction method for phasing, a selenomethionine derivative of the protein has also been overproduced, purified, and crystallized.

D2AM, a beamline with a high-intensity point-focusing fixed-exit monochromator for multiwavelength anomalous diffraction experiments.

D2AM is a french CRG beamline installed at the ESRF (European Synchrotron Radiation Facility) in Grenoble, with half of the time dedicated to biological macromolecule crystallography and half to materials science studies (diffraction, wide-angle and small-angle scattering). It is constructed at the front-end BM02 of the ESRF storage ring, using the X-ray beam from a 0.8 T bending magnet. D2AM entered into routine operation at the end of 1994, and is used either for single-wavelength or for multiwavelength anomalous diffraction studies. The beam is monochromated by an Si[111] two-crystal monochromator with a resolution of about 2 x 10(-4). The first crystal is water cooled. The X-ray photon energy covers the range between 6.5 keV (lambda approximately 1.9 A) and 17 keV (lambda approximately 0.7 A), a domain of energy with many K or L absorption edges of heavy atoms of interest for biological macromolecules studies and in materials science. The X-ray beam is focused in the vertical plane by two long curved mirrors and in the horizontal plane by the second crystal of the monochromator which is given an adjustable sagittal curvature. A spot size of 0.3 x 0.1 mm (FWHM) is measured at the sample position. Both mirrors are cut out of a 6"-diameter 1.1 m-long Si single crystal, polished and coated with a 400 A Pt thin film. The rugosity is better than 4 A r.m.s. and the longitudinal slope error is better than 5 x 10(-6) rad r.m.s. The first mirror is water cooled, the second is not. The beam intensity on the sample is about 10(11) photon s(-1) on a 0.3 x 0.3 mm focus area at 100 mA in the storage ring of the ESRF. The harmonic rejection ratio obtained with the two mirrors is better than 10(-5) for lambda/3. The combined optical system, mirror/monochromating-crystals/mirror, used on D2AM constitutes altogether a high-intensity point-focusing fixed-exit monochromator, which has the additional property that the energy resolution is not dependent on the beam divergence in use. Its stability and resolution are perfectly adapted to multiwavelength anomalous diffraction studies. The alignment of the mirrors and the monochromator is fully automated, taking 5 min, with the exception of the adjustment of the sagittal focusing. During multiwavelength diffraction experiments the wavelength is changed by a fast single monochromator rotation. Neither realignment of the mirrors nor readjustment of the beam focusing are necessary. The stability and reproducibility of the selected X-ray photon energy is better than 0.5 eV.

Crystal structure of UDP-N-acetylmuramoyl-L-alanine:D-glutamate ligase from Escherichia coli.

UDP-N-acetylmuramoyl-L-alanine:D-glutamate ligase (MurD) is a cytoplasmic enzyme involved in the biosynthesis of peptidoglycan which catalyzes the addition of D-glutamate to the nucleotide precursor UDP-N-acetylmuramoyl-L-alanine (UMA). The crystal structure of MurD in the presence of its substrate UMA has been solved to 1.9 A resolution. Phase information was obtained from multiple anomalous dispersion using the K-shell edge of selenium in combination with multiple isomorphous replacement. The structure comprises three domains of topology each reminiscent of nucleotide-binding folds: the N- and C-terminal domains are consistent with the dinucleotide-binding fold called the Rossmann fold, and the central domain with the mononucleotide-binding fold also observed in the GTPase family. The structure reveals the binding site of the substrate UMA, and comparison with known NTP complexes allows the identification of residues interacting with ATP. The study describes the first structure of the UDP-N-acetylmuramoyl-peptide ligase family.

Comparison of the structures of wild-type and a N313T mutant of Escherichia coli glyceraldehyde 3-phosphate dehydrogenases: implication for NAD binding and cooperativity.

The crystal structure of wild-type and N313T mutant glyceraldehyde 3-phosphate dehydrogenases from Escherichia coli was determined in the presence of NAD at 1.8 angstrom and 2.17 angstrom, respectively. The structure of the monomer and of the tetramer are similar to those observed for other GAPDHs. An exhaustive analysis of the hydrophobic clusters and the hydrogen bond networks explain the high degree of sequence conservation in GAPDHs. The structural effect of the N313T mutation is a change in the (phi,psi) angles of nearby residues Asn236 and Val237, while the structure around the mutated residue remains unchanged. A detailed comparison of the wild-type and N313T mutant E. coli GAPDH with the apo and holo forms of Bacillus stearothermophilus GAPDH is carried out in relation to the apo --> holo transition. An unbiased set of about 60 residues, whose C(alpha) atoms remain in the same relative position in the different forms of the tetramer, is defined as the tetramer "core" which acts as a fixed scaffold around which structural rearrangements occur during the apo --> holo transition. This core essentially includes beta-strands from the beta-sheets forming the O-P and Q-R interfaces, in particular strand beta1 which bears catalytic residue His176. During the apo --> holo transition, dimer O-P rotates around the molecular P-axis by about +1 degrees, and dimer O-R by about -1 degrees. Further rotations of the NAD binding domain relative to the catalytic domain are discussed in relation to the molecular symmetry. The possible effect on NAD binding cooperativity of mutations around the tetramer core is exemplified by residue 252. The presence of a conserved hydrophilic patch embedded in the hydrophobic O-P interface is highlighted. A mechanism for substrate binding, different from those currently proposed, is described where the hydroxyl group of the substrate C(2) atom is hydrogen bonded to Cys149N.

Crystallization and preliminary X-ray diffraction studies of Escherichia coli glyceraldehyde-3-phosphate dehydrogenase.

Phosphorylating glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is a key enzyme in glycolysis. Single crystals of NAD-dependent GAPDH from Escherichia coli have been obtained by vapour diffusion at room temperature using trisodium citrate as precipitant. In almost the same crystallization conditions, two kinds of crystals were found to be suitable for X-ray diffraction. The crystals with only one half of a tetramer in the asymmetric unit were chosen for high- resolution analysis. They belonged to space group C222(1), with cell dimensions a = 79.1, b = 189.6 and c = 122.2 A. These crystals diffracted to 1.8 A resolution.

Refined crystal structure of the 2[4Fe-4S] ferredoxin from Clostridium acidurici at 1.84 A resolution.

The crystal structure of the 2[4Fe-4S] ferredoxin from Clostridium acidurici has been determined at a resolution of 1.84 A and refined to an R-factor of 0.169. Crystals belong to space group P4(3)2(1)2 with unit cell dimensions a = b = 34.44 A and c = 74.78 A. The structure was determined by molecular replacement using the previously published model of an homologous ferredoxin and refined by molecular dynamics techniques. The model contains the protein and 46 water molecules. Only two amino acid residues, Asp27 and Asp28, are poorly defined in the electron density maps. The molecule has an overall chain fold similar to that of other [4Fe-4S] bacterial ferredoxins of known structure. The two [4Fe-4S] clusters display similar bond distances and angles. In both of them the co-ordination of one iron atom (bound to Cys11 and Cys40) is slightly distorted as compared with that of the other iron atoms. A core of hydrophobic residues and a few water molecules contribute to the stability of the structure. The [4Fe-4S] clusters interact with the polypeptide chain through eight hydrogen bonds each, in addition to the covalent Fe-Scys bonds. The ferredoxin from Clostridium acidurici is the most typical clostridial ferredoxin crystallized so far and the biological implications of the newly determined structure are discussed.

Effect of the anisotropy of anomalous scattering on the MAD phasing method.

The analysis of X-ray diffraction intensities is complicated by the anisotropy of anomalous scattering (AAS) that can occur due to resonance associated with transitions between core electrons and valence molecular orbitals. Substantial AAS has been observed directly in diffraction data near the K edge of selenium in selenolanthionine [Templeton & Templeton (1988). Acta Cryst. A44, 1045-1051] and in pleiochroism of X-ray absorption in selenobiotinyl streptavidin [Hendrickson, Pähler, Smith, Satow, Merritt & Phizackerley (1989). Proc. Natl Acad. Sci. USA, 86, 2190-2194]. The impact of AAS on the multiple-wavelength anomalous diffraction (MAD) method for phase determination is of particular interest in the context of this chemical state of selenium in the light of a general method that has been developed to incorporate selenomethionine into proteins for use in MAD phasing [Hendrickson, Horton & LeMaster (1990). EMBO J. 9, 1665-1672]. The first step of the MAD phasing method necessarily assumes that the anomalous-scattering factors are isotropic and our first aim here is to evaluate the effect of this approximation on initially determined phases. To obtain ultimate phases free from the effects of anisotropy, a least-squares procedure has been written in which global parameters (i.e. pertaining to the whole data set) are refined simultaneously with local parameters (i.e. pertaining to a given node h). The AAS is taken explicityly into account by considering f' and f" as tensors instead of scalars [Templeton & Templeton (1982). Acta Cryst. A38, 62-67], and the components of the f' and f" tensors are among the refinable global parameters. The effectiveness of this procedure is tested with data simulated from the refined atomic model of selenobiotinyl streptavidin. The application of this procedure to actual Photon Factory measurements is also described. The results show that AAS does not cripple the MAD method, and that phases uncorrupted by these effects can be recovered.