Crystallographic Refinement and Structure-Factor Time-Averaging by Molecular Dynamics in the Absence of a Physical Force Field

Abstract

The application of Molecular-Dynamics simulation in protein-crystallographic structure refinement has become common practice. In this paper, structure optimizations are described where the driving force is derived only from the crystallographic data and not from any physical potential energy function. Under this extreme condition ab initio structure refinement and the application of structure-factor time averaging was investigated using a small 9 atom test system. Success in ab initio refinement, where the starting atomic positions are randomly distributed, depends on the resolution of the crystallographic data used in the optimization. The presence of high resolution data introduces false minima in the X-ray energy profile, enhancing the search problem significantly. On the same system, we also tested the method of time-averaged crystallographically restrained Molecular Dynamics, again in the absence of a physical force field. In this method, the diffraction data is modelled by an ensemble of structures instead of one single structure. In comparison to conventional single-structure refinement, more reflections were required to determine a correct atomic distribution. A time-averaging simulation at 0.2 nm resolution (40 reflections) yielded an incorrect distribution, although a low R-factor was obtained. Simulations at 0.1 nm resolution (248 reflections) gave both low R-factors, 3 to 4%, and correct atomic distributions. The scale factor between the observed and time-averaged calculated structure factor amplitudes appeared to be unstable, when optimized during a time-averaging simulation. Tests of time-averaged restrained simulations with noise added to the observed structure-factor amplitudes, indicated that noise is modelled when no information in the form of constraints or restraints is available to distinguish it from real data.     

Correlations of atomic movements in lysozyme crystals.

Diffuse scattering data have been collected on two crystal forms of lysozyme, tetragonal and triclinic, using synchrotron radiation. The observed diffraction patterns were simulated using an exact theory for simple model crystals which relates the diffuse scattering intensity distribution to the amplitudes and correlations of atomic movements. Although the mean square displacements in the tetragonal form are twice that in the triclinic crystal, the predominant component of atomic movement in both crystals is accounted for by short-range coupled motions where displacement correlations decay exponentially as a function of atomic separation, with a relaxation distance of approximately 6 A. Lattice coupled movements with a correlation distance approximately 50 A account for only about 5-10% of the total atomic mean square displacements in the protein crystals. The results contradict various presumptions that the disorder in protein crystals can be modeled predominantly by elastic vibrations or rigid body movements.     

Crystal structure study of Opsanus tau parvalbumin by multiwavelength anomalous diffraction

The crystal structure of a small calcium-binding protein, the parvalbumin IIIf from Opsanus tau in which Tb was substituted for Ca, has been analysed by multiwavelength anomalous diffraction. Data at a resolution of 2.3 A were collected at three wavelengths near the L3 absorption edge of Tb (1.645-1.650 A), using the synchrotron radiation emitted by a storage ring and a multiwire proportional counter. The phases of the reflections were determined from this single derivative, without native data. Prior to any refinement, the resulting electron density map shows a good agreement with the model of the homologous carp parvalbumin in regions of identical amino-acid sequence.     

Approaching the molecular structure of ribosomes

Fifteen forms of three-dimensional crystals and three forms of two-dimensional sheets from ribosomal particles have been grown. In all cases only biologically active particles could be crystallized, the crystalline material retaining its integrity and biological activity for months. Cryastallographic data have been collected from crystals of 50 S ribosomal subunits, using synchrotron radiation, at temperatures between 19 and -180 degree C. Although at around 0 degrees C in the synchrotron X-ray beam the crystals rapidly lose their high-resolution reflections, at cryo-temperatures hardly any radiation damage occurs over long periods, and a complete set of diffraction data to about 6 A resolution could be collected from a single crystal. Heavy-atom clusters were used for soaking as well as for specific binding to the surface of the ribosomal subunits prior to crystallization. The 50 S ribosomal subunits from a mutant of Bacillus stearothermophilus which lacks the ribosomal protein BL11 crystallize isomorphously with the native form. Models of the entire 70 S ribosome and of the 50 S subunit have been reconstructed from two-dimensional sheets at 47 and 30 A, respectively. These models demonstrate the overall shape of the particles, the contact areas between large and small subunits, the space where protein biosynthesis may take place and a tunnel through the 50 S subunit which could provide a path for the nascent polypeptide chain.     

Initiating a crystallographic study of a class II fructose-1,6-bisphosphate aldolase.

We have reproducibly crystallized the metal-dependent Class II fructose-1,6-bisphosphate aldolase from Escherichia coli. Crystals in the shape of truncated hexagonal bipyramids have unit cell dimensions of a = b = 78.4 A, c = 290.6 A and are suitable for a detailed structural analysis. The space group has been identified as P6(1)22 or enantiomorph. Data sets to approximately 2.9 A resolution have been recorded using both the Rigaku R-AXIS IIc image plate area detector coupled to a copper target rotating anode X-ray source and using the MAR image plate systems with synchrotron radiation at the EMBL outstation DESY in Hamburg, and at S.R.S. Daresbury. Diffraction beyond 2.5 A has been observed when large freshly grown crystals are used with the synchrotron beam. A data set to this resolution has been collected. Several putative heavy-atom derivative data sets have also been measured using synchrotron radiation facilities and analysis of these data sets is in progress.     

Non-destructive three-dimensional evaluation of a polymer sponge by micro-tomography using synchrotron radiation

X-ray micro-tomography, a non-destructive technique is used to uncover the complex 3-D micro-architecture of a degradable polymer sponge designed for bone augmentation. The measurements performed at HASYLAB at DESY are based on a synchrotron radiation source resulting in a spatial resolution of about 5.4 microm. In the present communication we report the quantitative analysis of the porosity and of the pore architecture. First, we elucidate that synchrotron radiation at the photon energy of 9 keV has an appropriate cross section for this low-weight material. Modifications in sponge micro-architecture during measurement are not detected. Second, the treatment of the data, an amount of 2.5 Gbyte to generate binary data is described. We compare the 3-D with the 2-D analysis in a quantitative manner. The obtained values for the mean distance to material within the sponge calculated from 2-D and 3-D data of the whole tomogram differ significantly: 12.5 microm for 3-D and 17.6 microm for 2-D analysis. If the pores exhibit a spherical shape as frequently found, the derived mean pore diameter, however, is overestimated only by 6% in the 2-D image analysis with respect to the 3-D evaluation. This approach can be applied to different porous biomaterials and composites even in a hydrated state close to physiological conditions, where any surface preparation artifact is avoided.     

A model of the quaternary structure of the Escherichia coli F1 ATPase from X-ray solution scattering and evidence for structural changes in the delta subunit during ATP hydrolysis.

The shape and subunit arrangement of the Escherichia coli F1 ATPase (ECF1 ATPase) was investigated by synchrotron radiation x-ray solution scattering. The radius of gyration and the maximum dimension of the enzyme complex are 4.61 +/- 0.03 nm and 15.5 +/- 0.05 nm, respectively. The shape of the complex was determined ab initio from the scattering data at a resolution of 3 nm, which allowed unequivocal identification of the volume occupied by the alpha3beta3 subassembly and further positioning of the atomic models of the smaller subunits. The delta subunit was positioned near the bottom of the alpha3beta3 hexamer in a location consistent with a beta-delta disulfide formation in the mutant ECF1 ATPase, betaY331W:betaY381C:epsilonS108C, when MgADP is bound to the enzyme. The position and orientation of the epsilon subunit were found by interactively fitting the solution scattering data to maintain connection of the two-helix hairpin with the alpha3beta3 complex and binding of the beta-sandwich domain to the gamma subunit. Nucleotide-dependent changes of the delta subunit were investigated by stopped-flow fluorescence technique at 12 degrees C using N-[4-[7-(dimethylamino)-4-methyl]coumarin-3-yl]maleimide (CM) as a label. Fluorescence quenching monitored after addition of MgATP was rapid [k = 6.6 s-1] and then remained constant. Binding of MgADP and the noncleavable nucleotide analog AMP . PNP caused an initial fluorescent quenching followed by a slower decay back to the original level. This suggests that the delta subunit undergoes conformational changes and/or rearrangements in the ECF1 ATPase during ATP hydrolysis.     

The 3 A crystal structure of yeast initiator tRNA: functional implications in initiator/elongator discrimination.

A significantly improved molecular model of yeast initiator tRNA (ytRNA(iMet) has been prepared that gives insight into the structural basis of eukaryotic initiator tRNA's unique function. This study was made possible by X-ray data collected at synchrotron radiation sources with the newly developed technologies of 'imaging plates' and 'storage phosphors'. These data extend beyond the resolution limit of 4.0 A reported previously to a current limit of 3.0 A and are considerably more accurate. Refinement of the model against the new data (R factor = 21.5%) clearly reveals a novel modification and a set of tertiary interactions involving sequence features characteristic of eukaryotic initiator tRNAs. We hypothesize these to be the structural elements responsible for part of the special function of yeast tRNA(iMET).     

Crystallization and preliminary X-ray diffraction study of a chimaeric Fab' fragment of antibody binding tumour cells

Crystals have been obtained of a chimaeric Fab' fragment that binds to a tumour-associated mucin-like glycoprotein TAG72. The Fab' fragment comprises the variable heavy and light-chain domains of a murine monoclonal antibody, B72.3, coupled to human gamma 4 and kappa constant regions. The crystals are orthorhombic and belong to the space group P2(1)2(1)2(1), with unit cell dimensions a = 67.9 A, b = 94.2 A and c = 208.8 A. Diffraction to 2.6 A resolution was observed using synchrotron radiation. Despite the acute radiation sensitivity of the crystals a full native data set has been collected using the Weissenberg camera at the Photon Factory synchrotron. These data will be used for molecular replacement calculations in an attempt to elucidate the structure of this chimaeric Fab' fragment.     

Changes in crystallographic structure and thermostability of a Cu,Zn superoxide dismutase mutant resulting from the removal of a buried cysteine

In principle, protein thermostability depends on efficient interior packing of apolar residues and on avoidance of irreversible denaturation in the unfolded state. To study these effects, the single free cysteine in the highly stable enzyme bovine Cu,Zn superoxide dismutase was mutated to alanine (Cys6----Ala), and the recombinant protein was expressed in yeast, purified, characterized for reversible and irreversible denaturation, crystallized isomorphously to the wild-type enzyme, and used to determine the atomic structure. Removal of the chemically reactive thiol significantly decreased the rate of irreversible denaturation (as monitored by thermal inactivation at 70 degrees C), but the observed energetic cost (delta delta G of 0.7-1.3 kcal/mol as determined by differential scanning calorimetry) was much less than predicted from either the change in hydrophobicity or packing due to removal of the interior sulfur atom. X-ray diffraction data were collected to 2.1-A resolution using an area detector, and the atomic model for the mutant enzyme was determined by fitting to electron density difference maps, followed by reciprocal space refinement both with stereochemical restraints using PROLSQ and with molecular dynamics using X-PLOR. The refined 2.1-A resolution crystallographic structure suggests that small concerted and compensating shifts (less than 0.5 A) of the surrounding side chains and of the adjacent N- and C-terminal beta-strands significantly reduced the energetic cost of the interior mutation by improving packing and stereochemistry in the mutant enzyme. Taken together, these results differentiate between the effects of reversible and irreversible processes as they impact the design of thermostable proteins and suggest that relatively subtle concerted shifts can significantly reduce the energetic cost of evolutionary variation in internal residues of proteins with Greek key beta-barrel folds.     

Metal substitution in transferrins: the crystal structure of human copper-lactoferrin at 2.1-A resolution.

The structural consequences of binding a metal other than iron to a transferrin have been examined by crystallographic analysis of human copper-lactoferrin, Cu2Lf. X-ray diffraction data were collected from crystals of Cu2Lf, using a diffractometer, to 2.6-A resolution, and oscillation photography on a synchrotron source, to 2.1-A resolution. The structure was refined crystallographically, by restrained least-squares methods, starting with a model based on the isomorphous diferric structure from which the ligands, metal ions, anions, and solvent molecules had been deleted. The final model, comprising 5321 protein atoms (691 residues), 2 Cu2+ ions, 2 (bi)carbonate ions, and 308 solvent molecules has good stereochemistry (rms deviation of bond lengths from standard values of 0.018 A) and gives a crystallographic R value of 0.196 for 43,525 reflections in the range 7.5-2.1-A resolution. The copper coordination is different in the two binding sites. In the N-terminal site, the geometry is square pyramidal, with equatorial bonds to Asp 60, Tyr 192, His 253, and a monodentate anion and a longer apical bond to Tyr 92. In the C-terminal site, the geometry is distorted octahedral, with bonds to Asp 395, Tyr 435, Tyr 528, and His 597 and an asymmetrically bidentate anion. The protein structure is the same as for the diferric protein, Fe2Lf, demonstrating that the closure of the protein domains over the metal is the same in each case irrespective of whether Fe3+ or Cu2+ is bound and that copper could be transported and delivered to cells equally well as iron. The differences in metal coordination are achieved by small movements of the metal ion and anion within each binding site, which do not affect the protein structure.     

Radioprotection of mouse colony forming units-spleen against heavy-charged particle damage by WR 2721

The effectiveness of S-2-(3-aminopropylamino)ethylphosphorothioic acid (WR 2721) to protect against the heavy-charged particle beams with dose-averaged LET infinity's ranging from 26 to 260 keV/micron was studied using the marrow colony forming units-spleen as a model system. WR 2721 (400 mg/kg) was injected ip 30 min before whole-body irradiation in the plateau ionization region of the Bragg curve. Significant protection was observed at 26, 51, and 135 keV/micron LET values where the data were collected with 20Ne, 28Si, and 40Ar ions, respectively. The largest component of protection was the slope change, where at LET values of 26 and 51 keV/micron the DMFs (slope) were 2.1 and 2.3, respectively, which are very close to the gamma-ray value of 2.4 (gamma LET approximately equal to 0.2 keV/micron). Protection, however, decreased with increase in LET from 51 to 135 keV/micron to the DMF value of 1.2 and no significant protection was observed against 56Fe ions at 260 keV/micron. Significant increases in extrapolation number occurred with gamma rays and neon particles. The results are discussed in terms of charged particle track structure, radiation chemistry, and potential clinical applications.     

Atomic structure of a CK2alpha human kinase by microfocus diffraction of extra-small microcrystals grown with nanobiofilm template

Extra-small microcrystals of a human kinase CK2alpha were obtained for the first time by the optimization of a recent protein crystallization method based on highly packed protein nanofilm template. Protein crystal induction and growth appear indeed optimal at high surface pressure of the film template yielding high protein orientation and packing. The resulting extra-small CK2alpha microcrystals (of about 20 microm in diameter) was subsequently used for synchrotron radiation diffraction data collection, which proves possible by means of the Microfocus Beamline at the ESRF Synchrotron in Grenoble. The quality of the resulting crystal diffraction patterns and of its resulting atomic structure at 2.4 A resolution proves the unique validity of the above two combined frontier technologies in defining a new approach to structural proteomics capable to solve the atomic structure of proteins so far never been crystallized and of pharmaceutical relevance. Physical explanation in terms of template dipole moments and possibility of generalization of this method to the wide class of proteins not yet crystallized are finally discussed. The structure of our CK2alpha mutant is in the Protein Data Bank (PDB ID Code 1NA7, deposited on 27 November 2002).     

Monitoring and validating active site redox states in protein crystals

High resolution protein crystallography using synchrotron radiation is one of the most powerful tools in modern biology. Improvements in resolution have arisen from the use of X-ray beamlines with higher brightness and flux and the development of advanced detectors. However, it is increasingly recognised that the benefits brought by these advances have an associated cost, namely deleterious effects of X-ray radiation on the sample (radiation damage). In particular, X-ray induced reduction and damage to redox centres has been shown to occur much more rapidly than other radiation damage effects, such as loss of resolution or damage to disulphide bridges. Selection of an appropriate combination of in-situ single crystal spectroscopies during crystallographic experiments, such as UV-visible absorption and X-ray absorption spectroscopy (XAFS), allows for effective monitoring of redox states in protein crystals in parallel with structure determination. Such approaches are also essential in cases where catalytic intermediate species are generated by exposure to the X-ray beam. In this article, we provide a number of examples in which multiple single crystal spectroscopies have been key to understanding the redox status of Fe and Cu centres in crystal structures. This article is part of a Special Issue entitled: Protein Structure and Function in the Crystalline State.     

Structure of oxidized poplar plastocyanin at 1.6 A resolution

The structure of poplar plastocyanin in the oxidized (CuII) state at pH 6.0 has been refined, using 1.6 A resolution counter data. The starting co-ordinates were obtained from the 2.7 A electron density map computed with phases derived by the multiple isomorphous replacement method. The model was refined successively by constrained real space, unrestrained reciprocal space, and restrained reciprocal space least-squares methods. The final residual R value is 0.17 for 8285 reflections (I greater than 2 sigma (I)). It is estimated that the root-mean-square standard deviation of the atomic positions is 0.1 A when averaged over all atoms, and 0.05 A for the Cu ligand atoms alone. The refined structure retains all the essential features of the 2.7 A model. The co-ordination geometry of the copper atom is confirmed as being distorted tetrahedral. The two Cu-N(His) bonds, 2.10 and 2.04 A, are within the range normally found in low molecular weight CuII complexes with Cu-N(imidazole) bonds. The Cu-S(Cys) bond, 2.13 A, is also normal, but the Cu-S(Met) bond, 2.90 A, is sufficiently long to raise important questions about its significance. The hydrogen-bonding and secondary structure can now be assigned confidently. Forty-four water molecules are included in the final model. Repetition of the refinement, using new data to 1.9 A resolution recorded from crystals at pH 4.2, has led to a residual R value of 0.16 for 6060 reflections (I greater than sigma (I)). There are few significant changes in the structure of poplar CuII-plastocyanin between pH 6.0 and pH 4.2. In particular, the geometry of the copper site is not affected. The observed changes in redox behaviour of plastocyanin at low pH are therefore unlikely to be connected with structural changes in the oxidized form of the protein. A number of features of the molecular structure appear to be directly related to the function of plastocyanin as an electron carrier in photosynthesis. Comparison between the known amino acid sequences of 67 plant plastocyanins reveals 52 conserved and 11 conservatively substituted residues in a total of 99. If three algal plastocyanin sequences are included in the comparison, there are still 26 conserved and 12 conservatively substituted residues. In many cases, the importance of these residues in determining the tertiary structure can be rationalized.     

X-ray diffraction from a left ventricular wall of rat heart

We studied x-ray diffraction from the left ventricular wall of an excised, perfused whole heart of a rat using x rays from the third-generation synchrotron radiation facility, SPring-8. With the beam at right angles to the long axis of the left ventricle, well-oriented, strong equatorial reflections were observed from the epicardium surface. The reflections became vertically split arcs when the beam passed through myocardium deeper in the wall, and rings were observed when the beam passed into the inner myocardium of the wall. These diffraction patterns were explained by employing a layered-spiral model of the arrangement of muscle fibers in the heart. In a quiescent heart with an expanded left ventricle, the muscle fibers at the epicardium surface were found to have a (1,0) lattice spacing smaller than in the rest of the wall. The intensity ratio of the (1,0) and (1,1) equatorial reflections decreased on contraction with a similar time course in all parts of the wall. The results show that it is possible to assign the origin of reflections in a diffraction diagram from a whole heart. This study offers a basis for interpretation of x-ray diffraction from a beating heart under physiologically and pathologically different conditions.     

Binding of the plant hormone kinetin in the active site of Mistletoe Lectin I from Viscum album

The crystal structure of the ribosome inhibiting protein Mistletoe Lectin I (ML-I) derived from the European mistletoe, Viscum album, in complex with kinetin has been refined at 2.7? resolution. Suitably large crystals of ML-I were obtained applying the counter diffusion method using the Gel Tube R Crystallization Kit (GT-R) on board the Russian Service Module on the international space station ISS within the GCF mission No. 6, arranged by the Japanese aerospace exploration agency (JAXA). Hexagonal bi-pyramidal crystals were grown during three months under microgravity. Before data collection the crystals were soaked in a saturated solution of kinetin and diffraction data to 2.7? were collected using synchrotron radiation and cryogenic techniques. The atomic model was refined and revealed a single kinetin molecule in the ribosome inactivation site of ML-I. The complex demonstrates the feasibility of mistletoe to bind plant hormones out of the host regulation system as part of a self protection mechanism.     

Electron diffraction analysis of the M412 intermediate of bacteriorhodopsin.

High resolution electron diffraction data have been recorded for glucose-embedded purple membrane specimens in which bacteriorhodopsin (bR) has been trapped by cooling slowly to below--100 degrees C under continuous illumination. Thin films (OD approximately 0.7) of glucose-embedded membranes, prepared as a control, showed virtually 100% conversion to the M state, and stacks of such thin film specimens gave very similar x-ray diffraction patterns in the bR568 and the M412 state in most experiments. To be certain that any measured differences in diffraction intensity would be real, two independent sets of electron diffraction intensities were recorded for near-equatorial, i.e. (hkO), reflections. Little correlation was indeed observed between these two sets for delta F values at low resolution (15-5.0 A, 49 reflections), but the correlation coefficient is approximately 0.3 at high resolution (5.0-3.3 A, 218 reflections). Thus, while most of the measured difference is error, the mean delta F and the correlation coefficient can be used to estimate the smaller, true delta F due to structural changes occurring in the M state. The magnitude of this estimated true mean delta F is equal to what would be produced if approximately five to seven nonhydrogen atoms were moved to structurally uncorrelated (i.e., new) positions in the M state. Movements of a few amino acid side chains, and repositioning of atoms of the retinal group and the associated lysine side chain after trans-cis isomerization, are the most probable causes of the observed intensity changes in the M state.(ABSTRACT TRUNCATED AT 250 WORDS)     

Near tubule and intertubular bovine dentin mapped at the 250 nm level

In this study, simultaneous diffraction and fluorescence mapping with a (250 nm)², 10.1 keV synchrotron X-ray beam investigated the spatial distribution of carbonated apatite (cAp) mineral and elemental Ca (and other cations including Zn) around dentin tubules. In 1 μm thick sections of near-pulp root dentin, where peritubular dentin (PTD) is newly forming, high concentrations of Zn, relative to those in intertubular dentin (ITD), were observed adjacent to and surrounding the tubule lumens. Some but not all tubules exhibited hypercalcified collars (high Ca signal relative to the surrounding ITD), and, when present, the zone of high Ca did not extend around the tubule. Diffraction rings from cAp 00.2 and 11.2 + 21.1 + 30.0 reflections were observed, and cAp was the only crystal phase detected. Profiles of Ca, Zn and cAp diffracted intensities showed the same transitions from solid to tubule lumen, indicating the same cAp content and organization in ITD far from the tubules and adjacent to them. Further, the matching Ca and diffraction profiles demonstrated that all of the Ca is in cAp or that any noncrystalline Ca was uniformly distributed throughout the dentin. Variation of 00.2 and 11.2 + 21.1 + 30.0 diffracted intensity was consistent with the expected biaxial crystallographic texture. Extension of X-ray mapping from near 1 μm resolution to the 250 nm level, performed here for dentin and its tubules, will provide new understanding of other mineralized tissues.     

Construction of low-resolution x-ray crystallographic electron density maps of the ribosome

Advances in X-ray crystallography now allow biological macromolecules of almost any size to be imaged at atomic resolution. Here, I outline the strategy that allowed for the solution of the 70S ribosome structure to 7.8-A resolution. The most important factors involve the effective use of synchrotron radiation and the application of existing crystallographic software to very large structures.