X-Ray Small Angle Scattering: A New Deconvolution Method for Evaluating Electron Density Distributions from Small Angle Scattering Diagrams

The direct determination of the electron density distributions of multilayered specimens with a small number of unit cells from X-ray small angle scattering experiments via the Q-function method of Hosemann and Bagchi includes the deconvolution of the so-called Q_o-function, the generalized Patterson function of one unit cell. In this paper a new and direct deconvolution method on the basis of Fourier series is presented which is suitable for one-dimensional centrosymmetrical (or antisymmetrical) density distributions. A FORTRAN-program has been written which has an execution time of ca. 20 s on an UNIVAC 1106-computer. The procedure has been successfully tested on some convolution functions generated by membrane-type electron density distributions.     

Axial arrangement of crossbridges in thick filaments of vertebrate skeletal muscle.

X-ray intensity data to 1.8 Å resolution were collected from native trigonal crystals of bovine trypsinogen. The orientation and position of the trypsinogen molecules within their crystal cells were determined by Patterson search techniques using the refined model of bovine trypsin (Bode &; Schwager, 1975), and by subsequent R factor refinement. The translation functions allowed discrimination between the enantiomorphic space groups P3₂21 and P3₁21. After one constrained crystallographic refinement cycle, which reduced the crystallographic reliability factor (R) from 35% to 31%, a preliminary difference Fourier map showed several interesting details. Several refinement cycles reduced the value of R to 23%. The overall chain folding is very similar to trypsin. The chain segments, including residues 184 to 193² and 217 to 223, which form the specificity pocket in trypsin, are flexible in trypsinogen. The autolysis loop is partially mobile between residues 142 and 152. There is no continuing electron density for the N terminal residues preceding Tyr20. This indicates that the N terminus may be only weakly fixed to the rest of the molecule or may even float freely in solution.     

Helical channels in crystals of gramicidin A and of a cesium--gramicidin A complex: an x-ray diffraction study.

X-ray crystallographic studies of gramicidin A crystallized from methanol (P2₁) and ethanol (P2₁2₁2₁), and of a Cs⁺ gramicidin A complex crystallized from methanol (P222₁, P2₁2₁2 or P2₁2₁2₁) are reported here. The asymmetric unit consists of two molecules of gramicidin A in the native crystals and four molecules in the cesium complex crystal. Patterson analyses show that gramicidin A in these crystals forms a cylindrical helical channel. In the two types of native gramicidin crystals, the diameter of this channel is about 5 å and its length is about 32 å. Cesium ions are bound inside this channel in crystals of the cesium-gramicidin A complex. The channel in this complex is considerably shorter (26 Å) and wider (6·8Å) than in the native forms. The Patterson maps of these three crystal forms are compatible with either the single-stranded β-helix (Urry, 1971) or the double-stranded parallel or anti-parallel, β-helix (Veatch et al., 1974).     

Molecular Symmetry of the ClpP Component of the ATP-dependent Clp Protease,anEscherichia coliHomolog of 20 S Proteasome

The ClpP component Clp protease fromEscherichia colihas been crystallized and examined by X-ray crystallography and self-rotation function calculations. The crystal belongs to the monoclinic space groupP2₁with unit cell dimensions ofa=196.9 Å,b=104.3 Å,c=162.4 Å and β=98.3°. The X-ray diffraction pattern extends at least to 2.5 Å Bragg spacing when exposed to CuKα X-rays. Self-rotation function analyses indicate that the ClpP oligomer has 72-point group symmetry. This symmetry suggests that the ClpP oligomer is a tetradecamer, (ClpP)₁₄, consisting of two heptamers, (ClpP)₇stacked on top of each other in a head-to-head fashion. The measurement of crystal density indicates that two independent copies of the ClpP oligomers are present in the asymmetric unit, giving a crystal volume per protein mass (V_M) of 2.73 ų/Da and a solvent content of 54.9% (v/v). Self-rotation function calculations are consistent with the presence of two ClpP tetradecamers in the asymmetric unit. The Patterson function suggests that a translation ofx=0.5 andy=0.5 relates a pair of ClpP oligomers in one asymmetric unit to another pair in the other asymmetric unit. And the two independent tetradecamers in one asymmetric unit are related by a relative rotation of about 18° around the 7-fold axis.     

The Conversion of Nitrite to Nitrogen Oxide(s) by the Constitutive NAD(P)H-Nitrate Reductase Enzyme from Soybean

A two-step purification protocol was used in an attempt to separate the constitutive NAD(P)H-nitrate reductase [NAD(P)H-NR, pH 6.5; EC 1.6.6.2] activity from the nitric oxide and nitrogen dioxide (NO_(x)) evolution activity extracted from soybean (Glycine max [L.] Merr.) leaflets. Both of these activities were eluted with NADPH from Blue Sepharose columns loaded with extracts from either wild-type or LNR-5 and LNR-6 (lack constitutive NADH-NR [pH 6.5]) mutant soybean plants regardless of nutrient growth conditions. Fast protein liquid chromatography-anion exchange (Mono Q column) chromatography following Blue Sepharose affinity chromatography was also unable to separate the two activities. These data provide strong evidence that the constitutive NAD(P)H-NR (pH 6.5) in soybean is the enzyme responsible for NO_(x) formation. The Blue Sepharose-purified soybean enzyme has a pH optimum of 6.75, an apparent K_m for nitrite of 0.49 millimolar, and an apparent K_m for NADPH and NADH of 7.2 and 7.4 micromolar, respectively, for the NO_(x) evolution activity. In addition to NAD(P)H, reduced flavin mononucleotide (FMNH₂) and reduced methyl viologen (MV) can serve as electron donors for NO_(x) evolution activity. The NADPH-, FMNH₂-, and reduced MV-NO_(x) evolution activities were all inhibited by cyanide. The NADPH activity was also inhibited by p-hydroxymer-curibenzoate, whereas, the FMNH₂ and MV activities were relatively insensitive to inhibition. These data indicate that the terminal molybdenum-containing portion of the enzyme is involved in the reduction of nitrite to NO_(x). NADPH eluted both NR and NO_(x) evolution activities from Blue Sepharose columns loaded with extracts of either nitrate- or zero N-grown winged bean (Psophocarpus tetragonolobus [L.]), whereas NADH did not elute either type of activity. Winged bean appears to contain only one type of NR enzyme that is similar to the constitutive NAD(P)H-NR (pH 6.5) enzyme of soybean.     

Myelin Membrane Structure As Revealed by X-Ray Diffraction

The present work consists of a new interpretation of the data presented in the article entitled “X-Ray Diffraction of Myelin Membrane. II” by C. K. Akers and D. F. Parsons (1970, Biophys. J. 10:116). It will be shown that the projection of the electron density onto the normal to the myelin multilayer derived by these authors is no more consistent with their data than another electron density function, or, perhaps, its negative. (A density function and its negative are related as follows: one of them is a certain density distribution, the other is the same function subtracted from a constant uniform density. Two density functions so related produce identical diffracted intensities.) The Fourier series for the projection of the electron density onto the normal to the myelin multilayer has coefficients ±[hI(h)]^1/2 where I(h) are the intensities of the five orders of reflection; data from which these can be estimated are presented by Akers and Parsons. The sequence of signs found here is + - - + + for the positive density (or - + + - - for the negative one). Quantitative agreement exists between the five X-ray diffraction data of Akers and Parsons and the same intensities calculated from the new model of the myelin structure described here. In this model the myelin double layer, 171 A thick, consists of a central lipid layer 72.4 A thick covered on both surfaces by protein layers 6.9 A thick; these protein layers are covered, in turn, by other lipid layers 42.4 A thick. Minor modifications of this model will no doubt be required to produce agreement between the observed and calculated intensities of the higher order reflections.     

The Interpretation of Low-Angle X-Ray Data from Planar and Concentric Multilayered Structures: The Use of One-Dimensional Electron Density Strip Models

The use of one-dimensional electron density strip models in interpreting low-angle X-ray data from planar and concentric multilayered structures is described. Diffraction formulas for an n-strip model are given. Fourier transforms, normalization constants, and Patterson functions are derived for certain strip models.     

Rhodium(III) cis-dihydrido complexes with 3,6-bis(2′-pyridyl)pyridazine (dppn) and bidiazines. Crystal and molecular structure of [Rh(H)2(dppn)(PPh3)2]PF6· CH2Cl2

The acetone complex [Rh(H)₂(acetone)₂(PPh₃)₂]- PF₆ reacts with bidiazines and 3,6-bis(2′-pyridyl)- pyridazine (dppn) giving the air stable cis-dihydrido rhodium(III) [Rh(H)₂(L)(PPh₃)₂]PF₆ complexes. The structure of the dichloromethane solvate of [Rh(H)₂(dppn)(PPh₃)₂]PF₆ has been determined by X-ray crystal structure analysis. Crystals are monoclinic, space group P2₁/a, with a = 18.629(6), b = 15.339(5), c = 17.146(5) Å, β = 101.02(3)° and Z = 4. The structure has been solved from diffractometer data by Patterson and Fourier methods and refined by block-matrix least-squares to R = 0.076 for 6225 observed reflections. In the structure discrete [Rh(H)₂(dppn)(PPh₃)₂]⁺ cationic complexes, PF₆⁻ anions and dichloromethane solvent molecules are present. The Rh atom is octahedrally surrounded by two cis hydride ligands and by two cis nitrogen atoms from a dppn molecule acting as a bidentate chelating ligand through two neighbouring pyridyl and pyridazinyl nitrogen atoms. Two P atoms from PPh₃, ligands in trans apical positions complete to octahedral the coordination of Rh.     

Note on the Theory of X-Ray Diffraction by Spherical Shell Structures

An equation is derived, which connects two functions P(r) and g(x), the first being related to the scattering intensity by a simple transformation, the second to the elctron density distribution of a spherically symmetric structure. This relation seems to be a suitable starting point for an analysis of shell structures from diffraction patterns.     

Cytochrome c4 from Pseudomonas aeruginosa

The dihaem cytochrome c₄ from Pseudomonas aeruginosa has been crystallized in space group P6₅22 with cell dimensions $\text{a = b = 62.4}\text{A}\text{?}\text{, c = 174.2}\text{A}\text{?}$, and one molecule per asymmetric unit. Two heavy-atom derivatives, UO₂(NO₃)₂ and K₂Pt(NO₂)₄, which substitute at one and three sites, respectively, have allowed a low-resolution electron density map to be obtained. This shows clearly the two domains of the molecule.     

The preparation and crystal structure analysis of bis(L-Arginine)Cu(II)(acetate)2trihydrate

The crystal structure of bis(L-arginine)Cu(II)(acetate)₂trihydrate has been determined by X-ray analysis. The complex crystallizes in the monoclinic space group P2₁, with cell dimensions a = 15.948(2), b = 16.878(2), c = 10.378(2) Å, β = 108.47(1)°, Z = 4. There are two independent formula units in the asymmetric unit. The Cu atoms were located from a Patterson synthesis and the remaining atoms from difference Fourier syntheses. The structure was refined by least-squares to R = 0.079 and R = 0.11. Each copper atom has an essentially square planar coordination with the two arginine molecules chelated via the carboxy oxygens and the α-amino nitrogens, but with distorted six-fold coordinations completed by weak Cu…O (acetate) interactions. Electrostatic interactions between the acetates and the protonated ends of the amino acid residues link the two independent [Cu(L-arginine)₂(acetate)₂] units into dimers, which are then connected via hydrogen bonds, also involving the water molecules, into an infinite network.     

An inspection into the class of bis(alkyne)-undecacarbonyl-quadro-tetraruthenium complexes. Crystal structure and dynamic behaviour of Ru4(CO)11 (μ4, η2-MeC2Ph)2

The reactions of the butterfly complex Ru₄(CO)₁₂(MeC₂Ph) with several alkynes give the quasiplanar derivatives Ru₄(CO)₁₁(MeC₂Ph)(Alkyne) in almost quantitative yields.The structure of Ru₄(CO)₁₁(MeC₂Ph)₂ has been determined by X-ray methods. Crystals are monoclinic, space group C2/c, with Z = 4 in a unit cell of dimensions a 22.383(16), b 9.048(8), c 18.268(12) Å, β = 127.25(4)°. The structure has been solved from diffractometer data by Patterson and Fourier methods and refined by full-matrix least-squares to R = 0.034 for 1420 observed reflections. The complex, having an imposed C₂ symmetry, presents a tetranuclear metal cluster in which the Ru atoms are in a tetrahedrally-distorted square arrangement. Ten carbonyls are terminal and one symmetrically bridges an edge of the cluster. Each of the two alkyne ligands is σ-bonded to two Ru atoms on the opposite vertices of the cluster and π-bonded to the other two. The organometallic cluster has a Ru₄C₄ core in which the metal and carbon atoms occupy the vertices of a triangulated dodecahedron.     

Non-crystallographic symmetry in the crystal dimer of wheat germ agglutinin

Three isomorphous heavy atom derivatives of wheat germ agglutinin crystals, KAu(CN)₂, K₂Pt(NH₃)₂(NO)₂ and mersalyl, have been examined at high resolution. Heavy atom sites were located from difference Patterson maps in three dimensions at 2.15 Å resolution for the gold and platinum derivatives and with less certainty in the centrosymmetric [010] projection for the mersalyl derivative. These sites are distributed in the crystallographic asymmetric unit such that one half of them can be related to the other half by a 180 ° rotation about an axis parallel to a, and an additional translation of about 6.35 Å along that axis. It is suggested that the two subunits of the wheat germ agglutinin dimer, which represent the asymmetric unit of the C2 unit cell, are related by the same symmetry axis, causing heterologous subunit contacts due to the 6.35 Å translation of one relative to the other subunit.     

Cross-Correlation Functions for a Neuronal Model

Cross-correlation functions, R_XY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, R_XY(t,τ) = f_U [θ-h(τ), t + τ] {h′(τ) + E_U [u′(t + τ)]} for positive values of this quantity, where f_U(u,t) is the probability density function of U(t) and E_U [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in R_XY(t,τ) for a neuron subjected only to excitation. (3) For large τ, R_XY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) R_XY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.     

Probabilistic Model of Microbial Cell Growth,Division, and Mortality

After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability P_d(t)δt, dead with probability P_m(t)δt, or alive but undivided with the probability 1 − [P_d(t) + P_m(t)]δt, where t is time, P_d(t) expresses the probability of division for an individual cell per unit of time, and P_m(t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat''s properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population''s size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With P_d(t) and P_m(t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data.     

Histochemical Approach to Properties of Vicia faba Guard Cell Phosphoenolpyruvate Carboxylase

Properties of phosphoenolpyruvate carboxylase in guard cells dissected from frozen-dried Vicia faba L. leaflets were studied using quantitative histochemical techniques. Control experiments with palisade cells and whole leaflet extract proved that the single cell approach was valid. Most characteristics of enzyme activity in guard cells were identical to those in the leaflet extract. The activities were highly dependent on temperature, with maximum activity at 25 to 35 C. Half-maximum activity (with 1 millimolar phosphoenolpyruvate [PEP]) was observed at 0.1 millimolar Mg²⁺. Two-hundred millimolar NaCl inhibited the reaction by 50%. With frozen-dried leaflet extract, the apparent K_m(PEP) was 0.15 millimolar at pH 7.7; with guard cells, the values were 1.49, 0.5 to 0.8, and 0.24 millimolar in three successive experiments. Additional experiments showed that apparent K_m(PEP) of guard cell activity from plants within a single growth lot was reproducible and did not change during stomatal opening. Mixed extract experiments proved that soluble compounds were not responsible for the difference observed between leaflet and guard cell activities. The differences in apparent K_m(PEP) of guard cell activity could not be unambiguously interpreted. The physiological implications of the properties of this enzyme in guard cells are discussed.     

Multi-isomorphous replacement phasing of the earthworm fibrinolytic enzyme component A from Eisenia fetida

Earthworm fibrinolytic enzyme component A (EFEa) from Eisenia fetida, a protein functioning not only as a direct fibrinolytic enzyme, but also as a plasminogen activator, has been crystallized in P2₁2₁2₁ space group with 3 protein molecules per asymmetric unit. Four heavy atom derivatives were prepared using a mother liquor containing 1.4 mol · L^-1 Li₂SO₄ and 0.1 mol · L^-1 MOPS buffer (pH7.2) and used to solve the protein’s diffraction phase. The heavy atom binding sites in the derivative crystals were determined using difference Patterson and difference Fourier methods and were refined in combination to yield the initial protein’s structure phase at 0.25 nm resolution. The non-crystallographic symmetry relationship of the three independent protein molecules in the asymmetric unit was determined using the correlative heavy atom sites and used for the averaging of the initial electron density. As a result, the electron density was significantly improved, providing a solid foundation for subsequent structure determination.     

Recognition of ribonuclease A by 3'-5'-pyrophosphate-linked dinucleotide inhibitors: a molecular dynamics/continuum electrostatics analysis

The proteins of the pancreatic ribonuclease A (RNase A) family catalyze the cleavage of the RNA polymer chain. The development of RNase inhibitors is of significant interest, as some of these compounds may have a therapeutic effect in pathological conditions associated with these proteins. The most potent low molecular weight inhibitor of RNase reported to date is the compound 5′-phospho-2′-deoxyuridine-3-pyrophosphate (P→5)-adenosine-3-phosphate (pdUppA-3′-p). The 3′,5′-pyrophosphate group of this compound increases its affinity and introduces structural features which seem to be unique in pyrophosphate-containing ligands bound to RNase A, such as the adoption of a syn conformation by the adenosine base at RNase subsite B₂ and the placement of the 5′-β-phosphate of the adenylate (instead of the α-phosphate) at subsite P₁ where the phosphodiester bond cleavage occurs. In this work, we study by multi-ns molecular dynamics simulations the structural properties of RNase A complexes with the ligand pdUppA-3′-p and the related weaker inhibitor dUppA, which lacks the 3′ and 5′ terminal phosphate groups of pdUppA-3′-p. The simulations show that the adenylate 5′-β-phosphate binding position and the adenosine syn orientation constitute robust structural features in both complexes, stabilized by persistent interactions with specific active-site residues of subsites P₁ and B₂. The simulation structures are used in conjunction with a continuum-electrostatics (Poisson-Boltzmann) model, to evaluate the relative binding affinity of the two complexes. The computed relative affinity of pdUppA-3′-p varies between −7.9 kcal/mol and −2.8 kcal/mol for a range of protein/ligand dielectric constants (ε_p) 2–20, in good agreement with the experimental value (−3.6 kcal/mol); the agreement becomes exact with ε_p = 8. The success of the continuum-electrostatics model suggests that the differences in affinity of the two ligands originate mainly from electrostatic interactions. A residue decomposition of the electrostatic free energies shows that the terminal phosphate groups of pdUppA-3′-p make increased interactions with residues Lys⁷ and Lys⁶⁶ of the more remote sites P₂ and P₀, and His¹¹⁹ of site P₁.     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

The Role of Active Oxide Species for Electrochemical Water Oxidation on the Surface of 3d‐Metal Phosphides

Transition metal phosphides (TMPs) have recently been utilized as promising electrocatalysts for oxygen evolution reaction (OER) in alkaline media. The metal oxides or hydroxides formed on their surface during the OER process are hypothesized to play an important role. However, their exact role is yet to be elucidated. Here unambiguous justification regarding the active role of oxo(hydroxo) species on O‐Ni_(1?x)Fe_xP₂ nanosheet with pyrite structure is shown. These O‐Ni_(1?x)Fe_xP₂ (x = 0.25) nanosheets demonstrate greatly improved OER performance than their corresponding hydroxide and oxide counterparts do. From density function theory (DFT) calculations, it is found that the introduction of iron into the pyrite‐phased NiP₂ alters OER steps occurred on the surface. Notably, the partially oxidized surface of O‐Ni_(1?x)Fe_xP₂ nanosheets is vital to improve the local environment and accelerate the reaction steps. This study sheds light on the OER mechanism of the 3d TMP electrocatalyst and opens up a way to develop efficient and low‐cost electrocatalysts.