An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Design of Peptides Using α,β-Dehydro-residues: Synthesis,Crystal Structure and Molecular Conformation of N-Boc-L-Val-ΔPhe–ΔPhe-L-Ala-OCH3

To obtain general rules of peptide design using α,β-dehydro-residues, a sequence with two consecutive ΔPhe-residues, Boc-L -Val-ΔPhe–ΔPhe- L -Ala-OCH₃, was synthesized by azlactone method in solution phase. The peptide was crystallized from its solution in an acetone/water mixture (70:30) in space group P6₁ with a=b=14.912(3) Å, c= 25.548(5) Å, V=4912.0(6) ų. The structure was determined by direct methods and refined by a full matrix least-squares procedure to an R value of 0.079 for 2891 observed [I?3σ(I)] reflections. The backbone torsion angles ?₁=?54(1)°, ψ₁= 129(1)°, ω₁=?177(1)°, ?₂ =57(1)°, ψ₂=15(1)°, ω₂ =?170(1)°, ?₃=80(1)°, ψ₃ =7(2)°, ω₃=?177(1)°, ?₄ =?108(1)° and ψ^T₄=?34 (1)° suggest that the peptide adopts a folded conformation with two overlapping β-turns of types II and III′. These turns are stabilized by two intramolecular hydrogen bonds between the CO of the Boc group and the NH of ΔPhe³ and the CO of Val¹ and the NH of Ala⁴. The torsion angles of ΔPhe² and ΔPhe³ side chains are similar and indicate that the two ΔPhe residues are essentially planar. The folded molecules form head-to- tail intermolecular hydrogen bonds giving rise to continuous helical columns which run parallel to the c-axis. This structure established the formation of two β-turns of types II and III′ respectively for sequences containing two consecutive ΔPhe residues at (i+2) and (i+3) positions with a branched β-carbon residue at one end of the tetrapeptide.     

On the Analysis of Variance for Time Sequenced Samples

The 3 way nested ANOVA model y_ijk = μ + a_i + B_ij + γ_k + (αγ)_ik + epsilon_ijk With α (treatment or group effects) and γ (time) both being fixed effects and B (the individual effects) random and nested within α, is introduced and explored. The problems associated with the usual approach are explained. The alternative model Is developed and a method of evaluation via the method of linear contrasts is recomended. The test statistic has the distribution of a convolution of F-distributions. Further, a method of investigating the assumptions of the model is offered and a further generalization using path spaces (of dim. K) is developed. Here again the appropriate test statistic has the distribution of a convolution of F-distributions. This combined with the method of linear contrasts offers an elegant solution to the BEHRENS-FISHER problem. y_ijk = f_ik + B_ij + epsilon_ijk     

An Unbalanced Mixed Model with Random Effects Having Unequal Variances

Consider the mixed model where x_ijk's are known constants, β_k are unknown parameters and a_i, e_ij are random variables independently and normally distributed with zero means and variances σd_i and σ² respectively, where it is assumed that the d_i's are known (d_i >0). This paper presents procedures for estimating the variance components σ, σ², for testing the hypothesis σ = 0, and for making transformations to random variables with uncorrelated errors and constant variances in order to estimate as well as to test hypothesis concerning the β_k's in the model.     

Partitioning of mesophyll conductance for CO2 into intercellular and cellular components using carbon isotope composition of cuticles from opposite leaf sides

We suggest a new technique for estimating the relative drawdown of CO₂ concentration (c) in the intercellular air space (IAS) across hypostomatous leaves (expressed as the ratio c_d/c_b, where the indexes d and b denote the adaxial and abaxial edges, respectively, of IAS), based on the carbon isotope composition (δ¹³C) of leaf cuticular membranes (CMs), cuticular waxes (WXs) or epicuticular waxes (EWXs) isolated from opposite leaf sides. The relative drawdown in the intracellular liquid phase (i.e., the ratio c_c/c_bd, where c_c and c_bd stand for mean CO₂ concentrations in chloroplasts and in the IAS), the fraction of intercellular resistance in the total mesophyll resistance (r_IAS/r_m), leaf thickness, and leaf mass per area (LMA) were also assessed. We show in a conceptual model that the upper (adaxial) side of a hypostomatous leaf should be enriched in ¹³C compared to the lower (abaxial) side. CM, WX, and/or EWX isolated from 40 hypostomatous C₃ species were ¹³C depleted relative to bulk leaf tissue by 2.01–2.85‰. The difference in δ¹³C between the abaxial and adaxial leaf sides (δ¹³C_AB ? ¹³C_AD, Δ_b–d), ranged from ??2.22 to +?0.71‰ (??0.09 ± 0.54‰, mean ± SD) in CM and from ??7.95 to 0.89‰ (??1.17 ± 1.40‰) in WX. In contrast, two tested amphistomatous species showed no significant Δ_b–d difference in WX. Δ_b–d correlated negatively with LMA and leaf thickness of hypostomatous leaves, which indicates that the mesophyll air space imposes a non-negligible resistance to CO₂ diffusion. δ¹³C of EWX and 30-C aldehyde in WX reveal a stronger CO₂ drawdown than bulk WX or CM. Mean values of c_d/c_b and c_c/c_bd were 0.90 ± 0.12 and 0.66 ± 0.11, respectively, across 14 investigated species in which wax was isolated and analyzed. The diffusion resistance of IAS contributed 20 ± 14% to total mesophyll resistance and reflects species-specific and environmentally-induced differences in leaf functional anatomy.

     

Crystallization and preliminary X-ray crystallographic studies of ketosteroid isomerase from Pseudomonas putida biotype B

The Δ⁵-3-ketosteroid isomerase from Pseudomonas putida biotype B has been crystallized. The crystals belong to the space group P2₁2₁2₁ with unit cell dimensions of a = 36.48 Å, b = 74.30 Å, c = 96.02 Å, and contain one homodimer per asymmetric unit. Native diffraction data to 2.19 Å resolution have been obtained from one crystal at room temperature indicating that the crystals are quite suitable for structure determination by multiple isomorphous replacement.     

Purification,crystallization, and preliminary X-ray diffraction analyses of the bacterial chemotaxis receptor modifying enzymes

Bacterial chemotaxis receptor modifying enzymes from Salmonella typhimurium have been crystallized using microseeding techniques. The crystals of the S-adenosyl-L -methionine-dependent methyl transferase, CheR, belong to the monoclinic space group P2₁ with cell constants a = 55.1 Å, b = 48.1 Å, c = 63.1 Å, β = 112.3°. The crystals of the catalytic domain of the methylesterase, CheB, belong to the trigonal space group P3₂21 or P3₁21 with unit cell dimensions of a = b = 63.4 Å, c = 86.8 Å. Both crystals contain one molecule per asymmetric unit and have calculated Matthews' volumes of 2.4 ų/Da. © 1995 Wiley-Liss, Inc.     

Syntheses of 1-[2-(Phosphonomethoxy)Alkyl]Thymine Monophosphates and an Evaluation of their Inhibitory Activity Toward Human Thymidine Phosphorylase

A series of new monophosphates of 1-[2-(phosphonomethoxy)alkyl]thymines, such as PMPTp_, 3-MeO-PMPTp, HPMPTp, and FPMPTp, were synthesized and tested for their ability to inhibit human thymidine phosphorylase. Kinetic measurements of enzyme activity were performed using thymidine and inorganic phosphate as the substrates. The data show that some monophosphates provide a considerable increase of the multisubstrate inhibitory effect. The highest inhibitory potency was found with (R)-FPMPTp 4c (K _i ^dT = 4.09 ± 0.47 μM, K _i(P_i) = 2.13 ± 0.29 μM) and (R) 3-MeO-PMPTp 4d (K _i ^dT = 5.78 ± 0.71 μM, K _i(P_i) = 2.71 ± 0.37 μM).     

Crystallization and preliminary X-ray studies of ornithine decarboxylase from Trypanosoma brucei

Trypanosoma brucei ornithine decarboxylase, expressed and purified from E. coli, has been crystallized by the vapor diffusion method using PEG 3350 as a precipitant. The crystals belong to the monoclinic space group P2₁ and have cell constants of a = 66.3 Å, b = 151.8 Å, c = 83.7 Å, and β = 101.2°. While larger crystals are twinned, smaller crystals (0.4 × 0.3 × 0.05 mm³) are single.     

Stereodynamics of Small 1,2-Dialkyldiaziridines

Diaziridines are very interesting representatives of organic compounds containing stereogenic nitrogen atoms. In particular, 1,2-dialkyldiaziridines show extraordinarily high stereointegrity. The lone electron pairs of the nitrogen atoms are in trans configuration, avoiding a four-electron repulsive interaction. Furthermore, the trans configuration of the substituents at the nitrogen atoms is energetically favored because of reduced steric interactions. Therefore only two stereoisomers (enantiomers) are observed. At elevated temperatures the enantiomers are interconverting because of the limited stereointegrity of the chirotopic nitrogen atoms. The enantiomerization rate constants and the activation parameters of interconversion are of great interest. Here, we investigated the stereodynamics of a set of small 1,2-dialkyldiaziridines bearing short substituents (Me, Et, iPr, tBu), using enantioselective dynamic gas chromatography (DGC). Separation of enantiomers of all compounds, including the highly volatile 1,2-dimethyldiaziridine, was achieved using heptakis(2,3-di-O-ethyl-6-O-tert-butyldimethylsilyl)-β-cyclodextrin in 50% PS086 (w/w) as chiral stationary phase in fused silica capillaries with a length of up to 50 m. Measurements at variable temperatures were performed and reaction rate constants were determined using the unified equation of chromatography implemented in the software DCXplorer. The activation barriers at room temperature for 1-(tert-butyl)-2-ethyldiaziridine, ΔG^╪_298K = 123.8 kJ mol^–1 (ΔH^╪ = 115.5 ± 2.9 kJ mol^–1, ΔS^╪ = –28 ± 1 J mol^–1 K^–1), and 1-ethyl-2-isopropyldiaziridine, ΔG^╪_298K = 124.2 kJ mol^–1 (ΔH^╪ = 113.1 ± 2.4 kJ mol^–1, ΔS^╪ = –37 ± 2 J mol^–1 K^–1), were determined, representing some of the highest values observed for nitrogen inversion in diaziridines. Chirality 00:000–000, 2013. © 2013 Wiley Periodicals, Inc.     

Models of Plant Disease Epidemics. II: Gradients of Bean Rust

The spread of bean rust from three types of inoculum sources (area, line, and point) was studied under field conditions in two seasons. Disease intensity (y) over time was quantified as incidence of diseased plants, incidence of diseased leaves, and disease severity at distances (d) of 0.3, 0.7, 1.5, 2.7, 4.3, 6.5, and 8.7 m from the inoculum sources. Seven curvilinear models were compared and the models that best explained the gradients of bean rust were y = ad^?b exp(cd), y = a exp(–bd^c) and y = a exp(–bd); where a was proportion of disease near the source, d was distance in metres, b was the slope, and c was a shape parameter. For general analysis to compare the slopes of the gradients, the gradient curves were linearized by ln(y) versus d and the parameters ln(a) (intercept) and b (slope) were estimated. The three measures of disease intensity and the three types of inoculum sources had estimated gradient parameters that were statistically different. The incidence of diseased plants rapidly approached y = 1.0 and the gradient slopes were near zero. Also with the ln(y) linearization, the gradients of the incidence of diseased leaves had slopes flatter than the gradients of disease severity. The gradient slopes from area sources of inoculum were flatter than from line sources, which in turn were flatter than from point sources. Late in the epidemics, the b-values became similar for all combinations of inoculum sources × assessment types. The interpretation of flattening of the gradients was confounded because aberrations in transformations occurred with most models. That is, when the intensity of disease (incidence or severity) approached the maximum, the increases in the intercepts were restricted and this restriction was responsible for most of the flattening. No flattening of gradients occurred over time when the gompit gradient model [–ln(–ln(y/y_max)) = –ln(–ln(a))?b ln(d)] was used for these same disease values. The fitting of models to the gradients served little purpose except to classify the curves in a general way. A new statistic, the area under the disease gradient curve (AUDGC), is proposed to compare epidemics.     

Thermodynamic parameters for the helix-coil thermal transition of ribonuclease-S-peptide and derivatives from 1H-NMR data

Values for the thermodynamic quantities, ΔH° = 11.8 ± 2.0 Kcal/mole and ΔS° = 43.6 ± 6.0 e.u., of the 3-13 helix–coil equilibrium of isolated S-peptide (19 residue N-terminal fragment of ribonuclease A) in aqueous solution (3 m M, 1M NaCl, pD 5.4) have been determined from a joint analysis of the Thr 3γ, Ala 6β, Phe 8meta, and Phe 8para ¹H chemical shift vs temperature curves (?7 to 80°C) in several aqueous–trifluorethanol mixtures. Chemical shifts in the coil and in the helix have been determined for up to 16 protons belonging to the 3-13 fragment. Thermodynamic parameters have also been determined for C-peptide (13 residue fragment) and a number of S-peptide derivatives. From the variation of the values of the thermodynamic parameters at pD 2.5, 5.4, and 8.0, a quantitation of the two helix-stabilizing side-chain interactions can be made: (1) Δ(ΔH°) ? 5 Kcal/mole and Δ(ΔS°) ? 18 e.u. for the salt bridge Glu 2^? … Arg 10⁺ and (2) Δ(ΔH°) ? 3 Kcal/mole and Δ(ΔS°) = 9 e.u. for the one in which the His 12⁺ imidazolium group is involved, presumably a partial stacking with the Phe 8 side chain.     

Peptide design 310-helical conformation of a linear pentapeptide containing two dehydrophenylalanines,Boc-Gly-ΔZPhe-Leu-ΔZPhe-Ala-NHCH3

α, β-Dehydroamino acids are expected to provide conformational constraint to the peptide backbone. A pentapeptide containing two dehydrophenylalanines (Δ^ZPhe) separated by one L -amino acid has been synthesized and its solid state conformation determined. The pentapeptide, Boc-Gly-Δ^ZPhe-Leu-Δ^ZPhe-Ala-NHCH₃, crystallizes from aqueous methanol in the orthorhombic space group P2₁2₁2₁. There are four formula units, C₃₅H₄₆N₆O₇, in a unit cell of dimensions a = 10.155(3), b = 15.175(1), and c = 23.447(2) Å, at room temperature. The structure was solved by direct methods program, SIR88, and refined to a final R = 0.038 based on 3049 reflections with I > 2σ(I). All the peptide links are trans and the backbone conformation of the pentapeptide can be described as a 3₁₀-helix, with mean ?, ψ values of ?65.1° and ?22.8° (the value is averaged over the first four residues). There are four intramolecular 4 → 1 type hydrogen bonds characteristic of 3₁₀-type helices. In the crystal, the helices are held together by intermolecular N? H…?O?C head-to-tail and lateral hydrogen bonding between symmetry related molecules. This mode of packing is similar to the packing motifs observed so often in other oligopeptides that adopt a 3₁₀-helical structure. © 1993 John Wiley & Sons, Inc.     

Conformational properties of Pro-Pro sequences. I. Crystal structures of two dipeptides with L-Pro-L-Pro and L-Pro-D-Pro sequences

The crystal structures of Bu^tCO-L -Pro-L -Pro-NHMe, H₂O (1: monoclinic; P2₁; a = 6.662, b = 11.067, c = 12.205 Å; β = 96.28°) and Bu^tCO-L -Pro-D -Pro-NHMe (2: monoclinic; P2₁; a = 10.770, b = 15.039, c = 11.325 Å; β = 110.00°) have been solved by x-ray diffraction. Structure 1 accommodates an open disposition with intermolecular interactions involving the water molecule, while 2 is βII-folded by an intramolecular i + 3 → i hydrogen bond. In both derivatives, small thermal parameters are indicative of fairly fixed conformations for the proline rings. Comparison between conformations of either isolated or adjacent L -Pro residues in the crystal structures of unstrained oligopeptides shows that the conformational properties of L -Pro-L -Pro sequences are probably a simple combination of those found for isolated L -Pro residues.     

α,β-Dehydro-amino acid residues in the design of peptide structures: Synthesis,crystal structure,and molecular conformation of two homologous peptides—N-Ac-Dehydro-Phe-L-Leu-OCH3 and N-Ac-Dehydro-Phe-NorVal-OCH3

The dehydro-residue containing peptides N-Ac-dehydro-Phe-L -Leu-OCH₃ ( I ) and N-Ac-dehydro-Phe-NorVal-OCH₃ ( II ) were synthesized by the usual workup procedures. The peptides crystallize from their solutions in methanol in space group P6₅: ( I ) a = b = 12.528(2) Å, c = 21.653(5) Å; ( II ) a = b = 12.532(2) Å, c = 21.695(4) Å. The structures were determined by direct methods. Both peptides adopt similar conformations with ?,ψ of dehydro-Phe as follows: ( I ) ?57.0(5)° and ?37.0(5)°; ( II ) ?56.0(5),° and ?37.5(5)°. The observed data on dehydro-Phe when placed at the (i + 1) position show that the ?,ψ values of dehydro-Phe are either ?60°, 140° or ?60°, ?30°. The conformation of ?60°, 140° can be accommodated only with a flexible residue at the (i + 2) position while the ?,ψ values of ?60°, ?30° are obtained with a bulky residue at the (i + 2) position as in the present structures. The molecules are packed in a helical way along the c axis. These are held by two strong intermolecular hydrogen bonds involving both NH as donors and acetyl group and dehydro-Phe oxygen atoms as acceptors. © 1994 John Wiley & Sons, Inc.     

Purification,crystallization, and preliminary X-ray studies on the rhizome lectin from stinging nettle and its complex with NN′N″-triacetylchitotriose

Single crystals were grown from affinity-purified stinging nettle lectin and from its complex with the specific trisaccharide NN′N″ -triacetylchitotriose by vapor diffusion at room temperature. The lectin crystallizes in space group P2₁2₁2₁ with unit cell dimensions a = 54.3 (1) Å, b = 62.2 (1) Å, and c = 92.4 (2) Å, and diffracts to 3.0 Å resolution. The asymmetric unit contains three lectin monomers. The crystals of the lectin-trisaccharide complex have space group P2₁2₁2₁ with cell constants a = 37.69 (4) Å, b = 48.97 (6) Å, and c = 57.32 (4) Å. These crystals diffract to at least 2.0 Å resolution and the asymmetric unit contains one lectin monomer. A three-dimensional X-ray structure determination is on its way. © 1993 Wiley-Liss, Inc.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

The crystal structure of the photosynthetic inhibitors DCMU and DTPU

X-ray diffraction studies have been carried out on a single crystal of the photosynthetic inhibitors N-(3,4-dichlorophenyl)-N′-dimethylurea (DCMU) and its newly synthesized spin-labeled analog N-(3,4-dichlorophenyl)-N′-(3,3,5,5-tetramethylpiperidine-4-oxyl)-urea (DTPU). The synthesis of DTPU as well as its crystallographic data are reported. The crystal system of both compounds is monoclinic with a space group P2₁/c. The cell constants of DCMU are a = 7.759(1), b = 14.737(3), c = 9.233(2) Å, β = 100.99(6)°; of DTPU they are a = 6.976(1), b = 11.998(2), c = 23.585(3) Å, β = 91.38(5)°. Comparison of conformational parameters of DCMU and DTPU reveal differences in the dihedral angle between the aromatic ring and the ureido plane. The measured volumes of DCMU and DTPU are 259.1 and 493.3 ų, respectively. These figures suggest the size of the binding site of the inhibitors in the photosynthetic membrane.     

Experimental conformational study of two peptides containing α-aminoisobutyric acid. Crystal structure of N-acetyl-α-aminoisobutyric acid methylamide

Some theoretical studies have predicted that the conformational freedom of the α-aminoisobutyric acid (H-Aib-OH) residue is restricted to the α-helical region of the Ramachandran map. In order to obtain conformational experimental data, two model peptide derivatives, MeCO-Aib-NHMe 1 and Bu^tCO-LPro-Aib-NHMe 2 , have been investigated. The Aib dipeptide 1 crystallizes in the monoclinic system (a = 12.71 Å, b = 10.19 Å, c = 7.29 Å, β = 110.02°, Cc space group) and its crystal structure was elucidated by x-ray diffraction analysis. The azimuthal angles depicting the molecular conformation (? = ?55.5°, ψ = ?39.3°) fall in the α-helical region of the Ramachandran map and molecules are hydrogen-bonded in a three-dimensional network. In CCl₄ solution, ir spectroscopy provides evidence for the occurrence of the so-called ₅ and C₇ conformers stabilized by the intramolecular i → i and i + 2 → i hydrogen bonds, respectively. The tripeptide 2 was studied in various solvents [CCl₄, CD₂Cl₂, CDCl₃, (CD₃)₂SO, and D₂O] by ir and pmr spectroscopies. It was shown to accommodate predominantly the βII folded state stabilized by the i + 3 → i hydrogen bond. All these experimental findings indicate that the Aib residue displays the same conformational behavior as the other natural chiral amino acid residues.