An Unbalanced Two-way Model With Random Effects Having Unequal Variances

Consider the model y_ijk=u ± a_i ± b_i ± c_ij ± e_ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n_ij where μ is a constant and a_i, b_i, c_ij are distributed independently and normally with zero means and variances Δ₂ Δ2/bd_ij and δ₂ respectively. It is assumed that d_i's, and d_ij's are known (positive) constants (for all i and j). In this paper procedures for estimating the variance components (Δ₂, Δ²_b and Δ²_a) and for testing the hypothesis H_oc:Δ²_c/Δ² = y₃ and H_oa:Δ²_b/Δ² = y₄ (where y₂, y₃, and y₄, are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.     

Variation of photosynthetic performance, nutrient uptake, and elemental composition of different generations and different thallus parts of Saccharina japonica

In order to illustrate the physiological variation of different generations and different thallus parts of Saccharina japonica, physiological parameters such as maximum and effective PSII photochemical efficiency, nutrient uptake, and elemental composition were determined in the laboratory. Photosynthetic analysis in different generations indicated that, although gametophytes had higher pigment contents than the sporophyte, they had lower values of F _v/F _m and ΔF/F′_m. The highest Chl a/Chl c ratio was found in sporophyte generation (3.98?±?0.01) and in the basal part of fresh thallus (2.66?±?0.02). The sporophyte had significantly higher values of nitrate uptake but lower values of phosphorus uptake than the gametophytes. The contents of nitrogen and carbon as well as C/N in gametophytes were significantly higher than those in sporophytes. In addition, the basal part of the S. japonica thallus had the highest C content (22.31?±?1.50 %) but the lowest N content (2.02?±?0.16 %), as well as the highest value of C/N (11.02?±?0.34).     

The effect of calcium on the thermotropic properties of bovine blood coagulation factors IX and X and their activation intermediates and products

The thermotropic properties of bovine blood coagulation Factors IX and X, as well as the activation intermediates and products of these proteins, have been investigated by differential scanning microcalorimetry in the presence and absence of Ca²⁺. Bovine Factor IX displays a single thermal-denaturation transition characterized by a temperature midpoint (T_M) of 54.5 ± 0.5 °C and a calorimetric enthalpy (ΔH_c) of 105 ± 15 kcal/mol, in the absence of Ca²⁺. In the presence of Ca²⁺ concentrations sufficient to saturate its sites on Factor IX, the T_m value is increased to 57.0 ± 0.5 °C and the ΔH_c is virtually unchanged. When the activation intermediate, Factor IXα, is similarly analyzed in the absence of Ca²⁺, a broad, diffuse thermogram was obtained which did not lend itself to calculation of thermodynamic parameters. In the presence of Ca²⁺, Factor IXα displayed thermograms characterized by a T_M of 51.0 ± 0.5 °C and a ΔH_c of 109 ± 10 kcal/mol. The activated product, Factor IXaα, in the absence of Ca²⁺ (the values in the presence of saturating Ca²⁺ are given in parentheses), undergoes thermal denaturation with a T_M of 54.5 ± 0.5 °C (57.0 ± 0.5 °C) and a ΔH_c of 158 ±10 kcal/mol (156 ± 10 kcal/mol). Similarly, the terminal-activation product, Factor IXaβ, displays a T_M of 51.5 ± 0.5 °C (54.0 ± 0.5 °C) and a ΔH_c of 85 ± 5 kcal/mol (126 ± 10 kcal/mol). Bovine blood coagulation Factor X has been analyzed in this same fashion, and shows very similar thermal properties to Factor IX. The thermal denaturation of Factor X is represented by a T_M of 54.0 ± 0.5 °C (55.0 ± 0.5 °C) and a ΔH_c of 102 ± 10 kcal/mol (118 ± 10 kcal/mol), whereas its activated form, Factor Xaβ, possesses a T_M of 55.0 ± 0.5 °C (55.0 ± 0.5 °C) and a ΔH_c of 92.0 ± 5 kcal/mol (136 ± 10 kcal/mol). These studies indicate that, for many of these proteins, Ca²⁺ induces a conformational alteration to a more thermally stable form, which also requires the absorption of greater amounts of heat for thermal denaturation.     

Stretching and overstretching of DNA in pulsed field gel electrophoresis. I. A quantitative study from the steady state birefringence decay

Using a sensitive birefringence instrument, the birefringence arising from the orientation of the DNA chain during electrophoretic transport has been recorded. This birefringence is shown to proceed both from the alignment (stretching) of the molecule in the direction of the electric field and from the extension of the length of its primitive path (overstretching). The contribution of these two processes can be separated in the decay of the birefringence after the end of the application of the electric field. The fast relaxation of the overstretching occurs first and is demonstrated to be the main contribution to the birefringence. The orientation factor of the remaining stretched state and its decay can be quantitatively understood using the biased reptation model. It provides, in addition, a high value for the tube diameter or gel pore size a (4500 ± 450 Å for a 0.7% agarose gel with a c^?0.6_g dependence in the agarose concentration c_g) and a low value for the effective charge per base pair (0.2e as compared to 0.5e using the condensation hypothesis). The contribution of overstretching to the birefringence is also quantitatively interpreted in term of the change in the mean length l of DNA inside a pore size a. The dynamics of decay of this overstretching is well represented by a stretched exponential with a stretching exponent α = 0.44. The mean decay time decreases slightly with increasing fields and scales with the overall DNA length close to N²₀. © 1993 John Wiley & Sons, Inc.     

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.     

Crystallographic structure of the turbine C-ring from spinach chloroplast F-ATP synthase

In eukaryotic and prokaryotic cells, F-ATP synthases provide energy through the synthesis of ATP. The chloroplast F-ATP synthase (CF₁F_O-ATP synthase) of plants is integrated into the thylakoid membrane via its F_O-domain subunits a, b, b’ and c. Subunit c with a stoichiometry of 14 and subunit a form the gate for H⁺-pumping, enabling the coupling of electrochemical energy with ATP synthesis in the F₁ sector.Here we report the crystallization and structure determination of the c14-ring of subunit c of the CF₁F_O-ATP synthase from spinach chloroplasts. The crystals belonged to space group C2, with unit-cell parameters a=144.420, b=99.295, c=123.51 Å, and β=104.34° and diffracted to 4.5 Å resolution. Each c-ring contains 14 monomers in the asymmetric unit. The length of the c-ring is 60.32 Å, with an outer ring diameter 52.30 Å and an inner ring width of 40 Å.     

Adsorption of the polypeptides on a solid surface. III. Behavior of stiff chains in a pore

A strict analytical theory has been developed describing the behavior of a model lattice polymer chain of arbitrary stiffness in a slitlike pore at polymer–adsorbent interaction energies –ε. The thermodynamic characteristics of the system were calculated. It was shown that the transition of the macromolecule from the solution volume inside a pore occurs by the first-order phase transition with evolution of latent heat of adsorption. The transition point –ε = –ε_c is determined by the chain stiffness and is independent of the pore width D. It is shown that in the precritical range, –ε < –ε_c, the free energy ΔF of the macromolecules in the pores is adequately described by the universal dependence ΔF = ΔF(D*/A), where D* is some effective pore width depending on the value of –ε, and A is the length of the Kuhn segment. At high attraction energies, –ε ? –ε_c, the macromolecules are bonded to the pore walls by a great number of units and their free energy depends only on –ε and the chain stiffness, ΔF = ΔF(A, ε). Close to the critical energy –ε ? –ε_c (transition range), ΔF is determined by both the stiffness of the macromolecule and the pore width D: ΔF ～ A²D^?1 for fairly high values of A and D. The possibilities of using porous media as protein stabilizers are discussed, and the value of the stabilizing effect depending on the chain stiffness is estimated.     

Effects of habitat loss and limitation on effective population size and inbreeding rates of Walia ibex (Capra walie) in Ethiopia

The effects of habitat loss and limitation on effective population size and inbreeding rates of Walia ibex (Capra walie) were assessed at Simien Mountains National Park. Total direct census was conducted in 2009. Historical data were obtained from park offices and literatures. Effective population sizes (N_e), inbreeding rates (ΔF) and heterozygosity losses to the whole and subdivided population per habitat were estimated. Correlations (r) between the two repeated direct censuses were positive (r = 0.99, P < 0.01). The mean N_e and ΔF (%/year) per study sites were 65.34 ± 59.45 and 0.0286 ± 0.032, respectively. The ΔF of the whole population of C. walie was 0.228 ± 0.011. The ΔF was negatively correlated with N_e (r = ?0.799, P < 0.05). The mean ΔF per fragmented habitat ranged from 0.3 (Cheneck) to 7.7% (Buait ras). The highest ΔFs per year were observed in Buait ras (7.7%), Adarmaz (7.4%) and Sankaber (4.5%). The mean heterozygosity loss per total population was 0.235 ± 0.42, which was about 23.5%. The differences in N_e and ΔF among the population per habitat were the results of habitat limitation, which in turn reduce the genetic variability and foster losses of heterozygosity.     

Cytochrome c interaction with membranes. The enthalpy of oxidation of cytochromes c, c2, and a1,2.

The enthalpy of oxidation of horse-heart cytochrome c bound to phospholipid vesicles was found to be 14.6 ± 0.3 kcal/mole at 25 °C, pH 7.0, equal to the value for oxidation of the free form of the cytochrome. The affinity constants for binding of the reduced and oxidized forms of cytochrome c were the same at 4 °C and 30 °C, indicating that ΔH ° of binding contributes negligibly to the overall enthalpy of oxidation of the bound cytochrome c. The free energy (ΔG °′) of oxidation of the bound cytochrome c was 1.3 kcal/mole smaller than that for the free form, the difference being due to the change in entropy favoring the oxidized state of the cytochrome in the bound state. Measurement of the ΔH °′ for the oxidation of cytochrome a relative to the ferri/ferrocyanide couple shows it to be the same, within the limits of experimental error to that for the oxidation of cytochrome c.     

Large contributions of coupled protonation equilibria to the observed enthalpy and heat capacity changes for ssDNA binding to Escherichia coli SSB protein

Many macromolecular interactions, including protein‐nucleic acid interactions, are accompanied by a substantial negative heat capacity change, the molecular origins of which have generated substantial interest. We have shown previously that temperature‐dependent unstacking of the bases within oligo(dA) upon binding to the Escherichia coli SSB tetramer dominates the binding enthalpy, ΔH_obs, and accounts for as much as a half of the observed heat capacity change, ΔC_p. However, there is still a substantial ΔC_p associated with SSB binding to ssDNA, such as oligo(dT), that does not undergo substantial base stacking. In an attempt to determine the origins of this heat capacity change, we have examined by isothermal titration calorimetry (ITC) the equilibrium binding of dT(pT)₃₄ to SSB over a broad pH range (pH 5.0–10.0) at 0.02 M, 0.2 M NaCl and 1 M NaCl (25°C), and as a function of temperature at pH 8.1. A net protonation of the SSB protein occurs upon dT(pT)₃₄ binding over this entire pH range, with contributions from at least three sets of protonation sites (pK_a1 = 5.9–6.6, pK_a2 = 8.2–8.4, and pK_a3 = 10.2–10.3) and these protonation equilibria contribute substantially to the observed ΔH and ΔC_p for the SSB‐dT(pT)₃₄ interaction. The contribution of this coupled protonation (∼ −260 to −320 cal mol⁻¹ K⁻¹) accounts for as much as half of the total ΔC_p. The values of the “intrinsic” ΔC_p,0 range from −210 ± 33 cal mol⁻¹ °K⁻¹ to −237 ± 36 cal mol⁻¹K⁻¹, independent of [NaCl]. These results indicate that the coupling of a temperature‐dependent protonation equilibria to a macromolecular interaction can result in a large negative ΔC_p, and this finding needs to be considered in interpretations of the molecular origins of heat capacity changes associated with ligand‐macromolecular interactions, as well as protein folding. Proteins 2000;Suppl 4:8–22. © 2000 Wiley‐Liss, Inc.     

Helix-coil transition of Poly(L-glutamic acid) in N-methylacetamide

The folding of randomly coiled poly(L -glutamic acid) to the helical state has been studied in N-methylacetamide by titration methods. Since this solvent would be expected to form amide-peptide group hydrogen bonds with the unfolded form of the polymer, to a first approximation no helix stabilization could come from intrapolymer hydrogen bonds. The titration data, collected from 30 to 70°C yield the following values per residue for the thermodynamic parameters governing the coil-helix reaction for the uncharged polymer: ΔG_30°C°, ?1. 9 ± 0.1 kcal; Δ H°, 0 ± 0.1 kcal; ΔS_30°C°, 6.3 ± 0.6 eu. In N-methyl acetamide, the helix is an order of magnitude more stable than in water, and this stabilization appears to be entirely the result of the entropy gained by solvent molecules which are released from the polymer upon folding.     

H+ transport and coupling by the F0 sector of the ATP synthase: Insights into the molecular mechanism of function

The F₀ sector of the ATP synthase complex facilitates proton translocation through the membrane, and via interaction with the F₁ sector, couples proton transport to ATP synthesis. The molecular mechanism of function is being probed by a combination of mutant analysis and structural biochemistry, and recent progress on theEscherichia coli F₀ sector is reviewed here. TheE. coli F₀ is composed of three types of subunits (a, b, andc) and current information on their folding and organization in F₀ is reviewed. The structure of purified subunitc in chloroform-methanol-H₂O resembles that in native F₀, and progress in determining the structure by NMR methods is reviewed. Genetic experiments suggest that the two helices of subunitc must interact as a functional unit around an essential carboxyl group as protons are transported. In addition, a unique class of suppressor mutations identify a transmembrane helix of subunita that is proposed to interact with the bihelical unit of subunitc during proton transport. The role of multiple units of subunitc in coupling proton translocation to ATP synthesis is considered. The special roles of Asp61 of subunitc and Arg210 of subunita in proton translocation are also discussed.     

Letter: X-ray data for four crystalline forms of serum albumin

Cell dimensions, space groups and crystal densities are reported for a monoclinic form of human serum albumin (a = 126.5, b = 39.2, c = 135.2Å, β = 93.3 °, C2, Z = 4), tetragonal human serum albumin (a = 84.0, c = 276Å, P4₁2₁2, Z = 8), a mercury dimer of human serum albumin (a = 155, b = 83, c = 122Å, P2₁2₁2₁, Z = 4) and a hexagonal form of equine serum albumin (a = 96.6, c = 144.5Å, P6₁, Z = 6).     

Fluorescence F 0 of photosystems II and I in developing C3 and C4 leaves,and implications on regulation of excitation balance

This work addresses the question of occurrence and function of photosystem II (PSII) in bundle sheath (BS) cells of leaves possessing NADP-malic enzyme-type C₄ photosynthesis (Zea mays). Although no requirement for PSII activity in the BS has been established, several component proteins of PSII have been detected in BS cells of developing maize leaves exhibiting O₂-insensitive photosynthesis. We used the basal fluorescence emissions of PSI (F _0I) and PSII (F _0II) as quantitative indicators of the respective relative photosystem densities. Chl fluorescence induction was measured simultaneously at 680 and 750 nm. In mature leaves, the F _m(680)/F ₀(680) ratio was 10.5 but less in immature leaves. We propose that the lower ratio was caused by the presence of a distinct non-variable component, F _c, emitting at 680 and 750 nm. After F _c was subtracted, the fluorescence of PSI (F _0I) was detected as a non-variable component at 750 nm and was undetectably low at 680 nm. Contents of Chls a and b were measured in addition to Chl fluorescence. The Chl b/(a + b) was relatively stable in developing sunflower leaves (0.25–0.26), but in maize it increased from 0.09 to 0.21 with leaf tissue age. In sunflower, the F _0I/(F _0I + F _0II) was 0.39 ± 0.01 independent of leaf age, but in maize, this parameter was 0.65 in young tissue of very low Chl content (20–50 mg m^?2) falling to a stable level of 0.53 ± 0.01 at Chl contents >100 mg m^?2. The values of F _0I/(F _0I + F _0II) showed that in sunflower, excitation was partitioned between PSII and PSI in a ratio of 2:1, but the same ratio was 1:1 in the C₄ plant. The latter is consistent with a PSII:PSI ratio of 2:1 in maize mesophyll cells and PSI only in BS cells (2:1:1 distribution). We suggest, moreover, that redox mediation of Chl synthesis, rather than protein accumulation, regulates photosystem assembly to ensure optimum excitation balance between functional PSII and PSI. Indeed, the apparent necessity for two Chls (a and b) may reside in their targeted functions in influencing accumulation of PSI and PSII, respectively, as opposed to their spectral differences.     

The crystal and molecular structure of tri-o-ethylamylose (tea 3)

The crystal and molecular structure of a tri-O-ethylamylose polymorph, TEA 3, has been solved by stereochemical conformation and packing analysis, combined with X-ray fibre diffraction analysis. The unit cell is orthorhombic, space group P2₁2₁2₁, with a  15.36 (±0.03) Å, b  12.18 (±0.05) Å, and c (fibre repeat)  15.48 (±0.01) Å. The actual chain conformation is a 4₃ helix with the EtO-6 group in the tg position, as was found in the polymorph TEA 1.     

An improved purification of ECF1 and ECF1F0 by using a cytochrome bo-deficient strain of Escherichia coli facilitates crystallization of these complexes

A novel strategy, which employs a cytochrome bo-lacking strain (GO104) and a modified isolation procedure provides an effective approach for obtaining much purer preparations of ECF₁F₀ than described previously, as well as for isolating homogeneous and protein-chemically pure ECF₁. ECF₁ obtained in this way could be crystallized by vapor-diffusion using polyethylene glycol (PEG) as a precipitant in a form suitable for X-ray diffraction analysis. The crystals belong to the orthorhombic space group P2₁2₁2₁, with lattice parameters a=110, b=134, and c=269 Å, and diffract to a resolution of at least 6.4 Å.     

An aminopeptidase from Agave americana thermodynamic studies

Purified Agave aminopeptidase was characterized with respect to the thermodynamic properties of the reaction catalysed by the enzyme. Kinetic studies were conducted at different temperatures ranging from 7.8 to 45°. The energy of activation, E_a, as well as the constants ΔH, ΔF and ΔS were calculated for both the formation of the enzyme-substrate complex, and the dissociation of the enzyme-product complex. Kinetic studies in buffers with varying dielectric constants enabled the determination of the electrostatic as well as the non-electrostatic components of ΔS. These results fit well into the overall kinetic picture of this enzyme-catalysed reaction as reported previously.     

Form birefringence as applied to biopolymer and inorganic material supraorganization

Abstract

I review here form, or textural, birefringence (Δ_F) in the context of advances in the field, as well as with regard to findings and applications in the physics of photonic devices, fibers maintaining polarization, photonic crystal fibers, and in biopolymers present in extracellular matrices and the myelin sheath. Some advantages of applying knowledge of Δ_F to biological fields involving biopolymers, especially collagen fibers, are considered in more detail. Tendon and cartilage collagen fibers have been regarded as a model of dense, highly aggregated biopolymers with preferential orientations. Owing to their supramolecular organization, such materials may be used to study molecular order by using anisotropic optical properties, especially Δ_F. Differences between collagen type I- and collagen type II-rich structures, and similarities between collagen crimp and second harmonic generation images are reported. Based on data reported here, it is possible to deduce that collagen type I supramolecular organization has nonlinear optical properties and that tendon segments can conduct red laser light. With respect to nerve fibers, the detection and measurements of Δ_F have allowed the myelin sheath to be considered a smectic liquid crystal.