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.     

Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

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.     

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.     

Molecular hybridization of 4-azahexacyclo[5.4.1.0(2,6).0(3,10).0(5,9).0(8,11)]dodecane-3-ol with sigma (σ) receptor ligands modulates off-target activity and subtype selectivity

A series of N-substituted 4-azahexacyclo[5.4.1.0^2,6.0^3,10.0^5,9.0^8,11]dodecan-3-ols incorporating the respective arylalkyl subunits from several known sigma (σ) receptor ligands were synthesized and evaluated for their affinity against σ receptors and dopamine receptors. The hybrid trishomocubane-derived ligands (4-6) showed good selectivity for σ₁ and σ₂ receptors over multiple dopamine receptors. The molecular hybrid obtained from haloperidol and 4-azahexacyclo[5.4.1.0^2,6.0^3,10.0^5,9.0^8,11]dodecan-3-ol (4, σ₁K_i = 27 nM, σ₂K_i = 55 nM) showed reduced affinity for D₁-D₅ dopamine receptors when compared to haloperidol itself. The compound with the greatest σ₁ affinity in the series, benzamide 4 (σ₁K_i = 7.6 nM, σ₂K_i = 225 nM) showed a complete reversal of the subtype selectivity displayed by the highly σ₂ selective parent benzamide, RHM-2 (3, σ₁K_i = 10412 nM, σ₂K_i = 13.3 nM).     

Bayesian Estimation in a Generalized Negative Binomial Distribution

A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θ^x (1 - θ)^m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ^?1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n^?1 for different values of k..     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

Enzymatic Properties of β-Xylosidase from Malbranchea pulchella var. sulfurea No. 48

Some enzymatic properties of Malbranchea β-xylosidase were investigated. The β- xylosidase activity was inhibited by Hg²⁺, Zn²⁺, Cu²⁺, N-bromosuccinimide, p-chloromercuribenzoate and sodium laurylsulfate, while this activity was activated by Ca²⁺. The enzyme released xylose as the end product even from 10% xylobiose solution without forming any xylooligosaccharides. The enzyme well acted on aryl-β-d-xylosides, but showed no activity on alkyl-β-d-xylosides, and it was practically free from glucosidase activity. The Km and V_max values of this enzyme for xylobiose were calculated to be 2.86 × 10^?8 m and 34.5 μmoles/mg/min, respectively, and these values determined for phenyl-β-d-xyloside were 3.01 × 10^?8 m and 16.2 μmoles/mg/min, respectively.     

Asymptotical Tests on the Equivalence,Substantial Difference and Non‐inferiority Problems with Two Proportions

Let d = p₂ ? p₁ be the difference between two binomial proportions obtained from two independent trials. For parameter d, three pairs of hypothesis may be of interest: H₁: d ≤ δ vs. K₁: d > δ; H₂: d ? (δ₁, δ₂) vs. K₂: d ∈ (δ₁, δ₂); and H₃: d ∈ [δ₁, δ₂] vs. K₃: d ? [δ₁, δ₂], where H_i is the null hypothesis and K_i is the alternative hypothesis. These tests are useful in clinical trials, pharmacological and vaccine studies and in statistics generally. The three problems may be investigated by exact unconditional tests when the sample sizes are moderate. Otherwise, one should use approximate (or asymptotical) tests generally based on a Z‐statistics like those suggested in the paper. The article defines a new procedure for testing H₂ or H₃, demonstrates that this is more powerful than tests based on confidence intervals (the classic TOST – two one sided tests – test), defines two corrections for continuity which reduce the liberality of the three tests, and selects the one that behaves better. The programs for executing the unconditional exact and asymptotic tests described in the paper can be loaded at http://www.ugr.es/~bioest/software.htm. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

F-tests for Hypotheses with Block Matrices and Under Conditions of Orthogonality in the General Multivariate Gauss-Markoff Model

The multivariate general Gauss-Markoff (MGM) model (U, XB, ∑?σ²V) when the matrices V ≥ 0 and ∑ > 0 are known and the scalar σ² > 0 is unknown, is considered. The present paper is a continuation of two earlier works (Oktaba, 1988a, b). If XB = X₁Σ + X₂Δ, then the F-test for verification the hypothesis WΣA = 0 is presented. Moreover, under conditions of orthogonality the decomposition of the matrix S_A (?BCA)′L^?(?BCA) into the sum of s = r(L) matrices is given, where ?BCA is the estimator of the parametric estimable functions ?BCA, Cov (?BCA) = A′ ∑?σ²L = ?C₄?′, B? = (X′T^?X)^?X′T^?U, C₄ = (X′T^?X)^?M, where M = M′ is any arbitrary matrix such that R(X) ? R(T), T=V+XMX′; T^? is any c-inverse. R(A) is the linear space generated by the colums of A. Then under additional assumption on normality of U the statistics F for testing ?BA = 0 is deduced. Under conditions of normality of U and decomposition of S_A, the statistics F₁, …, F_s for the hypotheses jⁱ BA = 0 (i = 1,…, s) are established.     

NICOTINE AND α-BUNGAROTOXIN BINDING TO AXONAL AND NON-NEURAL TISSUES1

Abstract— Nicotine binds to homogenates of lobster walking leg nerve (K_d= 1.1 ± 0.3 μm , B_max= 2.4 ± 0.5 nmol/g wet tissue), horseshoe crab leg nerve (K_d= 0.11 ± 0.06 μm , B_max= 1.3 ± 0.6nmol/g), and kidney from 18-month-old rats (K_d= 0.8 ± 0.2 μm , B_max= 23 ± 9 nmol/g). The pharmacological sensitivities of nicotine binding to lobster and horseshoe crab leg nerve homogenates are similar to that of the axonal cholinergic binding macromolecule (ACBM) (Denburg et al., 1972) of lobster leg. nerve membrane, while the binding to rat kidney is sensitive to α-bungarotoxin but not atropine or curare. There was no nicotine binding to rat heart or spleen, or to kidney from younger rats; little or no binding to blue crab nerve or to Torpedo electroplax motor nerve; and little binding (around 0.1 nmol/g) to rat liver. [³H]α-Bungarotoxin bound reversibly (0.17 nmol/g) to lobster leg nerve membrane The implications of these results for the distribution and function of the ACBM, and for the specificity of α-bungarotoxin, are discussed.     

Stable resistance to bacterial blight disease in rice

Ten rice cultivars were evaluated for stable resistance to 18 isolates of Xanthomonas campestris pv. oryzae. Stable performance of the host cultivar was evaluated by regressing the cultivar means on the mean level of pathogenicity of the isolates averaged over all cultivars. A cultivar with low disease incidence, a regression coefficient near or equal to zero (b= 0) and the deviation from regression as small as possible (S²_d= 0) was considered highly stable while that with low disease incidence, b= 1 -0 and S²_d= 0 was considered to possess average stability. Accordingly, cvs TKM-6, CB II, DV 85 and Ramakrishna were considered to possess average stability while IR 20 and Indira were the most stable. Cvs Cemposelak, IR 1545, BJ 1 and IR 8 showed high response to disease incidence with relatively small changes in level of pathogenicity of the isolates and hence were considered most unstable. The regression technique was considered as a valuable tool for identification of stable resistance to bacterial blight disease of rice.     

ISOLATION OF HYDROPHOBIC PROTEINS BINDING AMINO ACIDS: γ-AMINOBUTYRIC ACID BINDING IN THE RAT CEREBRAL CORTEX

—The binding of [¹⁴C]GABA to nerve-ending membranes isolated from rat cerebral cortex follows a hyperbolic curve saturating at 0·4pmol/μg protein. This binding is about 60% inhibited by chloropromazine, and about 40%, inhibited by bicuculline. A hydrophobic protein fraction binding [¹⁴C]GABA was separated from the total. lipid extract of nerve-ending membranes. The binding follows a hyperbolic curve that saturates at 10·5 pmol of [¹⁴C]GABA/μg of protein, with an apparent K_d= 30 μm . The binding is competitively inhibited by bicuculline with a K_i= 273 μm . These results are compared with those previously obtained on a GABA binding protein from crustacean muscle.     

Anti-Barnacle Activities of Isothiocyanates Derived from β-Citronellol and Their Structure–Activity Relationships

Antifouling agents with low toxicity are in high demand for sustaining marine industries and the environment. This study aimed to synthesize 15 isothiocyanates derived from β-citronellol and evaluate their antifouling activities and toxicities against cypris larvae of the barnacle Amphibalanus amphitrite. The synthesized isothiocyanates exhibited effective antifouling activities (EC₅₀=0.10–3.33 μg mL⁻¹) with high therapeutic ratios (LC₅₀/EC₅₀ >30). Four isothiocyanates with an amide or isocyano group showed great potential as effective antifouling agents (EC₅₀=0.10–0.32 μg mL⁻¹, LC₅₀/EC₅₀=104–833). The enantiomers of the isothiocyanates only slightly differed in their antifouling activities. These results may serve as a basis for further research and development of β-citronellol-derived isothiocyanates as effective low-toxic antifouling agents. To the best of our knowledge, this study is the first to report the antifouling activities of isothiocyanates derived from accessible natural products.     

Unconditional Confidence Interval for the Difference between Two Proportions

In applied statistics it is customary to have to obtain a one‐ or two‐tail confidence interval for the difference d = p₂ – p₁ between two independent binomial proportions. Traditionally, one is looking for a classic and non‐symmetric interval (with respect to zero) of the type d ∈ [δ_L;δ_U], d ≤ δ₀ or d ≥ δ₀. However, in clinical trials, equivalence studies, vaccination efficacy studies, etc., and even after performing the classic homogeneity test, intervals of the type |d| ≤ Δ₀ or |d| ≥ Δ₀, where Δ₀ > 0, may be necessary. In all these cases it is advisable to obtain the interval by inverting the appropriate test. The advantage of this procedure is that the conclusions obtained using the test are compatible with those obtained using the interval. The article shows how this is done using the new exact and asymptotic unconditional tests published. The programs for performing these tests may be obtained at URL http://www.ugr.es/~bioest/software.htm.     

The beta-adrenergic receptor in human lymphocytes: subclassification by the use of a new radio-ligand, (+/-)-125 Iodocyanopindolol

(±)?¹²⁵Iodocyanopindolol (ICYP), a new radio-ligand with high affinity and specificity to β-adrenoceptors was used to identify and characterized β-adrenergic receptors in human lymphocytes. Binding of ICYP was saturable with 1.56 ± 0.2 fmol ICYP specifically bound/10⁶ cells at maximal occupancy of the sites and of high affinity (K_D=57 ± 7.1pM, N=4. In contrast to ¹²⁵Iodohydroxybenzylpindolol ICYP-binding was not affected by phentolamine (up to 10^?4M) or serotin (up to 10^?5M). Analysis of inhibition of ICYP-binding via a pseudo-Scatchard-plot (“Hofstee-plot”) by β_1-selective (practocol, metaprolol) and β_2-selective (IPS 339, zinterol) adrenergic drugs resulted in linear plots suggesting the existence of a homogeneous population of β-adrenergic receptorsin human lymphocytes. From the resulting K_D-values for practolol (16.8 μM), metoprolol (4.11 μM), zinterol (0.08 μM) and IPS 339 (0.002 μM) is concluded that the β-adrenergic receptor present in human lymphocytes is of the β₂-subtype. According to its low non-specific binding and its high specificity to β-adrenergic receptors ICYP appears to be an ideal ligand for long-term studies on the regulation of β-adrenergic receptors of human lymphocytes.     

Binding of spermine and ifenprodil to a purified,soluble regulatory domain of the N‐methyl‐d‐aspartate receptor

The binding of spermine and ifenprodil to the amino terminal regulatory (R) domain of the N‐methyl‐D ‐aspartate receptor was studied using purified regulatory domains of the NR1, NR2A and NR2B subunits, termed NR1‐R, NR2A‐R and NR2B‐R. The R domains were over‐expressed in Escherichia coli and purified to near homogeneity. The K_d values for binding of [¹⁴C]spermine to NR1‐R, NR2A‐R and NR2B‐R were 19, 140, and 33 μM, respectively. [³H]Ifenprodil bound to NR1‐R (K_d, 0.18 μM) and NR2B‐R (K_d, 0.21 μM), but not to NR2A‐R at the concentrations tested (0.1–0.8 μM). These K_d values were confirmed by circular dichroism measurements. The K_d values reflected their effective concentrations at intact NR1/NR2A and NR1/NR2B receptors. The results suggest that effects of spermine and ifenprodil on NMDA receptors occur through binding to the regulatory domains of the NR1, NR2A and NR2B subunits. The binding capacity of spermine or ifenprodil to a mixture of NR1‐R and NR2A‐R or NR1‐R and NR2B‐R was additive with that of each individual R domain. Binding of spermine to NR1‐R and NR2B‐R was not inhibited by ifenprodil and vice versa, indicating that the binding sites for spermine and ifenprodil on NR1‐R and NR2B‐R are distinct.     

PHOTOSYNTHESIS AND CALCIFICATION BY EMILIANIA HUXLEYI (PRYMNESIOPHYCEAE) AS A FUNCTION OF INORGANIC CARBON SPECIES

To test the possibility of inorganic carbon limitation of the marine unicellular alga Emiliania huxleyi (Lohmann) Hay and Mohler, its carbon acquisition was measured as a function of the different chemical species of inorganic carbon present in the medium. Because these different species are interdependent and covary in any experiment in which the speciation is changed, a set of experiments was performed to produce a multidimensional carbon uptake scheme for photosynthesis and calcification. This scheme shows that CO₂ that is used for photosynthesis comes from two sources. The CO₂ in seawater supports a modest rate of photosynthesis. The HCO is the major substrate for photosynthesis by intracellular production of CO₂ (HCO+ H⁺→ CO₂+ H₂O → CH₂O + O₂). This use of HCO is possible because of the simultaneous calcification using a second HCO, which provides the required proton (HCO+ Ca²⁺→ CaCO₃+ H⁺). The HCO is the only substrate for calcification. By distinguishing the two sources of CO₂ used in photosynthesis, it was shown that E. huxleyi has a K_½ for external CO₂ of “only” 1.9 ± 0.5 μM (and a V_max of 2.4 ± 0.1 pmol·cell⁻¹·d⁻¹). Thus, in seawater that is in equilibrium with the atmosphere ([CO₂]= 14 μM, [HCO]= 1920 μM, at fCO₂= 360 μatm, pH = 8, T = 15° C), photosynthesis is 90% saturated with external CO₂. Under the same conditions, the rate of photosynthesis is doubled by the calcification route of CO₂ supply (from 2.1 to 4.5 pmol·cell⁻¹·d⁻¹). However, photosynthesis is not fully saturated, as calcification has a K_½ for HCO of 3256 ± 1402 μM and a V_max of 6.4 ± 1.8 pmol·cell⁻¹·d⁻¹. The H⁺ that is produced during calcification is used with an efficiency of 0.97 ± 0.08, leading to the conclusion that it is used intracellularly. A maximum efficiency of 0.88 can be expected, as NO uptake generates a H⁺ sink (OH⁻ source) for the cell. The success of E. huxleyi as a coccolithophorid may be related to the efficient coupling between H⁺ generation in calcification and CO₂ fixation in photosynthesis.     

Light/Dark Cycle and Temperature-Their Impact on Phosphate-Limited Growth of Oscillatoria redekei VAN GOOR in Semicontinuous Culture

Phosphate-limited growth of Oscillatoria redekei in semicontinuous culture has been studied under conditions of continuous illumination at 20 °C as well as in a 12/12 hours light-dark cycle at temperatures between 5 °C and 20 °C. The subsistence quota (q₀) amounted to 0.052 μmol mm⁻³ under all conditions, when the phosphate quota was expressed on the basis of cell volume. The interaction between temperature and phosphate quota and its impact on growth rate are described by the following model: Parameter values are t_opt=24.5 °C, t_min=0.95 °C, μ_max =0.873 d⁻¹. The maximum phosphate quota was found to depend on temperature and to increase along with declining temperature.