A Generalized Intrinsic Rank Test for k Independent Samples

The original intrinsic rank test is generalized in that the sizes of the k samples may now be arbitrary, and the number of intrinsic rank intervals need not equal the number of samples. Furthermore, the size of these intervals can be made variable, subject only to relatively mild constraints. These generalizations permit the formulation and testing of more specific hypotheses concerning the commonality of the sample distributions. A generalized intrinsic rank function is used to transform the usual ordinal ranks, obtained from the combined samples, into intrinsic ranks. Original sample identity and intrinsic ranks are then cross-tabulated and evaluated as 2-way contingency table.     

Reactivation and refolding of reassociated dimers of rabbit muscle creatine kinase

Creatine kinase (ATP:creatine N-phosphotransferase, EC 2.7.3.2) is a good model for studying dissociation and reassociation during unfolding and refolding. This study compares self-reassociated CK dimers and CK dimers that contain hybrid dimers under proper conditions. Creatine kinase forms a monomer when denatured in 6 M urea for 1 h which will very quickly form a dimer when the denaturant is diluted under suitable conditions. After modification by DTNB, CK was denatured in 6 M urea to form a modified CK monomer. Dimerization of this modified subunit of CK occurred upon dilution into a suitable buffer containing DTT. Therefore, three different types of reassociated CK dimers including a hybrid dimer can be made from two different CK monomers in the proper conditions. The CK monomers are from a urea-denatured monomer of DTNB-modified CK and from an unmodified urea dissociated monomer. Equal enzyme concentration ratios of these two monomers were mixed in the presence of urea, then diluted into the proper buffer to form the three types of reassociated CK dimers including the hybrid dimer. Reassociated CK dimers including all three different types recover about 75% activity following a two-phase course (k ₁ = 4.88 × 10^–3 s^–1, k ₂ = 0.68 × 10^–3 s^–1). Intrinsic fluorescence spectra of the three different CK monomers which were dissociated in 6 M urea, dissociated in 6 M urea after DTNB modification, and a mixture of the first two dissociated enzymes were studied in the presence of the denaturant urea. The three monomers had different fluorescence intensities and emission maxima. The intrinsic fluorescence maximum intensity changes of the reassociated CK dimers were also studied. The refolding processes also follow biphasic kinetics (k ₁ = 3.28 × 10^–3 s^–1, k ₂ = 0.11 × 10^–3 s ^–1) after dilution in the proper solutions. Tsou's method [Tsou (1988), Adv. Enzymol. Rel. Areas Mol. Biol. 61, 381–436] was also used to measure the kinetic reactivation rate constants for the different three types of reassociated CK dimers, with different kinetic reactivation rate constants observed for each type. CK dissociation and reassociation schemes are suggested based on the results.     

Estimation of the Power of the Kruskal-Wallis Test

Power calculations of a statistical test require that the underlying population distribution(s) be completely specified. Statisticians, in practice, may not have complete knowledge of the entire nature of the underlying distribution(s) and are at a loss for calculating the exact power of the test. In such cases, an estimate of the power would provide a suitable substitute. In this paper, we are interested in estimating the power of the Kruskal-Wallis one-way analysis of variance by ranks test for a location shift. We investigated an extension of a data-based power estimation method presented by Collings and Hamilton (1988), which requires no prior knowledge of the underlying population distributions other than necessary to perform the Kruskal-Wallis test for a location shift. This method utilizes bootstrapping techniques to produce a power estimate based on the empirical cumulative distribution functions of the sample data. We performed a simulation study of the extended power estimator under the conditions of k = 3 and k = 5 samples of equal sizes m = 10 and m = 20, with four underlying continuous distributions that possessed various location configurations. Our simulation study demonstates that the Extended Average × & Y power estimation method is a reliable estimator of the power of the Kruskal-Wallis test for k = 3 samples, and a more conservative to a mild overestimator of the true power for k = 5 samples.     

Comparing Power Behaviours for Some Goodness-of-Fit Test Statistics in Sparse Multinomials

This paper is concerned with the power behaviour of four goodness-of-fit test statistics in sparse multinomials with k cells. Most previous work has been concerned only with both Pearson's X² and the likelihood ratio test statistics. We consider in this study, two additional test statistics, namely, the Cressie-Read test statistic – I(2/3) and the modified Freeman-Tukey test (FT) statistic. Because k ≥ 10 in this study, a Monte Carlo procedure based on 1000 simulated samples is used to estimate the powers for the four test statistics. Alternatives on various line segments are employed. Results suggest that none of the test statistics completely dominate the other and that the choice of which test to use depends on the nature of the alternative hypothesis. These results are consistent with those obtained by West and Kempthorne (1972), although, the Pearson's χ² test statistic may be preferred because of its closer approximation to the χ² distribution in terms of the attained α levels.     

Interaction of magnesium ions with poly A and poly U

The binding of Mg⁺⁺ to poly A and poly U has been measured quantitatively by using the metallochromic indicator calmagite. The method is described in detail. It is shown that there is electrostatic interaction between the binding sites, viz., the phosphate groups, and the intrinsic association constant, for the specific binding can be determined. After extrapolation to zero ionic strength we find that, for the binding of Mg⁺⁺ to poly A, k_int = 4 × 10⁴ and for that, to poly U, k_int = 3 × 10⁴. The intrinsic enthalpy of association is negative. The effect of Mg⁺⁺ on the secondary structure of poly A and poly U has been studied by measuring the ultraviolet absorbance, optical rotatory dispersion and viscosity as a function of the amount of added Mg⁺⁺ ions. It was found that Mg⁺⁺ promotes the formation of a more ordered secondary structure by neutralizing or screening the negative charges. It is concluded from the absorbance measurements that for poly A at pH ? 7 and for poly U at pH >xs 9 this ordering involves stacking of the bases. Likewise, in solutions of UDP with a pH around 10, base stacking occurs on addition of Mg⁺⁺.     

The concentration dependence of sedimentation for polysaccharides

The relationship between the sedimentation coefficient s₀ and its concentration coefficient k_s obtained in experiments on velocity sedimentation for polysaccharides is discussed. The values of s₀, k_s and an independently determined molecular weight reported by different authors for different polysaccharides are considered. It was established that the scaling relation. k_s∼ s₀ ^v unambiguously relates to the scaling relation s₀∼ M^b. The values of the sedimentation parameter β _s introduced on the basis of Svedberg's equation for s₀ and on the basis of the expression k_s = B 〈h²〉^3/2M^–1 are discussed and the generalized Wales-van Holde-Rowe equation M_KS = (N_A/β _S)^3/2[s]^3/2 k_S ^1/2 is used for evaluation of the molecular weights of polysaccharides. The adequacy of this evaluation is illustrated by taking as an example the determination of the unit length weight of an extra-rigid polysaccharide chain and of the equilibrium rigidity of rigid-chain, semi-rigid-chain and flexible-chain polysaccharides. The pair of experimental values s₀ and k_S obtained in a single series of experiments give the same information as may be obtained from the other pairs of hydrodynamic values such as [η] and s₀ or [η] and D₀, where [η] is the intrinsic viscosity and D₀ is the translational diffusion coefficient. Accepted: 11 December 1996     

Comparisons of Some Chi-Squared Goodness-of-Fit Test Statistics in Sparse One-Way Multinomials

The behavior of Pearson's X² test, the likelihood ratio test Y² and the two of its derivatives, G² and G_k², the Freeman-Tukey test (FT) and the Cressie and Read test Statistic I(2/3) are examined in this study. Estimated attained α levels based on 1000 simulated samples when the approximating distribution is χ_k-1², are computed for these tests for the various values of k, n and seven null hypotheses. Results from estimated power computations indicate that none of the test statistics has a clear advantage over any others, and that the choice of which test to use must therefore rest mainly on the performances with regards to the attained α levels when the χ² approximation is invoked. In this respect, the log-normal approximation proposed by Lawal and Upton (1980) is strongly recommended. This is closely followed by the I(2/3).     

New insights into testing for density dependence

The reasons why tests for density dependence often differ in their results for a particular time-series were investigated using modelled time-series of 20 generations in lenght. The test of Pollard et al. (1987) is the most reliable; it had the greatest power with the three forms of density dependent data investigated (mean detection rates of 50.8–61.1%) and was least influenced by the form of the density dependence in time-series. Bulmer's first test (Bulmer 1975) had slightly lower power (mean detection rates of 27.4–56.8%) and was more affected by the form of density dependence present in the data. The mean power of the other tests was lower and detection rates were more variable. Rates were 24.6–46.2% for regression of k-value on abundance, 6.4–32.6% for regression of k-value on logarithmic abundance and 0.2–13.7% for Bulmer's second test (Bulmer 1975). Bulmer's second test is not useful because of low power. For one method, regression of k-value on abundance. density dependence was detected in 19.9% of timeseries generated using a random-walk model. For regression of k-value on logarithmically-transformed abundance the equivalent figure was 18.3% of series. These rates of spurious detection were significantly (P<0.001) greater than the generally accepted 5% level of type 1 errors and so these methods are not suitable for the analysis of time-series data for density dependence. Levels of spurious detection (from random-walk data) were around the 5% level and hence were acceptable for Bulmer's first test, Bulmer's second test, and the tests of Pollard et al. (1987), Reddinguis and den Boer (1989) and Crowley (1992). For all tests, except Bulmer's second test, the rate of detection and the amount of autocorrelation in time-series were negatively correlated. The degree of autocorrelation accounted for as much as 59.5–77.9% of the deviance in logit proportion detection for regression of k-value on abundance, Bulmer's first test, and the tests of Pollard et al. and Reddingius and den Boer. For regression of k-value on abundance this relationship accounted for less of the deviance (29.4%). Independent effects of density dependence were largely absent. It is concluded that these are tests of autocorrelation, not density dependence (or limitation). Autocorrelation was found to become positive (which is similar to values from random-walk data) as the intrinsic growth rate became either small or large. As the strength of density dependence (in the discrete exponential logistic equation) is dependent on the product of the intrinsic growth rate and the density dependent parameter it is unclear whether this is because of variation in the strength of density dependent mortality or reproduction per se. However, small values of the intrinsic grwoth rate cause the amount of variation in the data to become small, which might hinder detection of density dependence, and large values of the intrinsic growth rate are coincident with determinstic chaos which hinders detection. The user of these tests for density dependence should be aware of their potential weakness when variation within time-series is small (which itself is difficult to judge) or if the intrinsic growth rate is large so that chaotic dynamics might result. Power and levels of variability in rates of detection using Reddingius and den Boer's test were intermediate between those of the test of Pollard et al. and Bulmer's first test. This, combined with the strong relationship between rates of detection of limitation and the value of the autocorrelation coefficient, make testing for limitation similar to testing for density dependence. Crowley's test of attraction gave the widest range of mean detection rates from density dependent data of all the tests (20.4–60.6%). The relative rates of detection for the three forms of density dependent data were opposite to those found for Bulmer's first test and the test of Pollard et al. I conclude that testing for attraction is a complementary concept to testing for density dependence. As dynamics represented in time-series generated using a stochastic form of the exponential logistic equation became chaotic, Bulmer's first test, the test of Pollard et al. and regression of k on abundance failed to detect density dependence reliably. Conversely, Crowley's test was capable of detecting attraction with a power between 96 and 100% with time-series containing both stochastically and deterministically chaotic dynamics. This difference from other tests is in agreement with the lower influence of autocorrelation.     

A Monte Carlo Study to Evaluate the Performance of Selected Tests of Homogeneity in Sparse Contingency Tables

We address the problem of tests of homogeneity in two-way contingency tables in case-control studies when the case category is subdivided into k subcategories. In this situation, we have two cells with large frequencies and 2 X k cells with frequencies that become small as k increases. We propose two ad hoc statistics in which a statistic for the sparse cells is combined with a statistic for the cells with large frequencies. We will study these tests along with the Pearson test (using a chi-square approximation) in a Monte Carlo simulation study. Two sets of null hypothesis models and two sets of alternative hypothesis models are considered. The best test for the models considered is the usual Pearson test (using an approximate chi-square distribution) although the ad hoc models are more powerful under one alternative model considered.     

An application of the logistic equation to the population dynamics of salt-marsh gastropods

The logistic equation for population growth N = K/(1 + be^−rt) with modifications for environmentally influenced changes in habitat carrying capacity K, and species intrinsic growth rate r, can satisfactorily simulate density levels of real populations of herbivores. The model assumes that carrying capacity is a function of incident solar energy while intrinsic growth rate is a function of temperature and salinity.Test animals were Cerithidea and Assiminea from Mission Bay, San Diego, California.     

Application of a novel method for age estimation of a baleen whale and a porpoise

Eyeballs from 121 fin whales (Balaenoptera physalus) and 83 harbor porpoises (Phocoena phocoena) were used for age estimation using the aspartic acid racemization (AAR) technique. The racemization rate (k_Asp) for fin whales was established from 15 fetuses (age 0) and 15 adult whales where age was estimated by reading growth layer groups (GLGs) in the earplugs. The (k_Asp) for harbor porpoises was derived from 15 porpoises (two calves and 13 > 1 yr old) age‐estimated by counting GLGs in the teeth and two calves classified to age based on length. The (k_Asp) values were estimated by regression of GLGs against D/L ratios. For the fin whales an (k_Asp) of 1.15 × 10^?3/yr (SE ± 0.00005) and a D/L ratio at birth [(D/L)₀] of 0.028 (SE ± 0.0012) were estimated, which is in agreement with rates for other mysticeti. For the harbor porpoises a (k_Asp) of 3.10 × 10^?3/yr (SE ± 0.0004) and a (D/L)₀ value of 0.023 (SE ± 0.0018) were estimated, which is considerably higher than found for other cetaceans. Correlation between chosen age estimates from AAR and GLG counts indicated that AAR might be an alternative method for estimating age in marine mammals.     

Contributions of water transfer energy to protein‐ligand association and dissociation barriers: Watermap analysis of a series of p38α MAP kinase inhibitors

In our previous work, we proposed that desolvation and resolvation of the binding sites of proteins can serve as the slowest steps during ligand association and dissociation, respectively, and tested this hypothesis on two protein‐ligand systems with known binding kinetics behavior. In the present work, we test this hypothesis on another kinetically‐determined protein‐ligand system—that of p38α and eight Type II BIRB 796 inhibitor analogs. The k_on values among the inhibitor analogs are narrowly distributed (10⁴ ≤ k_on ≤ 10⁵ M^?1 s^?1), suggesting a common rate‐determining step, whereas the k_off values are widely distributed (10^?1 ≤ k_off ≤ 10^?6 s^?1), suggesting a spectrum of rate‐determining steps. We calculated the solvation properties of the DFG‐out protein conformation using an explicit solvent molecular dynamics simulation and thermodynamic analysis method implemented in WaterMap to predict the enthalpic and entropic costs of water transfer to and from bulk solvent incurred upon association and dissociation of each inhibitor. The results suggest that the rate‐determining step for association consists of the transfer of a common set of enthalpically favorable solvating water molecules from the binding site to bulk solvent. The rate‐determining step for inhibitor dissociation consists of the transfer of water from bulk solvent to specific binding site positions that are unfavorably solvated in the apo protein, and evacuated during ligand association. Different sets of unfavorable solvation are evacuated by each ligand, and the observed dissociation barriers are qualitatively consistent with the calculated solvation free energies of those sets.     

Cation binding to β-casein. a comparison of electrostatic models

The binding of cations of β-casein at pH 6.6 was considered previously. Available for three sodium concentiations, I = 0.04, 0.08, or 0.16 M are: [1] proton releases between I and [2] for each I, as calcium activity is increased, correlated sequences of monomer net charge, proton release, site bound calcium and protein Solvation- Models for ion binding are examined. Critical considerations are the intrinsic binding constants between hydrogen[H], calcium[Ca] and sodium[Na] ions and phosphate[P] and caiboxyIate[C] sites, and the effects of electrostatic interaction between sites as influenced by spatial fixed charge distribution, ionic strength and dielectric constant [D]. Anticipated intrinsic binding constants are k_H,P^o = 3 × 10⁶, k_Ca,P^o = 120, k_Na,P^o = 1, k_H,C^o = 7 × 10⁴ and k_Ca,C^o = 5.6Distributed charge models, either surface or volume, are inadequate since any reasonable monomer size yields fixed charge densities requiring k_H,P^o and k_Ca,C^o which are too low when the maximum in D is 75. Also, with increasing calcium binding, calculated proton release is only 0.4 to 0.5 of that observed.Discrete charge models accept anticipated k^o and yield calculated sequences of calcium binding and proton release which are in good agreement with those observed provided that: (1) using the known amino acid sequence of the phosphate-containing acidic peptide portion of the molecule, pep tide fixed charge is distributed at the lowest I so as to minimize electrostatic free energy; (2) in the region of fixed charge, D is approximately 5; (3) the distances between peptide fixed charges decrease with increasing ionic strength or calcium binding and (4) while protein is in solution, the acidic peptide and the remainder of the molecule are essentially electrostatically independent.     

On Combination of Ratio and PPS Estimators

AGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample-values. In this paper, an estimator depending on estimated optimum value of k based on sample-values, under pps sampling scheme is proposed and studied.     

Evidence for an inhibitory LIM domain in a rat brain agmatinase-like protein

We recently cloned a rat brain agmatinase-like protein (ALP) whose amino acid sequence greatly differs from other agmatinases and exhibits a LIM-like domain close to its carboxyl terminus. The protein was immunohistochemically detected in the hypothalamic region and hippocampal astrocytes and neurons. We now show that truncated species, lacking the LIM-type domain, retains the dimeric structure of the wild-type protein but exhibits a 10-fold increased k_cat, a 3-fold decreased K_m value for agmatine and altered intrinsic tryptophan fluorescent properties. As expected for a LIM protein, zinc was detected only in the wild-type ALP (∼2 Zn²⁺/monomer). Our proposal is that the LIM domain functions as an autoinhibitory entity and that inhibition is reversed by interaction of the domain with some yet undefined brain protein.     

Use of glucose oxidase system in measuring aeration capacity of fermentors. Comparison of the dynamic and steady-state methods of kla measurement

A steady-state method for k_la determination has been presented using the Michaelis–Menten two-substrate kinetic equation for oxidation of glucose in the presence of the enzymes glucose oxidase and excess catalase. The conditions have been specified where spontaneous hydrolysis of lactone is sufficiently rapid, thus eliminating inhibitory action of lactone on the oxidation. In glucose oxidase-free batches, the k_la values were determined using various modification of the dynamic method. The dynamic methods in which gas interchange was effected without interrupting aeration and agitation of the batch yielded erroneously lower k_la values as compared to the results of steady-state methods if the measured k_la value was higher than 0.03 s^?1. The values yielded by the dynamic method in which the gas interchange was effected at the same time with turning on aeration and agitation of the batch agreed with values resulting from the steady-state method provided that the measured k_la values were lower than 0.08^?1 and the simultaneous interfacial transport of nitrogen and oxygen had been taken into account in the evaluation. At k_la values higher than 0.08 ^?1, this modification of the dynamic method also yielded lower k_la values as compared with the outcome of the steady-state method. The experiments performed do not, however, allow one to decide unambiguously on the whether these lower k_la values are due to failure of the adopted model to describe adequately the dynamic behavior of the system or whether they are true values differing from those yielded by the steady-state method on account of different physical properties of compared batches.     

Comparing treatment-induced changes for k independent samples of paired observations

In a recent paper, MARASCUILO [19] has provided an asymptotic solution to the important question on how to test for differences in change parameters when paired observation of binary type (+, -) have been made on two or more independent samples of individuals. In this article, an alternative approach is presented implying asymptotic as well as exact tests for changes. They are based on pre-post test designs from clinical research and allow for controlled evaluation of one treatment modality as well as for comparing 2 or more than 2 treatment modalities. The rationale of the tests is based on McNEMARS [21] test for paired binary observations in one, two, or k samples.     

Intracellular ionic activities in frog skin

Summary Asymmetrical displacement currents are measured in the absence and in the presence of the lipophilic anion dipicrylamine (DPA) in the extracellular solution of nerve fibres of the frogRana esculenta. DPA (30nM-3 M) enhances the current by a component that has the properties expected for a translocation current of DPA ion across the lipid membrane. Analysis in terms of a single-barrier model yields the translocation rate constant (k), the total surface density of DPA absorbed to the membrane (N _t ), and the equidistribution voltage (). The value ofk of about 10⁴ s^–1 is similar to that for a solvent-free artificial bilayer formed by the Montal-Mueller method. The surface densityN _t varies with the DPA concentration as it does in the artificial bilayer, but is about tenfold smaller at all concentrations. The DPA ions sense an intrinsic electric field that is offset by a transmembrane voltage between 0 and 30 mV (inside positive). The part of the axolemma probed by the DPA ion appears as a thin (<2.5 nm), fluid bilayer of lipids. DPA ions seem, however, to be excluded from the major part of the axolemma as if this area is occupied by integral proteins or negative charges.     

A Note on Non-Parametric Tests for the Interaction in Two-Way Layouts

A suggestion is given of how to prove main and interaction effects in two-way layouts independent of each other even if the data are just ordinally scaled. Starting from HILDEBRAND'S (1980a, b) non-parametric approach which presupposes interval-scaled data, transformations of ranks are settled before analysis per analogy to the H-test takes place. That is, the same formula of an asymptotically X²-distributed test-statistic results but mean ranks are used instead of mean scores in order to partialize, for instance, main effects while testing interaction effect. Finally an allusion is given of how to handle ties as well as unequal sample sizes.     

Release of vitamin B-12 in vitro from intrinsic factor-vitamin B-12 complex Purification and characterization of a releasing factor from rat ileal brush border

Vitamin B-12 is released from the purified gastric intrinsic factor-[⁵⁷Co]vitamin B-12 (intrinsic factor- [⁵⁷Co]vitamin B-12) complex, when incubated with rat intestinal mucosa. Maximum specific activity for splitting the complex is localized in ileal brush border. Release of [⁵⁷Co]vitamin B-12 is not due to its mere exchange during incubation with endogenous non-radioactive vitamin B-12. The splitting process has specific requirement for Ca²⁺ and ATP and it is thermolabile, time- as well as temperature-dependent. It is also inactivated by the presence of p-chloromercuribenzoate. Further, the vitamin B-12-releasing factor has been isolated from solubilized brush border and is purified 70-fold by (NH₄)₂SO₄ precipitation, gel filtration and Con. A-Sepharose 4B affinity chromatography. In SDS-polyacrylamide gel electrophoresis, it is resolved into a single band of about 25 kDa, indicating its purity. The releasing factor exhibits maximum activity at pH 7.4; isoelectric focusing reveals only one major form with pI 7.52. With intrinsic factor-[⁵⁷Co]vitamin B-12-complex as the substrate, apparent K_m and V_max values obtained are 128.2·10⁻¹² M/1 and 117.6 pg·h⁻¹ 100 μg protein, respectively. Amino acid and carbohydrate analyses reveal the glycoprotein nature of the factor. Intrinsic factor-[⁵⁷Co]vitamin B-12 complex is not susceptible to unspecific proteolytic digestion/ Similarly, the releasing factor does not hydrolyse other proteins. Thus, the observed substrate-specificity of the releasing factor differentiates it from other known proteolytic enzymes of ileal brush borders.