Sensitivity Profiles of Diversity Indices

The author previously described special sensitivity measures for diversity indices. These measures make possible on analytical treatment of the index sensitivity. In the article a detailed analysis of sensitivity properties of the Hurlbert indices is presented. In the first step the abundances n_k were sequenced in an increasing order. Plotting the sensitivity against n_k or log n_k, essential sensitivity properties can be observed. For example, one can study the sensitivities to changes in the dominant and subdominant abundances, the site of the “nearly neutral” abundance and the site of local sensitivity maxima in the domain of the relatively rare categories. The observations are supported by mathematical reasoning.     

Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors

Given independent multivariate random samples {X_ij: j = 1, …, n_i} from F_i, for i = 1,2, a test is desired for H₀: F₁ = F₂ against general alternatives. Consider the k · (n₁ + n₂) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let S_k be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed S_k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kS_k, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.     

Characterizations of the Exponential Distribution by Local Maximum Random Variables

Let {X_n, n≧1} be a sequence of independent and identically distributed random variables. Suppose n(K)=min n for which X_n>X_k, with K fixed and n>K. We will characterize the exponential distribution by considering the distributional properties of X_k and X_k and X_n(k).     

Species abundance distributions in neutral models with immigration or mutation and general lifetimes

We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate λ. Thus, the population size is a homogeneous, binary Crump–Mode–Jagers process (which is not necessarily a Markov process). We assume that types are clonally inherited. We consider two classes of speciation models in this setting. In the immigration model, new individuals of an entirely new species singly enter the population at constant rate μ (e.g., from the mainland into the island). In the mutation model, each individual independently experiences point mutations in its germ line, at constant rate θ. We are interested in the species abundance distribution, i.e., in the numbers, denoted I _n (k) in the immigration model and A _n (k) in the mutation model, of species represented by k individuals, k = 1, 2, . . . , n, when there are n individuals in the total population. In the immigration model, we prove that the numbers (I _t (k); k ≥ 1) of species represented by k individuals at time t, are independent Poisson variables with parameters as in Fisher’s log-series. When conditioning on the total size of the population to equal n, this results in species abundance distributions given by Ewens’ sampling formula. In particular, I _n (k) converges as n → ∞ to a Poisson r.v. with mean γ/k, where γ : = μ/λ. In the mutation model, as n → ∞, we obtain the almost sure convergence of n ⁻¹ A _n (k) to a nonrandom explicit constant. In the case of a critical, linear birth–death process, this constant is given by Fisher’s log-series, namely n ⁻¹ A _n (k) converges to α ^k /k, where α : = λ/(λ + θ). In both models, the abundances of the most abundant species are briefly discussed.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.     

A singular dispersion relation arising in a caricature of a model for morphogenesis

In 1983 Oster et al. proposed a model for morphogenesis consisting of a system of partial differential equations in which the dispersion relation for the problem linearised about the zero solution has a singularity. That is, the initial growth rate of a small perturbation of wave number k from the zero solution tends to positive or negative infinity as k tends to some critical value k _c from above or below respectively. We consider here as a caricature of the model a single partial differential equation with a similar dispersion relation in a bounded one-dimensional domain. The wave number, or equivalently the domain size, may be thought of as a bifurcation parameter. For the Neumann problem a phenomenon arises in which, as the domain size l increases past a critical value l _l ,the linear stability of the n-th mode jumps from one solution to a remote solution. That is, for l _n the trivial solution is unstable and a certain non-trivial solution is stable to perturbations of mode n, whereas for l>l _n the opposite is true. For the Dirichlet or the Robin problem a linear stability change in the trivial solution occurs, but no corresponding change in any other solution has been found. The corresponding initial boundary value problems are then considered. An asymptotic analysis is performed in the weakly nonlinear limit in the particular case in which only one mode is unstable and gives an asymptotic solution for two classes of nonlinearity, one symmetric and the other asymmetric about u=0. A development of the method of harmonic balance is then used to obtain approximate solutions in the strongly nonlinear case and when more than one mode may be unstable.     

Effects of hydrocarbon additions on gas-liquid mass transfer coefficients in biphasic bioreactors

The effects of aliphatic hydrocarbons (n-hexadecane andn-dodecane) on the volumetric oxygen mass transfer coefficient (k _L a) were studied in flat alveolar airlift reactor and continuous stirred tank reactors (CSTRs). In the flat alveolar airlift reactor, high aeration rates (>2 vvm) were required in order to obtain efficient organic-aqueous phase dispersion and reliablek _L a measurements. Addition of 1% (v/v)n-hexadecane orn-dodecane increased thek _l a 1.55-and 1.33-fold, respectively, compared to the control (superficial velocity: 25.8×10⁻³ m/s, sparger orifice diameter: 0.5 mm). Analysis of the gas-liquid interfacial areaa and the liquid film mass transfer coefficientk _L suggests that the observedk _L a increase was a function of the media's liquid film mass transfer. Addition of 1% (v/v)n-hexadecane orn-dodecane to analogous setups using CSTRs led to ak _L a increase by a factor of 1.68 and 1.36, respectively (superficial velocity: 2.1×10⁻³ m/s, stirring rate: 250 rpm). These results propose that low-concentration addition of oxygen-vectors to aerobic microbial cultures has additional benefit relative to incubation in purely aqueous media.     

The physiological factors which govern inert gas exchange

The decay constants (k _j ) of the equation of inert gas exchanges are the roots of an algebraic equation of degreen+1, wheren is the number of distinct absorbing tissues. The coefficients of this equation can be obtained numerically by certain independent experiments to measure the tissue parameters. Graphical solution of this equation yields theoretical values of thek _j . Combining these constants with the numerical values for the partial derivatives of thek _j then gives the per cent rate of change of thek _j as any one tissue parameter varies by a given fraction of its normal range. A numerical example of these calculations shows good conformity with experiment, and permits a quantitative estimate of variations in the speed of gas exchange from a knowledge of changes in the physiological state. The opinions expressed in this article are the private ones of the writers, and are not to be construed as reflecting the policies of the Navy Department or the Naval Service at large.     

Influence of membrane structure on ion transport through lipid bilayer membranes

Summary Charge-pulse relaxation studies with the positively charged PV-K⁺ complex (cyclo-(d-Val-l-Pro-l-Val-d-Pro)₃) and the negatively charged lipophilic ion dipicrylamine (DPA^–) have been performed in order to study the influence of structural properties on ion transport through lipid bilayer membranes. First, the thickness of monoolein membranes was varied over a wide range using differentn-alkanes and slovent-free membranes. The thickness (d) of the hydrocarbon core of these membranes varied between 4.9 and 2.5 nm. For both transport systems the partition coefficient was found to be rather insensitive to variations ind. The same was valid for the translocation rate constantk _MS of PV-K⁺, whereas a strong increase of the translocation rate constantk _i of DPA-with decreasingd was observed. In a further set of experimental conditions the structure of the lipids, such as number and position of the double bonds in the hydrocarbon chain and its chain length as well as the nature of the polar head group, was varied. The translocation constantk _MS of PV-K⁺ transport was found to be much more sensitive to these variations thank _i of DPA-.Much larger variations ink _i andk _MS were observed in membranes made from lipids with ether instead of ester linkages between glycerol backbone and hydrocarbon chain. The results are in qualitative agreement with the surface potentials of monolayers made from corresponding lipids. Increasing amounts of cholesterol in membranes of dioleoylphosphatidylcholine caused a strong decrease ofk _MS (PV-K⁺), whereask _i was found to be rather insensitive to this variation.In monoolein membranes cholesterol causes a decrease ofk _MS up to sixfold and a increase ofk _i up to eightfold. The partition coefficient of DPA^– was insensitive to cholesterol, whereas of PV-K⁺ was found to decrease about eightfold in these membranes. The influence of cholesterol onk _MS is discussed on the basis of viscosity changes in the membrane and the change ink _i of DPA^– and of PV-K⁺ on the basis of a possible change of the dipole potential of the membranes. The other sterols, epicholesterol and ergosterol cause no change in the kinetics of the two probes.The different influence of membrane properties like thickness, viscosity, and dipole potential on the two transport systems is discussed under the assumption that the adsorption planes of the two probes have different positions in a membrane. Possibly because of a larger hydrophobic interaction, the adsorption plane of PV-K⁺ is located more towards the hydrocarbon side and that of DPA^– more towards the aqueous side of the dipole layer.     

Prediction of protein secondary structure from amino acid sequence

The conformational parametersP _k for each amino acid species (j=1–20) of sequential peptides in proteins are presented as the product ofP _i,k , wherei is the number of the sequential residues in thekth conformational state (k=-helix,-sheet,-turn, or unordered structure). Since the average parameter for ann-residue segment is related to the average probability of finding the segment in the kth state, it becomes a geometric mean of (P _k )_av=(P _i,k ) ^1/n with amino acid residuei increasing from 1 ton. We then used ln(P_k)_av to convert a multiplicative process to a summation, i.e., ln(P _k ) _av =(1/n)P _i,k (i=1 ton) for ease of operation. However, this is unlike the popular Chou-Fasman algorithm, which has the flaw of using the arithmetic mean for relative probabilities. The Chou-Fasman algorithm happens to be close to our calculations in many cases mainly because the difference between theirP _k and our InP _k is nearly constant for about one-half of the 20 amino acids. When stronger conformation formers and breakers exist, the difference become larger and the prediction at the N- and C-terminal-helix or-sheet could differ. If the average conformational parameters of the overlapping segments of any two states are too close for a unique solution, our calculations could lead to a different prediction.     

怀槐细胞悬浮培养的结构化动力学模型

为探明怀槐细胞生长、异黄酮染料木素合成与底物消耗间的关系,建立了怀槐细胞悬浮培养的结构化动力学模型。模型预测分析了胞内外的蔗糖代谢、胞内结构组分变化、胞内中间组分的变化、细胞呼吸损失以及胞内外异黄酮染料木素的合成情况。模型各参数灵敏度的分析表明kM_b1、k_b2 和k_p是最为灵敏的参数,其调节10%时,目标函数变化的最大比例分别达12.8%、4.61%和2.54%,其它参数对目标函数变化的影响均小于0.5%。该模型预测值与实验值具有较好的吻合性。     

Kinetic analysis of biphasic protein modification reactions cooperative effects

A mathematical treatment of protein modification reactions is presented, and it is shown thai in these cases protein modification is described by a summation of exponential functions of reaction time, the number of exponentials being equal to the number of modified protein species. It is shown that in cases of protein modification cooperativity, there is a strict dependence of the coefficients of the multiexponential modification equation on the constants of the same equation. The conditions necessary for a reduction of a multiexponential protein modification equation to one of a summation of two exponentials only are examined. The possible formulae for the coefficients of a two-exponential-summation equation, used to describe the modification of protein models with two, three or four modifiable residues (as well as some aspects of models with five and six modifiable residues) per protein molecule are derived. It is seen that the number of such coefficients is severely limited. The most frequently obtained formula for the lower stoichiomelric coefficient of a 'wo-exponential-summation equation is Ak_a/(k_a-k_b). where k_b and k_b are the constants of the two exponentials of the equation, and A is a constant. The value most frequently arrived at for A is (n?1)/n, where n is the number of modifiable residues per protein molecule, while values such as 1/n, or a/n (where a is an integer, and also where a < n) are also possible. In most of the cooperative protein modification models worked out, k_a is identical with k_n, viz., k_a is identical with the rate constant for the first stoichiometric protein modification.     

Molecular Dynamics Simulation Studies of the Density and Temperature Dependence of Self-diffusion in a Cylindrical Micropore

We report Molecular Dynamics calculations of radial density profiles and self-diffusion coefficients of Lennard-Jones fluids in a cylindrical pore of radius 2σ, for a wide range of temperatures and densities. At n _p σ³ = 0.825 the self-diffusion coefficient parallel to the pore walls D _∥*. follows a monotonic (nearly linear) increase with kT/ε and is very similar to that of the bulk self-diffusion coefficient D _b *. At n _p σ³ = 0.4 and kT/ε ≤ 1.0 the curve of D _∥* vs. kT/ε shows a distinct inflection in the region 0.7 ≤ kT/ε ≤ 0.9 and values of D _∥* are much less than D _b * decreasing to near solid state values at very low temperatures. At the highest temperature studied, kT/ε = 2.98, D _∥* is almost inversely proportional to density and in a fairly close agreement with that of D _b *. At KT/ε = 0.49, D _∥* is much smaller than D _b *. The motion of adsorbate particles normal to the walls is also discussed.     

Some studies on catalysis by lysozyme

The preparation of some aryl β-glycosides of β-1, 4-linked oligosaccharides of (GlcNAc)_n, n = 2, 3, 4, is described. These compounds were tested as substrates for lysozyme from hens' egg white. The best of them, (GlcNAc)₄-3,4-DNP, had a value of k_cat/K_m which was about one-nintieth that for the hydrolysis of (GlcNAc)₆. The pH dependence of k_cat and k_cat/K_m for the hydrolysis of (GlcNAc)₄-3,4-DNP was similar to that for (GlcNAc)₆. (GlcNAc)₄-3,4-DNP was also a substrate for human lysozyme and lysozyme from ducks' egg white (II and III). An impure sample of (GlcNAc)₂F was prepared and this was hydrolyzed much more rapidly than (GlcNAc)₂-2,4-DNP by lysozyme. Compounds of type (GlcNAc)_n−1(XylNAc)Ar, where n = 2, 3, 4, were prepared and found not to be substrates for lysozyme. In the presence of (GlcNAc)₄ or (GlcNAc)₅, lysozyme-induced hydrolyses of (GlcNAc)-3,4-DNP and (Glc)-3,4-DNP were observed but not of (XylNAc)-3,4-DNP, (6-deoxy-GlcNAc)-3,4-DNP, (6-F-GlcNAc)-3,4-DNP, and (6-Cl-GlcNAc)-3,4-DNP. The significance of these results is discussed.     

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.     

Mining statistically-solid k-mers for accurate NGS error correction

Background

NGS data contains many machine-induced errors. The most advanced methods for the error correction heavily depend on the selection of solid k-mers. A solid k-mer is a k-mer frequently occurring in NGS reads. The other k-mers are called weak k-mers. A solid k-mer does not likely contain errors, while a weak k-mer most likely contains errors. An intensively investigated problem is to find a good frequency cutoff f₀ to balance the numbers of solid and weak k-mers. Once the cutoff is determined, a more challenging but less-studied problem is to: (i) remove a small subset of solid k-mers that are likely to contain errors, and (ii) add a small subset of weak k-mers, that are likely to contain no errors, into the remaining set of solid k-mers. Identification of these two subsets of k-mers can improve the correction performance.

Results

We propose to use a Gamma distribution to model the frequencies of erroneous k-mers and a mixture of Gaussian distributions to model correct k-mers, and combine them to determine f₀. To identify the two special subsets of k-mers, we use the z-score of k-mers which measures the number of standard deviations a k-mer’s frequency is from the mean. Then these statistically-solid k-mers are used to construct a Bloom filter for error correction. Our method is markedly superior to the state-of-art methods, tested on both real and synthetic NGS data sets.

Conclusion

The z-score is adequate to distinguish solid k-mers from weak k-mers, particularly useful for pinpointing out solid k-mers having very low frequency. Applying z-score on k-mer can markedly improve the error correction accuracy.

     

Minimum sample sizes for identifying chromosomal fragile sites from individuals: Monte Carlo estimation

A Monte Carlo simulation procedure was used to estimate the exact level of the standardized X ² test statistic (X _s ²) for randomness in the FSM methodology for the identification of fragile sites from chromosomal breakage data for single individuals. A random-number generator was used to simulate 10 000 chromosomal breakage data sets, each corresponding to the null hypothesis of no fragile sites for numbers of chromosomal breaks (n) from 1 to 2000 and at three levels of chromosomal band resolution (k). The reliability of the test was assessed by comparisons of the empirical and nominal α levels for each of the corresponding values of n and k. These analyses indicate that the sparse and discrete nature of chromosomal breakage data results in large and unpredictable discrepancies between the empirical and nominal α levels when fragile site identifications are based on small numbers of breaks (n < 0.5 k). With n≥ 0.5 k, the distribution of X _s ² appears to be stable and non-significant differences in the empirical and nominal α levels are generally obtained. These results are inherent to the nature of the data and are, therefore, relevant to any statistical model for the identification of fragile sites from chromosomal breakage data. For FSM identification of fragile sites at α = 0.05, we suggest that n≥ 0.5 k is the minimum reliable number of mapped chromosomal breaks per individual. Received: 28 April 1997 / Accepted: 1 July 1997     

Kinetics of the action of three selenides on Staphylococcus aureus growth as studied by microcalorimetry

The effect of three kinds of selenide on Staphylococcus aureus growth was studied by means of microcalorimetry. Differences in their capacities to inhibit the metabolism of this bacterium were observed. The rate constant k (in the log phase) in the presence of the compounds decreased with increasing concentrations of the compounds. The relationship of k and c is nearly linear for the selenium compounds. Judged from the rate constant, k, and the half-inhibitory concentration IC₅₀, the experimental results reveal that the sequence of antibiotic activity of the three tested selenides compounds is (2-hydroxy benzyl imino)ethyl n-hexyl selenide> n-butyl(2-hydroxy benzyl imino)ethyl selenide>bis[(2,4-dihydroxy benzyl imino)ethyl] selenide.     

Bioremediation of Soil Contaminated with Diesel Using Inorganic Nitrogen Sources: Incorporating nth-Order Algorithm in the Evaluation of Process Kinetics

In the present study, we investigated the effects of inorganic nitrogen sources—(NPK fertilizer, 15:15:15), (urea fertilizer, 46:0:0), (NH₄)₂SO₄ as well as monitored natural attenuation on the bioremediation of diesel-polluted soil. At the end of the 6-week study, the highest degradation was recorded in soil amended with NPK fertilizer (95 ± 2.77%) while the least total petroleum hydrocarbon removal was observed in monitored natural attenuation (89 ± 2.91%). Nth-order kinetics effectively described three of the treatments out of the four treatment plans. These include urea amendment (r² = 0.9925, average relative error (ARE) = 1.45%, root mean square error (RMSE) = 0.038, k_n = (3.57 ± 0.61) × 10^?2, n = 1.33), NPK fertilizer amendment (r² = 0.9751, ARE = 3.241%, RMSE = 0.086, k_n = (8.04 ± 0.23) × 10^?1, n = 0.74), and monitored natural attenuation (r² = 0.9697, ARE = 2.77%, RMSE = 0.073, k_n = (1.57 ± 0.50) × 10^?2, n = 1.16). The values of n from the nth-order kinetics parameter estimation indicated that all the treatments resulted in diesel degradation that followed a first-order kinetics path. Thus, the outcome of kinetic modeling showed that nth-order can be used as validating tool when many kinetic orders are under consideration. The phytotoxicity assay with Zea mays showed that the treatments plans resulted in germination indices of 17–55%.     

Modeling of calcium-induced solubility profiles of casein for biotechnology: Influence of primary structure and posttranslational modification

Summary Molecular biology holds the promise of new tools for the food industry which include proteins with tailor-made functionality. Without a fundamental knowledge of the molecular bases of these properties, implementation will be strictly empirical. For example, the phenomena of salt-induced precipitation of proteins (salting-out) and their resolubilization (salting-in) has heretofore been discussed only qualitatively. A quantitative method, using Wyman's theory of thermodynamic linkage, has been developed and tested on the calcium-induced solubility profiles of the major milk proteins, the caseins. Salting-out was described by a salt-binding constant,k ₁, andn, the number of moles of salt bound; salting-in was described by the corresponding termsk ₂ andm. The magnitude of these parameters indicated involvement of protein phosphate groups in binding and precipitation, but enzymatic dephosphorylation showed significant increases ink ₁ andk ₂ indicating involvement of carboxylate groups as well. Studies on two genetic variants of _s1-casein indicated the importance of a hydrophobically stabilized intramolecular ion pair in the functionality of the protein. These studies have led to a fuller understanding of the molecular basis for the solubility behavior of caseins and have laid the groundwork for future computer simulation of food protein functionality.