Sample Size Requirements of a Mixture Analysis Method with Applications in Systematic Biology

The available information on sample size requirements of mixture analysis methods is insufficient to permit a precise evaluation of the potential problems facing practical applications of mixture analysis. We use results from Monte Carlo simulation to assess the sample size requirements of a simple mixture analysis method under conditions relevant to biological applications of mixture analysis. The mixture model used includes two univariate normal components with equal variances but assumes that the researcher is ignorant as to the equality of the variances. The method used relies on the EM algorithm to compute the maximum likelihood estimates of the mixture parameters, and the likelihood ratio test to assess the number of components in the mixtures. Our results suggest that sample sizes close to 500 or 1000 data may be required to adequately solve mixtures commonly found in biology. Sample sizes of 500 or 1000 are difficult to achieve. However, use of this MA method may be a reasonable option when the researcher deals with problems which are intractable by other means. Copyright 1999 Academic Press.     

Combining gene annotations and gene expression data in model-based clustering: weighted method

It has been increasingly recognized that incorporating prior knowledge into cluster analysis can result in more reliable and meaningful clusters. In contrast to the standard modelbased clustering with a global mixture model, which does not use any prior information, a stratified mixture model was recently proposed to incorporate gene functions or biological pathways as priors in model-based clustering of gene expression profiles: various gene functional groups form the strata in a stratified mixture model. Albeit useful, the stratified method may be less efficient than the global analysis if the strata are non-informative to clustering. We propose a weighted method that aims to strike a balance between a stratified analysis and a global analysis: it weights between the clustering results of the stratified analysis and that of the global analysis; the weight is determined by data. More generally, the weighted method can take advantage of the hierarchical structure of most existing gene functional annotation systems, such as MIPS and Gene Ontology (GO), and facilitate choosing appropriate gene functional groups as priors. We use simulated data and real data to demonstrate the feasibility and advantages of the proposed method.     

Determination by photon correlation spectroscopy of particle size distributions in lipid vesicle suspensions.

A method of determining particle size distributions in lipid vesicle preparations is outlined. A vesicle suspension is modeled as a polydisperse mixture of spherical shells. The distribution of particle sizes in this mixture is approximated by a continuous, piecewise linear function called a first-order spline. Excellent simultaneous fits to photon correlation spectroscopy data gathered at several different angles are presented. An error analysis is included to indicate the resolution of the method.     

Application of isothermal titration calorimetry and column chromatography for identification of biomolecular targets

This protocol describes a method for identifying unknown target proteins from a mixture of biomolecules for a given drug or a lead compound. This method is based on a combination of chromatography and isothermal titration calorimetry (ITC) where ITC is used as a tracking tool. The first step involves the use of ITC to confirm the binding of ligand to a component in the biomolecular mixture. Subsequently, the biomolecular mixture is fractionated by chromatography, and the binding of the ligand with individual fractions (or subfractions) is verified by ITC. The iteration of chromatographic purification on the fractions combined with ITC results in identifying the target protein. This method is useful when the target protein or ligand is unknown and/or not amenable to labeling, chemical modification or immobilization. This protocol has been successfully used by our team and by others to identify both low-abundance and highly abundant target proteins present in biomolecular mixtures. With this protocol, it takes approximately 3-5 d to identify the target protein from a mixture.     

A rapid method for qualitative assay of both neomycin phosphotransferase II and β-glucuronidase activities in transgenic plants

A rapid and efficient method for assaying both NPT II and GUS activities was developed. In this method, which is modified from that of McDonnell et al. (1987), and Jefferson (1987), no sample processing procedures such as grinding and centrifugation are necessary. Cut plant tissues (leaves) or intact calli or cells expressing the genes of interest are placed in wells of a microtiter plate containing reaction mixture, and after incubation the reaction mixture is directly used for both NPT II and GUS assays. For the NPT II assay, aliquots of the reaction mixture are blotted onto Whatman P81 paper through a manifold, and the product of the reaction is detected by autoradiography. For GUS activity, aliquots or the rest of the reaction mixture are observed for fluorescent emission under a hand-held UV light or read in a fluorimeter after adding stop buffer to the reaction mixture. This method is the simplest, cheapest, and quickest assays for NPT II and GUS reported to date, and is extremely efficient and suitable for assaying small amounts of samples (as little as 0.3 mg tissue), such as in transient expression assays, or for the quick screening of large numbers of samples, such as in studies of gene inheritance in transgenic plants. In our laboratory, it has been used successfully in assaying NPT II activities for transient and stable gene expression in transformed protoplasts, calli, and leaf tissues of various transgenic plants. It has also been used for detecting both NPT II and GUS activities in transgenic rice plants, in which more than 400 samples could be assayed per day per person.     

Implications of a statistical occurrence model for mixture toxicity estimation

This study provides a method for characterizing the effects of concentration variability and correlation among co-acting compounds on mixture toxicity, considering the implications of missing chemical data. The method is explored by developing a set of multiple occurrence scenarios for mixtures of related chemicals. The calculations are performed for hypothetical mixtures of a group of ten synthetic antibiotics that have been tested on marine bacterium to fit dose-response relationships for long-term bioluminescence inhibition of Vibrio fischeri. Mixture toxicities are computed and compared for the assumptions of independent joint action theory and concentration/dose addition theory. The study results show that higher variability in concentrations is associated with higher effective (average) mixture toxicity, in this application by as much as a factor of ten for mixtures with highly variable component concentrations. Moreover, omitting the most toxic compounds caused mixture toxicities to be underestimated by a factor of approximately two. We recommend a pre-assessment of the effect of different chemical occurrence patterns and variability on mixture toxicity to help prioritize needs for further co-occurrence data and toxicity studies.     

Antioxidant Effect of the Reaction Mixture of Dehydroascorbic Acid with Tryptophan

Antioxidant activities as measured by the peroxide value, and the thiobarbituric acid or oxygen uptake methods were observed on a reaction mixture of dehydroascorbic acid with tryptophan. This was stronger than any of the activities of similar amino-carbonyl reaction mixtures tested and was comparable to BHA. The strongest activity was developed when an equimolar mixture of the reactants in 95% ethanol were heated for 30 min in a boiling water bath. In the antioxidant action, the presence of α-tocopherol acted synergistically. When the mixture was fractionated by TLC on a cellulose plate a brown colored fraction proved strongly effective by the POV method. Another fraction, effective in the oxygen uptake method but not in the POV method, was found mainly consisting of ascorbic acid. Other fractions which were identified before and related to the free radical formation were all inactive.     

杀虫剂混用方法——抗性治理的一种策略

本文根据种群遗传学的基本原理,采用计算机数值模拟的方法定量比较了合理混用、轮用、棋盘式使用等用药策略对害虫抗性增长的影响.结果表明,对半显性遗传,两性繁殖的害虫来说,在较有利的条件下合理混用与轮用效果基本一致,而优于棋盘式用药;在条件不利(抗性基因初始频率高,稀释作用小等)时,合理混用的方法明显优于其他两种方法.因此合理混用是一种有希望的抗性治理方法.     

A new method for analysis of components in a mixture without preseparation: evaluation of the concentration ratio and protein-protein interaction

A new method for evaluating the ratio of two structurally different proteins or other compounds in a mixture that does not require any preseparation steps and is based on using the aqueous two-phase partition technique is described. Mathematical analysis of the partitioning of a mixture of two solutes demonstrates its ability to quantitatively evaluate the ratio of the concentrations of the solutes in the initial mixture. It also provides the means for detecting interactions between the two solutes. Experimental results confirm the analysis to be correct for mixtures of low-molecular-weight compounds as well as for mixtures of structurally different proteins. An example of analysis of a clinically relevant mixture of two proteins-transferrin and carbohydrate-deficient transferrin-is provided. An analysis of interactions between two proteins and/or peptides is also illustrated using two examples.     

A psychophysical investigation of Beidler's mixture equation

Beidler's mixture equation (1971) describes the relationshipbetween the concentration and composition of a binary mixtureand the magnitude of the neural response. Later this equationwas generalized to a psychophysical level. The purpose of thepresent study is to show that Beidler's mixture equation canbe tested appropriately with indirect psychophysical methods,without the necessity of making assumptions about the magnitudeof the maximum responses to the single compounds which constitutethe mixture. Experiments were carried out using glucose andfructose as tastants. Concentrations of fructose and three equiratiomixture types containing glucose and fructose were matched inperceived sweetness intensities to five different glucose concentrationsusing the method of constant stimuli. The results showed thatBeidler's mixture equation describes accurately the taste interactionbetween glucose and fructose at low sweetness levels. At highsweetness levels the taste system is more efficient, as couldbe expected on the basis of Beidler's mixture equation, becausethe experimentally determined mixture concentrations were lowerthan those predicted by the mixture equation. The findings suggestthat glucose and fructose share common receptors, but that eitherone or both have additional secondary binding mechanisms.     

An efficient and practical synthesis of beta-(1 --> 3)-linked xylooligosaccharides

A facile and practical method was developed for the synthesis of beta-(1 --> 3)-linked xylooligosaccharides. Dibezoylation of allyl alpha-D-xylopyranoside (1) afforded 2,4-dibenzoate 6 as the major product. Chloroacetylation of 6, followed by deallylation and trichloroacetimidation, gave a 1:3 alpha/beta imidate (10 and 11) mixture. Coupling of the imidate mixture with 6 gave a disaccharide 13, whose dechloroacetylation afforded the disaccharide acceptor 16. Condensation of perbenzoylated xylosyl alpha/beta imidate (7 and 8) mixture with 6 gave the disaccharide 12. Deallylation of 12, followed by trichloroacetimidation, furnished the disaccharide donor as a 1:1 alpha/beta mixture. Coupling of the disaccharide donor mixture with the disaccharide acceptor 16 yielded the tetrasaccharide 17. Reiteration of deallylation and trichloroacetimidation transformed 17 to the tetrasaccharide donor mixture. Condensation of the tetrasaccharide donor mixture with the acceptor 16 gave the hexasaccharide 21. Debenzoylation with saturated ammonia-methanol afforded beta-(1 --> 3)-linked allyl xylotetraoside and xylohexaoside.     

Manometric method for determining bicarbonate content in plant leaves.

A method is described for manometric determination of bicarbonate (as little as 0.25 μmoles) in leaves. Conditions such as optimum pH and inactivation of carbonic anhydrase are introduced to stabilize the bicarbonate. Crude leaf extracts are purified with chloroform and Darco G-60. An ionic mixture is separated from macromolecular compounds by elution from a column of Sephadex G-25. Carbon dioxide is released by acidifying the ionic mixture and is determined with a respirometer.     

Determination of the concentration of ligand-specific molecules, found in mixtures with ligand-nonspecific molecules

A new method, which allows determination of the concentration of ligand-specific molecules in a mixture of these molecules with biochemically similar but ligand-unspecific molecules, is suggested. The method is based on a partial exhaustion of the mixture on a column with immobilized ligand and determination of the part of ligand-specific molecules presented in exhausted mixture. The concentration of monoclonal antibodies specific to bovine serum albumin in a commercial "Sigma" preparation and concentration of polyreactive immunoglobulins in a commercial "Sigma" preparation of bovine immunoglobulins were determined by suggested method.     

A kinetic method for the simultaneous determination of isoenzymes activities in mixture. Application to A2 and A3 horseradish peroxidases

A graphical method for the simultaneous determination of the activity of two isoenzymes in a mixture, is presented. The method is based on the different kinetic behaviour of the isoenzymes to the changes in the substrate concentrations. Having determined the reaction rates for the enzyme mixture at different substrate concentrations, the activity of both isoenzymes can be derived graphically. An algebraic method for two or more isoenzymes is mentioned, as well. The applications of the graphical and the algebraic method to A2 and A3 horseradish isoperoxidases demonstrated that the difference between the actual activities of the two isoperoxidases and those determined by the proposed method was around 5% of the actual activities. The scope of application of this method could be extended to isoenzymes of clinical importance.     

Exploiting the functional and taxonomic structure of genomic data by probabilistic topic modeling

In this paper, we present a method that enable both homology-based approach and composition-based approach to further study the functional core (i.e., microbial core and gene core, correspondingly). In the proposed method, the identification of major functionality groups is achieved by generative topic modeling, which is able to extract useful information from unlabeled data. We first show that generative topic model can be used to model the taxon abundance information obtained by homology-based approach and study the microbial core. The model considers each sample as a “document,” which has a mixture of functional groups, while each functional group (also known as a “latent topic”) is a weight mixture of species. Therefore, estimating the generative topic model for taxon abundance data will uncover the distribution over latent functions (latent topic) in each sample. Second, we show that, generative topic model can also be used to study the genome-level composition of “N-mer” features (DNA subreads obtained by composition-based approaches). The model consider each genome as a mixture of latten genetic patterns (latent topics), while each functional pattern is a weighted mixture of the “N-mer” features, thus the existence of core genomes can be indicated by a set of common N-mer features. After studying the mutual information between latent topics and gene regions, we provide an explanation of the functional roles of uncovered latten genetic patterns. The experimental results demonstrate the effectiveness of proposed method.     

Enhanced production of fructose palmitate by lipase-catalyzed esterification in ionic liquids

For the enhancement of enzyme activity, application of ultrasound irradiation on lipase-catalyzed esterification of fructose with palmitic acid in ionic liquids (ILs) mixture containing supersaturated fructose solution was investigated. In the mixture of [Bmim][TfO] and [Omim][Tf₂N] (1:1, v/v), 1.44 times higher enzyme activity (29.2 μmoL/min/g) was achieved under ultrasound irradiation. Besides, ultrasound irradiation enhanced enzyme stability in viscous ILs mixture. After 5 times reuse of Novozym 435 and ILs mixture, 84.4% of initial enzyme activity was remained under ultrasound irradiation, while the residual activity using magnetic stirring only method was 76.2%. These results show that enzymatic reaction in viscous ILs mixture under ultrasound irradiation is an effective method for enzyme activity, as well as, enzyme stability resulting in economic competitiveness of green process.     

Calculating affinity constants of substrate mixtures in a chemostat

An “oversimplified” method for calculating affinity constants in substrate mixtures is evaluated concerning its validity. It is shown that the real affinity to the mixture as determined by using the correct method is always higher, i.e., leads to a lower affinity constant, as compared to the wrong method frequently used.     

A Universal Method for Species Identification of Mammals Utilizing Next Generation Sequencing for the Analysis of DNA Mixtures

Species identification can be interesting in a wide range of areas, for example, in forensic applications, food monitoring and in archeology. The vast majority of existing DNA typing methods developed for species determination, mainly focuses on a single species source. There are, however, many instances where all species from mixed sources need to be determined, even when the species in minority constitutes less than 1 % of the sample. The introduction of next generation sequencing opens new possibilities for such challenging samples. In this study we present a universal deep sequencing method using 454 GS Junior sequencing of a target on the mitochondrial gene 16S rRNA. The method was designed through phylogenetic analyses of DNA reference sequences from more than 300 mammal species. Experiments were performed on artificial species-species mixture samples in order to verify the method’s robustness and its ability to detect all species within a mixture. The method was also tested on samples from authentic forensic casework. The results showed to be promising, discriminating over 99.9 % of mammal species and the ability to detect multiple donors within a mixture and also to detect minor components as low as 1 % of a mixed sample.     

Detecting Specific Populations in Mixtures

Mixed stock analysis (MSA) estimates the relative contributions of distinct populations in a mixture of organisms. Increasingly, MSA is used to judge the presence or absence of specific populations in specific mixture samples. This is commonly done by inspecting the bootstrap confidence interval of the contribution of interest. This method has a number of statistical deficiencies, including almost zero power to detect small contributions even if the population has perfect identifiability. We introduce a more powerful method based on the likelihood ratio test and compare both methods in a simulation demonstration using a 17 population baseline of sockeye salmon, Oncorhynchus nerka, from the Kenai River, Alaska, watershed. Power to detect a nonzero contribution will vary with the population(s) identifiability relative to the rest of the baseline, the contribution size, mixture sample size, and analysis method. The demonstration shows that the likelihood ratio method is always more powerful than the bootstrap method, the two methods only being equal when both display 100% power. Power declines for both methods as contribution declines, but it declines faster and goes to zero for the bootstrap method. Power declines quickly for both methods as population identifiability declines, though the likelihood ratio test is able to capitalize on the presence of 'perfect identification' characteristics, such as private alleles. Given the baseline-specific nature of detection power, researchers are encouraged to conduct a priori power analyses similar to the current demonstration when planning their applications.