CONDUCTING PHYLOGENETIC COMPARATIVE STUDIES WHEN THE PHYLOGENY IS NOT KNOWN

A method is proposed to conduct phylogenetic analyses of comparative or interspecific data when the true phylogeny is not known. Standard models of speciation and/or extinction or other methods are used to generate a sample from the set of all possible phylogenies for the measured species. The comparative data are then analyzed on each of the possible trees to obtain a distribution of possible evolutionary statistics for these data. The mean of this distribution is proposed as a reasonable estimate of the true evolutionary statistic of interest. Ways of obtaining confidence intervals and of developing hypothesis tests for this mean statistic are also proposed. The method can be used with any comparative method or phylogenetic analysis technique when phylogenetic relationships among species are not known or when branch lengths for a phylogeny in units of expected character change (as required by most methods) are not available. Computer programs to conduct the analyses are available on request.     

Assessing the numerical accuracy of the impedance method

The impedance method has been used extensively to calculate induced electric fields and currents in tissue as a result of applied electromagnetic fields. However, there has previously been no known method for an a priori assessment of the numerical accuracy of the results found by this method. Here, we present a method which permits an a priori assessment of the numerical accuracy of the impedance method applied to physiologically meaningful problems in bioengineering. The assessment method relies on estimating the condition number associated with the impedance matrix for problems with varying shapes, sizes, conductivities, anisotropies, and implementation strategies. Equations have been provided which predict the number of significant figures lost due to poor matrix conditioning as a function of these variables. The results show that, for problems of moderate size and uncomplicated geometry, applied fields should be measured or calculated accurately to at least five or six significant figures. As resolutions are increased and material properties are more widely divergent even more significant figures are needed. The equations provided here should ensure that solutions found from the impedance method are calculated accurately.     

A New Distribution-Free Approach to Constructing the Confidence Region for Multiple Parameters

Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.     

A novel method for estimating the number of species within a region

Ecologists are often required to estimate the number of species in a region or designated area. A number of diversity indices are available for this purpose and are based on sampling the area using quadrats or other means, and estimating the total number of species from these samples. In this paper, a novel theory and method for estimating the number of species is developed. The theory involves the use of the Laplace method for approximating asymptotic integrals. The method is shown to be successful by testing random simulated datasets. In addition, several real survey datasets are tested, including forests that contain a large number (tens to hundreds) of tree species, and an aquatic system with a large number of fish species. The method is shown to give accurate results, and in almost all cases found to be superior to existing tools for estimating diversity.     

Specific assay for endotoxin using immobilized histidine and Limulus amebocyte lysate.

The LAL test is inhibited or enhanced by many substances. To overcome these problems, we have developed a specific endotoxin assay method using an ultrafiltration unit, a fluorometric LAL reagent, and immobilized histidine (which is a specific adsorbent for endotoxins). This method is composed of two steps. The first step is the adsorption of endotoxins. Using immobilized histidine, endotoxins are quantitatively adsorbed on the adsorbent, and the adsorbed endotoxins are separated from LAL-inhibiting or -enhancing substances by the ultrafiltration unit. The second step is the reaction of adsorbed endotoxins with the LAL reagent. The endotoxins adsorbed on immobilized histidine are directly reacted with the LAL reagent in a filter cup and show enough activity for assay. The reproducibility and the accuracy of this method are high, and the recovery of endotoxins from a sample solution is more than 95%. The new endotoxin assay method using immobilized histidine can be utilized for the determination of endotoxins in a solution containing LAL-inhibiting or -enhancing substances such as amino acids and antibiotics instead of requiring employment of the more common gel-clot technique.     

Method for the mapping of a female partial-sterile locus on a molecular marker linkage map

The female gametophyte is an absolutely essential structure for angiosperm reproduction, and female sterility has been reported in a number of crops. In this paper, a maximum-likelihood method is presented for estimating the position and effect of a female partial-sterile locus in a backcross population using the observed data of dominant or codominant markers. The ML solutions are obtained via Bailey’s method. The process for the estimating of the recombination fractions and the viabilities of female gametes are described, and the variances of the estimates of the parameters are also presented. Application of the method is demonstrated using a set of simulated data. This method circumvents the problems of the traditional mapping methods for female sterile genes which were based on data from seed set or embryo-sac morphology and anatomy.     

In situ detection of enzymes in yeast

A very simple method that allows for the rapid in situ assay of enzyme activity in yeast is described. Single colonies are collected on sticks (or glass micropipets), or multiple colonies are collected on sandpaper, and crushed onto nitrocellulose filters. The filters in turn are stained for the enzyme of interest using a histochemical assay. The method is quantitative and was found to work well for four enzymes in yeast.     

Isolation of protein subpopulations undergoing protein-protein interactions

A new method is described for isolating and identifying proteins participating in protein-protein interactions in a complex mixture. The method uses a cyanogen bromide-activated Sepharose matrix to isolate proteins that are non-covalently bound to other proteins. Because the proteins are accessible to chemical manipulation, mass spectrometric identification of the proteins can yield information on specific classes of interacting proteins, such as calcium-dependent or substrate-dependent protein interactions. This permits selection of a subpopulation of proteins from a complex mixture on the basis of specified interaction criteria. The new method has the advantage of screening the entire proteome simultaneously, unlike the two-hybrid system or phage display, which can only detect proteins binding to a single bait protein at a time. The method was tested by selecting rat brain extract for proteins exhibiting calcium-dependent protein interactions. Of 12 proteins identified by mass spectrometry, eight were either known calcium-binding proteins or proteins with known calcium-dependent protein interactions, indicating that the method is capable of enriching a subpopulation of proteins from a complex mixture on the basis of a specific class of protein interactions. Because only naturally occurring interactions of proteins in their native state are observed, this method will have wide applicability to studies of protein interactions in tissue samples and autopsy specimens, for screening for perturbations of protein-protein interactions by signaling molecules, pharmacological agents or toxins, and screening for differences between cancerous and untransformed cells.     

Evolutionary Change of Restriction Cleavage Sites and Phylogenetic Inference

Mathematical formulas are developed for the evolutionary change of restriction cleavage sites in a DNA sequence, allowing unequal rates between transitional and transversional types of nucleotide substitution. Formulas are also developed for the probability of having a particular pattern of site changes among evolutionary lineages, such as parallel gains or losses of sites, and for inferring the presence or absence of a restriction site in an ancestral sequence from data on the present-day sequences. The unordered compatibility method is proposed for inferring the phylogenetic relationships among relatively closely related organisms, treating restriction sites as cladistic characters. Formulas are derived for the probability (P+) of obtaining the correct network for a given number (N) of informative sites for the cases of four and five species. These formulas are applied to evaluate the performance of the method and to estimate the N value required for P+ to be 95% or larger. The method performs well when the branches between ancestral nodes and the branches leading to the two most recent species are more or less equal in length, but performs poorly when the latter two branches are considerably longer than the former.     

Modeling of identity-by-descent processes along a chromosome between haplotypes and their genotyped ancestors

Identity-by-descent probabilities are important for many applications in genetics. Here we propose a method for modeling the transmission of the haplotypes from the closest genotyped relatives along an entire chromosome. The method relies on a hidden Markov model where hidden states correspond to the set of all possible origins of a haplotype within a given pedigree. Initial state probabilities are estimated from average genetic contribution of each origin to the modeled haplotype while transition probabilities are computed from recombination probabilities and pedigree relationships between the modeled haplotype and the various possible origins. The method was tested on three simulated scenarios based on real data sets from dairy cattle, Arabidopsis thaliana, and maize. The mean identity-by-descent probabilities estimated for the truly inherited parental chromosome ranged from 0.94 to 0.98 according to the design and the marker density. The lowest values were observed in regions close to crossing over or where the method was not able to discriminate between several origins due to their similarity. It is shown that the estimated probabilities were correctly calibrated. For marker imputation (or QTL allele prediction for fine mapping or genomic selection), the method was efficient, with 3.75% allelic imputation error rates on a dairy cattle data set with a low marker density map (1 SNP/Mb). The method should prove useful for situations we are facing now in experimental designs and in plant and animal breeding, where founders are genotyped with relatively high markers densities and last generation(s) genotyped with a lower-density panel.     

Using proteomics to mine genome sequences

We present a method for mining unannotated or annotated genome sequences with proteomic data to identify open reading frames. The region of a genome coding for a protein sequence is identified by using information from the analysis of proteins and peptides with MALDI-TOF mass spectrometry. The raw genome sequence or any unassembled contigs of an organism are theoretically cleaved into a number of equal sized but overlapping fragments, and these are then translated in all six frames into a series of virtual proteins. Each virtual protein is then subjected to a theoretical enzymatic digestion. Standard proteomic sample preparation methods are used to separate, array, and digest the proteins of interest to peptides. The masses of the resulting peptides are measured using mass spectrometry and compared to the theoretical peptide masses of the virtual proteins. The region of the genome responsible for coding for a particular protein can then be identified when there are a large number of hits between peptides from the protein and peptides from the virtual protein. The method makes no assumptions about the location of a protein in a particular gene sequence or the positions or types of start and stop codons. To illustrate this approach, all 773 proteins of Pseudomonas aeruginosa contained in SWISS-PROT were used to theoretically test the method and optimize parameters. Increasing the size of the virtual proteins results in an overall improvement in the ability to detect the coding region, at the cost of decreasing the sensitivity of the method for smaller proteins. Increasing the minimum number of matching peptides, lowering the mass error tolerance, or increasing the signal-to-noise ratio of the simulated mass spectrum, improves the ability to detect coding regions. The method is further demonstrated on experimental data from Mycobacterium tuberculosis and is also shown to work with eukaryotic organisms (e.g., Homo sapiens).     

Method to optimize high-pressure, multicomponent gas mixing.

By use of the equations derived herein, a method is outlined to determine the optimum filing sequence and to obtain the maximum possible pressure when two or more pure high-pressure gases are to be transferred to a receiver cylinder in order to prepare a multicomponent gas mixture. The method is valid for any number of gas components, originating from high-pressure storage cyclinders of arbitrary size and pressure and for a receiver cylinder to contain initially one or more of the component gases. Percentage concentrations within 1% of desired are easily obtained with this method.     

Spreadsheet Method for Evaluation of Biochemical Reaction Rate Coefficients and Their Uncertainties by Weighted Nonlinear Least-Squares Analysis of the Integrated Monod Equation

A convenient method for evaluation of biochemical reaction rate coefficients and their uncertainties is described. The motivation for developing this method was the complexity of existing statistical methods for analysis of biochemical rate equations, as well as the shortcomings of linear approaches, such as Lineweaver-Burk plots. The nonlinear least-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods that involve inversion of data are unreliable since several important assumptions of linear regression are violated. Furthermore, when linearized methods are used, there is no basis for calculation of the uncertainties in the rate coefficients. Uncertainty estimates are crucial to studies involving comparisons of rates for different organisms or environmental conditions. The spreadsheet method uses weighted least-squares analysis to determine the best-fit values of the rate coefficients for the integrated Monod equation. Although the integrated Monod equation is an implicit expression of substrate concentration, weighted least-squares analysis can be employed to calculate approximate differences in substrate concentration between model predictions and data. An iterative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of squared weighted errors. The uncertainties in the best-fit values of the rate coefficients are calculated by an approximate method that can also be implemented in a spreadsheet. The uncertainty method can be used to calculate single-parameter (coefficient) confidence intervals, degrees of correlation between parameters, and joint confidence regions for two or more parameters. Example sets of calculations are presented for acetate utilization by a methanogenic mixed culture and trichloroethylene cometabolism by a methane-oxidizing mixed culture. An additional advantage of application of this method to the integrated Monod equation compared with application of linearized methods is the economy of obtaining rate coefficients from a single batch experiment or a few batch experiments rather than having to obtain large numbers of initial rate measurements. However, when initial rate measurements are used, this method can still be used with greater reliability than linearized approaches.     

Locating regions of differential variability in DNA and protein sequences.

In the comparison of DNA and protein sequences between species or between paralogues or among individuals within a species or population, there is often some indication that different regions of the sequence are divergent or polymorphic to different degrees, indicating differential constraint or diversifying selection operating in different regions of the sequence. The problem is to test statistically whether the observed regional differences in the density of variant sites represent real differences and then to estimate as accurately as possible the location of the differential regions. A method is given for testing and locating regions of differential variation. The method consists of calculating G(x(k)) = k/n - x(k)/N, where x(k) is the position of the kth variant site along the sequence, n is the total number of variant sites, and N is the total sequence length. The estimated region is the longest stretch of adjacent sequence for which G(x(k)) is monotonically increasing (a hot spot) or decreasing (a cold spot). Critical values of this length for tests of significance are given, a sequential method is developed for locating multiple differential regions, and the power of the method against various alternatives is explored. The method locates the endpoints of hot spots and cold spots of variation with high accuracy.     

Crossintervalograms for analysis of electrical activity of the brain

A method of construction of crossintervalograms for electroencephalograms is proposed. Particular points or EEG fragments of particular shape are used as time-locked events, and the intervals between these reference points are analyzed. The method is theoretically substantiated. Examples of crossintervalograms constructed for EEG extrema and derivative EEGextrema are given. The information validity of these crossintervalograms is demonstrated and their features are indicated. Comparison crossintervalograms with crosscorrelograms is performed. The possibilities of further development and applications of a method are specified. It is suggested that the method will be useful for investigation of operative interaction of brain subsystems.     

Data mining applied to linkage disequilibrium mapping

We introduce a new method for linkage disequilibrium mapping: haplotype pattern mining (HPM). The method, inspired by data mining methods, is based on discovery of recurrent patterns. We define a class of useful haplotype patterns in genetic case-control data and use the algorithm for finding disease-associated haplotypes. The haplotypes are ordered by their strength of association with the phenotype, and all haplotypes exceeding a given threshold level are used for prediction of disease susceptibility-gene location. The method is model-free, in the sense that it does not require (and is unable to utilize) any assumptions about the inheritance model of the disease. The statistical model is nonparametric. The haplotypes are allowed to contain gaps, which improves the method's robustness to mutations and to missing and erroneous data. Experimental studies with simulated microsatellite and SNP data show that the method has good localization power in data sets with large degrees of phenocopies and with lots of missing and erroneous data. The power of HPM is roughly identical for marker maps at a density of 3 single-nucleotide polymorphisms/cM or 1 microsatellite/cM. The capacity to handle high proportions of phenocopies makes the method promising for complex disease mapping. An example of correct disease susceptibility-gene localization with HPM is given with real marker data from families from the United Kingdom affected by type 1 diabetes. The method is extendable to include environmental covariates or phenotype measurements or to find several genes simultaneously.     

Low volume processing of protein blots in rolling drums

We have evaluated an improved method for processing protein blots on nitrocellulose or nylon membranes using cylindrical plastic containers. The method, which is directly analogous to the commonly used method of photographic processing in rolling drums, uses small values of reagents which are constantly washed over the blotting membrane by rotating the drum horizontally on a roller mixer. Volumes of reagents used are typically less than one-10th of those required for conventional methods using plastic bags or trays. The efficiency of probing and washing steps are greatly improved, giving an all-round increase in sensitivity, ease of processing, and economy of reagents.     

NON-STEADY-STATE ANALYSIS OF CELLULAR DEVELOPMENT

A discrete, compartmental, representation is proposed for cellular development. Equations describing the kinetics of cellular development (with or without cell proliferation) are derived in both differential and integral form. Using an integral formulation, a method is proposed for the computation of compartment transit times (maturation times) which does not require the use of radioactive or other tracers. Although some restrictive conditions are imposed, the applicability of the method does not depend on strictly steady-state conditions, nor on purely exponential growth or decay. The method permits analysis of cellular development in certain non-steady cases for which existing analytical methods are inadequate. It is possible that patterns of cellular development during embryogenesis, recovery from insults, or growth in culture (e.g. of normal and leukaemic human granulocytes) could be examined using this method of analysis.     

A colorimetric method for the enzymatic analysis of gases: the determination of ethanol and formaldehyde vapors using solid alcohol oxidase

A novel enzymatic approach to the direct determination of ethanol vapors in the gas phase is described. The system is composed of alcohol oxidase, peroxidase, and the color indicator 2,6-dichloroindophenol dispersed on microcrystalline cellulose (avicel). Simple devices are developed for the semiquantitative determination of ethanol in the breath. The devices are optimized to produce a sharp color change at a set time of 1 min for ethanol concentrations above the legal limit for driving (kinetic method) or a stable final color after 5 min (equilibrium method). Such color changes are detectable by simple visual observation. Using TLC plastic sheets and a transmittance densitometer, the system can also be used as a quantitative method for the determination of ethanol or formaldehyde vapors. Dehydrated enzymes may be useful for the analysis of hazardous gases.