On testing biological data for the presence of a boundary

Under the boundary line model for a biological data set, where one variable is a biological response (e.g. crop yield) to an independent variable (e.g. available water content of the soil), we interpret the upper (or lower) boundary on a plot of the dependent variable (ordinate) against the independent variable (abscissa) as representing the maximum (or minimum) possible response for a given value of the independent variable. This concept has been widely used in soil science, agronomy and plant physiology; but it has been subject to criticism. In particular, no methods that are used to analyse the boundary line quantify the evidence that the envelope of the plot represents a boundary (in the sense of some limiting response to the independent variable) rather than simply being a fringe of extreme values of no intrinsic biological interest. In this article, we present a novel procedure that tests a data set for evidence of a boundary by considering its statistical properties in the region of the proposed boundary. The method is demonstrated using both simulated and real data sets.     

Fitting piecewise linear regression functions to biological responses

An iterative approach was achieved for fitting piecewise linear functions to nonrectilinear responses of biological variables. This algorithm is used to estimate the parameters of the two (or more) regression functions and the separation point(s) (thresholds, sensitivities) by statistical approximation. Although it is often unknown whether the response of a biological variable is adequately described by one rectilinear regression function or by piecewise linear regression function(s) with separation point(s), an F test is proposed to determine whether one regression line is the optimal fitted function. A FORTRAN-77 program has been developed for estimating the optimal parameters and the coordinates of the separation point(s). A few sets of data illustrating this kind of problem in the analysis of thermoregulation, osmoregulation, and the neuronal responses are discussed.     

An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory

Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(Xi, Xj; t), which expresses the percentage change in the value of a dependent variable Xi at a time t in response to an infinitesimal percentage change in the value of an independent variable Xj at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.     

NNAlign: a web-based prediction method allowing non-expert end-user discovery of sequence motifs in quantitative peptide data

Recent advances in high-throughput technologies have made it possible to generate both gene and protein sequence data at an unprecedented rate and scale thereby enabling entirely new "omics"-based approaches towards the analysis of complex biological processes. However, the amount and complexity of data that even a single experiment can produce seriously challenges researchers with limited bioinformatics expertise, who need to handle, analyze and interpret the data before it can be understood in a biological context. Thus, there is an unmet need for tools allowing non-bioinformatics users to interpret large data sets. We have recently developed a method, NNAlign, which is generally applicable to any biological problem where quantitative peptide data is available. This method efficiently identifies underlying sequence patterns by simultaneously aligning peptide sequences and identifying motifs associated with quantitative readouts. Here, we provide a web-based implementation of NNAlign allowing non-expert end-users to submit their data (optionally adjusting method parameters), and in return receive a trained method (including a visual representation of the identified motif) that subsequently can be used as prediction method and applied to unknown proteins/peptides. We have successfully applied this method to several different data sets including peptide microarray-derived sets containing more than 100,000 data points. NNAlign is available online at http://www.cbs.dtu.dk/services/NNAlign.     

Association models for a multivariate binary response

Models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.     

Combining intensity correlation analysis and MALDI imaging to study the distribution of flavonols and dihydrochalcones in Golden Delicious apples

Mass spectrometry-based imaging techniques applied to small molecules complement the growing research field of metabolomics and can be used to interpret many important biological processes occurring in plants. In untargeted imaging applications, chemical identification is a critical step since it cannot take advantage of separative techniques applied to neutral molecules (e.g. liquid chromatography). The use of high resolution spectrometers is of great help, but fragmentation experiments are often necessary. In many cases, the information on ion fragmentation is embedded in the data sets, because analytes break up during ionization, but the extraction of this information is not easy considering the complexity of the imaging data files. Here an approach is proposed for applying conventional untargeted MALDI (matrix-assisted laser desorption ionization) profiling and advanced data analysis to perform imaging of metabolites in apple tissues. The pipeline, based on intensity correlation analysis, is used to extract fragmentation information from untargeted, high resolution, wide range mass spectra and to reconstruct compound-specific images which can be used for interpretation purposes. The proposed approach was used to investigate the distribution of glycosylated flavonols and dihydrochalcones in Golden Delicious apples. The results indicate that the method is effective, showing a high potential for ascertaining detailed metabolite localization.     

Abstracts of papers to be presented at the Fiftieth Annual Meeting of the American Association of physical anthropologists Detroit,Michigan April 22–25, 1981

The critical problem confronting all allometric studies is the choice of an appropriate size variable, especially when body mass or some other measure of total size is unavailable. A method proposed by Jolicoeur (1963a,b) claims to generate an internal size variable by a principal components analysis of the covariance matrix of logarithmically transformed data, from which allometric coefficients can be computed. Despite the current popularity of this method, the precise relationship and degree of compatibility between such multivariate coefficients and the exponent of the bivariate power function (Y = βX^α) is unknown. This study evaluates the comparability and interpretability of allometric values computed by Jolicoeur's procedure and by standard bivariate regressions (least squares and major axis). Two primate data sets with known measures of size were utilized for these purposes: (1) longitudinal growth data from radiographs of two species of capuchin monkeys, Cebus apella and Cebus albifrons; and (2) interspecific osteometric data from a series of adult lemurs, species of prosimians from Madagascar. Consistent differences exist between multivariate and bivariate allometric coefficients for both ontogenetic and static data sets. Multivariate analysis underestimated the coefficients in the former and overestimated them in the latter. The internal size variable generated by principal components analysis is clearly not equivalent to, and hence not a suitable substitute for, known measures of size. Moreover, multivariate coefficients are very sensitive to the composition of variables in a given data set; α values of a variable changed appreciably depending on the other variables included in the analysis. The multivariate coefficients are also sample-specific, and provide misleading biological information when compared between samples (e.g., between species of capuchin monkey). For allometric investigations designed to evaluate scaling parameters relative to total size, alternative analytical solutions to the Jolicoeur method should be considered.     

An evaluation of fitting methods for the sum of two hyperbolas: application to uptake studies

Analysis of data in terms of the sum of two rectangular hyperbolas is frequently required in solute uptake studies. Four methods for such analysis have been compared. Three are based on least-squares fitting whereas the fourth (partition method I) is an extension of a single hyperbola fitting procedure based on non-parametric statistics. The four methods were tested using data sets which had been generated with two primary types of random, normal error in the dependent variable: one of constant error variance and the other of constant coefficient of variation. The methods were tested on further data sets which were obtained by incorporating single 10% bias errors at different positions in the original two sets. Partition method I consistently gave good estimates for the four parameters defining the double hyperbola and was highly insensitive to the bias errors. The least-squares procedures performed well under conditions satisfying the least-squares assumptions regarding error distribution, but frequently gave poor estimates when these assumptions did not hold. Our conclusion is that in view of the errors inherent in many solute uptake experiments it would usually be preferable to analyse data by a method such as partition method I rather than to rely on a least-squares procedure.     

The Burrows-Wheeler similarity distribution between biological sequences based on Burrows-Wheeler transform

This work aims at the similarity of biological sequences. Based on the Burrows-Wheeler transform, a definition of Burrows-Wheeler similarity distribution of two sequences is proposed to compare two sequences. Some distance measures are naturally followed by the distribution. The expectation and entropy of the similarity distribution are used to construct phylogenetic trees on two independent data sets. The result demonstrates that the method is efficient and powerful.     

Modeling kappa for measuring dependent categorical agreement data

A method for analysing dependent agreement data with categorical responses is proposed. A generalized estimating equation approach is developed with two sets of equations. The first set models the marginal distribution of categorical ratings, and the second set models the pairwise association of ratings with the kappa coefficient (kappa) as a metric. Covariates can be incorporated into both sets of equations. This approach is compared with a latent variable model that assumes an underlying multivariate normal distribution in which the intraclass correlation coefficient is used as a measure of association. Examples are from a cervical ectopy study and the National Heart, Lung, and Blood Institute Veteran Twin Study.     

Stabilized procedure for the determination of urokinase fibrinolytic potency

A stabilized procedure for the determination of urokinase (UK) fibrinolytic potency is described in which method response is dependent on urokinase concentration and independent of normal variation in assay parameters. The method is a selective stability-indicating procedure for UK active enzyme. It is suitable for evaluation of both high molecular weight as well as low molecular weight urokinase fractions and is calibrated against the World Health Organization International Reference Preparation for UK code 66/46 using a biological six-point parallel line log-log dose-response approach where sample and standard are compared under essentially identical conditions. High method stability and sensitivity are achieved through the use of appropriate levels of purified human plasminogen and human plasma (source of fibrinogen) as primary and secondary substrates, respectively. Method precision versus house reference standard (%RSD less than or equal to 2%) is suitable for research and pharmaceutical purposes. The absolute UK potency reference plane established in the calibrated procedure is equivalent to that established by other investigators in the fibrinolytic field.     

Mixed effect regression analysis for a cluster-based two-stage outcome-auxiliary-dependent sampling design with a continuous outcome

Two-stage design is a well-known cost-effective way for conducting biomedical studies when the exposure variable is expensive or difficult to measure. Recent research development further allowed one or both stages of the two-stage design to be outcome dependent on a continuous outcome variable. This outcome-dependent sampling feature enables further efficiency gain in parameter estimation and overall cost reduction of the study (e.g. Wang, X. and Zhou, H., 2010. Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling. Biometrics 66, 502-511; Zhou, H., Song, R., Wu, Y. and Qin, J., 2011. Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome. Biometrics 67, 194-202). In this paper, we develop a semiparametric mixed effect regression model for data from a two-stage design where the second-stage data are sampled with an outcome-auxiliary-dependent sample (OADS) scheme. Our method allows the cluster- or center-effects of the study subjects to be accounted for. We propose an estimated likelihood function to estimate the regression parameters. Simulation study indicates that greater study efficiency gains can be achieved under the proposed two-stage OADS design with center-effects when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a dataset from the Collaborative Perinatal Project.     

A parametric copula model for analysis of familial binary data

Modeling the joint distribution of a binary trait (disease) within families is a tedious challenge, owing to the lack of a general statistical model with desirable properties such as the multivariate Gaussian model for a quantitative trait. Models have been proposed that either assume the existence of an underlying liability variable, the reality of which cannot be checked, or provide estimates of aggregation parameters that are dependent on the ordering of family members and on family size. We describe how a class of copula models for the analysis of exchangeable categorical data can be incorporated into a familial framework. In this class of models, the joint distribution of binary outcomes is characterized by a function of the given marginals. This function, referred to as a "copula," depends on an aggregation parameter that is weakly dependent on the marginal distributions. We propose to decompose a nuclear family into two sets of equicorrelated data (parents and offspring), each of which is characterized by an aggregation parameter (alphaFM and alphaSS, respectively). The marginal probabilities are modeled through a logistic representation. The advantage of this model is that it provides estimates of the aggregation parameters that are independent of family size and does not require any arbitrary ordering of sibs. It can be incorporated easily into segregation or combined segregation-linkage analysis and does not require extensive computer time. As an illustration, we applied this model to a combined segregation-linkage analysis of levels of plasma angiotensin I-converting enzyme (ACE) dichotomized into two classes according to the median. The conclusions of this analysis were very similar to those we had reported in an earlier familial analysis of quantitative ACE levels.     

The generality of empirical and theoretical explanations of behavior

For theoretical explanations of data, parameter values estimated from a single dependent measure from one procedure are used to predict alternative dependent measures from many procedures. Theoretical explanations were compared to empirical explanations of data in which known functions and principles were used to fit only selected dependent measures. The comparison focused on the ability of theoretical and empirical explanations to generalize across samples of the data, across dependent measures of behavior, and across different procedures. Rat and human data from fixed-interval and peak procedures, in which principles (e.g., scalar timing) are well known, were described and fit by a theory with independent modules for perception, memory, and decision. The theoretical approach consisted of fitting closed-form equations of the theory to response rate gradients calculated from the data, simulating responses using parameter values previously estimated, and comparing theoretical predictions with dependent measures not used to estimate parameters. Although the empirical and theoretical explanations provided similar fits to the response rate gradients that generalized across samples and had the same number of parameters, only the theoretical explanation generalized across procedures and dependent measures.     

Ratio‐dependent significance thresholds in reciprocal 15N‐labeling experiments as a robust tool in detection of candidate proteins responding to biological treatment

Metabolic labeling of plant tissues with ¹⁵N has become widely used in plant proteomics. Here, we describe a robust experimental design and data analysis workflow implementing two parallel biological replicate experiments with reciprocal labeling and series of 1:1 control mixtures. Thereby, we are able to unambiguously distinguish (i) inherent biological variation between cultures and (ii) specific responses to a biological treatment. The data analysis workflow is based on first determining the variation between cultures based on ¹⁵N/¹⁴N ratios in independent 1:1 mixtures before biological treatment is applied. In a second step, ratio‐dependent SD is used to define p‐values for significant deviation of protein ratios in the biological experiment from the distribution of protein ratios in the 1:1 mixture. This approach allows defining those proteins showing significant biological response superimposed on the biological variation before treatment. The proposed workflow was applied to a series of experiments, in which changes in composition of detergent resistant membrane domains was analyzed in response to sucrose resupply after carbon starvation. Especially in experiments involving cell culture treatment (starvation) prior to the actual biological stimulus of interest (resupply), a clear distinction between culture to culture variations and biological response is of utmost importance.     

Reconstruction of the probe angular distribution from a series of electron spin resonance spectra of tilted oriented samples.

Model-independent methods for the reconstruction of the nitroxide spin probe angular distribution of labeled oriented biological assemblies from electron spin resonance (ESR) spectra were investigated. We found that accurate probe angular distribution information could be obtained from the simultaneous consideration of a series of ESR spectra originating from a sample at differing tilt angles relative to the Zeeman magnetic field. Using simulated tilt series data sets, we developed a consistent criteria for judging the reliability of the simulated fit to the data as a function of the free spectral parameters and thereby have increased the significance of the model-independent reconstruction of the probe angular distribution derived from the fit. We have also enhanced the angular resolution measurable with the model-independent methodology by increasing the rank of the order parameters that we can reliably deduce from a spectrum. This enhancement allows us to accurately deduce higher resolution features of the spin probe distribution. Finally we investigated the usefulness of fitting the tilt series data in multiple data sets such that tilt series data from many identical sample preparations are fitted simultaneously. This method proved to be useful in rapidly reducing a large amount of data by eliminating any redundant computations in the application of the enhanced model-independent analysis to identical sets of tilt series data. We applied the methodology developed here to ESR spectra from probe labeled muscle fibers to study the orientation of myosin cross-bridges in fibers. This application is described in the accompanying paper.     

A scheme to account quantitatively for the action of phytochrome in etiolated and light-grown plants

Abstract A scheme to account for the phytochrome responses of dark grown and green plants is presented. In contrast to some other models (e.g. Smith, 1970; Schäfer, 1975) it is proposed that both Pfr and the photoconversions of phytochrome are effectors of phytochrome action and interact to promote the observed responses. Under conditions where Ptot is not strongly wavelength dependent (e.g. with short pulses of light and in plants grown for prolonged periods in the light), responses will be predominantly related to Pfr concentration. Where Ptot is the major wavelength dependent variable (e.g. in the ‘high irradiance reaction’ of etiolated seedlings) it is proposed that the photoconversion process itself predominates in controlling the ultimate response. Some responses predicted by the scheme are compared with relevant published data.     

Vesicular stomatitis virus Indiana glycoprotein as a T-cell-dependent and -independent antigen.

The neutralizing immunoglobulin M (IgM) response to vesicular stomatitis virus (VSV) has been shown to be largely T-cell independent in several T-cell-deficient models of mice. By using different antigen froms of VSV, VSV antigen doses could be graded in vivo (infectious > > UV inactivated > formalin inactivated). The present study reveals a T-cell-dependent component of the neutralizing IgM response in nude mice given intravenous injections of low doses of noninfectious UV-inactivated VSV serotype Indiana (VSV-IND) only if the mice are transfused with VSV-IND-specific helper T cells. Instead, nude mice immunized with infectious VSV, which leads to greater antigen doses in vivo, were able to mount an IgM response in the absence of T cells. These results indicate that the IgM response to low doses of VSV-IND glycoprotein (G) is T-cell dependent. Nude mice immunized with infectious VSV also made a variable but low VSV-IND-neutralizing IgG response. A VSV-IND matrix (M)-specific helper T-cell line rendered this response more consistent, much higher, and longer lasting. Thus (i) VSV-G induces a mostly T-cell-independent but partially T-cell-dependent IgM (the latter can be visualized best at low doses of antigen) and (ii) the antibody response to VSV in nude mice proceeds through steps, i.e., IgM and IgG, that are dose dependent. The results suggest that the predominant role of helper T cells may be to expand and maintain the individual steps of differentiating B cells.     

Analysis of the Distribution of Bootstrap Tree Lengths Using the Maximum Parsimony Method

The bootstrap is an important tool for estimating the confidence interval of monophyletic groups within phylogenies. Although bootstrap analyses are used in most evolutionary studies, there is no clear consensus as how best to interpret bootstrap probability values. To study further the bootstrap method, nine small subunit ribosomal DNA (SSU rDNA) data sets were submitted to bootstrapped maximum parsimony (MP) analyses using unweighted and weighted sequence positions. Analyses of the lengths (i.e., parsimony steps) of the bootstrap trees show that the shape and mean of the bootstrap tree distribution may provide important insights into the evolutionary signal within the sequence data. With complex phylogenies containing nodes defined by short internal branches (multifurcations), the mean of the bootstrap tree distribution may differ by 2 standard deviations from the length of the best tree found from the original data set. Weighting sequence positions significantly increases the bootstrap values at internal nodes. There may, however, be strong bootstrap support for conflicting species groupings among different data sets. This phenomenon appears to result from a correlation between the topology of the tree used to create the weights and the topology of the bootstrap consensus tree inferred from the MP analysis of these weighted data. The analyses also show that characteristics of the bootstrap tree distribution (e.g., skewness) may be used to choose between alternative weighting schemes for phylogenetic analyses.