Sabina Bijlsma

Assessing the performance of statistical validation tools for megavariate metabolomics data.

Statistical model validation tools such as cross-validation, jack-knifing model parameters and permutation tests are meant to obtain an objective assessment of the performance and stability of a statistical model. However, little is known about the performance of these tools for megavariate data sets, having, for instance, a number of variables larger than 10 times the number of subjects. The performance is assessed for megavariate metabolomics data, but the conclusions also carry over to proteomics, transcriptomics and many other research areas. Partial least squares discriminant analyses models were built for several LC-MS lipidomic training data sets of various numbers of lean and obese subjects. The training data sets were compared on their modelling performance and their predictability using a 10-fold cross-validation, a permutation test, and test data sets. A wide range of cross-validation error rates was found (from 7.5% to 16.3% for the largest trainings set and from 0% to 60% for the smallest training set) and the error rate increased when the number of subjects decreased. The test error rates varied from 5% to 50%. The smaller the number of subjects compared to the number of variables, the less the outcome of validation tools such as cross-validation, jack-knifing model parameters and permutation tests can be trusted. The result depends crucially on the specific sample of subjects that is used for modelling. The validation tools cannot be used as warning mechanism for problems due to sample size or to representativity of the sampling.

Matrix correlations for high-dimensional data

MOTIVATION Modern functional genomics generates high-dimensional datasets. It is often convenient to have a single simple number characterizing the relationship between pairs of such high-dimensional datasets in a comprehensive way. Matrix correlations are such numbers and are appealing since they can be interpreted in the same way as Pearsons correlations familiar to biologists. The high-dimensionality of functional genomics data is, however, problematic for existing matrix correlations. The motivation of this article is 2-fold: (i) we introduce the idea of matrix correlations to the bioinformatics community and (ii) we give an improvement of the most promising matrix correlation coefficient (the RV-coefficient) circumventing the problems of high-dimensional data. RESULTS The modified RV-coefficient can be used in high-dimensional data analysis studies as an easy measure of common information of two datasets. This is shown by theoretical arguments, simulations and applications to two real-life examples from functional genomics, i.e. a transcriptomics and metabolomics example. AVAILABILITY The Matlab m-files of the methods presented can be downloaded from http://www.bdagroup.nl.

Dynamic metabolomic data analysis : A tutorial review

In metabolomics, time-resolved, dynamic or temporal data is more and more collected. The number of methods to analyze such data, however, is very limited and in most cases the dynamic nature of the data is not even taken into account. This paper reviews current methods in use for analyzing dynamic metabolomic data. Moreover, some methods from other fields of science that may be of use to analyze such dynamic metabolomics data are described in some detail. The methods are put in a general framework after providing a formal definition on what constitutes a ‘dynamic’ method. Some of the methods are illustrated with real-life metabolomics examples.

Estimating rate constants and pure UV-vis spectra of a two-step reaction using trilinear models

This paper describes the estimation of reaction rate constants and pure species UV‐vis spectra of the consecutive reaction of 3‐chlorophenylhydrazonopropane dinitrile with 2‐mercaptoethanol. The reaction rate constants were estimated from the UV‐vis measurements of the reacting system using the generalized rank annihilation method (GRAM) and the Levenberg–Marquardt/PARAFAC (LM‐PAR) algorithm. Both algorithms can be applied in cases where the contribution of different species in the mixture spectra is of exponentially decaying character. From a single two‐way array, two two‐way datasets are formed by means of splitting such that there is a constant time lag between the two two‐way datasets. By stacking these two two‐way datasets, the reaction rate constants can be estimated very easily from the third dimension. GRAM, which is fast and non‐iterative, decomposes the trilinear structure using a generalized eigenvalue problem (GEP). The iterative algorithm LM‐PAR consists of a combination of the Levenberg–Marquardt algorithm and alternating least squares steps of the PARAFAC model using GRAM results as a set of initial starting values. Pure spectra of the absorbing species were estimated and compared with their measured pure spectra. LM‐PAR performed the best, giving the lowest relative fit error. However, the relative fit error obtained with GRAM was acceptable. Since a lot of measurements are based on exponentially decaying functions, GRAM and LM‐PAR can have many applications in chemistry. Copyright

Application of curve resolution based methods to kinetic data

Abstract Two methods for estimating reaction rate constants from spectral data are compared. The first method is a weighted curve resolution method. The second method is an improved curve resolution method. If some of the pure spectra of species in a reacting system are known, this can be incorporated into the second algorithm. Hence, spectral information that is known a priori is used. Both methods are applied to UV–VIS recorded spectra of the two-step consecutive reaction of 3-chlorophenylhydrazonopropane dinitrile, which is an uncoupler of oxidative phosphorylation in cells, with 2-mercaptoethanol in order to estimate the reaction rate constants involved. In order to perform quality assessment, upper and lower error bounds of estimates of reaction rate constants were estimated using a jackknife procedure. Application of the second method led to lower standard deviations of the estimated reaction rate constants, compared to the first method, due to extra spectral information that is used in this second method.

Estimating reaction rate constants from a two-step reaction: a comparison between two-way and three-way methods

In this paper, two different spectral datasets are used in order to estimate reaction rate constants using different algorithms. Dataset 1 consists of short‐wavelength near‐infrared (SW‐NIR) spectra taken in time of the two‐step epoxidation of 2,5‐di‐tert‐butyl‐1,4‐benzoquinone using tert‐butyl hydroperoxide and Triton B catalyst. This dataset showed moderate reproducibility. Dataset 2 consists of UV‐VIS recorded spectra of the consecutive reaction of 3‐chlorophenylhydrazonopropane dinitrile with 2‐mercaptoethanol. This dataset showed good reproducibility. Two‐way and three‐way methods were used in order to estimate the reaction rate constants for both datasets. For the SW‐NIR dataset the lowest standard deviations for the reaction rate constants were obtained with a two‐way method. The lowest standard deviations for the reaction rate constant estimates for the UV‐VIS dataset were obtained with a two‐way method which uses spectral information that is known in advance. In this case the pure spectrum of two reacting absorbing species is known in advance and this information was used by the two‐way method. For one two‐way method and a few three‐way methods which do not use spectral information that is known in advance, pure spectra of the reacting absorbing species of the UV‐VIS dataset were estimated which showed excellent agreement with the recorded pure spectra. The pure spectra of the reacting absorbing species for the SW‐NIR dataset were not estimated, because it was not possible to record the real pure spectra of these species. For both spectral datasets, quality assessment has been performed using a jackknife method. Copyright

Rapid estimation of rate constants using on-line SW-NIR and trilinear models

Abstract In this paper, two algorithms are presented to estimate reaction rate constants from on-line short-wavelength near-infrared (SW-NIR) measurements. These can be applied in cases where the contribution of the different species in the mixture spectra is of exponentially decaying character. From a single two-dimensional dataset two two-way datasets are formed by splitting the original dataset such that there is a constant time lag between the two two-way datasets. Next, a trilinear structure is formed by stacking these two two-way datasets into a three-way array. In the first algorithm, based on the generalized rank annihilation method (GRAM), the trilinear structure is decomposed by solving a generalized eigenvalue problem (GEP). Because GRAM is sensitive to noise it leads to rough estimations of reaction rate constants. The second algorithm (LM–PAR) is an iterative algorithm, which consists of a combination of the Levenberg–Marquardt algorithm and alternating least squares steps of the parallel factor analysis (PARAFAC) model using the GRAM results as initial values. Simulations and an application to a real dataset showed that both algorithms can be applied to estimate reaction rate constants in case of extreme spectral overlap of different species involved in the reacting system.

Correlation network analysis reveals relationships between diet-induced changes in human gut microbiota and metabolic health

Background:Recent evidence suggests that the gut microbiota plays an important role in human metabolism and energy homeostasis and is therefore a relevant factor in the assessment of metabolic health and flexibility. Understanding of these host–microbiome interactions aids the design of nutritional strategies that act via modulation of the microbiota. Nevertheless, relating gut microbiota composition to host health states remains challenging because of the sheer complexity of these ecosystems and the large degrees of interindividual variation in human microbiota composition.Methods:We assessed fecal microbiota composition and host response patterns of metabolic and inflammatory markers in 10 apparently healthy men subjected to a high-fat high-caloric diet (HFHC, 1300 kcal/day extra) for 4 weeks. DNA was isolated from stool and barcoded 16S rRNA gene amplicons were sequenced. Metabolic health parameters, including anthropomorphic and blood parameters, where determined at t=0 and t=4 weeks.Results:A correlation network approach revealed diet-induced changes in Bacteroides levels related to changes in carbohydrate oxidation rates, whereas the change in Firmicutes correlates with changes in fat oxidation. These results were confirmed by multivariate models. We identified correlations between microbial diversity indices and several inflammation-related host parameters that suggest a relation between diet-induced changes in gut microbiota diversity and inflammatory processes.Conclusions:This approach allowed us to identify significant correlations between abundances of microbial taxa and diet-induced shifts in several metabolic health parameters. Constructed correlation networks provide an overview of these relations, revealing groups of correlations that are of particular interest for explaining host health aspects through changes in the gut microbiota.

Estimating reaction rate constants: comparison between traditional curve fitting and curve resolution

Abstract A traditional curve fitting (TCF) algorithm is compared with a classical curve resolution (CCR) approach for estimating reaction rate constants from spectral data obtained in time of a chemical reaction. In the TCF algorithm, reaction rate constants are estimated from the absorbance versus time data obtained from selective wavelengths. In this case, wavelengths are selected at which mainly one species is absorbing in time. In CCR, pure spectra of reacting absorbing species and the reaction rate constants are estimated simultaneously. Both TCF and CCR have been applied to experimental data. The reaction rate constants and the individual pure spectra of the reacting absorbing species were estimated simultaneously from the UV–VIS spectra taken in time of the two-step biochemical consecutive reaction of 3-chlorophenylhydrazonopropane dinitrile with 2-mercaptoethanol. This reaction was performed under second order and pseudo-first order conditions. For both conditions, the signal-to-noise ratio was approximately the same. However, if second order conditions are chosen, the first reaction step is very slow, which results in small absorbance differences in time. For the pseudo-first order dataset, the best precision of the reaction rate constant estimates has been obtained with TCF. For the second order dataset, CCR performed the best with respect to the precision of the reaction rate constant estimates.

Applications and new developments of the direct exponential curve resolution algorithm (DECRA). Examples of spectra and magnetic resonance images

Recently, a new multivariate analysis tool was developed to resolve mixture data sets, where the contributions (‘concentrations’) have an exponential profile. The new approach is called DECRA (direct exponential curve resolution algorithm). DECRA is based on the generalized rank annihilation method (GRAM). Examples will be given of resolving nuclear magnetic resonance spectra resulting from a diffusion experiment, spectra in the ultraviolet/visible region of a reaction and magnetic resonance images of the human brain. Copyright