Generic framework for high-dimensional fixed-effects ANOVA

In functional genomics it is more rule than exception that experimental designs are used to generate the data. The samples of the resulting data sets are thus organized according to this design and for each sample many biochemical compounds are measured, e.g. typically thousands of gene-expressions or hundreds of metabolites. This results in high-dimensional data sets with an underlying experimental design. Several methods have recently become available for analyzing such data while utilizing the underlying design. We review these methods by putting them in a unifying and general framework to facilitate understanding the (dis-)similarities between the methods. The biological question dictates which method to use and the framework allows for building new methods to accommodate a range of such biological questions. The framework is built on well known fixed-effect ANOVA models and subsequent dimension reduction. We present the framework both in matrix algebra as well as in more insightful geometrical terms. We show the workings of the different special cases of our framework with a real-life metabolomics example from nutritional research and a gene-expression example from the field of virology.     

ANOVA-simultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data

MOTIVATION: Datasets resulting from metabolomics or metabolic profiling experiments are becoming increasingly complex. Such datasets may contain underlying factors, such as time (time-resolved or longitudinal measurements), doses or combinations thereof. Currently used biostatistics methods do not take the structure of such complex datasets into account. However, incorporating this structure into the data analysis is important for understanding the biological information in these datasets. RESULTS: We describe ASCA, a new method that can deal with complex multivariate datasets containing an underlying experimental design, such as metabolomics datasets. It is a direct generalization of analysis of variance (ANOVA) for univariate data to the multivariate case. The method allows for easy interpretation of the variation induced by the different factors of the design. The method is illustrated with a dataset from a metabolomics experiment with time and dose factors.     

An ultra-fast metabolite prediction algorithm

Small molecules are central to all biological processes and metabolomics becoming an increasingly important discovery tool. Robust, accurate and efficient experimental approaches are critical to supporting and validating predictions from post-genomic studies. To accurately predict metabolic changes and dynamics, experimental design requires multiple biological replicates and usually multiple treatments. Mass spectra from each run are processed and metabolite features are extracted. Because of machine resolution and variation in replicates, one metabolite may have different implementations (values) of retention time and mass in different spectra. A major impediment to effectively utilizing untargeted metabolomics data is ensuring accurate spectral alignment, enabling precise recognition of features (metabolites) across spectra. Existing alignment algorithms use either a global merge strategy or a local merge strategy. The former delivers an accurate alignment, but lacks efficiency. The latter is fast, but often inaccurate. Here we document a new algorithm employing a technique known as quicksort. The results on both simulated data and real data show that this algorithm provides a dramatic increase in alignment speed and also improves alignment accuracy.     

Individual differences in metabolomics: individualised responses and between-metabolite relationships

Many metabolomics studies aim to find ‘biomarkers’: sets of molecules that are consistently elevated or decreased upon experimental manipulation. Biological effects, however, often manifest themselves along a continuum of individual differences between the biological replicates in the experiment. Such differences are overlooked or even diminished by methods in standard use for metabolomics, although they may contain a wealth of information on the experiment. Properly understanding individual differences is crucial for generating knowledge in fields like personalised medicine, evolution and ecology. We propose to use simultaneous component analysis with individual differences constraints (SCA-IND), a data analysis method from psychology that focuses on these differences. This method constructs axes along the natural biochemical differences between biological replicates, comparable to principal components. The model may shed light on changes in the individual differences between experimental groups, but also on whether these differences correspond to, e.g., responders and non-responders or to distinct chemotypes. Moreover, SCA-IND reveals the individuals that respond most to a manipulation and are best suited for further experimentation. The method is illustrated by the analysis of individual differences in the metabolic response of cabbage plants to herbivory. The model reveals individual differences in the response to shoot herbivory, where two ‘response chemotypes’ may be identified. In the response to root herbivory the model shows that individual plants differ strongly in response dynamics. Thereby SCA-IND provides a hitherto unavailable view on the chemical diversity of the induced plant response, that greatly increases understanding of the system.     

STATegra EMS: an Experiment Management System for complex next-generation omics experiments

High-throughput sequencing assays are now routinely used to study different aspects of genome organization. As decreasing costs and widespread availability of sequencing enable more laboratories to use sequencing assays in their research projects, the number of samples and replicates in these experiments can quickly grow to several dozens of samples and thus require standardized annotation, storage and management of preprocessing steps. As a part of the STATegra project, we have developed an Experiment Management System (EMS) for high throughput omics data that supports different types of sequencing-based assays such as RNA-seq, ChIP-seq, Methyl-seq, etc, as well as proteomics and metabolomics data. The STATegra EMS provides metadata annotation of experimental design, samples and processing pipelines, as well as storage of different types of data files, from raw data to ready-to-use measurements. The system has been developed to provide research laboratories with a freely-available, integrated system that offers a simple and effective way for experiment annotation and tracking of analysis procedures.     

Simplivariate models: ideas and first examples

One of the new expanding areas in functional genomics is metabolomics: measuring the metabolome of an organism. Data being generated in metabolomics studies are very diverse in nature depending on the design underlying the experiment. Traditionally, variation in measurements is conceptually broken down in systematic variation and noise where the latter contains, e.g. technical variation. There is increasing evidence that this distinction does not hold (or is too simple) for metabolomics data. A more useful distinction is in terms of informative and non-informative variation where informative relates to the problem being studied. In most common methods for analyzing metabolomics (or any other high-dimensional x-omics) data this distinction is ignored thereby severely hampering the results of the analysis. This leads to poorly interpretable models and may even obscure the relevant biological information. We developed a framework from first data analysis principles by explicitly formulating the problem of analyzing metabolomics data in terms of informative and non-informative parts. This framework allows for flexible interactions with the biologists involved in formulating prior knowledge of underlying structures. The basic idea is that the informative parts of the complex metabolomics data are approximated by simple components with a biological meaning, e.g. in terms of metabolic pathways or their regulation. Hence, we termed the framework 'simplivariate models' which constitutes a new way of looking at metabolomics data. The framework is given in its full generality and exemplified with two methods, IDR analysis and plaid modeling, that fit into the framework. Using this strategy of 'divide and conquer', we show that meaningful simplivariate models can be obtained using a real-life microbial metabolomics data set. For instance, one of the simple components contained all the measured intermediates of the Krebs cycle of E. coli. Moreover, these simplivariate models were able to uncover regulatory mechanisms present in the phenylalanine biosynthesis route of E. coli.     

Design and analysis of experiments with high throughput biological assay data

The design and analysis of experiments using gene expression microarrays is a topic of considerable current research, and work is beginning to appear on the analysis of proteomics and metabolomics data by mass spectrometry and NMR spectroscopy. The literature in this area is evolving rapidly, and commercial software for analysis of array or proteomics data is rarely up to date, and is essentially nonexistent for metabolomics data. In this paper, I review some of the issues that should concern any biologists planning to use such high-throughput biological assay data in an experimental investigation. Technical details are kept to a minimum, and may be found in the referenced literature, as well as in the many excellent papers which space limitations prevent my describing. There are usually a number of viable options for design and analysis of such experiments, but unfortunately, there are even more non-viable ones that have been used even in the published literature. This is an area in which up-to-date knowledge of the literature is indispensable for efficient and effective design and analysis of these experiments. In general, we concentrate on relatively simple analyses, often focusing on identifying differentially expressed genes and the comparable issues in mass spectrometry and NMR spectroscopy (consistent differences in peak heights or areas for example). Complex multivariate and pattern recognition methods also need much attention, but the issues we describe in this paper must be dealt with first. The literature on analysis of proteomics and metabolomics data is as yet sparse, so the main focus of this paper will be on methods devised for analysis of gene expression data that generalize to proteomics and metabolomics, with some specific comments near the end on analysis of metabolomics data by mass spectrometry and NMR spectroscopy.     

A Global Parallel Model Based Design of Experiments Method to Minimize Model Output Uncertainty

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.     

Current progress in computational metabolomics

Being a relatively new addition to the 'omics' field, metabolomics is still evolving its own computational infrastructure and assessing its own computational needs. Due to its strong emphasis on chemical information and because of the importance of linking that chemical data to biological consequences, metabolomics must combine elements of traditional bioinformatics with traditional cheminformatics. This is a significant challenge as these two fields have evolved quite separately and require very different computational tools and skill sets. This review is intended to familiarize readers with the field of metabolomics and to outline the needs, the challenges and the recent progress being made in four areas of computational metabolomics: (i) metabolomics databases; (ii) metabolomics LIMS; (iii) spectral analysis tools for metabolomics and (iv) metabolic modeling.     

Precursor mass prediction by clustering ionization products in LC-MS-based metabolomics

Liquid chromatography-mass spectrometry (LC-MS) is becoming the dominant technology in metabolomics, involving the comprehensive analysis of small molecules in biological systems. However, its use is still limited mainly by challenges in global high-throughput identification of metabolites: LC-MS data is highly complex, particularly due to the formation of multiple ionization products from individual metabolites. To address the limitation in metabolite identification, we developed a principled approach, designed to exploit the multi-dimensional information hidden in the data. The workflow first clusters candidate ionization products of the same metabolite together which typically have similar retention time, then searches for mass relationships among them in order to determine their ion types and metabolite identity. The robustness of our approach was demonstrated by its application to the LC-MS profiles of cell culture supernatant, which accurately predicted most of the known media components in the samples. Compared to conventional methods, our approach was able to generate significantly fewer candidate metabolites without missing out valid ones, thus reducing false-positive matches. Additionally, improved confidence in identification is achieved since each prediction comes with a probable combination of known ion types. Hence, our integrative workflow provides precursor mass predictions with high confidence by identifying various ionization products which account for a large proportion of detected peaks, thus minimizing false positives.     

Identifying functional gene sets from hierarchically clustered expression data: map of abiotic stress regulated genes in Arabidopsis thaliana

We present MultiGO, a web-enabled tool for the identification of biologically relevant gene sets from hierarchically clustered gene expression trees (http://ekhidna.biocenter.helsinki.fi/poxo/multigo). High-throughput gene expression measuring techniques, such as microarrays, are nowadays often used to monitor the expression of thousands of genes. Since these experiments can produce overwhelming amounts of data, computational methods that assist the data analysis and interpretation are essential. MultiGO is a tool that automatically extracts the biological information for multiple clusters and determines their biological relevance, and hence facilitates the interpretation of the data. Since the entire expression tree is analysed, MultiGO is guaranteed to report all clusters that share a common enriched biological function, as defined by Gene Ontology annotations. The tool also identifies a plausible cluster set, which represents the key biological functions affected by the experiment. The performance is demonstrated by analysing drought-, cold- and abscisic acid-related expression data sets from Arabidopsis thaliana. The analysis not only identified known biological functions, but also brought into focus the less established connections to defense-related gene clusters. Thus, in comparison to analyses of manually selected gene lists, the systematic analysis of every cluster can reveal unexpected biological phenomena and produce much more comprehensive biological insights to the experiment of interest.     

Proposed minimum reporting standards for chemical analysis

There is a general consensus that supports the need for standardized reporting of metadata or information describing large-scale metabolomics and other functional genomics data sets. Reporting of standard metadata provides a biological and empirical context for the data, facilitates experimental replication, and enables the re-interrogation and comparison of data by others. Accordingly, the Metabolomics Standards Initiative is building a general consensus concerning the minimum reporting standards for metabolomics experiments of which the Chemical Analysis Working Group (CAWG) is a member of this community effort. This article proposes the minimum reporting standards related to the chemical analysis aspects of metabolomics experiments including: sample preparation, experimental analysis, quality control, metabolite identification, and data pre-processing. These minimum standards currently focus mostly upon mass spectrometry and nuclear magnetic resonance spectroscopy due to the popularity of these techniques in metabolomics. However, additional input concerning other techniques is welcomed and can be provided via the CAWG on-line discussion forum at or . Further, community input related to this document can also be provided via this electronic forum. The contents of this paper do not necessarily reflect any position of the Government or the opinion of the Food and Drug Administration Sponsor: Metabolomics Society http://www.metabolomicssociety.org/ Reference: http://msi-workgroups.sourceforge.net/bio-metadata/reporting/pbc/ http://msi-workgroups.sourceforge.net/chemical-analysis/ Version: Revision: 5.1 Date: 09 January, 2007     

A fast reconstruction algorithm for electron microscope tomography

We have implemented a Fast Fourier Summation algorithm for tomographic reconstruction of three-dimensional biological data sets obtained via transmission electron microscopy. We designed the fast algorithm to reproduce results obtained by the direct summation algorithm (also known as filtered or R-weighted backprojection). For two-dimensional images, the new algorithm scales as O(N(theta)M log M)+O(MN log N) operations, where N(theta) is the number of projection angles and M x N is the size of the reconstructed image. Three-dimensional reconstructions are constructed from sequences of two-dimensional reconstructions. We demonstrate the algorithm on real data sets. For typical sizes of data sets, the new algorithm is 1.5-2.5 times faster than using direct summation in the space domain. The speed advantage is even greater as the size of the data sets grows. The new algorithm allows us to use higher order spline interpolation of the data without additional computational cost. The algorithm has been incorporated into a commonly used package for tomographic reconstruction.     

New strategy for the representation and the integration of biomolecular knowledge at a cellular scale

The combination of sequencing and post-sequencing experimental approaches produces huge collections of data that are highly heterogeneous both in structure and in semantics. We propose a new strategy for the integration of such data. This strategy uses structured sets of sequences as a unified representation of biological information and defines a probabilistic measure of similarity between the sets. Sets can be composed of sequences that are known to have a biological relationship (e.g. proteins involved in a complex or a pathway) or that share similar values for a particular attribute (e.g. expression profile). We have developed a software, BlastSets, which implements this strategy. It exploits a database where the sets derived from diverse biological information can be deposited using a standard XML format. For a given query set, BlastSets returns target sets found in the database whose similarity to the query is statistically significant. The tool allowed us to automatically identify verified relationships between correlated expression profiles and biological pathways using publicly available data for Saccharomyces cerevisiae. It was also used to retrieve the members of a complex (ribosome) based on the mining of expression profiles. These first results validate the relevance of the strategy and demonstrate the promising potential of BlastSets.     

Physiological time-series analysis using approximate entropy and sample entropy

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.     

Toward supportive data collection tools for plant metabolomics

Over recent years, a number of initiatives have proposed standard reporting guidelines for functional genomics experiments. Associated with these are data models that may be used as the basis of the design of software tools that store and transmit experiment data in standard formats. Central to the success of such data handling tools is their usability. Successful data handling tools are expected to yield benefits in time saving and in quality assurance. Here, we describe the collection of datasets that conform to the recently proposed data model for plant metabolomics known as ArMet (architecture for metabolomics) and illustrate a number of approaches to robust data collection that have been developed in collaboration between software engineers and biologists. These examples also serve to validate ArMet from the data collection perspective by demonstrating that a range of software tools, supporting data recording and data upload to central databases, can be built using the data model as the basis of their design.     

Untargeted large-scale plant metabolomics using liquid chromatography coupled to mass spectrometry

Untargeted metabolomics aims to gather information on as many metabolites as possible in biological systems by taking into account all information present in the data sets. Here we describe a detailed protocol for large-scale untargeted metabolomics of plant tissues, based on reversed phase liquid chromatography coupled to high-resolution mass spectrometry (LC-QTOF MS) of aqueous methanol extracts. Dedicated software, MetAlign, is used for automated baseline correction and alignment of all extracted mass peaks across all samples, producing detailed information on the relative abundance of thousands of mass signals representing hundreds of metabolites. Subsequent statistics and bioinformatics tools can be used to provide a detailed view on the differences and similarities between (groups of) samples or to link metabolomics data to other systems biology information, genetic markers and/or specific quality parameters. The complete procedure from metabolite extraction to assembly of a data matrix with aligned mass signal intensities takes about 6 days for 50 samples.     

SWISS MADE: Standardized WithIn Class Sum of Squares to Evaluate Methodologies and Dataset Elements

Contemporary high dimensional biological assays, such as mRNA expression microarrays, regularly involve multiple data processing steps, such as experimental processing, computational processing, sample selection, or feature selection (i.e. gene selection), prior to deriving any biological conclusions. These steps can dramatically change the interpretation of an experiment. Evaluation of processing steps has received limited attention in the literature. It is not straightforward to evaluate different processing methods and investigators are often unsure of the best method. We present a simple statistical tool, Standardized WithIn class Sum of Squares (SWISS), that allows investigators to compare alternate data processing methods, such as different experimental methods, normalizations, or technologies, on a dataset in terms of how well they cluster a priori biological classes. SWISS uses Euclidean distance to determine which method does a better job of clustering the data elements based on a priori classifications. We apply SWISS to three different gene expression applications. The first application uses four different datasets to compare different experimental methods, normalizations, and gene sets. The second application, using data from the MicroArray Quality Control (MAQC) project, compares different microarray platforms. The third application compares different technologies: a single Agilent two-color microarray versus one lane of RNA-Seq. These applications give an indication of the variety of problems that SWISS can be helpful in solving. The SWISS analysis of one-color versus two-color microarrays provides investigators who use two-color arrays the opportunity to review their results in light of a single-channel analysis, with all of the associated benefits offered by this design. Analysis of the MACQ data shows differential intersite reproducibility by array platform. SWISS also shows that one lane of RNA-Seq clusters data by biological phenotypes as well as a single Agilent two-color microarray.