Note: Our subscriber list is managed using Mailman, the GNU Mailing List Manager. To subscribe or unsubscribe, please visit https://mail.cs.ualberta.ca/mailman/listinfo/MetaboNews

Current and back issues of this newsletter can be viewed from the newsletter archive (http://www.metabonews.ca/archive.html).

Theory of Chemometrics

Feature article contributed by Jeroen Jansen, Lionel Blanchet, and Lutgarde Buydens, Laboratory of Analytical Chemistry, Radboud University Nijmegen, Netherlands

The Laboratory of Analytical Chemistry (LAC) at the Radboud University Nijmegen, headed by Prof. Lutgarde Buydens, is one of the oldest chemometrics groups in the world. Chemometrics is the research field interested in the analysis of complex chemical data. Omics data are therefore logically of particular chemometric interest and a key element in our research portfolio. Conversely, scientific and technological developments in metabolomics require ever-more advanced statistical methods that answer the very complex biological research questions. Such synergy between both fields may induce a next generation of thought-provoking challenges that stretch current methods to the limits and thereby spark the development of new approaches.

The field of chemometrics until recently relied heavily on two methods: Principal Component Analysis to describe the chemistry of complex analytical measurements, and Partial Least Squares Regression to predict specific properties from these measurements. Any literature search for 'analysis of metabolomics data' shows how the love for these methods flourishes on. However, LAC aims to ascend on these specific methods, to reach a strong theoretical—currently lacking—basis for chemometrics. For this we started a public-private partnership, through the Netherlands 'Top Institute for COmprehensive Analytical Science and Technology' (TI-COAST). In this project, called 'Analysis of Large data sets By Enhanced Robust Techniques' (ALBERT), several Dutch (bio)chemical companies collaborate with chemometricians and statisticians from the Universities of Nijmegen and Groningen to create a pipeline. In this line the information quality within any metabolomics (or other chemical) dataset can be quantitatively evaluated, based on solid theoretical grounds (Figure 1). This then forms the basis for the pre-processing to remove identified artefacts and thereby highlight the biologically relevant data. This can then be analysed by PCA or PLS, but potentially by more advanced methods that are tailor-made to answer the biological questions at hand. Also, here the theoretical basis is maintained, because each step in the pipeline is supported by two essential, but often overlooked aspects: validation and visualisation. This pipeline will assure peer metabolomics researchers they can both trust and understand results from the high-quality chemometric models at the basis of a joint publication.



Figure 1. Schematic depiction of the steps in the ALBERT pipeline.

Our laboratory has applied this pipeline and their interconnection in several studies. For example, we Intuitively expect that the concentration of a compound within a particular metabolic pathway changes proportionally to other metabolites in the same pathway. However, in reality, these concentration changes may follow much more complex behaviour: metabolic systems—biological problems in general—are inherently non-linear. The chemometrician's best friends (PCA and PLS) are unable to detect these relations in such cases and more advanced methods are required. Kernel transformations are particularly promising for this, for two reasons. Kernels can linearize almost any type of relation, which are then open for exploration by PCA or PLS. Although kernel-based methods are generally recognized as powerful, their use was severely hampered by the impossibility of visualizing the biological information (metabolites) that underlie the model, e.g., in a 'biplot'. Our group recently solved this problem, by implementing 'pseudo-samples' [1] that reconstruct the role of each metabolite in the model, even for nonlinear biological differences. This aspect can even be further extended to the linear and non-linear complementary information that GC-MS and NMR generate for complex diseases like Multiple Sclerosis (Figure 2) [2].



Figure 2. Loading plot of pseudo-samples trajectories for selected NMR and GC-MS variables, adapted from reference [2].

Another forte of chemometrics that is very useful to metabolomics, is the strong analytical basis that underlies it. This is not only reflected in analytical chemistry but also in the thought processes that lie beneath. Chemometrics therefore forms an abstract plane, on which concepts from remote scientific fields like psychology and marketing may cross-fertilize with those in systems biology. A prominent field in these social science disciplines is the study of 'individual differences' that can be very useful to create an 'individualized metabolomic fingerprint'. In collaboration with the Biosystems Data Analysis group at the University of Amsterdam, we have modeled the ecological response of a group of plants to herbivory, specifically the heterogeneity in this response between otherwise completely comparable plants and the emergence of sub-groups—chemotypes—in this response. For this we adapted the Simultaneous Component Analysis with Individual Differences constraints (SCA-IND) method [3], originally developed for assessing differences between sensory panel members for product tests. This method provided a view on this heterogeneity that was both ecologically and biochemically understandable (Figure 3). We believe this method can be applied broadly in metabolomic studies. Specifically its application in Personalized Health and Medicine, which focuses on the heterogeneity among patients, seems extremely promising. This is another very clear example of how chemometrics may facilitate cross-fertilization between research fields, even within biology.



Figure 3. SCA-IND model on the ecological plant response. A. Raw data (circles: control plants, triangles: attacked plants; grey: 1 day after attack, white: 7 days after, black: 14 days after. A negative relation between NEO and GBC clearly emerges during the experiment i. plant with high level of Neoglucobrassicin (NEO), and ii. High-Glucobrassicin Plant); B. This emergence becomes clear in the 'Group-level' scores of attacked plants; C. Loadings show this heterogeneity mainly associates with Glucobrassicin and Neoglucobrassicin; D. The Individual-level scores of the model show distinct Glucobrassicin and Neoglucobrassicin-responding plant groups, 14 days after attack—the emergence of 'Response Chemotypes'; plants i. and ii. from panel A are indicated.



References

1. Postma, G.J., P.W.T. Krooshof, and L.M.C. Buydens, Opening the kernel of kernel partial least squares and support vector machines. Analytica Chimica Acta, 2011. 705(1–2): p. 123-134. [PMID: 21962355]
   
2. Smolinska, A., et al., Interpretation and Visualization of Non-Linear Data Fusion in Kernel Space: Study on Metabolomic Characterization of Progression of Multiple Sclerosis. PLoS ONE, 2012. 7(6): p. e38163. [PMID: 22715376]
   
3. Jansen, J., et al., Individual differences in metabolomics: individualised responses and between-metabolite relationships. Metabolomics, 2012. 8(0): p. 94-104. [PMID: 22593723]