Analysis of time-resolved postprandial metabolomics data can enhance our knowledge about the human metabolism by providing a better understanding of regulation of subgroups of metabolites (e.g., lipids) and variations in postprandial responses of subgroups of people, with the potential to ultimately advance precision medicine. However, characterizing postprandial metabolomics response and understanding group differences is a challenging task since it requires the analysis of large-scale metabolomics data from a large set of individuals containing measurements of a wide set of metabolites at multiple time points. Such data is in the form of a three-way array: subjects by metabolites by time points. The state-of-the-art analysis methods mainly focus on clustering temporal profiles relying on summaries of the data across subjects or univariate analysis techniques studying one metabolite at a time, and fail to associate subgroups of subjects and subsets of metabolites with the dynamic time profile simultaneously.

In this study, we use NMR (nuclear magnetic resonance) spectroscopy measurements of plasma samples (of over three hundred individuals from the COPSAC2000 cohort) collected at multiple time points during a challenge test.  We use a multi-way analysis technique called the CANDECOMP/PARAFAC (CP) model to extract interpretable patterns from the time-resolved data. We compare the analysis of postprandial data, fasting state-corrected data and only fasting state data, and demonstrate the differences between different analysis approaches.

Our results show that the CP model reveals biologically meaningful patterns capturing how certain metabolite groups and their temporal profiles relate to various meta variables, in particular, BMI (body mass index), confirming already known biological knowledge as well as revealing new biological insights.

Background: Analysis of dynamic metabolomics data holds the promise to improve our understanding of underlying mechanisms in metabolism. For example, it may detect changes in metabolism due to the onset of a disease. Dynamic or time-resolved metabolomics data can be arranged as a three-way array with entries organized according to a subjects mode, a metabolites mode and a time mode. While such time-evolving multiway data sets are increasingly collected, revealing the underlying mechanisms and their dynamics from such data remains challenging. For such data, one of the complexities is the presence of a superposition of several sources of variation: induced variation (due to experimental conditions or inborn errors), individual variation, and measurement error. Multiway data analysis (also known as tensor factorizations) has been successfully used in data mining to find the underlying patterns in multiway data. In this paper, we study the use of multiway data analysis to reveal the underlying patterns and dynamics in time-resolved metabolomics data.

Results: We focus on simulated data arising from different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, and a human cholesterol model. We generate data with induced variation as well as individual variation. Systematic experiments are performed to demonstrate the advantages and limitations of multiway data analysis in analyzing such dynamic metabolomics data and their capacity to disentangle the different sources of variations. We choose to use simulations since we want to understand the capability of multiway data analysis methods which is facilitated by knowing the ground truth.

Conclusion: Our numerical experiments demonstrate that despite the increasing complexity of the studied dynamic metabolic models, tensor factorization methods CANDECOMP/PARAFAC(CP) and Parallel Profiles with Linear Dependences (Paralind) can disentangle the sources of variations and thereby reveal the underlying mechanisms and their dynamics.