Bilinear and trilinear modelling of three-way data obtained in two factor designed metabolomics studies

摘要

Metabolomic studies of biological samples using experimentally designed experiments at different levels produce large multivariate datasets which can be arranged in three-way data structures and modelled using bilinear and trilinear factor decomposition methods. The goal of these studies is the discovery of the hidden sources of data variability to facilitate their biochemical interpretation. In this paper, the relationship between the effects of the experimental design factors, the structure of the generated three-way datasets and their more appropriate modelling (bilinear or trilinear) are investigated. As example of study, the effects of the dose of a chemical drug on the changes over time in the concentration of lipids in multiple samples of a biological organism are investigated in detail. Different scenarios are considered depending on the type of effects and interactions between the experimental factors. The optimal data modelling results are obtained in case of having reproducible multiplicative effects between the experimental design factors, because in this case the data decomposition can be performed using a trilinear model and the correct lipid profiles are recovered. In the other data scenarios, even in the presence of only additive effects and no interaction between design factors, the correct recovery of the different lipid profiles describing the behavior of the system is not guaranteed and the subsequent rotation ambiguities associated to the bilinear model decompositions can still be present.