A new approach to graphical and numerical analysis of links between plant chemotaxonomy and secondary metabolism from HPLC data smoothed by a simplex mixture design

Summary. HPLC analysis of secondary metabolites represents an efficient tool for the studying of plant chemical diversity under different aspects: chemotaxonomy, metabolomics, adaptative responses to ecological factors, etc. Statistical analyses of HPLC databases, e.g. correlation analysis between HPLC peaks, can reliably provide information on the similarity/dissimilarity degrees between the chemical compounds. The similarities, corresponding to positive correlations, can be interpreted in terms of analogies between chemical structures, synchronic metabolisms or co-evolution of two compounds under certain environment conditions, etc. . In terms of metabolism, positive correlations can translate precursor-product relationships between compounds; negative correlations can be indicative of competitive processes between two compounds for a common precursor(s), enzyme(s) or substrate(s). Furthermore, the correlation analysis under a metabolic aspect can help to understand the biochemical origins of an observed polymorphism in a plant species. With the aim of showing this, we present a new approach based on a simplex mixture design, Scheffé matrix, which provides a correlation network making it possible to graphically visualise and to numerically model the metabolic trends between HPLC peaks. The principle of the approach consisted in mixing individual HPLC profiles representative of different phenotypes, then from a complete mixture set, a series of average profiles were calculated to provide a new database with a small variability. Several iterations of the mixture design provided a smoothed final database from which the relationships between the secondary metabolites were graphically and numerically analysed. These relationships were scale-dependent, namely either deterministic or systematic: the first consisted of a monotonic global trend covering the whole variation field of each metabolites’ pair; the second consisted of repetitive monotonic variations which gradually attenuated or intensified along a global trend. This new metabolomic approach was illustrated from 404 individual plants of Astragalus caprinus (Leguminoseae), belonging to four chemical phenotypes (chemotypes) on the basis of flavonoids analysed in their leaves. After smoothing, the relationships between flavonoids were numerically fitted using linear or polynomial models; therefore the co-response coefficients were easily interpreted in terms of metabolic affinities or competitions between flavonoids which would be responsible of the observed chemical polymorphism (the four chemotypes). The statistical validation of the approach was carried out by comparing Pearson correlations to Spearman correlations calculated from the smoothed and the crude HPLC database, respectively. Moreover, the signs of the smoothed relationships were finely supported by analogies and differences between the chemical structures of flavonoids, leading to fluent interpretation in relation to the pathway architecture.