Background. Olive oils (OOs) show high chemical variability due to several factors of genetic, environmental and anthropic types. Genetic and environmental factors are responsible for natural compositions and polymorphic diversification resulting in different varietal patterns and phenotypes. Anthropic factors, however, are at the origin of different blends’ preparation leading to normative, labelled or adulterated commercial products. Control of complex OO samples requires their (i) characterization by specific markers; (ii) authentication by fingerprint patterns; and (iii) monitoring by traceability analysis. Methods. These quality control and management aims require the use of several multivariate statistical tools: specificity highlighting requires ordination methods; authentication checking calls for classification and pattern recognition methods; traceability analysis implies the use of network-based approaches able to separate or extract mixed information and memorized signals from complex matrices. Results. This chapter presents a review of different chemometrics methods applied for the control of OO variability from metabolic and physical-chemical measured characteristics. The different chemometrics methods are illustrated by different study cases on monovarietal and blended OO originated from different countries. Conclusion. Chemometrics tools offer multiple ways for quantitative evaluations and qualitative control of complex chemical variability of OO in relation to several intrinsic and extrinsic factors.

Metabolisms represent highly organized systems characterized by strong regulations obeying to mass conservation law. This makes a whole chemical resource to be competitively shared between several biosynthesis components (ways) at both intra-and inter-molecular scales. Statistically, the whole shared-resource principle can be considered under a constant sum-unit constraint which represents the basis of simplex mixture rule. In this work, a new simplex-based chemometric approach was developed to extract scaffold information on different biosynthesis regulation factors responsible for the chemical structural diversity at atomic and molecular scales within a large metabolic system. This approach consisted in combining different (p) molecular clusters into a complete set of N mixtures containing a same constant (n) number of molecules which were randomly sampled by gradually varying the relative weights (n_j/n) of combined clusters j. The complete set of N combinations was initially given by the Scheffé’s mixture matrix. At the output of Scheffé’s design, each molecular mixture was represented by a theoretical average (barycentric) molecule which was trained by the characteristics of the different weighted clusters. The mixture design was iterated several (K) times by applying bootstrap technique leading to extensively explore chemical variability between and within clusters. Finally, the K response matrices issued from the K applications of Scheffé’s mixture design were averaged to obtain a smoothed matrix containing scaffold information on different regulation factors responsible for molecular diversification at inter- and intra- (atomic) molecular scales. This matrix was used as a backbone for graphical analysis of different positive and negative trends between atomic characteristics (chemical substitutions) at both mentioned scales. This new simplex approach was illustrated by cycloartane-based saponins of Astragalus genus by considering three desmosylation clusters (mono-, bi- and tridesmoside saponins) characterized by relative glycosylation levels of different aglycones’ carbons.

This communication presents a two decades-updating on different applications of a new simulation method using simplex rule for smoothing regulation processes of several cooperative or competing components of complex mixture systems in biology and chemistry. Application fields covers different matter scales varying from atomes to ecosystems via molecular and biological organism levels. Simulation results issued from simplex approach helped for better understanding (i) inter-atomic regulation ways of molecular synthesis, (ii) organization metabolic pathways from chromatographic data, (iii) feeding behaviors of multi-prey foraging animal species. Application perspectives of the simplex machine-learning method are widely opened for highlighting multidirectional and multiscale regulation processes of polymorphism and diversification of multi-cluster complex systems from big data satisfying mass conservation principle.

A mass conservation law-based chemometric approach was developed to extract smoothed processes governing inter- and intra-molecular variability of structural diversity in metabolic pools. The approach consisted of a machine-learning method using simplex rule to calculate a complete set of smoothed barycentric molecules from iterated linear combinations between molecular classes (glycosylation classes). An application to four glycosylation levels (GLs) of Caryophyllaceae saponins highlighted aglycone-dependent variations of glycosylations, especially for gypsogenic acid (GA) which showed high 28-glucosylation levels. Quillaic acid (QA) and gypsogenin (Gyp) showed closer variation ranges of GLs, but differed by relationships between glycosylated carbons toward different sugars. Relative GLs of carbons C3 and C28 showed associative (positive), competitive (negative) or independent (unsensitive) trends conditioned by the aglycone type (GA, Gyp) and molecular (total) GLs (the four classes): 28-glucosylation and 28-xylosylation showed negative global trends in Gyp vs GLs-depending trends in QA. Also, relative levels of 3-galactosylation and 3-xylosylation varied by unsensitive ways in Gyp vs positive trends in QA. These preliminary results revealed higher metabolic tensions (competitions) between considered glycosylations in Gyp vs more associative processes in QA. In conclusion, glycosylations of GA and QA were relatively distant whereas Gyp occupied intermediate position.