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 satisfying the mass conservation principle. This makes a whole chemical resource to be competitively shared between several ways at both intra-and inter-molecular scales. Whole resource sharing can be statistically associated with a constant sum-unit constraint which represents the basis of simplex mixture rule. In this work, a new simplex-based simulation approach was developed to learn scaffold information on metabolic processes controlling molecular diversity from a wide set of observed chemical structures. Starting from a dataset of chemical structures classified into p clusters, a machine learning process was applied by linearly combining the p clusters j and randomly sampling a constant number (n) of molecules according to different clusters’ weights (wj/w) given by Scheffé’s mixture matrix. At the output of mixture design, molecular linear combinations lead to calculate barycentric molecules integrating the characteristics of the different weighted clusters. The N mixtures-design was iterated by bootstrap technique leading to extensive exploration of chemical variability between and within clusters. Finally, the K response matrices issued from K iterated mixture designs were averaged to calculate a smoothed matrix containing scaffold information on regulation processes responsible for molecular diversification at inter- and intra-molecular (atomic) scales. This matrix was used as a backbone for graphical analysis of 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 combining three desmosylation clusters characterized by relative glycosylation levels of different aglycones’ carbons.

Astragalus genus represents the widest terrestrial plant taxon with more than 2500 species of herbs or shrubs. Under phytochemical aspect, this genus was characterized by a high structural diversity of saponins essentially based on cycloartane. The high number and diversity of saponins offers a strong basis for analysis of structural properties and metabolic trends governing molecular synthesis. Such trends can be highlighted by significant correlations between chemical substitution types/positions and aglycone forms. Beyond general biosynthetic machinery, structure-activity trends represent more specific aspects which are essential to be analyzed for highlighting structural factors influencing activity. These two complementary aims were considered in this paper by statistically analyzing structure-structure (SS) and structure-activity (SA) trends in saponins based on different cycloartane forms of Astragalus genus. For that, 193 saponin structures were statistically analyzed by ordination method to highlight positive and negative trends between different chemical substitutions and aglycone forms. In ordination analysis, the most published pharmacological activities of Astragalus saponins (immunomodulatory, cytotoxic) were considered to identify SA trends which were statistically evaluated by Fisher’s exact test. Results revealed significant contributions of cycloartane forms, glucosylation and/or hydroxylation positions on different studied pharmacological activities. Finally, using the significantly influent structural variables, SAR models were developed by logistic regressions. Statistical analysis of cumulated bibliographic data provides interesting integrative way for understanding biosynthetic rules governing structural diversity and influencing pharmacological activities within a wide metabolites’ family.

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.

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.