**1. Introduction**

Extra-virgin olive oil (EVOO) comes from the supernatant phase of juice obtained after cold pressing of *Olea europaea* fruits and is the fundamental dressing of any Mediterranean dish. It is considered the liquid gold in food trading because of its crucial role in the healthy way of life model called "Mediterranean Diet" [1]. Many scientific studies reveal that the chemical composition of EVOO is a perfect balance leading to countless benefits for humans [2–5]. The positive biological activities are reasonably due to the suitable presence of vegetable sterols [6], liposoluble polyphenols [7] and other anti-oxidant hydrocarbons [8] joined to the most abundant presence of mono-unsaturated tri-acyl-glycerol esters among the vegetable oils. Albeit the oleic ester in EVOOs is considered the overwhelming main mono-unsaturated fatty ester so far, this work casts another important mono-unsaturated fat potentially playing important biological roles. The wide impact of EVOOs composition accounts for the constantly updated European Regulation stating the chemical and taste features, limits and o fficial analytical techniques recognized for olive oil trade [9,10]. In the last decades, the traditional food analysis was shocked by the nuclear magnetic resonance (NMR) as alternative quantitative (qNMR) approach [11] flanking the o fficially recognized separation techniques. The nondestructive NMR spectroscopy allows the *in-situ* detection of several chemical species without the requirement of a real physical separation [8,12,13]; moreover qNMR is feasible directly or through a clever data throughput [14,15]. The definite advantages of the NMR analyses are: a) minimal sample treatment [8], b) simultaneous detection of a grea<sup>t</sup> amount of data [16], c) reduction of systematic errors controlled by the intrinsic instrumental stability, d) constant and direct dependence between signal integration and quantitative values because of the constant nuclear magnetic momentum for the measured nuclei [17]. Criticism toward NMR concerned mainly sensitivity; however, it actually depends on the machine, on sample type, on used solvent, on observed nuclei and on specific experimental runs; this is the reason it should be evaluated from case to case [18]. After several years of research on EVOOs composition, Rotondo et al. have developed a Multi-Assignment Recovered Analysis (MARA-NMR) involving multi-nuclear 1H and {1H}13C-NMR experiments processed by an accustomed processing "MARA" algorithm [19]. This method successfully and quickly achieves the quantification of many components in EVOOs samples through high-resolution spectroscopy at 500 MHz (500 MHz HR-NMR). On the other hand, the "first" MARA-NMR scheme did not take into account some 13C-NMR resonances whose intensity was significant, but these were associated to EVOO minor components (theoretically negligible and contributing for less than 1%) and, for these studies, the best fitting goodness never reached the expected convergence. Since the o fficial method for the quantitative determination of glyceryl fatty esters consists in the gas-chromatographic analysis of the corresponding methyl esters using the gas-chromatographic flame ionization detection (GC-FID) [20], this work focused on the data comparison between NMR and GC-FID on oils in order to solve inconsistent "leftovers" from literature. The paper evidences the neat importance of *cis*-vaccenic fatty ester in EVOOs as its content is around 3%; however, it was neglected so far because, according the o fficial method, it is included in the level of oleic ester.

#### **2. Materials and Methods**

#### *2.1. Materials and Samples*

Deuterated chloroform with a small amount of Tetra-Methyl-Silane (TMS), used as internal reference, was purchased at reagen<sup>t</sup> grade from Cambridge Isotope Laboratories (CIL) Inc. Extra-virgin olive oils were samples from awarded cultivars of di fferent provenience representing top level food in the seasons 2014–2015. These samples were kindly given by producers in order to carry out scientific projects belonging to the BIOOIL program, aiming to improve knowledge about top quality products.

Some seeds were isolated from *Capparis spinosa* fruits (known in Sicily as "cucunci"). Afterward seeds were dried in oven at 30 ◦C for 2 h. The matter was grinded in a mortar until the formation of a raw powder. This matter (20 g) was extracted in 100 mL of hexane, sonicated for 30 min at 30 ◦C and stirred overnight. The solution was then filtrated, and the hexane removed from the solution by using, at first, the rotating evaporator and later N2 flow over the sample. Finally, cucunci's seed oil (CSO) was recovered (yield 15% *w*/*w*).

#### *2.2. GC-FID Analysis for the Comparative Tests*

Fatty acids methyl esters (FAMEs) analysis was performed according to European Union (EU) Regulations [10]. It consists of the hydrolysis of tri-acyl-glycerides and cold transesterification with a methanol KOH solution; in particular, the methyl esters were prepared by vigorously shaking solution of the oil in heptane (0.1 g in 2 mL) with 0.2 mL of the methanolic KOH solution. The resulting solution was then injected into a gas chromatograph DANI MASTER GC-FID (Milan, Italy), equipped with a fused silica capillary column Phenomenex Zebron ZB-WAX (polar phase in polyethylene glycol) with a length of 30 m, internal diameter of 0.25 mm and film thickness of 0.25 μm. Helium was used as a carrier gas at a column flow rate of 1.2 mL/min, with a split ratio of 1:100. The temperature of the injector (split/splitless) and detector was of 220 ◦C and 240 ◦C, respectively. The oven was programmed as follows: initial temperature at 130 ◦C, final temperature at 200 ◦C (10 min) with an increase of 3 ◦C/min. The fatty acid methyl esters were identified by comparing the retention times with those of standard compounds. The relative percentage area of the fatty acids was obtained using the following relationship: %FAX = [AX/AT] × 100, where FAX stands for fatty acids to quantify, AX is the area of the methyl-esters and AT is the total area of the identified peaks in the chromatogram [21]. This analytical strategy is chosen for data comparison because it is officially recognized for the fatty esters quantification, on another hand the reader should be aware that the hydrolysis-esterification step is always tedious, laborious and time consuming, decreasing accuracy and precision. This is the reason why, lately, alternative analytical chromatographic methods have also been proposed [22], still showing limitations.

#### *2.3. Sample Preparation for NMR*

Sample preparation follows the same procedure successfully used by our group several years ago [7,8,12,19]. Briefly, all the CDCl3 solutions were kept homologous by mixing 122 μL of oil and 478 μL of deuterated chloroform (CDCl3) into a 5 mm test-tube (EVOO or CSO in a 13.5% weight ratio). In this study we used the same EVOOs studied in Reference 19; however, these were dissolved as different samples and the experiments were repeated in light of the new assignments. Tubes were immediately sealed to prevent solvent evaporation; it would affect the sample concentration influencing the chemical shift of many signals, especially the unsaturated and carbonyl 13C signals. These samples were readily used for the NMR scheduled analysis so that outcomes could be suitably processed and compared to each other.

## *2.4. NMR Analysis*

All the samples were analyzed at a constant temperature of 298 K on a 500 MHz Avance III NMR spectrometer endowed with a gradient assisted probe (SMARTprobe, Faellanden, Switzerland). The shimming procedure was carried out until the field homogeneity was assessed by less than 1.5 Hz of half-height line-width for the TMS signal.

The 1D 1H and 13C{1H} NMR spectra were run at 499.74 and 125.73 MHz, respectively. This research exploited the analytical procedure including two experiments: a) the standard 1H experiment with 64 scans; b) the standard 13C NMR experiment with 32 scans. The entire procedure takes around 30 min of experimental time for any sample including preparation. Hard pulse for the maximum sensitivity (90◦ pulse), was calibrated and constantly checked for 1H throughout the samples being always 8.2 ± 0.1 μs at −6 dB. 1H-NMR experiments (type A) were run with a spectral width of 12 ppm, 64 scans, 10 s of acquisition time and 5 s of recycle delay in order to overcome problems coming from the differences in the proton relaxation times. For the same reason the 13C spectra (type B) were acquired with the 90◦ hard pulse (11.2 ± 0.3 us at 6 dB) with 32 scans, 5 s of acquisition time and 20 s for the time delay. Thanks to the MARA-NMR algorithm, these experimental elements were conveyed together for the overall quantitative evaluation.

#### *2.5. NMR Processing and Data Treatment*

All the spectra were processed through three main software programs (ACDLab/NMR 2012 (Toronto, Ontario, Canada), MestreNova 6.6.2 (Galicia, Spain), Topspin 4.0.5 (Bruker, Milan, Italy) and using several procedures for the coherent alignment, spectral phasing, calibration, base-line correction and integration procedure. The best processing choices are here reported regardless the many other adoptable procedures. Topspin processed data were selected with manual phase-correction, parametric base-line correction with an implemented polynomial curve (for example, for experiment I *absd 16* command). Calibration of experiment A was performed on the methyl group of the β-sitosterol signal to (δH = 0.738 ppm) with the TMS always being (δ = 0.0 ± 0.005 ppm); for 13C calibration of experiment B the divinyl- methylene group of the linoleate glycerols (L11; δ13C = 25.6614 ppm) was used always keeping the known TMS 13C signal to δ13C = 0.0 ± 0.05 ppm. The TMS calibration would not really change the results; here, the calibration over internal signals is preferred because these are less dependent on random conditions as explained elsewhere [19].

The serial integration of 100 regions for all the A-type experiments, and of 90 regions for experiment B profiles, provided a pretty big matrix whose columns were the 40 studied samples EVOO and rows represented 190 homologous integrations (see Supplementary Materials). Every column of this matrix was processed by the mentioned MARA algorithm [19]; this theoretical architecture is modified according to the original knowledge and assignments concerning *cis*-vaccenic esters (V). The experimental coherences simply confirm the presence of a relevant amount of V, also improving consistency assessed by low best fitting goodness (ρ) values. The extended procedure outputs up to 20 quantitative parameters [7,8,19] (Table 1) but this manuscript focuses on the 11 quantitative parameters showing sound precision and important significance (Table 2). The data validation and experimental error is evaluated through reproducibility (several samplings) and repeatability (analyses in different days of the same sample).


**Table 1.** Abbreviations used to indicate quantitative values.

**Table 2.** Quantitative data and relative deviation for 11 main variables (whose code is reported in Table 1), as measured through Multi-Assignment Recovered Analysis-Nuclear Magnetic Resonance (MARA-NMR) processing method working on mono dimensional 1H and 13C-NMR experiments for 33 samples. Standard deviations were measured through 9 different experiments on 3 identical samples analyzed on three different days.


#### *2.6. Mathematical Background of MARA-NMR and Updates*

The used algorithm MARA-NMR was invented in this laboratory, exploiting the very simple idea that all NMR signals rise from active nuclei that belong to compounds and contribute according to: a) relative concentration, b) number of resonating nuclei, c) possible overlaps with homologous nuclei maybe belonging to other compounds [19]. If this theoretical statement and a suitable assignment is correct, the experimental profile should perfectly match our theoretical reconstruction. As explained in the original paper [18] experimental data are not ideal data-points, however we have designed this algorithm able to optimize quantitative parameters in order to minimize the overall deviations between experimental and theoretical outcomes enclosed in the function ρ which is the best-fitting goodness.

$$\rho = \sum\_{\mathbf{i}:\mathbf{j}=\mathbf{x}1}^{\mathbf{x}\mathbf{f}} \omega\_{\mathbf{x}\mathbf{j}} \left( \frac{\mathbf{y}\_{\mathbf{x}\mathbf{j}} \, \mathbf{I}\_{\mathbf{x}\mathbf{j}}}{\mathbf{I}\_{\mathbf{ref}}} - \frac{\sum\_{\mathbf{i}=\mathbf{a}}^{\mathbf{n}} \mathbf{N}^{\diamond} \mathbf{N} \mathbf{U} \mathbf{C}\_{\mathbf{i}} \ast \mathbf{C}\_{\mathbf{i}}}{\mathbf{N}^{\diamond} \mathbf{N} \mathbf{U} \mathbf{C}\_{\mathbf{ref}} \ast \mathbf{C}\_{\mathbf{ref}}} \right)^{2}. \tag{1}$$

The intensity of any signal in the spectrum Ixj respect to a reference signal Iref should even out the relative concentration (Ci against Cref) of the magnetically active nuclei NUCi actually assigned to that signal. Coefficients ω and γ are empirical parameters able to reduce experimental deviation improving the algorithm; theoretically speaking the best fitting goodness ρ should be 0 but in the real world we accept low values. The introduction of 18 new assignments for the *cis*-vaccenic ester, by enhancing just one quantitative parameter referred to the "new" component greatly lowered the best fitting goodness giving the proof of concept about the assignment. The 20 quantitative parameters are derived by 11 expressions derived from A experiments and 65 expressions derived from B experiments put together in the same expression as equation (1) containing 76 *xj* members and 20 *i* compounds. In order to preserve the quantitative proportion of 13C integrations, despite the uneven nOe relayed on total decoupled carbon nuclei, adopted equations in the sum (1) are divided in blocks of nuclei with the same chemical environment (methyl terminal carbons, methylene inner chain carbons, vynil-methylene, etc.). It is demonstrated that MARA-NMR keeps the quantitative information as reported in Supplementary Materials and in Reference [19].
