**3. Results**

#### *3.1. Modelization of Aromatic "Minerality" Based on the Chemical Composition of Wines*

For the study of the data obtained by the panel, a principal component analysis (PCA) of each attribute was performed, which was calculated from the average scores of the panel members. A correlation matrix was obtained for each attribute (wines in rows and tasters in columns). Thus, each of the attributes was represented in a factorial plane where the projections of each taster were placed around 360◦ of the correlation circle. With the average data of the scores established by each panel, a principal component analysis (PCA) was performed to evaluate the results obtained by the panel of non-producing tasting experts.

The PCA of each attribute was calculated with the average scores of the sensory judge members of the panel. For those descriptors in which the judges were grouped in the same part of the plane, it was interpreted as a sign that the panel had the same criteria in the interpretation of the attribute. On the contrary, those attributes in which the PCA showed the projection of the judges distributed throughout the plane could be explained as:


For this reason, only those attributes that showed a PCA with a projection of at least 60% of the judges in the same plane were taken into account for the correlation analysis shown in Table 2.


**Table 2.** Chemical compounds with correlation at a confidence level of 90% with the olfactory phase (in bold letters with significant differences; \* *p* < 0.1; \*\* *p* < 0.05).

Table 2 describes the results obtained in the correlation study (*p* < 0.1; 90% significance level) among the scores obtained by the panel of tasters, consisting of processors for the olfactory "minerality" descriptor, and volatile and non-volatile chemical compounds from the study samples. In bold are the variables with their correlation coefficients. Only the compounds isobutyric acid, octanoic acid, β-phenylethanol, isoamyl acetate, ethyl acetate, ethyl decanoate, isoamyl alcohol and 4-mercapto-4-4-methyl-2-2-pentanone were shown to be significant for the olfactory "minerality" descriptor, so these are included in the final PLS model. The crucial fact that isobutyric acid, isoamyl acetate and isoamyl alcohol correlate negatively must also be considered.

Next, a correlation study based on the proposed model was conducted for the "minerality" attribute and the variables that show a more positive or negative correlation among the quantified analytes.

Shown below is the proposed mathematical model once the statistical program was applied:

Aromatic minerality = 2.33 − 0.009 × isobutyric acid + 0.023 × octanoic acid − 0.026 × isoamyl acetate − 0.074 × ethyl acetate + 0.328 × ethyl decanoate − 0.074 × isoamyl alcohol + 0.016 × benzyl mercaptan.

In the graph of quality of fit (Figure 1B), we observe how values of 0.58 of cumulative Q<sup>2</sup> are reached, close therefore to the value of 0.6 required to ensure that the results are interesting. The Q<sup>2</sup> cumulated index measures the overall goodness of fit and the predictive quality of the models proposed.

**Figure 1.** (**A**) Quality of fit of partial least squares (PLS) model; (**B**) Distribution of the seventeen wine samples of the study based on the volatile profile of wines for the olfactory "minerality" descriptor.

The corresponding bar chart shown in Figure 1A enables us to visualize the quality of the partial least squares regression as a function of the number of components.

The closer the cumulated R2Y and R2X that correspond to the correlations between the explanatory (X) and dependent (Y) variables and the components are to 1, the better the partial least squares model.

Likewise, the graph of distribution of samples shows how they are projected in a linear way, and how in none of them do the residual values for the model exceed the maximum value of 2 (Figure 1A). These parameters indicate a good fit for the proposed model.

#### *3.2. Modelization of Aromatic "Minerality" Based on the Sensory Properties of Wines*

In a similar manner to that followed in the study, a partial least squares (PLS) regression analysis was carried out with data regarding the chemical composition and the volatile fraction of the wines in relation to the aromatic "minerality" attribute, taking into account the sensory attribute scores provided by the panel of expert judges. To choose the descriptors with significant differentiating capacity, those that showed a correlation of up to 90% level of confidence with the olfactory "minerality" descriptor were taken into account. As was stated in the review, it is reported that other descriptors such as granite, limestone, rock, etc., were associated with minerality [9]. However, only "minerality" was included in the sensory analysis so as not to distract the judges from the aim of this study.

The results are described in Table 3. In bold are the descriptors with significant values (*p* < 0,1; 90% significance level) for the "minerality" olfactory descriptor oak, empyreumatic, animal, plant chlorophyll and oxidation, so that these are included in the mathematical predictive model.

**Table 3.** Sensorial attributes from the sensory analysis performed on seventeen wine samples with correlation at a significant level of 90% with the olfactory "minerality" attribute (in bold letters with significant differences; \* *p* < 0.1; \*\* *p* < 0.05).


Next, on the proposed PLS model, a study of the correlation between the "minerality" olfactory attribute and other sensory descriptors with higher correlation was conducted. The proposed mathematical model is shown here:

Aromatic minerality = 2.32 − 0.39 × oak + 0.28 × empyreumatic + 0.483 × plant chlorophyll + 0.26 × oxidation.

#### *3.3. Modelization of Aromatic "Minerality" Based on the Chemical Composition and the Sensory Properties of Wines*

A third model was elaborated taking into account chemical data with significant correlation (*p* < 0.1, 90%) with the descriptor of "minerality" descriptor, as well as the scores of from descriptors with significant correlation with the aromatic "minerality" descriptor. The proposed model is presented here:

Aromatic minerality = 3.32 + 0.57 × plant/chlorophyll + 0.225 × oxidation − 0.015 × isobutyric acid + 0.003 × octanoic acid − 0.025 × phenylethyl alcohol − 0.004 × isoamyl acetate − 0.11 × ethyl acetate + 0.449 × ethyl decanoate − 0.081 × isoamyl alcohol + 0.008 × benzyl mercaptan.

The graph of quality of fit (Figure 2B) shows that Q<sup>2</sup> values of 0.69 are reached. Since a 1.0 Q<sup>2</sup> value is considered an optimal fit, we can judge the proposed model as satisfactory.

In the graphic representation of the samples (Figure 2A), we can see how they are distributed in a linear way, and how in none of them do the residual values found for the model exceed the maximum value of 2. It can also be seen that the residual values found are generally very low.

Figure 3 shows the standardized regression coefficients, in which it can be seen that all the variables of the model are within the recommended range of −1.96 to 1.96. Likewise, it can be observed that, according to this model, the "minerality" olfactory descriptor is positively correlated with the presence of organic acids such as octanoic acid as well as benzyl mercaptan. The model also indicates a relationship between herbaceous notes and oxidation with the "minerality" olfactory descriptor.

**Figure 2.** (**A**) Quality of fit of PLS model; (**B**) Distribution of the seventeen wine samples of the study in the predictive model of aromatic "minerality" considering the chemical and sensory profile.

**Figure 3.** Standardized coefficients of the linear regression in the predictive model of aromatic "minerality" descriptor constructed according to the chemical and sensory profile of the seventeen wine samples of the study.

On the other hand, as noted in the model built based on active olfactory analysis, compounds such as ethyl acetate, nail lacquer aroma and glue, and other compounds such as isoamyl alcohol, fusel or distinctly fruity notes [10,11], as in the case of the banana-scented isoamyl acetate, contribute negatively to the mineral attributes. It is not surprising that the presence of fruity aromas such as those produced by organic esters contribute negatively or contrary to the perception of "minerality", previously described this hypothesis by Par et al. [12–14].

#### *3.4. Modelization of the Gustatory "Minerality"*

Similar to what was done with sensory results of the "minerality" attribute at olfactory level, a partial least squares regression (PLS) analysis was conducted with chemical and sensory data regarding gustatory "minerality" obtained by the panel of expert tasters.

Those compounds with a relationship in concentration between the maximum and minimum value greater than 2 were considered, because it is assumed that they are compounds that can make significant differences in gustatory perception. A second criterion was established for this analysis, taking into account only those compounds whose concentration regarding the gustatory sensory threshold was >1. Gustatory thresholds in the case of anions and cations were those considered as known in the water matrix [15], since there are no publications related to wine.

Statistical analyses of the gustatory "minerality" attribute previously analyzed already showed that the results of the ANOVA were significant (*p* < 1.35 × <sup>10</sup>−2) for the set of white and red wines, but less so when the white wines (*p* < 8.61 × <sup>10</sup>−4) and the red wines (*p* < 5.61 × <sup>10</sup>−2) were analyzed separately (data not shown here). Therefore, it was decided to analyze subgroups of white and red wines separately.

#### *3.5. Gustatory "Minerality" Based on the Chemical Composition of White Wines*

An initial approach through correlation to a 90% significance level revealed that there was only one compound with a positive correlation between the gustatory "minerality" and the chemical compounds studied. Therefore, it was decided to reduce the level of significance to 60%. A study of correlation was performed for each of the compounds with gustatory capacity, which fulfilled the criteria referred to above, in order to evaluate their discriminatory capacity and include them in the partial least squares regression model. Table 4 describes the results obtained in the correlation study (*p* < 0.4; 60% significance level) of the scores obtained by the tasting panel for the gustatory "minerality" descriptor and the analytical results of compounds related to the gustatory sensations. Descriptors with significant values are highlighted in bold.

**Table 4.** Chemical compounds from the eleven white wine samples of the study with correlation at a significant confidence level of 60% with the gustatory "minerality" attribute in white wines (in bold letters with significant differences; \* *p* < 0.4; \*\* *p* < 0.1; \*\*\* *p* < 0.05).


Variables: volatile acidity, pH, L-lactic acid, tartaric acid, glucose and fructose, boron, magnesium and potassium were shown to be significant, contributing to the definition of the gustatory "minerality" descriptor in white wines, and are therefore included in the model (Figure 4).

**Figure 4.** Standardized coefficients of the linear regression model for the gustatory "minerality" descriptor in the eleven white wines of the study constructed on the chemical profile.

Compounds: succinic acid, L-malic acid, alcohol content, total acidity, glycerol, phosphorus, manganese and aluminum were eliminated from the model because its statistical quality improved after removal. Concerning the variable constituted by the sum of glucose and fructose, its coefficient or weight level in formula was very low (0.005), as may be expected, since a priori "minerality" is a difficult character to fit in sweet wines, although in this case we are speaking of dry wines. The proposed model is presented below:

> Gustatory minerality in white wines = 5.48 − 1.59 × pH + 0.34 × tartaric acid + 0.005 × glucose & fructose + 0.011 × magnesium − 0.001 × potassium.

Graph of quality of fit (Figure 5B) shows how the Q<sup>2</sup> value lies in values greater than 0.6, which is the necessary minimum to obtain representative results (0.66). Likewise, none of the wines show residual values greater than 2.0, as shown in the graph of samples dispersion (Figure 5A); therefore, all were retained for the construction of the PLS model.

**Figure 5.** (**A**) Quality of fit of PLS model; (**B**) Distribution of samples of the predictive model for the gustatory "minerality" descriptor based on the chemical profile constructed from the eleven white wines of the study.

It can be noted how the gustatory "minerality" descriptor in white wines was positively related to the increase in acidity. Therefore, the results indicate that increasing levels in tartaric acid and decreasing pH levels favor the emergence of the gustatory "minerality" descriptor in white wines. The model also suggests a positive relationship between the degree of sweetness and "minerality", which is somewhat surprising, but may be due to the fact that one of the wines in the study from the Riesling variety was an "off-dry" style, with 5–7 g/<sup>L</sup> of residual sugar.

#### *3.6. Gustatory "Minerality" Based on the Sensory Attributes of White Wines*

Similarly to what was conducted previously with chemical compounds, a correlation of the gustatory "minerality" attribute with the tasting parameters evaluated in the gustatory phase of the sensory analysis was performed; the results are shown in Table 5 from the scores obtained by the tasting panel for the gustatory "minerality" descriptor and the scores of "minerality". Descriptors with significant values are highlighted in bold.

**Table 5.** Sensory descriptors with correlation at 60% confidence level with the gustatory "minerality" attribute in the eleven white wines analyzed (in bold letters with significant differences; \* *p* < 0.4; \*\* *p* < 0.1; \*\*\* *p* < 0.05).


Below is the model proposed if taking only into account only the gustatory attributes:

Gustatory minerality in white wines = 0.19 + 0.32 × sweetness + 0.234 × acidity + 0.25 × acidity (freshness) + 0.31 × alcohol (sweetness) − 0.30 × tannin (concentration) + 0.43 × body (feeling of weight) + 0.67 × bitterness − 0.31 × balance.

Again, there is a positive correlation between increasing levels of acidity and the gustatory "minerality" observed by the judges on the panel of tasters. The proposed model reached in this case a value of 0.58 for accumulated index Q2, which gives the model moderate credibility, since it does not reach the critical value of 0.6.

#### *3.7. Gustatory "Minerality" Based on the Chemical Composition and the Sensory Properties of White Wines*

Finally, a third model was developed taking into account both the chemical data with significant correlation (*p* < 0.4, 60%) with the gustatory "minerality" descriptor as well as the descriptors with significant correlation (*p* < 0.4, 60%) with the same descriptor. The proposed model is presented below:

Gustatory minerality in white wines = 2.29 − 0.89 × pH + 0.21 × tartaric acid + 0.004 × glucose & fructose + 0.014 × magnesium − 0.001 × potassium + 0.17 × sweetness

+0.15 × acidity level + 0.20 × alcohol (sweetness) + 0.27 × body + 0.44 × bitterness − 0.19 × balance.

Fit values found for Q<sup>2</sup> were 0.63 for the first components given that those values greater than 0.6 are acceptable, the proposed model was therefore considered valid.

In addition, and as can be seen in Figure 6, in which the standardized regression coefficients are shown, all the variables of the model are within the recommended range of −1.96 to 1.96. Similarly, it is noted that according to this model, the increasing values of acidity, sweetness and alcohol are

positively related to this descriptor. What is more, the absence of balance or the presence of some metals, such as potassium, can contribute negatively to mineral tastes.

**Figure 6.** Standardized coefficients of regression for the predictive model of the gustatory "minerality" descriptor based on the chemical and sensory profile from the eleven white wines of the study.

#### *3.8. Modelization of Gustatory "Minerality" Considering the Chemical Composition of Red Wines*

As in the white wines, a test was performed on the correlation between the scores of the "minerality" attribute and the concentrations of the different chemical compounds analyzed. The study revealed that there was only one compound with a positive correlation between gustatory "minerality" and the chemical compounds analyzed. Therefore, it was decided to decrease the level of significance to 60%. Only the compounds showing a significant correlation were considered for inclusion in the partial least squares regression model.

Table 6 shows the analytical results of the compounds related to the gustatory sensations. The variables with significant values providing differences between samples are shown in bold. The factors alcoholic strength, L-lactic acid, succinic acid, aluminum, manganese, phosphorus and potassium proved to be significant for the gustatory "minerality" descriptor in red wines and were therefore included in the mathematical model.

**Table 6.** Chemical compounds with correlation at a significant level of 60% with the gustatory "minerality" attribute in red wines constructed from the data extracted from the six red wines in the study (in bold letters with significant differences; \* *p* < 0.4; \*\* *p* < 0.1).


*Beverages* **2019**, *5*, 66

Below is the proposed PLS model that considers the active chemical composition in the mouth at the sensory level of red wines:

Gustatory minerality in red wines = 0.77 + 0.05 × alcoholic strength − 0.15 × l − lactic acid + 0.99 × succinic acid − 0.03 × aluminum − 0.17 × manganese + 0.001 × phosphorus + 0.0003 × potassium.

#### *3.9. Modelization of Gustatory "Minerality" Considering the Sensory Attributes of Red Wines*

Table 7 describes the results obtained in the study of correlation (*p* < 0.4; 60% significance level) of the scores obtained by the panel of expert tasters for the gustatory "minerality" descriptor in red wines

**Table 7.** Sensory descriptors with correlation at a significant level of 60% with the gustatory "minerality" attribute build from the data extracted from the six red wines of the study (in bold letters with significant di fferences; \* *p* < 0.4; \*\* *p* < 0.1; \*\*\* *p* < 0.05).


The proposed PLS model that considers the attributes of gustative sensory analysis is shown below:

Gustatory minerality in red wines = 1.07 − 0.49 × acidity (freshness) + 0.31 × alcohol (warmth) + 0.47 × tannin (concentration) − 0.34 × astringency of tannin + 0.29 × depth

+ 0.24 × gustatory persistence.

The quality of fit of the two models displayed in Sections 3.1 and 3.2 based on Q<sup>2</sup> parameters were 0.45 for the one which uses chemical parameters and 0.74 for the one which uses sensory attributes; the latter is therefore much more reliable.

In order to improve the fit of the formula that considered the chemical composition, di fferent models were performed eliminating variables whose importance in the projection was less than 0.8 (Figure 7B); however, the model initially proposed for the PLS accumulated the best fit and so it was maintained as valid.

In the sensory model, and as is shown in the Variable Importance in Projection (VIP) graph (Figure 7A), the descriptors tannin from oak and heartburn were eliminated from the model since the statistical quality improved after their removal. Additionally, all the descriptors that are part of the model exceeded the 0.8 cut-o ff values.

Concerning the chemical composition, it should be highlighted how the gustatory "minerality" descriptor in red wines is positively related to the alcoholic strength and does not seem to give importance to acidity, which was the case in white wines. However, a positive correlation of a compound with a saline character appears in the case of succinic acid. This relationship is already reflected in previous studies about "minerality" in wine.

Furthermore, in relation to the tasting attributes, similarly to what was seen in white wines, there is a positive correlation between the feeling of alcoholic warmth and gustatory "minerality". However, contrary to what happens in white wines, the gustatory acidity in red wines is not decisive in the detection of a mineral character.

**Figure 7.** (**A**) Variable Importance in Projection (VIP) graphic of the models proposed for the gustatory "minerality" descriptor in red wines constructed on the chemical profile of active gustatory compounds; (**B**) Idem based on the values of the descriptive sensory analysis from the data extracted from the six red wines in the study.

#### *3.10. Modelization of Gustatory "Minerality" in Red Wines Considering the Chemical Composition and the Sensory Attributes*

Finally, a third model was developed in red wines taking into account both chemical data with significant correlation (*p* < 0.4, 60%) with the gustatory "minerality" descriptor and the sensory tasting parameters. The proposed model is presented below:

Gustatory minerality in red wines = 1.84 − 0.29 × acidity (freshness) + 0.22 × alcohol (warmth) +0.29 × tannin (concentration) − 0.23 × astringency of tannin + 0.19 × depth + 0.17 × persistence + 0.74 × succinic acid − 0.25 × manganese + 0.0002 × potassium.

As shown in the graph of variable importance (Figure 8), alcoholic strength, l-lactic acid, aluminum and phosphorus were eliminated from the model since its statistical quality improved after their removal. The model shows a fit of 0.64 based on the accumulated Q<sup>2</sup> parameter, so it can be considered that it exceeds the cutoff threshold established at 0.6.

The model constructed shows how increasing values of alcohol sensations (warmth) and tannins, both at the level of astringency and phenolic concentration, are positively related to this descriptor, and how the model, once again, appears to give no importance to the acidity, as occurred in white wines. However, there is again a positive correlation with a compound with a saline character, succinic acid. The presence of metals is irrelevant, since some of them, such as manganese, contribute positively to the final pls mathematical model and others, like potassium, do so negatively.

**Figure 8.** Variable Importance in Projection (VIP) graph of the model proposed for the gustatory "minerality" descriptor in red wines, based on the chemical and sensory profile of the six red wine samples.
