The total content of phenolic compounds was determined using the Folin–Ciocalteu reagent. To prepare the reagent, 100 g of sodium tungstate (Na₂WO₄$\cdot$2H₂O) (Vekton, Saint Petersburg, Russia) and 25 g of sodium molybdate (Na₂MoO₄$\cdot$2H₂O) (Vekton) were sequentially dissolved in 700 cm³ of distilled water. Then, 50 cm³ of concentrated orthophosphoric acid (H₃PO₄, 85%, $\rho$₂₀ = 1.71 g/cm³) (Vekton), and 100 cm³ of concentrated hydrochloric acid (HCl, $\rho$₂₀ = 1.19 g/cm³) (Vekton) were added to the resulting solution, after which the mixture was brought to a boil and maintained under reflux for 10 hours. Then, 150 g of lithium sulfate (Li₂SO₄$\cdot$2H₂O) (Vekton) and a few drops of bromine (Vekton) were added, with boiling continued for another 15 minutes. After cooling to 20 $\pm$ 0.5 °C, distilled water was added to adjust the final volume to 1 dm³.

High-performance liquid chromatography (HPLC) was implemented to analyze phenolic substances in various forms (monomeric, oligomeric, and polymeric). The eluents used were methanol (Vekton) (solution A) and an aqueous solution of trifluoroacetic acid (C₂HF₃O₂) (Vekton) at a concentration of 0.6 g/100 cm³ (solution B). Standard samples of trans-resveratrol and syringic acid (all from Sigma-Aldrich Chemie GmbH, Steinheim, Germany), gallic acid, and caffeic acid (Fluka, Chemie GmbH, Buchs, Switzerland) were employed to identify individual phenolic compounds.

The antioxidant activity (AOA) evaluation was performed using an amperometric method based on the generated current measurement during the oxidation of antioxidant molecules. The current value directly depended on the concentration and chemical structure of the antioxidants in the sample. The standard used was 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox-C) (Sigma-Aldrich Chemie GmbH).

The colorimetric method is based on the ability of phenolic compounds to reduce phosphotungstic and phosphomolybdic acids, which are components in the Folin-Ciocalteu reagent, and form colored tungsten (W₈O₂₃) and molybdenum oxides (Mo₈O₂₃). The intensity of the blue coloration is proportional to the concentration of phenols and was measured colorimetrically. Measurements were performed in quartz cuvettes with a 1 cm optical path.

A calibration graph was constructed using gallic acid solutions in 100 cm³ volumetric flasks by adding 2.5, 5.0, 7.5, 10.0, 12.5, 15.0, 17.5, 20.0, and 25.0 cm³ of a gallic acid standard solution. Next, 1 cm³ of distilled water was added to the flask for the control solution. Then, 1 cm³ of Folin-Ciocalteu reagent, 15–20 cm³ of distilled water, and 10 cm³ of sodium carbonate solution were added to each flask, and distilled water was added until the final volume was achieved. After 30 minutes, the optical density was measured at a wavelength of 670 nm against the control solution. A calibration graph was plotted based on the obtained optical density values.

The qualitative and quantitative composition of phenolic substances in the studied samples was determined by HPLC in gradient mode using an Agilent Technologies chromatographic system (model 1100). A Zorbax SB-C18 chromatographic column with a size of 2.1–150 mm, packed with silica gel, with a grafted octadecylsilyl phase possessing a sorbent particle size of 3.5 µm, was used to separate the substances. The eluent composition during chromatography was changed according to the content of component B, and the following scheme was applied: 0 min 8%; 0–8 min 8–38%; 8–24 min 38–100%; 24–30 min 100%. The eluent flow rate was 0.25 cm³/min. The volume of the injected sample was 2 µL; column thermosetting was 40 °C. Chromatograms were recorded at the following wavelengths: 280 nm for gallic acid and 313 nm for hydroxycinnamic acid derivatives. Individual compounds were identified by comparing their spectral characteristics with those described in the literature and by matching the retention time of the peak being determined and the peak of the standard sample. The spectral characteristics of individual substances were confirmed using literature data [69, 70, 71, 72, 73, 74, 75]. The quantitative content of individual components was calculated using calibration graphs for the dependence of the peak area on the concentration of the substance, constructed using standard substance solutions. All determinations were performed in triplicate.

The electric current generated by the oxidation of antioxidant molecules in a test sample consisting of one or a mixture of substances on the surface of the working electrode at a certain potential was converted into a digital signal and compared with the signal obtained from the antioxidant standard under the same detection conditions. Calibration curves were constructed using a series of measurements of standard solutions with concentrations of 0.5, 1.0, 5.0, and 10.0 mg/dm³. Five consecutive measurements of the analyzer output signal were conducted for each parallel sample of the analyzed specimen, and the desired value (in terms of Trolox-C) was calculated for each input using the calibration characteristic. The arithmetic mean of the obtained values and the relative standard deviation were also calculated. Accordingly, a 2.2 mM H₃PO₄ solution was used as an eluent; the eluent flow rate varied from 1.0 to 5.0 cm³/min. The voltage potential varied from +2.0 to –2.0 V. Five consecutive measurements of the standard solution signals (output curve area) were carried out at different potentials. The arithmetic mean of five measurements (standard deviation no more than 5%) was recorded as the result. Based on the obtained data, a calibration graph was constructed with the coordinates: X represents the standard signal (output curve area); Y denotes the standard concentration, mg/dm³, described by the equation Y = aX + b. The approximation coefficient was 0.99. The reproducibility of the method relative to the Trolox-C standard was 8.6%, and the convergence of the results obtained was 5%. The calculation of the convergence and reproducibility of the method was carried out using the Spline program.

This study aimed to create unified methodological approaches to designing and modeling the composition and properties of products using stem extracts.

The objects of the study were mathematical models and methods for setting and solving problems in compiling and optimizing the composition of products using stem extracts.

A synthetic data augmentation method was used to increase the sample size and improve the statistical robustness of the models. The original values of phenolic compound concentrations were expanded by adding random noise distributed according to the normal law. In this case, the distribution parameters (mean and standard deviation) for each feature were determined based on the calculated statistical characteristics of the original data. Synthetic observations were generated for each grape variety and then combined with the original data by concatenation. This approach imitates the natural variability of phenolic concentrations and provides sufficient data for building reliable regression models and conducting other statistical analyses.

The values of the mass concentration of phenolic substances (MCPSs) and AOA of the aqueous ethanol extract experimental samples from white technical grape stems are presented in Fig. 1. According to our research, 11 phenolic compounds with the non-flavonoid structure were identified in the composition of the phenolic complex of the water–ethanol extracts from white grape stems (Aligote, Kokur white, Rhine Riesling, Rkatsiteli, Sauvignon green, Podarok Magaracha, Pervenets Magaracha) that reached technological maturity and were processed into wine.

The mass concentration of phenolic substances determined in the aqueous ethanol extracts from grape stems was between 7.95 and 16.40 g/dm³. The final result was taken as the arithmetic mean of two parallel determinations, the discrepancy between which did not exceed (for the measurement range of 3000–20,000 mg/dm³) 39 mg/dm³. The error limit for measuring the mass concentration of phenolic substances at a confidence probability of p = 0.95 for the specified measurement range was $\pm$39 mg/dm³. The antioxidant activity of these extracts ranged from 6.30 to 13.90 g/dm³. The final measurement result of the total content for the determined antioxidant in the sample (the third digit was rounded up) was noted as the arithmetic mean of the results of two parallel determinations, the discrepancy between which did not exceed the repeatability limit (r_abs = 5%). The error limit for measuring the antioxidant activity value at a confidence level of p = 0.95 was $\pm$56 mg/dm³.

A study of the qualitative and quantitative phenolic compositions of grape stems revealed that these 11 compounds include biologically active substances consisting of phenolic acids and their esters (caftaric acid, coutaric acid, caffeic acid, ferulic acid, p-coumaric acid, ellagic acid, gallic acid, protocatechuic acid, syringic acid, and the ethyl ether of p-coumaric acid) and stilbenes. Data presented in Table 1 show that white grape stems possess a diverse phenolic composition, with both similarities and differences in the qualitative and quantitative content of individual compounds and compound groups.

The aqueous–ethanolic extracts from grape stems include up to 4.4% of the mass concentration of phenolic substances of stilbenes compounds [39].

The qualitative and quantitative compositions of the aqueous ethanol extracts from grape stems of the most common European varieties in the southern regions of Russia: Aligote, Rhine Riesling, Rkatsiteli, and grape varieties of an interspecific selection from the NRC “Kurchatov Institute”—“Magarach”—Pervenets Magarach. Analysis of the qualitative and quantitative phenolic compositions for the aqueous ethanol extracts from grape stems showed that the content of biologically active compounds, such as hydroxybenzoic acids and stilbenes, in the extract samples from the Rkatsiteli grape variety, were higher by 47.8% and 17%, respectively, than those from other varieties.

A linear regression model was developed using the phenolic profile parameters as input data to predict the stilbene concentration. The resulting model demonstrated high accuracy, as evidenced by the determination coefficient R² = 0.95, calculated on the test set (Fig. 2). This confirms that the phenolic profile can be a reliable predictor of the stilbenes content in the samples.

In addition to a high coefficient of determination (R² = 0.95), the model demonstrated a low root mean square error (RMSE = 1.12 mg/dm³), indicating strong predictive accuracy. These metrics confirm the robustness of the model when applied to both original and synthetically augmented data.

Compared to traditional regression models, our approach integrates SHAP analysis, providing interpretability and allowing for the identification of key predictors. Moreover, the incorporation of synthetic data enhances model generalizability without compromising accuracy. The model was further validated on a subset of experimental data, demonstrating reliable predictive performance in real-world conditions.

When training the model, an expanded set was used, including both the original data and synthetically generated observations, which improved the generalization ability of the model. These data were randomly divided into training (75%) and testing (25%) subsets.

Fig. 2 compares the actual and predicted stilbenes concentrations from the model (actual vs. predicted). As demonstrated in Fig. 2, most points are concentrated along the diagonal line, indicating a high correspondence between the predictions and the actual data.

Subsequently, SHAP (SHapley Additive exPlanations) analysis was performed to assess the contribution of individual phenolic compounds in predicting the stilbenes concentration and to interpret the performance of the constructed regression model. This method allows for a quantitative assessment of the significance of each feature and its impact on the model output, which is especially important when analyzing complex multivariate data characterized by a high degree of multicollinearity and overlapping effects of individual compounds. A SHAP summary plot was constructed for non-flavonoid phenolic compounds as part of the analysis (Fig. 3), which ranks the features in order of their contribution to the model. This plot demonstrates which phenolic profile components contribute most to predicting the stilbenes concentration. The color scale displays the value of each feature in a specific observation (from low to high), which allows us to assess the significance of each compound and the direction of its influence (positive or negative). A SHAP dependence plot was constructed for the group of hydroxycinnamic acids and their esters (Fig. 4). This plot allows us to study the relationship between the SHAP value and the concentration of compounds in this group. The observed linear dependence indicates a direct contribution of these compounds to the predicted concentration of stilbenes.

Moreover, the color indication of the second feature (protocatechuic acid) allows us to evaluate the effect of interactions between the components, showing how the combined effect of several phenolic compounds is reflected in the model.

In general, the SHAP analysis results confirmed the high interpretability of the model and the biological validity of the selected predictors. These obtained dependencies allow us to assess both the contribution of each compound to the forecast and identify potential mechanisms involved in forming the phenolic profile of grape stems and their relationship with the accumulation of stilbenes. This makes the model a forecasting tool and an important means for an in-depth study of metabolic relationships within the phenolic complex.

The correlation analysis between phenolic compounds in grape stems allows us to identify stable patterns in their joint accumulation, which is especially important for understanding metabolic relationships and identifying key predictors for calculating the concentration of stilbenes. The correlation matrix for non-flavonoid phenolic compounds demonstrates a clear clustering into two main groups: hydroxycinnamic acids and their esters and hydroxybenzoic acids (Fig. 5).

Further, high positive correlations are observed (coefficients above 0.8) within each group, indicating similar trends in their variability and, probably, a common biosynthetic nature of these compounds. For example, hydroxycinnamic acids (caftaric, caffeic, and ferulic acids) demonstrate almost complete synchronicity in their concentrations, which suggests these compounds participate in common biochemical cascades. Interestingly, the relationship between the two main clusters is less pronounced—the correlation coefficients between hydroxycinnamic and hydroxybenzoic acids range from weakly negative to moderately positive values (from –0.2 to +0.4). This may indicate differences in the mechanisms involved in the biosynthesis or functional differentiation of these compound classes in the metabolism of grape stems. Thus, the construction and analysis of correlation matrices can allow the identification of groups of compounds with similar accumulation dynamics and the assessment of the degree of connectivity between key classes of phenolic compounds. The obtained data provide a basis for further studying the regulation of metabolic pathways and a reasonable choice of informative predictors when modeling the content of target metabolites, such as stilbenes.

Histograms of the concentration distribution of phenolic compounds not only allow an assessment of the overall variability of the data but also provide an opportunity to identify key distribution features for each class of compounds.

These graphs can aid researchers in determining which compounds are characterized by stable concentrations (narrow range of values) and which components are characterized by high variability (widespread). Moreover, histograms depicting the concentration distribution of phenolic compounds allow us to assess the variability and distribution pattern of values. The histograms for the non-flavonoid compounds are presented in Fig. 6 (with annotations from (A) to (M)).

These visualizations allow us to identify compounds with the most stable and variable concentrations, which is important for the subsequent interpretation of statistical indicators. Indeed, most hydroxycinnamic and hydroxybenzoic acids in the non-flavonoid phenolic compounds show distributions close to normal, with one distinct mode and a symmetrical pattern (Fig. 6). This suggests that these compounds accumulate relatively uniformly in the sample set. However, distributions with shifted modes or signs of bimodality are observed for some components, such as stilbenes and individual cinnamic acid esters, which may indicate the presence of subgroups in the sample or differences in metabolic pathways between grape varieties.

When analyzing histograms, special attention should be paid to the presence of outliers, especially in small samples. The presence of individual observations with extremely high or low concentrations may indicate both technological factors (e.g., sample processing features) and biological heterogeneity in the source material. These features must be considered during further data processing and the construction of predictive models.

Histograms serve not only as a tool for the initial assessment of the data structure but also as an important means for identifying potential artifacts, assessing the stability of individual predictors, and preliminarily identifying groups of compounds with high or low variability. All these aspects are critically important when preparing data for regression analysis and subsequent interpretation of the obtained models.

Analysis of the histograms illustrating the distribution of phenolic compound concentrations showed that most components have relatively stable distributions, which indicates the reliability of the original data and the correctness of the sampling procedure. At the same time, increased variability in concentrations was revealed for several compounds, which may indicate varietal or technological features in the formation of the phenolic profile. These identified distribution features were considered when forming a synthetic sample and in subsequent regression analyses to predict the concentration of stilbenes. These histograms allowed a visual assessment of the data structure and played an important role in creating a statistically valid model that considers the natural variability in the phenolic composition of grape stems.

One-way analysis of variance (ANOVA) was performed to assess the statistical significance of the differences in the phenolic compound concentrations between cultivars on the synthetically expanded sample. Table 2 presents the p-values for non-flavonoid phenolic compounds.

These results showed that the within-group variability increases significantly when homogenizing the synthetic data, leading to higher p-values, indicating no statistically significant differences between varieties in some cases.

Multiple factor analysis (MFA) was performed on non-flavonoid phenolic compound datasets to assess the data structure and identify sample groupings based on the phenolic profile (Fig. 7). The MFA allows the distribution of the grape stem samples to be visualized using the first two principal components; each point corresponds to a separate sample, and the color indication reflects the varietal affiliation. The observed clear separation of samples by varieties (Aligote, Rhine Riesling, Rkatsiteli, and Pervenets Magaracha) indicates the high information content of the non-flavonoid phenolic profile for varietal differentiation.

The first principal component (Dim 1) makes the greatest contribution to the differentiation of varieties and, according to the trait loading results, is determined mainly by the content of hydroxycinnamic acids and their esters. The second component (Dim 2) is largely associated with variations in the concentrations of hydroxybenzoic acids and stilbenes, which reflects the contribution of these compounds to the overall difference in phenolic profiles.

The MFA of independent datasets shows that non-flavonoid phenolic compounds are informative predictors of grape stem varietal affiliation. The clear clustering of samples by varieties indicates stable differences in phenolic profiles due to genetic features and the possible influence of growing conditions and technological factors. These results underline the importance of a comprehensive consideration of phenolic compounds in analyzing the quality and origin of raw grape materials.