Freshly harvested Roselle (Hibiscus sabdariffaL. var. vimto) calyxes in Tchatibali, a locality in Mayo-Danaï, Far North region, Cameroon, were oven-dried for 48 h at 45˚C before use. The acyl donors used in this study were Methyl Palmitate (MP) and Vinyl Laurate (VL), both from Sigma. Tert-amyl alcohol (Sigma) was used as a solvent. The immobilised lipase B from Candida antarctica on acrylic resin (≥ 5000 U/g, recombinant, expressed in Aspergillus niger, Sigma) was used as the catalyst.

2.2.1. Production Process of Roselle Calyx Acylated Anthocyanins and Data Collection

Purified Anthocyanins were obtained from Roselle calyx water extract and submitted to transesterification following the production process diagram presented in Figure 1.

Figure 1. Process diagram of the production of acylated anthocyanins from H.sabdariffa L. calyx.

The transesterification reaction was conducted in the dark in a 50 mL stirred reactor. For each run, 15 mL of solvent was added to 50 mg of freeze-dried anthocyanidin extract, followed by 2 mL of acyl donor. The experiments were conducted using a Circumscribed Centred Composite (CCC) experimental design. The reaction was initiated by adding a specified quantity of immobilised lipase with a defined specific activity. Control experiments were performed without enzymes. Calcium chloride was used in a guard tube to prevent the reaction medium from absorbing water.

100 µL of suspension was withdrawn from the reaction medium at the relevant time, dissolved in 0.9 mL of methanol, and filtered with a 0.2 µm syringe filter. A volume of 20 µL of this solution was then injected into the HPLC system to evaluate the conversion yield. At the end of the reaction time, the biocatalysts were removed by centrifugation. Each experiment was conducted three times, and the mean values were used for calculations.

2.2.2. Identification of Anthocyanins and Transesterification Reaction Monitoring

HPLC was performed using a Shimadzu HPLC system (Kyoto, Japan; LC-20AD pump, CTO-20A column oven, and SPO-M20A diode-array detector). A C18 column of 4.6 mm diameter and 250 mm length (Phenomenex Gemini) was used for the separation. Data were analysed using LC Real Time Analysis software. Preparative HPLC was also performed, and an aliquot was collected based on the retention time (RT). MS was performed to identify the compounds. The maximum absorption wavelength (λ_max) at which data were to be collected was determined by analysis of the absorption spectrum at pH one and pH 4.5 of a 1/50 to 1/5 diluted solution of 1 mg/mL anthocyanins contained in the pellets.

Elution for quantitative reaction monitoring was performed using a low-pressure gradient of 5% formic acid in Milli-Q water (solvent A) and ACN (solvent B) at a flow rate of 0.8 ml/min and a column temperature of 40˚C. The program was as follows: 2 min (10% B), 5 min (20% B), 10 min (30% B), 15 min (33% B), 20 min (30% B), 25 min (40% B), 30 min (50% B), 32 min (100% B), and 35 min (10% B). The initial quantity of solvent B was 10%. The different compounds were quantified at 330 and 520 nm. Each time, 20 µL of the sample was injected, and the resulting chromatogram was compared to the reference (at t = 0 s).

The conversion yield was calculated with the following formula:

where A t = 0 is the peak area at t = 0 s, and A t is the peak area at a given time.

2.2.3. System Predictive Modelling and Optimisation

Response Surface Methodology(RSM)

A 3-factor circumscribe central composite (CCC) experiment design was used. The system response (y) was the conversion yield. The reaction temperature X₁, the reaction time X₂, and the substrate-to-enzyme ratio X₃ were the explanatory variables. Absolute values were obtained by converting coded values with the formula:

where U j and x j are respectively a real variable j and its corresponding coded value. Δ U j which is the variation step, was calculated with:

Max and min were meant to represent the maximum and minimum value of a variable j (Real or coded), while U j 0 is the natural value at the centre of the range for each factor (Table 1).

Table 1. Process variable employed in the CCC design.

*Mass ratio.

The centre point was replicated 5 times, for a total of 20 experiments. The relationship between the response and the independent variables was obtained by fitting the acquired data into the following second-order polynomial equation:

Analysis of variance (ANOVA) was used to evaluate the variation of the response (y). The data were analysed using Statgraphic Centurion 15.1.

Artificial neural networks(ANNs)

CCC Additional runs were obtained through data augmentation. Before augmentation, dimensional effects were removed by normalisation to the range 0 – 1 of both input (original CCC matrix values) and output variable (experimental response, Yield). After generation, the synthetic data were denormalised to the original physical units to enable direct comparison with experimental observations. The following relations were used:

Python Code was used to define a Variational Autoencoder (VAE) model in TensorFlow. For each acyl, the VAE model was trained on the CCC matrix and the experimental system response to generate new rows in Google Colab (https://colab.research.google.com). The mean response of the centre points was used for the VAE; thus, only a 15-line matrix was used. The VAE used an encoder consisting of a single dense hidden layer with 64 neurons and ReLU activation, followed by a two-dimensional latent space parametrised by mean and log-variance vectors. The decoder mirrored this structure with a dense layer of 64 neurons and a sigmoid output layer. The model was trained for 100 epochs using the Adam optimiser (learning rate 0.001), minimising the sum of the binary cross-entropy reconstruction loss and the Kullback-Leibler divergence. Boundary filtering and physical consistency were used to ensure chemical plausibility.

A self-organising feature map network was used to predict the enzymatic conversion yields. The architecture of the feedforward incremental backpropagation network consisted of an input layer with three neurons (X₁, X₂, and X₃), one hidden layer, and an output layer. The incremental mode was chosen to achieve convergence within a few epochs, thereby reducing computational time. Several networks were developed to determine the number of neurons in the hidden layer by varying the number of neurons and observing changes in mean squared error (MSE) and R². The training was performed using a Levenberg-Marquardt backpropagation algorithm in MATLAB R2015b. The transfer functions chosen for the response (output layer) and the hidden layers were the linear function and the hyperbolic Sigmoid Tangent function (tansig). Training and testing were performed on the randomised experimental and augmented data, with 70% allocated to training, 15% to validation, and 15% to testing. The trained network was saved as a MATLAB. mat file for subsequent use.

Models’validation and comparison tools

Predicted values obtained from RSM and ANNs were compared with experimental data using statistical metrics such as the coefficient of determination (R²), the chi-square test statistic (χ²), the Absolute Average Deviation (AAD), the Root Mean Squared Error (RMSE), and the Standard Error of Prediction (SEP). They were calculated using the following equations:

where n is the number of experiments, y e and y p , experimental and predicted system response, and y e m , y p m their corresponding mean values.

Anthocyanin pellets extracted from Roselle aqueous freeze-dried extract represented up to 1.33 ± 0.05 g/5 g of dried calyx powder, and the λ_max for their analysis was found to be 518 nm. Three major compounds detected and identified in aliquots collected by preparative HPLC were analysed by FTMS-ESI in positive ion mode, yielding interesting results. The obtained results are presented in the following Table 2.

Table 2. Mass details of identified compounds.

Apart from the identified compounds, there can be other anthocyanins, which are unidentified, in the studied sample (others may not have been detected because of very low concentration). Although other studies have confirmed the presence of these compounds in Roselle calyx samples, our findings align with the most frequently reported compounds, Dp and Cy. After developing a selective extraction method for anthocyanins from dried Roselle calyces from Guerlé, Senegal, Segura-Carretero et al. [29] identified various components by exact mass and fragmentation patterns using CE-TOF-MS in positive-ion ESI mode. They identified Delphinidin-3-sambubioside and cyanidin-3-sambubioside as the main components. Cyanidin-3,5-diglucoside was identified as a minor component along with cyanidin-3-O-rutinoside and delphinidin-3-O-glucoside. Using HPLC with diode array detection coupled to electrospray TOF and IT tandem MS, Rodriguez-Medina et al. [30] also identified, using positive ionisation mode, Delphinidin-3-sambubioside and cyanidin-3-sambubioside as the main anthocyanins present in Roselle dried calyx. In a study published in 2013, Omotuyi et al. identified up to five classes of compounds and acetylated malvidin (m/z 391.33) as major anthocyanidins in H.S hydrolysate using Mass spectrophotometry [31]. The concerned were pelargonidin (m/z 271.23), Cyanidin (m/z 287), Peonidin (m/z 299.28), Delphinidin (m/z 301), and petunidin (m/z 317.31). In the present study, the significant component, Delphinidin, was followed during transesterification.

As described in the methods, the transesterification reaction was carried out on the Roselle calyx water extract, which contained the identified compounds at specified percentages. During the process, some of the anthocyanins present in the extract were not converted. Meanwhile, as shown in Figure 2, the chromatographic monitoring of Delphinidin-3-sambubioside, the most abundant compound, indicated complete disappearance. The corresponding conversion yield did not reach 100%. This apparent discrepancy can be attributed to competing hydrolysis reactions that produce non-acylated products, to the formation of non-detectable side esters at the monitoring wavelength, and/or to thermal degradation of anthocyanins under prolonged heating. The consumption of the parent substrate via parallel pathways has been shown to occur alongside the formation of target acylated derivatives [2][32]. These pathways may include anthocyanin degradation and secondary reactions during enzymatic modification.

Figure 2. Chromatograms of Hs anthocyanins before reaction (A); acylated Hs anthocyanidin after 72 h of acylation reaction with VL (B); acylated Hs anthocyanidins after 72 h of acylation reaction with MP (C).

As shown inFigure 3, the generated RSM and VAE-ANN data and predictions indicated optimal operating parameters for maximum conversion yield.

Figure 3. Data generation and computing approach.

The conversion yield obtained for each experiment without augmentation is presented inTable 3.

Table 3. Obtained experimental and predicted conversion yields from the CCC matrix without augmentation.

*Replication of the centre point.

3.3.1. Response Surface Methodology

Significant effects of process variables were determined by analysis of variance. The P-values less than 0.05 showed that four effects, Temperature (X₁), Time (X₂), the quadratic effect of Temperature (X₁²), and the quadratic effect of Time (X₂²), were significantly different from zero at the 95.0% confidence level on the conversion yield. It was observed that both temperature and time increased the conversion yield, with the effect of time being more pronounced. However, their quadratic effect reduced the system response due to enzyme behaviour at temperatures above their optimal values. The obtained models, expressed as coded factors, were transformed via variable changes and plotted. The substrate-to-enzyme ratio had the least effect on the conversion yield among the three factors and was therefore fixed at the midpoint of its range. The obtained models with absolute values were:

C_yield(MP) = −1257.81 + 39.12X₁ + 3.89X₂ – 0.02X₁X₂ – 0.30X₁² – 0.02X₂² (12)

And,

C_yield(VL) = −631.94 + 20.76X₁ – 1.05X₂ + 0.03X₁X₂ – 0.17X₁² – 0.00X₂² (13)

Corresponding response surface areas are presented in Figure 4.

Figure 4.Response surface of conversion yield for (A) VL and (B) MP under the effects of time and temperature.

The temperature was found to affect the reaction yields of both the VL and MP systems. This may be due to changes in the reaction medium’s viscosity, substrate solubility, activation, stability, and thermal denaturation of the enzyme [33]. It was observed that, in addition to temperature, time also influences the two systems; the obtained response surfaces show near-linear (VL) and curvature (MP) dependence of yield. The difference in the linearity of response observed between MP and VL systems can be explained by the physicochemical influence of the acyl chain on enzyme-substrate interaction. CAL-B is known to behave as a pocket-limited enzyme, in which acyl donors compete for a confined active site cavity [9][13]. Longer or bulkier chains impose steric hindrance at the entrance to the hydrophobic pocket of CAL-B, thereby altering activation energy and temperature sensitivity. In addition, differences in hydrophobicity modify mass-transfer resistance and substrate solubility in tert-amyl alcohol. Similar steric-governed rate behaviours have been reported for acylated flavonoids and sugar ester synthesis [3][32][33][34]. During the synthesis of phloridzin cinnamate via trans-esterification with Novozym 435® (CAL-B), Enaud et al. (2004) [35] showed that the reaction time depended on temperature: 15 h at 60˚C, 4 h at 80˚C, and 2 h at 100˚C. Turner and Vulfson [36] showed that this enzyme remains active without loss up to 130˚C, a temperature not considered in the present work due to the stability of the substrates. Other works [33][37]-[39] have, however, noted that despite its effectiveness, the effect of temperature lacks clarity and depends on the environment of the enzyme in the case of the synthesis of a sugar ester (as is the case of sambubioside linked to Delphinidin).

3.3.2. ANN Modelling and Optimisation

The AAD, SEP, and RMSE values for the initial non-augmented data and the dataset composed of experimental and augmented data showed that increasing the number of experimental points in the training dataset via VAE improved the network’s performance and, thus, its predictive ability.

The number of ANN hidden neurons was determined by trial observation and comparison of mean square error sums (MSE). Across hidden neuron counts from 1 to 20, the optimal VAE-ANN models were obtained with 15 neurons and 19 and 40 epochs for VL and MP, respectively. So, the topology selected for our network was 3-15-1. Figure 5shows the validation performances of the networks. For both systems, the best validation performance was achieved at epoch 13, with MP outperforming VL.

Figure 5. Validation performance of VL (A) and MP (B) built neural networks.

3.3.3. Comparison between ANN and RSM

RSM and ANN have shown that both can be excellent predictors of conversion efficiency in D-3-sambubioside transesterification in the ranges of considered factors. Figure 6 presents the predicted-experimental plots for VL and MP using RSM and ANN.

Figure 6.Scatter plots of RSM and ANN Experimental CCC matrix response values versus Predicted values for both VL and MP systems.

The values obtained for the statistical parameters used for comparison are presented in Table 4. Both methods have demonstrated good data-fitting and predictive performance.

Table 4. RSM and ANN Experimental and Predicted Optimum with corresponding statistical parameters

*Validation criterion.

The optimal predicted operating parameters for the transesterification of Roselle anthocyanins with VL were identical across both the RSM and ANN methods. With MP, the predicted optimum conditions differed; AAD, RMSE, and SEP values indicated that ANN was more accurate and thus more effective. Although ANN predicted a slightly higher optimum yield than RSM for MP, operating at higher temperatures and longer times may increase energy consumption. Conversely, RSM identified conditions involving lower temperature and reduced residence time for VL. Overall, for both systems and methods, the R² and AAD values fell within the acceptable ranges, indicating that both models were valid for prediction. ANNs (ANN and VAE-ANN) demonstrated superior performance for MP. In contrast, RSM exhibited competitive performance for VL, particularly with respect to χ², with minor discrepancies between experimental and predicted values, indicating that the two were very close. These observations suggest that different reaction mechanisms induced by acyl donor group structures may have influenced the performance of the fitting algorithms. In other words, the efficiency of fitting by minimising the sum of the squared differences between the experimental and predicted responses (RSM) and Backpropagation combined with the Marquart-Levenberg algorithm, which is also a combination of the gradient descent method and the Gauss-Newton method (ANN), may depend on the behaviour of the system and involved mechanisms. Although ANN is often described as the best-fitting method for nonlinear regression, many authors have found that RSM outperforms ANN, noting lower prediction deviation [40][41]. When using a Central Composite Rotatable Experimental Design (CCRD) to model lipase production from used engine oil as the substrate in Burkholderiacenocepacia ST8, Lau et al. [42] found that the RSM model had higher accuracy in predicting lipase activity yield.