Predicting the reaction rates between flavonoids and methylglyoxal by combining molecular properties and machine learning

The kinetics of the reaction between methylglyoxal (MGO) and epigallocatechin gallate have been investigated at pH 7.4 and 37 ◦ C, and the kinetic data were combined with previously obtained data of six other flavonoids to develop a model that allows to predict the trapping capacity of MGO based on the molecular properties of the seven flavonoids. The observed data were augmented by using synthetic minority oversampling technique forming a new data set that was used to create the predicting models for the trapping rate constant of MGO by flavonoids via principal component regression (PCR) and back-propagation neural network algorithm, respectively. The PCR model based on the first six principle components was robust and accurate comparing other created models, with an associated root-mean-square error value of 8.02 × 10 (cid:0) 7 on the testing set. This work provides quantitative structure-activity models for rapid and accurate prediction of the trapping rate constant of MGO by flavonoids


Introduction
Methylglyoxal (MGO) is a yellow hygroscopic liquid known as 2-oxopropanal, pyruvaldehyde, or 2-ketopropionaldehyde (Wang & Ho, 2012).MGO can be found in various foods and beverages (Nemet et al., 2006;Zhu et al., 2019) as well as in living organisms (Thornalley, 2008) where it is generated from sugar autoxidation, lipid degradation, microbial fermentation or the Maillard reaction (Wang & Ho, 2012).Investigations show that MGO may influence the quality of foods and cause adverse effects on humans due to its high reactivity (Lund & Ray, 2017).It is known that MGO can react with nucleophilic side chains (lysine, arginine and cysteine) on proteins (Fig. 1) leading to formation of advanced glycation end-products (AGEs) (Lo et al., 1994), and react with the ɑ-amino group of free amino acids generating Strecker aldehydes (Lund & Ray, 2017).Strecker aldehydes are responsible for off-flavour in food products such as ultra-high temperature (UHT) processed milk (Jansson et al., 2017), pilsner beer (Bravo et al., 2008), and juices (Perez-Cacho & Rouseff, 2008).MGO-derived structural modification of proteins may influence digestion and absorption lowering the nutritional values of foods (Nowotny et al., 2018).It is well-established that AGEs formed in vivo are associated with chronic diseases (Thornalley, 2008), while the role of dietary AGEs on human health is still a matter of debate (Hellwig & Henle, 2014).Therefore, controlling the content of MGO is of significant importance to improve food quality and human health.
Flavonoids are secondary metabolites in plants and considered natural scavengers of MGO (Shao et al., 2014;Zhu et al., 2020a).MGO is trapped at the C6 and C8 positions of the A-ring of flavonoids forming mono-and di-MGO adducts (Fig. 1) by an electrophilic substitution reaction (Shao et al., 2014;Zhu et al., 2019).The MGO trapping ability is mainly dependent on the molecular structure of flavonoids (Shao et al., 2014;Xie & Chen, 2013;Zhu et al., 2020a).An A-ring with a 5,7-dihydroxy structure is favourable for the trapping activity, while the number of hydroxyl groups on the B-ring seems not to influence the trapping ability (Shao et al., 2014;Xie & Chen, 2013).The heterocyclic C-ring can also influence the trapping efficiency of MGO; a double bond at C2 and C3 of the C-ring weakens the trapping capacity, while a hydroxyl group at C3 of the C-ring is beneficial for the trapping efficiency (Shao et al., 2014).This qualitative description of the molecular structure of flavonoids can be used to compare the reactivity of different flavonoids, but it is difficult to precisely predict kinetics for the trapping reaction of MGO by flavonoids.In our previous work, kinetics simulation for the competitive reaction between MGO with protein and flavonoids were performed in a sample system relevant to UHT milk (Zhu et al., 2020a).We found that some flavonoids could trap MGO, but it was difficult to efficiently inhibit the modification of protein by MGO due to the low trapping rate of flavonoids.Most studies concerning the trapping reactions of MGO by flavonoids focus on qualitative results rather than providing corresponding kinetics data (Shao et al., 2008;Yang et al., 2017).Therefore, the lack of kinetics data limits the understanding of how the structure of flavonoids affects the trapping capacity and hence limits the application of flavonoids to compete efficiently with nucleophilic sites on proteins for MGO.In addition, there are more than 5000 different structures of flavonoids in nature (Ross & Kasum, 2002), so it would be extremely laborious to determine rate constants for the reaction between MGO and all flavonoids.To close this gap, in-silico model techniques can be applied to create predicting models for the trapping rate constants of MGO by combining obtained kinetics data with molecular properties of flavonoids.
In the present work, the apparent second order rate constant for the reaction between epigallocatechin gallate (EGCG) and MGO was determined at pH 7.4 and 37 • C. The kinetics data of EGCG and the six flavonoids (trans-resveratrol, naringenin, apigenin, kaempferol, fisetin, epicatechin) previously studied (Zhu et al., 2019;2020a;2020b) were regarded as dependent variables of the observed data, and the corresponding properties of the molecules (i.e.molecular descriptors) were regarded as independent variables.The Pearson correlation between molecular properties of flavonoids and experimentally determined second-order rate constants of trapping MGO were analyzed to evaluate the effect of molecular properties on the trapping capacity.The observed data were augmented by using synthetic minority oversampling technique (SMOT), and the augmented data together with observed data were used to create predicting models by using principal component regression (PCR) and back-propagation neural network (BPNN) algorithms, respectively.Finally, the root mean squared error (RMSE) was used to compare the performance of different algorithm models.

Sample preparation of analytes
Stock solution of EGCG (5 mM) was prepared in ethanol, and MGO (0.1 M) was prepared in phosphate buffer (pH 7.4, 0.1 M).The stock solutions were stored at 4 • C and used within two days.EGCG stock solution (10 μL) was mixed with different volumes of MGO stock solution (10 μL, 15 μL, 20 μL, 25 μL, 30 μL) and phosphate buffer (pH 7.4, 0.1 M) making a series of mixtures with the final volume of 1 mL, which allowed concentration of EGCG and MGO of 0.05 mM and 1-3 mM, respectively.The concentrations of MGO were kept at least twenty times higher than the concentration of EGCG to create pseudo first-order reaction conditions.Reaction mixtures were incubated at 37 • C in a water bath from 0 to 20 min, and 10 μL glacial acetic acid was used to terminate the reaction between EGCG and MGO.Reaction mixtures were stored at − 20 • C until further analyses.Three independent replicates were conducted for all reaction conditions.

Determination of EGCG content
The content of EGCG in the samples was determined by HPLC analysis using a Dionex Ultimate 3000 system (Thermo Scientific, CA, USA) coupled with Diode Array Detector (DAD).A Zorbax Eclipse Plus C-18 column (Agilent Technologies, Glostrup, Denmark; 100 (L) × 2.1 (ID) mm, 1.8 μm particle size) with a guard column (Agilent Technologies, Glostrup, Denmark; 5 (L) × 2.1 (ID) mm, 1.8 μm particle size) was used for the separation.Column temperature was maintained at 25 • C, and the autosampler was set to 10 • C. The mobile phases were composed of 0.1% TFA in Milli-Q water (solvent A) and 100% acetonitrile (solvent B).The following gradient was used at a flow rate of 0.25 mL/min: 95%-60% solvent A from 0 to 14.1 min, 60%-5% solvent A from 14.1 to 14.2 min, constant flow of 5% solvent A from 14.2 to 15.8 min, 5%-95% solvent A from 15.8 to 15.9 min, and then 95% solvent A from 15.9 to 20.4 min.The injection volume was 10 μL, and the DAD was set at 320 nm.The calibration curve was y=0.1492x-0.0178(n=10, R 2 =0.9991), and the limit of detection (LOD) and limit of quantification (LOQ) were 5.5 and 16.6 μM, respectively.

Calculation of molecular properties
All computational analyses were performed using the Chem3D 16.0 program (Cambridge Soft., Cambridge, MA, USA).Molecular dipole, Fig. 1.Competitive reaction of MGO with nucleophilic side chains of proteins (lysine, arginine and cysteine) and EGCG.Only the substitution at C6 for the EGCG mono-adduct is presented for simplicity, but similar substitution may also occur at C8. potential energy (PE), total energy (TE), and Löwdin charge (LC) were calculated by using the GAMESS interface, and molecular geometries were optimized at B3LYP/6-31G (d, p) level of the density functional theory (DFT).TE is the sum of the PE and the kinetic energy (Tachikawa & Osamura, 2000).PE is used to represent the relationship between the energy of a molecule and its geometry (Lewars, 2016).The LC is a type of partial charge and used for a qualitative understanding of the structure and reactivity of molecules (Mondal et al., 2003).Other properties were computed after the energy minimization by using the MM2 force field with RMS (root mean square) gradient of 0.01.The energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) were computed by using the Molecular Orbital interface.Steric hindrance (SH), Gibbs Free Energy (GFE), LogP, LogS, molecular topological index (MTI), total connectivity (TC), total valence connectivity (TVC) were computed by using the Computer Properties interface.SH is one of steric descriptors associated with size and shape of the molecule (Hollett et al., 2006).Gibbs free energy is used to determine the spontaneity of a reaction and to represent relative stability of the molecule (Liu et al., 2019).LogP is a parameter used to describe the molecular hydrophobicity (Begnaud et al., 2016), while LogS is used to express the aqueous solubility of a compound (Sun, 2004).MTI is defined as a numerical descriptor of the molecular structure that is a numeric value or a sequence for a given molecular structure, which shows the physical, chemical and biological properties of a molecular graph (Raychaudhury & Pal, 2015).TC and TVC are two molecular topological indices that are related to the relative possibility of each bond in a molecule to have an encounter with another bond in the same molecule or in another neighbouring molecule during bimolecular collision (Eddy & Essien, 2017).The energy difference in a molecule between the HOMO and LUMO was recorded as ΔE gap .Dipole-x, dipole-y and dipole-z are the three components of the total dipole moment in three-dimensional Cartesian coordinate system.All molecular properties were calculated using default settings, and water was selected as the solvent for the GAMESS calculations.

Data augmentation
The data that were available for the seven flavonoids were not sufficient to create a model for the prediction of the rate constant between polyphenol and MGO, and therefore, it was necessary to augment the data before the construction of models.In the present work, new instances of 70 were synthesized (Supplementary materials, Table S1) based on the data of the seven original flavonoids by using the SMOT algorithm.The synthesized instances were generated from the feature space between original instances (data from seven flavonoids) by generating data points on the line segment connecting a randomly selected data point and one of its K-nearest neighbours (Elreedy & Atiya, 2019).

Creating models of prediction
The observed data were merged with the augmented data to form a new dataset that was randomly divided into a training set and a testing set in a ratio of 7:3.The training set was used to create predicting models for the trapping rate constants of MGO by flavonoids, while the testing set was used to evaluate performance of models by comparing the RMSE values.

Principal component regression
Principal component regression (PCR) is a multiple regression analysis that uses principal components of variables as predictors instead of observed variables leading to reduction of the dimensionality of model input and to overcome the multi-collinearity problem of variables (Umali & Barrios, 2014).
In the present work, the training set was normalized using the scale function in the R project before performing principal component analysis, and extracted principal scores were used as regressors to build a prediction model (Kawano et al., 2018).

Back-propagation neural network
Back-propagation neural network (BPNN) is known as error back propagation network and can minimize an error backwards while information is transmitted forward (Wang et al., 2015).A typical BPNN consists of one input layer, number of hidden layers, and one output layer.The input layer serves to pass the input vector to the network, the hidden layers play computation roles, and the output layer has the response for outputting values.A single hidden layer BPNN can approximate any continuous nonlinear function by arbitrary precision with a sufficient number of neurons (Wang et al., 2015).Therefore, it has been widely used to predict complex nonlinear systems.The number of neurons was the main tuning parameter during the training process, and a threshold of 0.001 was used as stopping criteria for training.In the present work, the number of neurons of the hidden layer was optimized in the range of 3-15.

Statistical data analysis
All curve fittings and calculation of rate constants between EGCG and MGO were carried out in the OriginPro 2016 software (OriginLab Co., Northampton, USA).The fitting parameters were estimated iteratively using the least square method based on the algorithm of Levenberg-Marquardt. Adjusted coefficients of determination (R 2 adj ) were used to evaluate the performance of the curve fitting.Pearson correlation analysis of variables and data visualization were performed in the R project (version 3.6.3)with the ggplot2 and packages.Data augmentation (SMOT algorithm), PCR and BPNN were performed in the R project (version 3.6.3)with the DMwR, factoextra, neuralnet package, respectively.The values of RMSE were also calculated in the R project (version 3.6.3).The statistical significance of the parameters of the PCR models were evaluated at the level of 0.001 (P<0.001).

Kinetics of the reaction between EGCG and MGO
The kinetics of the reaction between EGCG and MGO was investigated at pH 7.4 and 37 • C by measuring the change of EGCG concentration as a function of reaction time.EGCG was not stable during the process of incubation and degraded due to isomerization and polymerization (Komatsu et al., 1993).Therefore, the loss of EGCG during the process of incubation with MGO was due to both the trapping of MGO and its degradation.The degradation of EGCG has been reported to follow first-order kinetics in aqueous solution (Li et al., 2011), and the degradation rate constant (k deg ) could thus be obtained by fitting the change of concentration of EGCG incubated alone.In the present work, the change in chromatographic peak area of EGCG incubated alone was fitted to a single exponential decay curve (eq.(1)) as a function of incubation time (Fig. 2A), providing k deg of (1.1 ± 0.1) × 10 − 3 s − 1 .
In eq. ( 1), A t is the chromatographic peak area of EGCG, A 0 is the initial peak area of EGCG, and t is the incubation time.As shown in Fig. 2A, EGCG was almost completely degraded when it was incubated alone for 120 min indicating that it was possible to follow the full degradation process of EGCG by UHPLC analysis.
Similarly, the decay in chromatographic peak area of EGCG incubated together with an excess of MGO (at least 20 folds) was recorded and fitted to a double exponential equation (eq.(2)), providing the pseudo first order rate constant (k obs ) as shown in Fig. 2B.
In eq. ( 2), the sum of A 1 and A 2 is equal to the initial peak area of EGCG, and k deg is the degradation rate constant obtained from the EGCG incubation experiment (eq.( 1)).The fitted apparent k obs was almost eight folds higher than k deg when EGCG (0.05 mM) was incubated with MGO (3 mM), and the required time for complete consumption of EGCG was shortened to 20 min.This suggests that most of EGCG participated in the trapping process of MGO, while only minor levels were degraded.The k obs values were found to depend linearly on the MGO concentration, which allowed determination of the apparent second order rate constant (k 2 ) from the slope determined by linear regression; k 2 = (2.6 ± 0.1) M − 1 ⋅ s − 1 , as shown in Fig. 2C.
In our previous work, the apparent second order rate constants were reported for the reaction between MGO and six different flavonoids at the same reaction conditions as employed in the current work (pH 7.4, 37 • C) (Zhu et al., 2019;2020a;2020b).As show in Fig. S1 (Supplementary materials), the investigated polyphenols had different MGO trapping rate constants, which decreased in the following order: EGCG > epicatechin > naringenin > kaempferol > trans-resveratrol > apigenin > fisetin.Trans-resveratrol is a stilbenoid compound and was regarded as a flavonoid lacking the heterocyclic C-ring in the present work.Naringenin represents the flavanone compound, apigenin represents flavone compound, while kaempferol and fisetin represent flavonols with different positions of hydroxyl groups.EGCG and epicatechin represent a flavanonol compound with or without a galloyl group at C3, respectively.EGCG presented the highest trapping rate (Fig. S1, Supplementary materials).The lack of heterocyclic C-ring of trans-resveratrol and the existence of a double bond between C2 and C3 reduced the trapping rate, while the hydroxyl at C3 or C5 and the galloyl group at C3 increased the trapping rate.These results were consistent with previous published results (Lund & Ray, 2017;Xie & Chen, 2013), where electron-donating groups of flavonoids were found to increase the MGO trapping reactivity, while electron-withdrawing groups lowered the reactivity.The effect of functional groups of flavonoids on the trapping ability of MGO can be attributed to the change in the electronegativity of reactive sites, hereby influencing the electrophilic attack of the MGO.Moreover, slightly alkaline pH can increase the MGO trapping capacity due to increase of the nucleophilicity of the reactive sites of flavonoids (Shao et al., 2008).In our previous study, a Lederer-Manasse type reaction mechanism was suggested for the trapping of MGO by naringenin (Zhu et al., 2019).It was confirmed that the alkaline condition favours the deprotonation of flavonoids generating a nucleophilic phenolate, which increased partial electron density at the reactive sites of flavonoids (Zhu et al., 2019).Therefore, the electronegativity of active sites of flavonoids is very important on the trapping capacity of MGO.

Correlation between molecular properties and trapping rates
In the present work, eighteen molecular properties reported to affect reactivity (Begnaud et al., 2016;Cheng et al., 2018;Liu et al., 2020;Tachikawa & Osamura, 2000) were calculated for the seven selected flavonoids, and are listed in the Supplementary materials (Table S2) together with the corresponding trapping rates of MGO.The calculated eighteen molecular properties together with their Pearson correlation with trapping rate of MGO are described in a matrix in Fig. 3.The intensity of correlation was used to represent the effect of molecular properties of flavonoids on the trapping rate of MGO.Positive correlations represent promoting effects on trapping rates, while negative correlations represent properties that hinder trapping.Only five parameters were found to correlate strongly with the trapping rate constants of MGO; LogP, GFE, PE, TE, MTI had absolute values of correlation coefficients higher or equal to 0.85.LogP was a significant parameter frequently used in the development of quantitative structure-activity relationships (Begnaud et al., 2016).In the present work, the value of LogP of flavonoids was found to have the highest negative correlation with the trapping rate constants of MGO, which indicates that high hydrophilicity of flavonoids aids an effective trapping of MGO (Fig. 3, Table S2).A negative GFE value is necessary for a spontaneous chemical reaction, and a more negative GFE value implies a more powerful driving force towards the products (Zeng et al., 2017).All seven flavonoids had negative GFE values (Supplementary materials, Table S2), and had the same GFE difference between flavonoid and corresponding mono-adduct (Supplementary materials, Table S3).This result indicates that the reaction between flavonoids and MGO is spontaneous and explains the reason for GFE playing a strong negative correlation with the trapping rate constants of MGO (Fig. 3).Similarly, the PE of flavonoids also showed a strong negative correlation with the trapping rate constants of MGO (Fig. 3), because a low PE means low requirement of energy for the trapping reaction (Tachikawa & Osamura, 2000).TE is the sum of PE and kinetic energy and is therefore also negatively correlated to the trapping rate constants of MGO (Fig. 3).MTI is another important parameter and has previously been widely used for the investigation of quantitative structure-activity relationship (Liu et al., 2020;Raychaudhury & Pal, 2015).From our results, MTI of flavonoids was found to be positively correlated with the trapping rate constants of MGO (Fig. 3), which indicates that the use of MTI to predict the trapping rate constants is feasible.
Other parameters of flavonoids also presented certain negative/ positive correlations with the trapping rate constant of MGO; e.g., TC (− 0.48), SH (− 0.53), dipole-y (0.0.66), dipole (− 0.57), dipole-z (0.61), LUMO (0.51) and ΔEgap (0.49) (Fig. 3).Both TC and TVC have been found to correlate excellently with the properties of some molecules (Eddy & Essien, 2017).In the present work, TC and TVC showed negative correlations with the trapping rate constants of MGO.SH was also negatively correlated with the trapping rate constants of MGO, indicating that the attack of MGO was limited by the changes in molecular structure caused by the increase of SH.It has been reported that the shape and size of a molecule could influence the value of SH, and further to influence the physical and chemical properties of a molecule (Hollett et al., 2006).Dipole moment is used to represent the intermolecular interactions, and a higher dipole moment indicates stronger intermolecular interactions (Targema et al., 2013).In our study, the dipole moment presented a negative correlation with the trapping rate constants of MGO, and the absolute values of correlation coefficient between trapping rate constants of MGO and the components of dipole moment in Cartesian coordinate system (dipole-y and dipole-z) exceeded 0.6.It has been reported that the dipole moment increases with a decrease in ΔE gap (Wang et al., 2003).Therefore, ΔE gap showed a positive correlation with the trapping rate constants of MGO by flavonoids (Fig. 3).
It is known that the HOMO and LUMO orbitals represent electron donating and electron accepting ability, respectively, for a molecule.Therefore, high HOMO value would contribute to the electrophilic attack of MGO on flavonoids.However, the correlation coefficient was only − 0.02 between HOMO and the trapping rate constants of MGO, whereas LUMO had a correlation coefficient of 0.51 (Fig. 3).The value of HOMO was almost the same for all the investigated flavonoids (~11 eV), while the value of LUMO were highly influenced by the structure of flavonoid (~1 eV to ~ − 4 eV) (Supplementary materials, Table S2).In fact, the parameter ΔE gap has been reported to be more significant than the single HOMO or LUMO value for the reaction rate (Cheng et al., 2018), and ΔE gap was used to reflect the kinetic stability of a compound towards reactions involving electron transfer or rearrangement (Granold et al., 2018).Therefore, it was no surprise that ΔE gap had a positive correlation (0.49) with the trapping rate constants of MGO.
Furthermore, LogS presented a slightly positive correlation (0.32) with trapping rate constants, which means that the aqueous solubility of flavonoids could improve the trapping capacity of MGO.The small correlation coefficient of dipole-x and trapping rate constant (0.11) indicates that the horizontal component of dipole hardly influences the trapping reaction.In addition, it has been widely accepted that C-6 and C-8 of the A-ring (trans-resveratrol at C-4 and C-6, Fig. S1) are the active sites of trapping MGO.Löwding charge (a type of partial charge) of selected flavonoids did not present large correlation with the trapping rate constants of MGO (Fig. 3).

Creating and evaluation of predicting models
A good predicting model requires a large dataset, otherwise the obtained model will have poor prediction power (Antoniou et al., 2017).Most experimental data are often not easy to obtain or to determine as experiments can be laborious and costly.Currently, data augmentation technology is used to alleviate this challenge by using various transformations to generate new data from the actual data, but these transformations are normally performed in image classification or speech recognition.Reports on non-image data augmentation are still lacking, but SMOT is gaining increased interest among researchers (Jia et al., 2020).SMOT can produce synthetic data from actual data by randomly selecting nearest neighbours.Thus, if the actual data is highly representative, the production of new data will be more diverse.In the present work, the selected seven flavonoids were highly representative for typical flavonoids (Fig. S1, Supplementary materials), representing stilbene, flavanone, flavone, flavonol and flavanonol compounds.It is therefore expected that the augmented data produced via SMOT were diversified and would create a predicting model without any overfitting.
Three parameters of molecular structure including HOMO, dipole-x and LC(C8) were removed and were not used to create predicting models due to the extremely weak correlation with the trapping rate constants of MGO (HOMO: 0.02, dipole-x: 0.11, LC(C8): 0.09).In the present work, a typical BPNN was trained by using the training set, consisting of one input layer, one hidden layer and one output layer.The neuron number of the input layer is comprised by fifteen molecular properties of flavonoids, and the output layer had only one neuron, and its output is the predicted trapping rate constants of MGO by flavonoids.The number of neuron of the hidden layer was optimized in the range of 3-15, and the corresponding RMSE value in the training set and testing set for BPNN are shown in Table S4 (Supplementary materials).RMSE values in the training set were significantly lower than in the testing set, meaning that BPNN only presented a good performance on the training set and not on the testing set.This result could be attributed to the overfitting of trained BPNN because BPNN easily converges to a local minimum leading to a poor ability of generalization.In addition, the determined trapping rate constants covered the range of 4.4 × 10 − 3 to 2.6 M − 1 s − 1 (Table S2, Supplementary materials), which means that the current precision of BPNN is insufficient for the requirement of prediction.
The PCR method was therefore chosen to examine if it was possible to create a predicting model with higher accuracy.The PCR method decreases the requirement of data size via the reduction of variable dimensions.In other words, in the PCR process, one first performs a principal component analysis to reduce the number of variables and then selects a few components as new explanatory variables to develop a regression model (Kawano et al., 2018).As shown in Fig. 4, the first three components cumulatively contributed to 91.5% of the total variance, and their eigenvalues were >1.Therefore, the first three components were initially used to fit the regression model.The adjusted coefficients of determination (adjusted R 2 ) of the model reached 0.9375, and the p-value and all coefficients of the model reached significance levels (p<0.001,Table 1).However, this model based on the first three components did not exhibit good performance on the testing set, with most of data points being very different from the line y = x and the RMSE value only reached 1.54 × 10 − 1 (Fig. 5A), indicating that a relatively

Table 1
The evaluation of parameters for the first three components and the first six components created models. (

Fig. 2 .
Fig. 2. (A) The decay in the chromatographic peak area of EGCG (0.05 mM) incubated alone at pH 7.4 and 37 • C in 0.1 M phosphate buffer.The solid line fitted by an exponential decay curve was used to determine k deg , the corresponding first-order degradation rate constant.(B) The decay in the chromatographic peak area of EGCG during the reaction between EGCG (0.05 mM) and MGO (3 mM) at pH 7.4 and 37 • C in 0.1 M phosphate buffer.The solid line fitted by using equation (1) was used to determine k obs , the observed pseudo first-order rate constant between EGCG and MGO.(C) The observed pseudo first-order rate constants (k obs ) plotted against MGO concentration (1-3 mM) to determine the second-order rate constant (k 2 ) as the slope of the linear regression.

Fig. 3 .
Fig. 3. Correlogram of molecular properties and trapping rate constants for observed data.Positive correlations are displayed in red and negative correlations in blue colour.The intensity and area of colour are proportional to the correlation coefficient.RC, Rate Constant; LC (C8), Löwding charge (C8); LC (C6), Löwding charge (C6); MTI, Molecular topological index; SH, Steric hindrance; TE, Total energy; PE, Potential energy; GFE, Gibbs free energy; TVC, Total valence connectivity; TC, Total connectivity.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4 .
Fig. 4. Scree plot representing the eigenvalues (black histogram) and the cumulative variances percentage (red line-symbol) for the principal components.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 1) First three components created model