Estimation of Total Phenolic Compounds and Non-Targeted Volatile Metabolomics in Leaf Tissues of American Chestnut ( Castanea dentata ), Chinese Chestnut ( Castanea mollissima ) and the Backcross Breeding Generations

The American chestnut (Castanea dentata) was once a dominant tree species in the Appalachian Mountains and played a critical role in the ecological system. However, it was nearly eliminated by chestnut blight caused by the As-comycetous fungus Cryphonectria parasitica. Identification of compounds specific to species and backcross hybrids may help further refine disease resistance breeding and testing. Phenolic compounds produced by plants are significant to their defense mechanisms against fungal pathogens. Therefore, an analytical platform has been developed to estimate the total phenolic content in leaf tissues of the American chestnut, Chinese chestnut (Castanea mollissima), and their backcross breeding generations (B 3 F 2 and B 3 F 3 ) using the Folin-Ciocalteu reagent assay with UV/Vis spectrophotometry which may be used to predict blight resistance. Adsorption (765 nm) results from leaf tissue extraction in methanol/water (95%:5% v/v) and pH 2, show that the variations among these four tree species are significant (ANOVA p = 2.3 × chromatography and mass spectrometry was conducted to identify volatile organic compounds (VOCs) from the leaf of American chestnut, Chinese chestnut, and their backcross hybrids B 3 F 2 and B 3 F 3 . A total of 67 VOCs were identified among all chestnut types. Many of the metabolites associated with the Chinese chestnut have been reported to have antifungal properties, whe-reas the native and hybrid American chestnut metabolites have not. Most of the antifungal metabolites showed the strongest efficacy towards the Asco-mycota phylum. A partial least squares discriminant analysis (PLS-DA) model (R 2 X = 0.884, R 2 Y = 0.917, Q 2 = 0.584) differentiated chestnut species and hybrids within the first five principal component (PCs).


Introduction
The American chestnut tree (Castanea dentata) was a dominant native species in the eastern forests of the United States. Due to its rapid growth, large size, and nut production, it was critical to the U.S forest ecosystem and economy [1].
However, this tree species was devastated by a fungal pathogen, Cryphonectria parsitica [2] starting in 1904 and nearly wiped out by 1945. The virulent strains of the fungus attack the tree through penetration of wounds and bark fissures, killing the bark and cambium layer, preventing the transport of water and nutrients, and reducing the tree to short-statured sprouts or causing mortality [3] [4] [5]. It is difficult to know all the consequences however the loss of these dominant tree species likely significantly changed a wide range of ecosystem services dependent on this species [6]. Because the tree was nearly wiped out before modern forest research there is only speculation on how it affected soil chemistry and food webs. However, the chestnut was likely a more stable and abundant resource for wildlife than other tree species [7]. In addition, the long-term impact of the loss of a dominant tree species could affect local climate regulation [8], regional carbon balance [9], and flood control [10], as well as reducing biodiversity [11] and threatening the sustainable ecosystem [12]. Therefore, the restoration of American chestnuts has received attention and efforts have ensued to restore the species [13].
In the late 20 th century, backcross breeding programs were implemented to produce hybrids from pathogen resistant Asian chestnut species, primarily Chinese chestnut (Castaneamollissima) and American chestnut [14]. The hope is that the sixth generation (B 3 F 3 ) carries American chestnut morphology characteristics [15] but also resistance to the blight from Chinese chestnut [16]. However, the selection of trees with resistance is costly, labor intensive and time-consuming, as the determination of blight resistance can take up to 15 years and may change Journal of Agricultural Chemistry and Environment over time due to enhanced juvenile resistance. Traditionally, resistance tests involve pathogen inoculation in plantations, forest test plantings that receive natural blight pressure [17], or complex genomic sequencing [18]. Therefore, feasible and reliable alternative analysis methods are desired.
As indicated by Lafka et al. each plant has a unique composition of phenolics, therefore the development of optimal condition regarding phenolic extraction is critical [27]. To date, although plant phenolic extraction techniques such as supercritical fluid extraction (SFL) [28] and pressurized liquid extraction (PLE) [29] have been developed, the most commonly applied procedure is the organic solvent extraction. This is likely because both SFL and PLE require high pressure equipment not available in many labs. Common solvents like methanol, ethanol, ethyl acetate, and acetone have been applied to many plant materials [20]. However, the extracting solvent choice affects the recovery of phenolics. For example, methanol was shown to be more efficient in the extraction of lower molecular weight polyphenols [30], while aqueous acetone is better for higher molecular weight compounds such as flavanols [31]. Furthermore, the extracted phenolic profile could also be affected by solvent-to-solid ratio, extraction time, temperature, and extraction pH [32].
The complex, volatile organic compounds (VOCs) profiles emitted from plants have been successfully used in differentiating plant species [33] [34] [35] [36] [37]. A recent study further expanded VOCs pattern analysis to discriminate modified plant hybrids from their parents [38]. To date, many VOC sampling techniques have been developed. Extraction techniques such as steam distillation (SD), simultaneous distillation extraction (SDE), purge and trap, or dynamic headspace have been used in the research. In particular, nondestructive sampling methods such as solid-phase microextraction (SPME) have been extensively applied to sampling VOCs [39]. Furthermore, mass spectrometry based non-targeted metabolomics or metabolic profiling, which can screen biological alterations that correlate to phenotypic perturbations [40], is finding application in a wide range of research including plant biology [41]. For example, Zhao et al.
applied metabolic profiling with gas chromatography-mass spectrometry and successfully revealed plant growth interaction between carbon and nitrogen metabolism [42].
In this study, a Folin-Ciocalteu reagent assay was employed to optimize extraction conditions such as liquid/solid ratio, time, and pH to maximize the yield of total phenolic compounds from chestnut tree leaf tissues. In addition, the to-Journal of Agricultural Chemistry and Environment tal phenolic content (TPC) of species was compared. Extensive analysis using headspace SPME gas chromatography and mass spectrometry was conducted to identify VOCs from the leaf of American chestnut, Chinese chestnut, and their B 3 F 2 and B 3 F 3 hybrids.

Plant Material
American chestnut, Chinese chestnut, and their backcrossing generations B 3 F 2 , and B 3 F 3 were obtained from The American Chestnut Foundation (TACF) via the United States Department of Agriculture Forest Service who is collaborating with TACF on chestnut reintroduction [13]. Backcross hybrid (B 3 F 2 and B 3 F 3 ) experimental material consisted of progeny from orchard trees (open-pollinated) at TACF's Meadowview Orchard [43]. The BC 3 F 2 material consisted of progeny from one mother tree, and the BC 3 F 3 consisted of progeny from three mother trees, which were bulked together for this experiment. Chinese chestnut experimental material was collected from one open-pollinated tree in Asheville, NC that was surrounded by other Chinse chestnut trees, and progeny were thus  width) which usually occur at five to six months of growth. All samples from two independent tests were collected at the same time of the day (at 9-11 am) under Journal of Agricultural Chemistry and Environment uniform light conditions. For each sampling date, leaves from each species were randomly selected to harvest for chemical analysis.
Analysis of volatile organic compounds from leaves, SPME and GC/MS, were made on the same date as the sampling. VOCs samples preparation procedure was based on Chang et al. with modifications [34]. Fresh leaves were immediately chopped into small pieces, and 5 g samples were placed in 1 L glass jars (Environmental Sampling Supply, San Leandro, CA) and sealed with aluminum foil and parafilm. Samples were heated for 30 min in a 35˚C incubator before SPME extraction. SPME was done for 2 hours at room temperature and desorbed at a GC inlet for 5 min at 300˚C. VOCs samples labelled replication 1 to replication 6 were all from the first test, and replication 7 to replication 12 were from a second independent test. For the total phenolic determination, fresh leaves were collected and immediately frozen in liquid nitrogen and stored at −80˚C until they were freeze-dried for total phenolic measurements.

Solvent Extraction
The extraction of phenolic compounds from chestnut tree leaves was based on the procedures described by Lafka et al. with modifications [28]. Briefly, 20 mg of ground tree leaf tissue was placed in a sample vial (Hach, Loveland, CO) with n = 6 for each type of solvent. Samples were extracted with 2 mL of methanol/ water (v/v 95%/5%), ethanol, ethyl acetate, and acetone/water (v/v, 70%/30%) in a shaker (C-24 model, New Brunswick Scientific Co., INC. Edison, NJ) for different extraction times (30 min to 24 hours) at room temperature. The extract was centrifuged at 6000 G for 30 min and the supernatant was transferred and evaporated to dryness in a rotary evaporator (Organomation Associates, Inc, Berlin, MA). The solution was then dissolved in 4 mL ice-cold methanol for F-C assay analysis. For the pH study, prior to organic solvent extraction, the leaf tissue was acidified with HCl to pH range 2 to 6, and n-hexane was added 5:1 (v/w) for 20 min at room temperature. Six replicates (n = 6) of each chestnut tree family in two independent tests were made and analyzed under the same conditions.

Total Phenolic Content (TPC) Determination
The TPC procedure was based on Ainsworth et al. with changes [44]. In general, 10% (v/v) of F-C reagent was made with deionized water. The extracts were then mixed with 200 µL of the F-C reagent and vortexed thoroughly in a sample vial (Hach, Loveland, CO) for 1 minute. The solution was incubated for 10 min at room temperature before adding 0.8 mL of 700 mM Na 2 CO 3 solution into the tube. The mixture was then kept in the dark for 2 hours. The absorbance of the solution was measured at 765 nm using a GENESYS 30 UV/Visible spectrophotometer (Thermo Scientific, Waltham, MA) against deionized water blank. The value of the TPC was determined via a calibration curve (with R 2 = 0.99) prepared with a series of caffeic acid standards (0, 20, 40, 60, 80, 100, and 120 mg/ L). The TPC results were expressed as mg of caffeic acid equivalents per gram of fresh weight leaf tissue (mg CA/g FL).

Headspace SPME Extraction
The SPME technique is a non-destructive sampling method that can be used to collect VOCs in the headspace above samples. Commercially available SMPE fibers coated with 85 µm Carboxen-polydimethylsiloxane (CAR/PDMS) (Supelco, Sigma-Aldrich, PA, USA) were selected. All fibers were conditioned based on the supplier's recommendations at 300˚C for one h before first use. SPME extraction was performed by exposing fibers to the headspace above ground leaf samples for two hours in order to reach chemical and thermal equilibration. Six replicates (N = 6) of VOCs extraction of each chestnut tree family in two independent tests were made and analyzed under the same conditions.

GC/MS Condition
Extracted VOCs were analyzed with an Agilent gas chromatograph (Agilent Technologies 7890A) coupled with Agilent mass spectrometer (Agilent Technologies 5975C) system (GC/MS) with ChemStation software. Separations were done using a DB-1 capillary column (60 m × 320 µm × 1 µm) (Agilent J&W column, Santa Clara, CA). Samples were analyzed in splitless mode. The injector temperature was kept at 270˚C, and was equipped with a 0.7 mm ID SPME inlet liner (Supelco, Bellefonte, PA). The GC oven temperature operation conditions were applied as in previous studies [45]. Briefly, 45˚C for 9 min, 10˚C·min −1 to 85˚C, hold for 3 min, 3 min −1 to 110˚C, hold for 3 min, 3˚C·min −1 to 120˚C, hold for 3 min, and 10˚C·min −1 to 270˚C, hold for 5 min. The carrier gas supplied to the column was helium (99.9999% purity) at a constant flow rate of 2 mL/min.
For the MS detection, the electron impact (EI) was set as 70 eV with the ion source temperature at 230˚C and quadrupole temperature at 150˚C, respectively.

Data Analysis
GC-MS data files were preprocessed for noise filtering, baseline correction, and converted to CDF format with ChemStation(Agilent Technologies, Inc. Santa Clara, CA). The output files were uploaded to XCMS [46] software to process the peak detection, matching, and alignment with the default setting. The data set was then filtered by removing peaks with 75% missing values. The intensity of resultant peaks was further normalized with respect to the sum of the intensities, in which each peak intensity was divided by the sum of all peak intensities in the fraction. The final peak tables were uploaded to MetaboAnalysis [47] software for statistical analysis.
Prior to analysis, all variables were logarithm transformed and mean centered.
Nonparametric univariate method, Kruskal-Wallis Test, was performed to analyze the significance (p-value < 0.05) of peaks among the samples. The false discovery rates (FDR) test with p-values less than 0.05 (pFDR < 0.05) was applied to Journal of Agricultural Chemistry and Environment the results for further adjustment. Spearman correlation rank test was used to generate correlation matrices for the volatile metabolites. Differentiation of plant emissions was analyzed using principal component analysis (PCA) and partial lease squares discriminant analysis (PLS-DA). In addition, clustering techniques, such as K-means and Hierarchical cluster analysis (HCA) were applied.

Optimization of Solvent Extraction Variables
Prior to final analysis of phenolic content from the chestnut tree leaf, the organic solvent extraction procedure was optimized using pooled samples. The extraction of phenolics was further studied by varying extraction pH from 2 to 6 at room temperature for 24 hours. In addition, a set of non-acidified control samples were also extracted under the same experimental condition. As shown in Figure 2, acidification has a significant impact on phenolic extraction.
The addition of acid improved the extraction from methanol and ethanol with the highest extraction content of 14.7 mg/g and 14.3 mg/g respectively. However, acidification caused the loss of phenolic content in ethyl acetate and acetone/water solvents. Based on the high extraction yield and low sample variations, methanol was employed for the phenolic extraction of chestnut varieties.

The Extraction Kinetics
The kinetics of total phenolic extraction was analyzed to determine the extraction rate and appropriate time range. The solid/liquid extraction processes from plant materials were investigated with mathematical models [48] [49] [50]. The empirical models such as Pelog, second order, Elovich, and power law are commonly used to fit the experimental data (Section 1 Supplementary Material (SM)).  The extraction of total phenolics vs time is shown in Figure 3. Extraction kinetics could generally be considered to take place in two phases. A high initial rate of extraction can be observed for all solvents from 0.5 to about 3 hours followed by a slower extraction rate. It should be noted that previous studies suggest that long extraction time could cause degradation of phenolics, however, no decline was observed in extraction yield during 24 hours extraction for all solvents in this study. Several models were used to describe the experimental data with the empirical parameters shown in Table SM1. The R 2 (Table SM1) from model fitting indicates that the phenolic extraction process from chestnut tree leaf tissue is second-order for all solvents that were tested. The R 2 in secondorder models for methanol, ethanol, ethyl acetate, and acetone/water were 0.990, 0.998, 0.999, and 0.996, respectively.

Volatile Organic Compounds Analysis
HS-SPME was employed for VOC extraction from fresh leaves followed by GC/MS analysis to investigate VOCs emitted from four chestnut species (Casta-Journal of Agricultural Chemistry and Environment nea dentata, Castanea mollissima, and their hybrids B 3 F 2 and B 3 F 3 ). The identification of the VOCs in samples was based on the comparison of mass spectrum reference NIST MS library and assisted with the calculated Kovats index comparison with literature. The identified VOCs, their retention times, and the relative abundance (peak intensity) are detailed in Supplementary Information SM Table 2.
ChemStation software used on SPME-CC/MS chromatograms ( Figure 5) showed 52 peaks on average were detected in American chestnut, 30  As shown in Table SM2, a large portion of the identified VOCs were found in the four chestnut hybrids. However, chemicals such as ethyl 2-methylbutanoate, 2-nonen-1-ol, and γ-elemene were primarily detected in parental chestnuts tree leaves samples. Furthermore, compared to VOCs from parental Chinese chestnut, methyl acetate, heptanal, 4-hexen-1-ol acetate, β-phellandrene, p-xylene, caryophyllene, seychellene, and ylangene were identified mainly in American tree leaf samples. Regarding hybrids, (3E)-3,7-dimethyl-1,3,7-octatriene, γ-cadinene, (E)-2-pentene, and 2-methyl-furan was only discovered in B 3 F 2 . To verify whether the VOCs profiles can be used to discriminate the breeding generations and their parental species and to discover potential volatile metabolites that differ between hybrids and their parental Chestnut, chemometric analysis such as univariate (ANOVA) and multivariate analysis are required.

Chemometric Analysis of VOC Profiles from Chestnut Tree Species and Hybrids
Preliminary visual inspection of the TICs of GC/MSleaf VOCs profiles of American, Chinese, B 3 F 2 , and B 3 F 3 revealed a high degree of similarity ( Figure 5).  Table 1.
The K-means algorithm divides the data into a defined number of clusters (K). In this study, four clusters were defined (K = 4) and listed in  K-means clusters help to suggest that VOCs profiles of Chinese chestnut differ from both American chestnut and hybrids. Furthermore, the similarity between hybridized generations is considerably high. However, K-means does not reveal VOCs profile differences between American chestnut and hybrids. In addition to K-means, Hierarchical Cluster Analysis (HCA), aimed to uncover latent structure in terms of a hierarchy of embedded group clusters, was further applied to the dataset [50]. The resulting dendrogram shown in Figure 7 implies three major clusters organized by HCA, namely A, B, and C with some subclusters.
The first group (A) includes VOCs samples from hybrids, especially from the first independent test, and implied that B 3 F 2 and B 3 F 3 shared similar VOCs profiles. The second group (B) contains two subclusters, B 1 and B 2 . B 1 was mainly composed of American chestnut leaf samples, while B 2 primarily consisted of the hybrids. Finally, cluster C included mostly samples of Chinese chestnut except for a few B 3 F 2 samples from the second independent test and an American chestnut sample.

Discussion
Phenolic compounds are important secondary metabolites involved in plant protection against pathogens and pathogen resistance [62]. Therefore, knowing the total phenolic content of American, Chinese, B 3 F 2 , and B 3 F 3 could aid in the restoration of American chestnut and improve understanding of the differences between parental species and hybrids bred for resistance. However, an optimized extraction method needed to be established that takes into the chestnut's phenolic structural complexity and distribution diversity. In this study, extraction variables including solvent type, solvent/mass ratio, pH, and extraction kinetics were examined by colorimetric reaction with the Folin-Ciocalteu reagent and UV/Vis spectrophotometric method. It should be noted that the higher temperature and longer extraction time yield greater phenolic content [48]. However, according to Dai et al., phenolic compounds can be easily hydrolyzed and oxidized over time [20]. Therefore, in this study, the time of extraction was not extended beyond 24 h, and the extraction temperatures above ambient were not considered.
Conventional organic solvents such as methanol, ethanol, ethyl acetate, and acetone/water were selected using a solvent/mass ratio from 20:1 to 200:1 [44] [63] [64]. The highest phenolic extraction content was obtained using ethyl acetate. However, this extraction with ethyl acetate is not significantly different (p > 0.05) from the extractions with other solvents. The best extraction solvent/mass ratio was 150:1 among all the tested solvents.  [48]. In this study, Peleg's, second-order, Elovich and power models were applied to interpret extraction kinetics with second-order kinetics providing the best fits (R 2 over 0.99) for all tested solvents.
Plant phenolic extraction that follows a second-order kinetic process takes place in two subsequent phases. The fast phase occurs early, where the majority of phenolics get extracted quickly to the washing by the solvent. This is followed by a slower phase where the extraction process becomes steady and driven by diffusion [64]. The power law model describes the diffusion process during the extraction. The diffusion exponent n calculated from experimental data was less than 0.5 (n < 0.5), which indicates that Fickian diffusion [66] predominates during leaf tissue extraction.
The total phenolic content from American chestnut, Chinese chestnut, and their backcrossing generations B 3 F 2 and B 3 F 3 has been determined. The highest phenolic content was found in Chinese chestnut trees, the lowest was in the American chestnut, and the two backcross hybrids showed intermediate levels ( Figure 4). Student t-test suggests that the difference between Chinese chestnut, and other tree species were significant (p < 0.05). This suggests that phenolic Journal of Agricultural Chemistry and Environment content may be used to distinguish Chestnut species and hybrids, that are differentiated by blight resistance, Steiner et al. and [38]. In the present study, a total number of 66 volatile compounds were identified from all tree species.
Previous studies suggest the primary function of these varied sesquiterpenes is to deliver messages. This signaling function was found in both plant-microbe interactions [70] and in plant-plant interactions [71].
Almost all volatile metabolites associated with Chinese chestnut were reported to have antifungal or antimicrobial activity individually or constituent components of essential oil extracts (see Table 1). However, the 3 native chestnut metabolites did not show direct antifungal activity except for 2-nonen-1-ol, (E)-2-pentene, and y-cardinene from the hybrid chestnuts were reported to have antifungal efficacy properties.
The detection of variation in VOCs profiles from four tree species was highly dependent on robust statistical methods. The ANOVA test, which is a univariant analysis method, initially identified 18 VOCs as significantly different among tree species. Further analysis required chemometric methods, and the results from this multivariate modeling suggest that the separation of VOCs profiles can be established between American and Chinese chestnut, American chestnut and the hybrids, and Chinese chestnut and the hybrids. However, poor separations were obtained from the hybrids' (B 3 F 2 and B 3 F 3 ) VOC profiles. This supports the hypothesis that VOCs from hybrids are different from the parental species.
The differences between the parental species and the B 3 F 3 generation supports previous evidence that traditional breeding has not yet reached the goal of obtaining American chestnut characteristics while maintaining blight resistance of the Chinse chestnut [43] [57]. Similar behavior in VOCs profiles involving hy-Journal of Agricultural Chemistry and Environment brids, and their parental species have been observed in Citrus fruit [38] and peach tree siblings [72]. Moreover, the combination of univariate and PLS-DA approaches can be utilized when handling biological data [73] [74]. Therefore, the VIP from PLS-DA and p-values < 0.05, and the false discovery rates were calculated. As a result, 13 volatile chemicals showed significantly higher or lower levels among species.
Xuan et al. argued that using a set of data from complex biological samples may provide better discrimination power and more useful information [75].
Therefore, the identification of biomarkers was not considered in this study. The algorithms of cluster analysis focused on dividing data objects into groups or clusters based on shared common characteristics [76].
Two extensively applied cluster analysis methods in metabolomics, nonhierarchical K-means, and HCA were used in this study. The observation of Kmeans (Table 2) suggested the existence of a high similarity of VOCs collected from hybridized generations. In addition, compared to the other tree species, the VOCs profiles of Chinese chestnut leaves differ. However, K-means does not explain the variation between American chestnut leaves VOCs and the hybrids.
This phenomenon could be explained by the genotype intimacy between American chestnut and the hybrids since both B 3 F 2 and B 3 F 3 carried 15/16 portion of American chestnut genes.
HCA was further employed for clustering the individual sample using Euclidian distance and Ward's linkage method. The resulting clusters were represented in a dendrogram to indicate the similarity and distance of each sample in the dataset. HCA results suggest that VOC samples collected from parental species differ from their breeding generations. Clear separation of VOCs profiles can also be made between American chestnut and Chinese chestnut. However, a high similarity of VOCs profiles was found in the two hybrids. HCA was consistent with the PLS-DA results, where clear separation can be made between parental chestnut tree species while poor separation was made between hybrids.

Conclusions
In the present study, we have established an extraction method to determine the total phenolic content from chestnut tree leaf samples. Extraction conditions were optimized for solvent type, solvent/mass ratio, pH and extraction time.
Methanol was selected as an appropriate solvent for the extraction. The optimized solvent/mass ratio, extraction time, and pH were 100:1, 24 hours, and pH = 2, respectively. The highest conventional phenolic content was found in the Chinese chestnut, while the lowest was in the American chestnut. The simple analytical methods described here along with chemometrics have proven to be a powerful tool in chestnut hybrid discrimination.
This study also demonstrated the potential of using plant leaf tissue VOCs profiles to discriminate between American, Chinese, and their hybrids B 3 F 2 and B 3 F 3 via non-destructive headspace SPME sampling with untargeted volatile Journal of Agricultural Chemistry and Environment metabolomics. A total of 67 VOCs was identified from all tree species. A strong emission of cis-3-hexenyl acetate was found in all tested samples. Although there were high similarities among tree species' VOCs profiles, distinctions can be approached using chemometric analysis. A PLS-DA model showed that, compared with their parents, the VOCs from hybrids plant leaf is significantly different. The variations of thirteen VOCs among tree leaf samples were considered significant. The similarities of samples were analyzed and visualized by clustering analysis such as K-means and HCA. Results from this study provide a feasible and useful method to rapidly classify four chestnut tree species using a small amount of leaves. The results from the study indicate that the advanced breeding generation (BC 3 F 3 ) had markedly lower phenolic compounds than the Asian parent, which may be indicative of a reduced disease defense mechanism, as has been exhibited in other species. The BC 3 F 3 did not exhibit VOC leaf chemistry similar to the American parent, suggesting a departure from desired traits of having similar physiology/morphology of the American chestnut in all ways except blight resistance. However, results indicated slight improvements from traditional breeding in phenolic compound content. Future research using leaf chemistry may provide a better understanding of breeding effects on American chestnut restoration. Journal of Agricultural Chemistry and Environment

Section 1 Extraction Kinetics
The hyperbolic model, Peleg's model is expressed as: where C is the concentration at time t, K 1 is the initial extraction rate at t = 0, and K 2 is the maximum extraction yield.
The second-order kinetic model can be described by Equation (2): where: k is the extraction rate constant, C s is the extraction capacity, and C t is the concentration of phenolics in the solution at any time. Its linear form can be expressed: The initial extraction rate is represented as h, where The Elovich model is shown in Equation (6): q dq e dt β α − = (6) where q is the amount of absorbance at time t, and α, β are constants. Its linear form can be expressed as ( ) Under the diffusion controlled mechanism, the extracted amount can be described by the power law model: where C is a dimensionless quantity, B is a constant that describes the particleactive substance system, and n is the diffusion exponent. Journal of Agricultural Chemistry and Environment The PCA model derived from GC-MS spectra of all the VOCs samples was applied to the full data set, in which five principal components cumulatively account for 61.7% of the data variation ( Figure SM1) Figure SM1. The variations that explained by PCs from PCA modeling of VOC profiles from American, Chinese and two backcross hybrids generations of chestnut.