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. 2024 Jan 19;14(5):3186–3201. doi: 10.1039/d3ra07960k

A simple and reliable QSPR model for prediction of chromatography retention indices of volatile organic compounds in peppers†

Shahin Ahmadi a,✉, Shahram Lotfi b, Hamideh Hamzehali c, Parvin Kumar d
PMCID: PMC10797599  PMID: 38249679

Abstract

Worldwide, various types of pepper are used in food as an additive due to their unique pungency, aroma, taste, and color. This spice is valued for its pungency contributed by the alkaloid piperine and aroma attributed to volatile essential oils. The essential oils are composed of volatile organic compounds (VOCs) in different concentrations and ratios. In chromatography, the identification of compounds is done by comparing obtained peaks with a reference standard. However, there are cases where reference standards are either unavailable or the chemical information of VOCs is not documented in reference libraries. To overcome these limitations, theoretical methodologies are applied to estimate the retention indices (RIs) of new VOCs. The aim of the present work is to develop a reliable QSPR model for the RIs of 273 identified VOCs of different types of pepper. Experimental retention indices were measured using comprehensive two-dimensional gas chromatography coupled to quadrupole mass spectrometry (GC × GC/qMS) using a coupled BPX5 and BP20 column system. The inbuilt Monte Carlo algorithm of CORAL software is used to generate QSPR models using the hybrid optimal descriptor extracted from a combination of SMILES and HFG (hydrogen-filled graph). The whole dataset of 273 VOCs is used to make ten splits, each of which is further divided into four sets: active training, passive training, calibration, and validation. The balance of correlation method with four target functions i.e. TF0 (WIIC = WCII = 0), TF1 (WIIC = 0.5 & WCII = 0), TF2 (WIIC = 0 & WCII = 0.3) and TF3 (WIIC = 0.5 & WCII = 0.3) is used. The results of the statistical parameters of each target function are compared with each other. The simultaneous application of the index of ideality of correlation (IIC) and correlation intensity index (CII) improves the predictive potential of the model. The best model is judged on the basis of the numerical value of R2 of the validation set. The statistical result of the best model for the validation set of split 6 computed with TF3 (WIIC = 0.5 & WCII = 0.3) is R2 = 0.9308, CCC = 0.9588, IIC = 0.7704, CII = 0.9549, Q2 = 0.9281 and RMSE = 0.544. The promoters of increase/decrease for RI are also extracted using the best model (split 6). Moreover, the proposed model was used for an external validation set.

A simple and reliable QSPR model for the retention indices (RIs) of 273 identified volatile organic compounds (VOCs) of different types of pepper was developed with CORAL software. The proposed theoretical model is applied to estimate the retention indices (RIs) of new VOCs.graphic file with name d3ra07960k-ga.jpg

1. Introduction

Peppers are among the most ancient spices known to man and are extensively harvested all over the entire globe. Pepper fruits contain a high quantity of constituents advantageous to human health, such as antioxidants, minerals, vitamins (mainly A, C, and E), polyphenols and carotene. All types of pepper are eaten fresh or dried and are used in the food industry as additives (coloring and flavoring agents) because of their unique pungency, color, flavor, and aroma.1–3 The piperine alkaloid (as the (E,E)-isomer), which is responsible for pungency, and the volatile essential oils that provide flavour and aroma are primarily accountable for the quality of peppers as rated by humans.4,5 However, other compounds have also been identified in peppers, such as terpenes, flavonoids, steroids, unsaturated fatty acids, and polysaccharides. Furthermore, the essential oil derived from the distillation of pepper contains various taste and flavouring components: e.g. oxygenated monoterpenoid compounds, monoterpene hydrocarbons and oxygenated compounds, sesquiterpene hydrocarbons and oxygenated compounds, oxygenated sesquiterpenes, and phenolic compounds. These compounds are designated as volatile organic compounds (VOCs).4,6,7 The essential oils of peppers can also be employed as antioxidant, antiseptic, antibacterial, antimycotic, anti-epileptic, anti-inflammatory, diuretic, antipyretic, anthelminthic, and carminative agents.8,9

Numerous reports have been published for the identification and characterization of diverse VOCs of peppers.10–13 Gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) techniques are generally employed for the quantitative determination of volatile compounds in peppers.14,15 Other techniques such as proton-transfer-reaction time-of-flight mass spectrometry (PTR-ToF-MS), two-dimensional gas chromatography with flame ionization detection (GC × GC-FID), quadrupole mass spectrometry (GC × GC-qMS) and time-of-flight mass spectrometry (GC × GC/TOFMS) are also applied to identify VOCs.5,10,16

In chromatography, the chemical structure of compounds is identified by comparing obtained peaks with a reference standard. However, in some cases, reference standards may be unavailable or the chemical information about VOCs may not be registered in reference libraries. To reduce these limitations, theoretical techniques for estimating the retention index (RI) of new VOCs are employed. Hence, the quantitative structure–property/activity relationship (QSPR/QSAR) is employed to predict the retention index (RI).17 QSPR/QSAR is a significant theoretical technique used to establish mathematical models that predict the properties/activities or endpoints of compounds, which have been newly designed or are undeveloped.18,19

A literature survey revealed that CORAL (CORrelation And Logic software available at http://www.insilico.eu/coral) software can be implemented for the development of predictive QSPR/QSAR models. CORAL is freeware software designed to calculate one-variable QSPR/QSAR models between an endpoint and descriptors using the Monte Carlo algorithm. In this software, the optimal descriptor of correlation weight (DCW) is calculated using the SMILES (Simplified Molecular-Input Line-Entry System) notation of the molecular structure.20–22 According to a literature report, the index of ideality of correlation (IIC) and correlation intensity index (CII) are applied as new criteria for judging the predictive potential of the QSPR model. It is often mentioned in the literature that the numerical value of the coefficient of determination (R2) for the validation and calibration set is improved by the IIC, whereas the CII improves the numerical value of the coefficient of determination (R2) for all four sets: i.e. active training, passive training, calibration and validation.23–31

The objective of this study is to construct a predictive QSPR model using the Monte Carlo technique of the CORAL software for the retention index property of 273 VOCs recognized in peppers. Ten random splits are made and each split is divided into four subsets. The IIC and CII statistical parameters are employed to predict a better model. The balance of correlation method with four target functions, i.e. TF0 (WIIC = WCII = 0), TF1 (WIIC = 0.5 & WCII = 0), TF2 (WIIC = 0 & WCII = 0.3) and TF3 (WIIC = 0.5 & WCII = 0.3), is used to examine the robustness and accuracy of the constructed QSPR model.

2. Data and method

2.1. Data

The retention index (RI) data for 273 VOCs identified in 13 peppers were obtained from the literature by Rojas et al.32 Polydimethylsiloxane/divinylbenzene (PDMS/DVB) fiber was used for extraction of the VOCs. The peaks on the two-dimensional GC with a quadrupole mass spectrometric detection (GC × GC-qMS) chromatogram were identified by the column set comprising a non-polar molecule (5% phenyl polysilphenylenesiloxane) as the primary column and a polar molecule (polyethylene glycol) in the second column. Experimental retention indices were obtained using the van den Dool and Kratz equation and Adams' retention indices. Data preprocessing details were reported in the literature by Rojas et al.32 The range of values for the retention index (RI) went from 930 to 1790. The IDs of the compound, SMILES codes, and corresponding experimental and predicted RI are provided in Table S1.† Ten splits were prepared and each split was further split randomly into four subsets: i.e. an active training set (≈26%), a passive training set (≈20%), a calibration set (≈20%), and a validation set (≈34%). The role of each set was fixed and is well explained in the literature.33–36

2.2. Method

The methodology for obtaining the results from the CORAL software can be summarized as a group by the following steps:

(1) Data preparation involves converting the structure to SMILES and preparing the Total set file.

(2) The process of data splitting in CORAL software is carried out using random splitting. This can be done using the classical scheme or balance of correlation. In the balance of correlation the data is divided into four sets: active training, passive training, calibration, and validation sets. However, if the amount of data is small, the classical scheme is used and the data set includes training, calibration, and validation sets.

(3) The selection of descriptors is based on either SMILES or a graph, or a combination of both. The descriptors are chosen accordingly.

(4) The target function selection involves computing correlation weights using the Monte Carlo method and maximizing one of the target functions: namely TF0, TF1, TF2, or TF3. The formulas of these target functions are described in the corresponding section.

(5) Model building consists of two phases. In Phase 1, the preferable threshold and number of epochs are searched for using Monte Carlo optimization based on statistical results from the calibration set. In Phase II, the preferable model is constructed after optimization of the threshold and number of epochs.

(6) External validation is performed on the test sets after model building.

(7) Model interpretation is carried out in this step.

(8) New molecules can be designed based on the model interpretation.

2.3. Hybrid optimal descriptor

As previously mentioned in the preceding section, in CORAL software three types of optimal descriptors can be calculated: i.e., SMILES-based, graph-based, and hybrid descriptors (obtained by combining SMILES and graph-based). The graph-based descriptor can be computed by using a hydrogen-filled graph (HFG), a hydrogen-suppressed molecular graph (HSG) or a graph of atomic orbitals (GAO).37–39 A literature survey shows that QSPR models designed using the hybrid optimal descriptor provide robust models with higher statistical quality.40 Here, the QSPR model for the prediction of RI is designed by utilizing a hybrid optimal descriptor based on the correlation weights of SMILES attributes and vertex degrees in the hydrogen-filled graph (HFG).

The hybrid optimal descriptor of the correlation weights (DCW) is computed using the following equation:

DHybridCW(T*,N*) = DCWSMILES(T*,N*) + DCWHFG(T*,N*) 1

The DCW of HFG and SMILES are calculated via mathematical eqn (2) and (3).

DCWSMILES(T*,N*) = ∑CW(Sk) + ∑CW(SSk) + ∑CW(SSSk) + CW(BOND) + CW(MFCs) 2
DCWHFG(T*,N*) = ∑CW(EC0k) + ∑CW(EC1k) + ∑CW(pt2k) + ∑CW(VS2k) + ∑CW(nnk) + ∑CW(C5) + ∑(C6) 3

In eqn (2), the structural attributes Sk, SSk, and SSSk are single SMILES symbols (e.g., Cl or S), two SMILES symbols and a combination of three SMILES symbols, respectively. The BOND code demonstrates the existence or absence of double (=), triple (#), or stereochemical bonds (@ or @@). Here, the molecular feature contributions (MFCs) are the total number of oxygen atoms (O), the number of double bonds (=), and the number of triple bonds (#). Therefore, in eqn (3), the attributes EC0 and EC1 are the number of neighbors of a vertex degree and Morgan's connectivity of first order; pt2k is the number of paths of length 2; VS2 is the valence shells of radius 2 in the HFG; the nn symbol implies nearest neighbors; C5 and C6 are descriptors that represent the five- and six-membered rings in the molecular structure, respectively. T is the threshold to separate SMILES attributes into noise or active. The active SMILES are applied to construct the model. The noise SMILES are not involved in constructing the model. T* and N* are the optimum threshold and number of epochs of the Monte Carlo optimization method. T* and N* provide the maximum statistical quality for the calibration set. The numerical values for CWs are acquired from the Monte Carlo optimization and the optimal descriptor is computed with the optimal CWs. Then the calculated CWs are employed to design a predictive model of the RI according to the following equation:

RI = C0 + C1 × DCW(T*,N*) 4

2.4. The Monte Carlo optimization

Here to design robust QSPR models, four different kinds of target functions, TF0, TF1, TF2 and TF3, are used. Then, the outcomes of the statistical results are compared with each other.

The mathematical equations for each target function can be demonstrated follows:

TF0 = RATRN + RPTRN − |RATRN − RPTRN| × drweight 5
TF1 = TF0 + IICCAL × weight for IIC (IICweight) 6
TF2 = TF0 + CIICAL × weight for CII (CIIweight) 7
TF3 = TF0 + IICCAL × IICweight + CIICAL × CIIweight 8

Here, RATRN and RPTRN are the correlation coefficients between the observed and predicted RI for the active training and passive training sets, respectively. The numerical values for weights of index of ideality of correlation (IIC) and correlation intensity index (CII) are usually kept constant and here the numerical values of drweight, IICweight and CIIweight were 0.1, 0.5 and 0.3, respectively. IICCAL and CIICAL are computed for the calibration set using eqn (9).

2.4. 9

R CAL is the correlation coefficient between experimental values and calculated values of RI for the calibration set. The negative and positive mean absolute errors are indicated by −MAE and +MAE, which are computed as follows:

2.4. 10
2.4. 11
Δk = observedk − calculatedk 12

The ‘k’ is the index (1, 2, …, N) and the observedk and calculatedk are related to the endpoint.

2.4. 13

R 2 is the correlation coefficient for a set that contains n substances. Rk2 is the correlation coefficient for n − 1 substances of a set after removing the kth substance. Hence, if (Rk2 − R2) is greater than zero, the kth substance is an “oppositionist” for the correlation between experimental and predicted values of the set. A small sum of “protests” means a more “intensive” correlation.

2.5. Applicability domain

In QSPR/QSAR models, the applicability domain (AD) is used to specify whether the designed model interpolates (correct predictions) or extrapolates (incorrect predictions). In the CORAL software, the distribution of SMILES attributes in the active training, passive training, and calibration sets is used to calculate the AD. Therefore, the AD for the model acquired as a result of Monte Carlo optimization varies depending on the distribution of the datasets in the training and calibration sets. In the QSPR/QSAR models designed by CORAL software, the statistical defects of SMILES are employed to define the AD. The “statistical defect,” d(A) is computed according to the following mathematical equation:

2.5. 14

P ATRN(Ak), PPTRN(Ak) and PCAL(Ak) are the probability of attributes in the active training set, passive training set, and calibration set, respectively; NATRN(Ak), NPTRN(Ak), and NCAL(Ak) are frequencies of attributes in the active training, passive training and calibration sets, respectively.

The SMILES-statistical defect (D) can be calculated as the sum of statistical defects of all attributes:

2.5. 15

NA is the number of active SMILES attributes for the given compounds.

In CORAL, a SMILES is an outlier if:

2.5. 16

Inline graphic D is an average of statistical defects for the dataset of the active training set.

3. Results and discussion

3.1. QSPR modelling for RI

Based on ten initial QSPR models, three compounds (compounds 49, 205, and 265) were identified as outliers. Therefore, these compounds were excluded from the data set before further processing. Herein, to achieve consistent statistical performance, ten different QSPR models were built for each type of target function (TF0, TF1, TF2, and TF3) employing hybrid optimal descriptors. The summary of statistical results for all QSPR models is summarized in Table S2.† The numerical value of R2 calculated with TF3 for the validation set of all splits is higher than the R2 calculated with the other target functions (TF0, TF1 and TF2); thus the TF3 calculated with eqn (8) was selected as the best target function. A comparison of the determination coefficients of the validation set for all splits computed via four target functions is represented in Fig. 1.

Fig. 1. Comparison of determination coefficients computed with TF0, TF1, TF2 and TF3 of all ten splits.

Fig. 1

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The QSPR models for the ten splits formulated with TF3 for prediction of the RI of the VOCs are given below:

Split 1

RI = 73.8025(±7.0844) + 24.5924(±0.1499) × DCW(1,15) 17

Split 2

RI = 121.5622(±6.8196) + 26.4093(±0.1507) × DCW(1,15) 18

Split 3

RI = 315.0484(±6.5146) + 20.0374(±0.1270) × DCW(1,15) 19

Split 4

RI = 133.8434(±9.0780) + 16.6644(±0.1272) × DCW(1,15) 20

Split 5

RI = 120.8001(±5.6911) + 22.7349(±0.1122) × DCW(1,15) 21

Split 6

RI = 265.7739(±6.3219) + 23.9520(±0.1477) × DCW(1,15) 22

Split 7

RI = 107.8894(±7.4311) + 23.2382(±0.1417) × DCW(1,15) 23

Split 8

RI = 40.7742(±6.0698) + 25.9964(±0.1255) × DCW(1,20) 24

Split 9

RI = 25.2594(±6.5441) + 25.5860(±0.1587) × DCW(1,15) 25

Split 10

RI = 110.5639(±6.0444) + 21.8635(±0.1077) × DCW(1,15) 26

3.2. Model validation

In this study, the RI of the VOCs was predicted using QSPR models based on Monte Carlo optimization employing four target functions TF0 (WIIC = WCII = 0), TF1 (WIIC = 0.5 & WCII = 0), TF2 (WIIC = 0 & WCII = 0.3) and TF3 (WIIC = 0.5 &WCII = 0.3), and each target function was checked with ten random splits. The balance of correlation method was applied to generate QSPR models. The statistical results presented in Table S2† indicate that all designed QSPR models are within the standard range in terms of statistical criteria and have robust predictability. It can also be seen from Table S2† that simultaneously adding the weight IIC and CII to the target function increases its ability to predict RI as well as improving the statistical results. The numerical value of R2 for the validation set of split 6 (R2 = 0.9308, eqn (22)) was found to be higher than the numerical value of R2 for the other models created with TF3, so it was identified as the best model. Fig. 2 displays the plot between observed and calculated data of the RI for the QSPR models computed with TF3. A good correlation between observed RI and calculated RI, as well as a uniform distribution of RI for active training, passive training, calibration and validation sets can be seen in Fig. 2. Finally, the validation metrics for each model are calculated using three strategies: (i) internal validation or cross-validation with the training set data; (ii) external validation with the test set data; and (iii) Y-scrambling or data randomization. If CR2p > 0.5 for the created model in a Y-randomization test, the model is free of chance correlation. For all constructed QSPR models the numerical value of CR2p was more than 0.5, indicating the robustness of the developed models.

Fig. 2. Experimental versus predicted retention indices of split 1 to 10 for VOCs detected in peppers by the Monte Carlo method based on target function TF3.

Fig. 2

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3.3. Interpretation of the QSPR model

In the QSPR model developed by the CORAL software, mechanistic interpretation is defined as the description of structural attributes acquired from SMILES or hydrogen-filled graphs which are responsible for the increase or decrease of an endpoint. If the numerical value of correlation weights of these structural attributes is negative in three or more runs of the optimization, then these structural features are defined as a promoter of endpoint decrease. On the other hand, if the numerical value of correlation weights of these structural attributes is positive in three or more runs of the optimization, then these structural features are defined as a promoter of endpoint increase. However the structural attribute is undefined if the correlation weight of the structural descriptors has both positive and negative numerical values.

The promoters for endpoint RI increase or decrease were computed from the best model (split 6) and are displayed in Table 1. Morgan extended connectivity of zero-order for hydrogen atom as 1 (ec0-h…1…), Morgan extended connectivity of first-order for hydrogen atom as 4 (ec1-h…4…), Morgan extended connectivity of first-order for carbon atom as 7 (ec1-c…7…), Morgan extended connectivity of zero-order for carbon atom as 3 (ec0-c…3…), Morgan extended connectivity of first-order for carbon atom as 4 (ec1-c…10…), the number of paths of length 2 which started from a hydrogen atom is equal to 3 (pt2-h…3…), the number of paths of length 2 which started from a carbon atom is equal to 5 (pt2-c…5…), the number of paths of length 2 which started from a hydrogen atom is equal to 2 (pt2-h…2…), two sp3 hybridized carbon joined by branching (c…(…c…), the presence of two consecutive aliphatic carbons (c…c…) etc. were some significant promoters of endpoint increase. The nearest neighbours code for carbon equal to 413 (nnc-c…413), the nearest neighbours code for carbon equal to 440 (nnc-c…440), a combination of the carbon atom, oxygen and branching (c…o…(…), and 28 as a sum of vertex degrees which take place at a topological distance of 2 relatively to carbon vertex (vs. 2-c…28) etc. were some significant promoters of endpoint decrease.

The list of the promoters RI increase and decrease from splits 6 calculated with TF3.

No. Structural attributes CWs Probe 1 CWs Probe 2 CWs Probe 3 NSs NSc NSv Defect [SAk] Description
The promoters of RI increase
1 EC0-H…1… 0.0509 0.16064 0.34295 68 58 54 0 Morgan extended connectivity of zero-order for hydrogen atom as 1
2 EC1-H…4… 0.18025 0.22099 0.18401 68 57 54 0 Morgan extended connectivity of first-order for hydrogen atom as 4
3 PT2-H…3… 0.16527 0.2584 0.3257 68 57 54 0 The number of paths of length 2 which started from a hydrogen atom is equal to 3
4 C⋯C…… 0.44726 0.01345 0.30905 65 55 50 0.0003 The presence of two consecutive aliphatic carbons
5 EC1-C…7… 0.31326 0.46929 0.21017 63 56 50 0 Morgan extended connectivity of first-order for carbon atom as 7
6 VS2–H…6… 0.10836 0.05545 0.26739 63 56 50 0 6 as a sum of vertex degrees which take place at a topological distance of 2 relatively to hydrogen vertex
7 EC0-C…3… 0.56731 0.20537 0.33853 62 47 46 0.0006 Morgan extended connectivity of zero-order for carbon atom as 3
8 EC1-C…10 0.22378 0.25831 0.04221 61 52 47 0.0002 Morgan extended connectivity of first-order for carbon atom as 4
9 NNC-C…422 0.20503 0.01758 0.05181 60 53 48 0.0001 The nearest neighbours codes for carbon equal to 422
10 C…(…C… 0.29947 0.13954 0.33177 59 49 49 0.0004 Two sp3 hybridized carbon joined by branching
11 =…… 0.15273 0.45098 0.39027 56 43 44 0.0001 Presence of double covalent bond
12 1…… 0.26393 0.42999 0.64276 53 46 42 0 Presence of at least one ring
13 NNC-C…321 0.44352 0.72343 0.10398 53 39 38 0.0008 The nearest neighbours codes for carbon equal to 321
14 PT2-H…2… 0.06983 0.57052 0.40344 53 42 38 0.0008 The number of paths of length 2 which started from a hydrogen atom is equal to 2
15 PT2-C…5… 0.21029 0.22211 0.19676 52 42 39 0.0005 The number of paths of length 2 which started from a carbon atom is equal to 5
 
The promoters of RI decrease
1 NNC-C…413 −0.08801 −0.07644 −0.57505 67 57 52 0.0002 The nearest neighbours codes for carbon equal to 413
2 C…1…(… −0.30101 −0.02505 −0.28091 26 27 20 0.0003 Combination of aliphatic carbon, one ring and branching
3 NNC-C…440 −0.3105 −0.03567 −0.80092 26 27 20 0.0003 The nearest neighbours codes for carbon equal to 440
4 C⋯O…(… −0.39833 −1.30355 −0.7525 8 1 4 0.0036 Combination of the carbon atom, oxygen and branching
5 O…(…(… −0.15072 −1.42791 −2.29626 5 1 5 0.0019 Oxygen atom with two branching
6 VS2–C…28 −0.05713 −0.5657 −0.85747 5 8 4 0.0001 28 as a sum of vertex degrees which take place at a topological distance of 2 relatively to carbon vertex
7 3⋯C…1… −1.16603 −0.21466 −2.69557 1 6 1 0.0019
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3.4. A comparison of various QSPR models based on RI

A survey of the literature indicates that Rojas et al. (2019) reported only one QSPR model for retention index: the QSPR model for 273 VOCs of pepper.32 The molecular descriptors and molecular fingerprints were calculated using Dragon and PaDEL-Descriptor software. To create balanced subsets, the dataset was divided into training, validation, and test sets of molecules using the Balanced Subsets Method (BSM). Afterward, the Wootton, Sergent, and Phan-Tan-Luu (WSP) unsupervised variable reduction method was employed to reduce the presence of multicollinearity, redundancy, and noise among the initial pool of 4336 molecular descriptors and fingerprints. By implementing this method, a reduced pool consisting of 1664 descriptors was subjected to supervised selection through replacement method (RM) variable subset selection in order to establish a four-descriptor model. The efficacy of the model was assessed by evaluating the coefficient of determination and the root-mean-square deviation in fitting. Specifically, the values obtained for R2 and RMSD for training were 0.879 and 72.1, respectively. Similarly, R2 and RMSD were found to be 0.832 and 91.7 in the validation set, while R2 and RMSD were 0.915 and 55.4 in the test set. The minimal discrepancies observed among these parameters across the three sets indicate the stability and predictability of the QSPR model.

Table 2 displays a comparison of the statistical results of the present QSPR model with the reported QSPR model. The previously reported model was implemented with only one split, but in the present QSPR models, 10 splits were used to design 40 QSRR models employing four target functions (TF0, TF1, TF2 and TF3). Two significant criteria, the index of ideality correlation (IIC) and correlation intensity index (CII), are also addressed in this work, which were not studied in earlier work. In the present QSPR models, only one descriptor, DCW, was used to construct the QSPR models but in the previously reported model, four descriptors were applied. The numerical value of the determination coefficient (Rval2) of the QSPR model generated with TF3 for split 6 is 0.9308, which is much better than the value for the reported model. Thus, the presented QSPR models are more robust and predictable.

Comparison of present QSPR models with the previously reported study.

No. Set n Descriptor generator Regression method R 2 train RMSD IIC CII Ref.
1 Training 92 Dragon and PaDEL MLR 0.879 72.1 — — 32
Validation 91 0.832 91.7 — —
Test 90 0.915 55.4 — —
2 ActivTRN 68 CORAL package LR 0.885 62.7 0.658 0.928 Present work
PassTRN 58 0.900 70.8 0.677 0.943
Calib 54 0.904 51.6 0.951 0.944
Valid 90 0.931 54.4 0.770 0.955
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3.5. External validation of the proposed models

An external dataset of 115 VOCs reported by Rojas et al.32 was used to predict the RI of molecules outside the dataset for modeling. The RI properties of these compounds were predicted by ten models based on TF3 and average values were compared with external predictions by Rojas et al.Table 3 shows the average predicted RI of ten models, the prediction by Rojas et al.32 for the BPX5 and BP20 column coupled system, and experimental retention indices from the literature.

External set of common VOCs detected in peppers: name, CAS registry number, predicted retention indices based on the average prediction of models 1 to 10, and prediction by Rojas et al.32 for the BPX5 and BP20 column coupled system, experimental retention indices from the literature, and source.

No. Name CAS number RIpredicted (this study) RIpredicted (Rojas et al.) Experimental RIliterature Ref.
DB-5 column HP-5MS stationary phase HP-5 column DB-Wax stationary phase BPX5 column RTX-Wax stationary phase HP-20M column DB-5MS stationary phase BP20 column
1 Myrcenol 543-39-5 1164.719 1159.6 NA NAa NA NA NA NA NA NA NA 41
2 (E,E)-α-Farnesene 502-61-4 1483.631 1496.2 1508 NA NA NA NA NA NA NA NA 15, 42 and 43
α-Farnesene ─ ─ NA NA NA NA NA NA NA NA 41 and 44
3 Elemicin 487-11-6 1501.785 1565 1540 NA NA NA NA NA NA NA NA 43 and 45
1554
1556
4 Myristicin 607-91-0 1391.435 1546.5 1520 NA NA NA NA NA NA NA NA 43
5 Apiole 523-80-8 1541.468 1721.7 1679 NA NA NA NA NA NA NA NA 43
1680
1685
6 Dillapiole 484-31-1 1565.236 1709.1 1622 1622 NA NA NA NA NA NA NA 14,43
1644
7 Eugenol acetate 93-28-7 1568.772 1577.7 1524 NA NA NA NA NA NA NA NA 45
8 Carvone oxide 18 383-49-8 1239.442 1367.3 NA NA NA NA NA NA NA NA NA 41, 42 and 46–49
trans-Carvone oxide 33 204-74-9 ─ ─ NA NA NA NA NA NA NA NA NA 41
9 α-Bulnesene 3691-11-0 1484.066 1508.7 1493 1505 NA NA NA NA NA NA NA 41
1503
1505
δ-Guaiene ─ ─ NA NA NA NA NA NA NA NA NA 42 and 43
10 Dihydrocarveol 619-01-2 1164.505 1184.8 1192 NA 1195 1941 NA NA NA NA NA 41, 42, 44 and 46–49
1195
p-Menth-8-en-2-ol ─ ─ NA NA NA NA NA NA NA NA NA 42
trans-p-Menth-8-en-2-ol ─ ─ NA NA NA NA NA NA NA NA NA 47–49
Neo-dihydrocarveol 18 675-34-8 ─ ─ NA NA NA NA NA NA NA NA NA 41
11 cis-β-Terpineol 138-87-4 1196.492 1181 1159 NA NA NA NA NA NA NA NA 41
12 β-Bisabolol 15 352-77-9 1647.933 1604.1 NA NA 1668 NA NA NA 2021 NA NA 41 and 42
13 α-Bisabolol 515-69-5 1644.237 1594.9 1683 NA NA NA NA NA NA NA NA 14 and 44
1701
14 Squalene 111-02-4 2742.641 2726 2790 NA NA NA NA NA NA NA NA 6
15 δ-Terpinyl acetate 93 836-50-1 1382.135 1356 1313 NA NA NA NA NA NA NA NA 41
16 1,4-Cineole 470-67-7 1139.433 1117.1 1016 1016 NA 1171 NA NA NA NA NA 41
17 Cadina,1,4-dien-3-ol 1608.026 1636.1 NA NA NA NA NA NA NA NA NA 41
18 trans-Piperitone oxide 4713-38-6 1194.878 1303.8 1258 NA NA NA NA NA NA NA NA 50
19 3-Buten-2-ol 598-32-3 642.9435 758.6 NA NA NA NA NA NA NA NA NA 41
20 Vomifoliol 23 526-45-6 1573.99 1735.6 NA 1796 NA 3167 1814 NA NA NA NA 41
3175
21 Neryl isovalerate 3915-83-1 1578.39 1593 NA NA NA NA NA NA NA NA 1872 43
22 Retrofractamide B 54 794-74-0 2393.783 2624 NA NA NA NA NA NA NA NA NA 14
23 Guineensine 55 038-30-7 2568.907 2783.1 NA NA NA NA NA NA NA NA NA 14
24 Caryophyllene alcohol 472-97-9 1586.876 1548.9 1568 1560 1564 NA NA NA NA NA NA NA 42
Caryophyllenol ─ ─ NA NA NA NA NA NA NA NA NA 41, 44 and 46–49
25 Clovene 469-92-1 1440.777 1460 NA NA NA NA NA NA NA NA NA 42
26 Piperitol 491-04-3 1170.929 1143.6 NA NA NA NA NA NA NA NA NA 43
27 Humulene oxide II 19 888-34-7 1609.486 1589.6 1606 NA NA NA NA NA NA NA NA 41
1607
28 α-Cedrene 469-61-4 1447.516 1451.9 1409 1409 NA NA NA 1562 NA NA NA 43
1410
29 Hedycaryol 21 657-90-9 1627.43 1612.5 1530 NA NA NA NA NA NA NA NA 44
30 Germacrene D-4-ol 198 991-79-6 1594.602 1606.5 1511 1567 NA NA NA NA NA NA NA 43
1574
31 α-Eudesmol 473-16-5 1592.197 1595.8 1652 NA NA NA NA NA 2230 NA NA 41 and 43
32 Furanodiene 19 912-61-9 1586.736 1626.1 NA NA NA NA NA NA NA NA NA 43
33 cis-p-Menth-8-en-2-ol 1180.423 1193.1 NA NA NA NA NA NA NA NA NA 47–49
34 Isopulegol 89-79-2 1200.764 1141.3 1145 1146 NA 1879 NA NA NA NA NA 43
1879
35 Menthol 89-78-1 1190.85 1113.6 1173 NA NA 1626 NA NA 1646 NA NA 41
2103
36 cis-Sabinene hydrate 15 537-55-0 1144.655 975 1069 1101 NA 1465 NA NA NA NA NA 14 and 43
1070
1097
37 Cedrol 77-53-2 1583.856 1544.5 1596 NA NA NA NA NA NA NA NA 15, 41, 42 and 46–49
1604
38 (Z)-Isosafrole 17 627-76-8 1271.586 1391.8 1308 NA NA NA NA NA NA NA NA 41
1336
39 Nona-trans,cis-2,6-dienal 557-48-2 1102.993 1130.7 NA NA NA 1597 1605 NA NA NA NA NA 51
40 Howeveranediol 25 265-75-2 761.5132 733.4 NA NA NA NA NA NA NA NA NA 6
41 Ethyl-2-hexenol 50 639-00-4 993.1246 1003.4 NA NA NA NA NA NA NA NA NA 41
42 Hept-trans-3-en-2-one 1119-44-4 940.3034 900.1 NA NA NA NA NA NA NA NA NA 51
43 Nona-trans,trans-2,5- dien-4-one 61 759-51-1 1101.811 1085.6 NA NA NA NA NA NA NA NA NA 51
44 Hex-trans-2-enal 6728-26-3 838.5927 850.3 854 NA 857 1201 NA NA 1209 848 NA 51
(E)-2-Hexenal ─ ─ NA NA NA NA NA NA NA NA NA 41
45 1-Hepten-3-ol 4938-52-7 902.912 925.4 NA NA NA NA NA NA NA NA NA 41
46 (E)-3-Octenol 18 185-81-4 1063.265 1043.7 NA NA NA NA NA NA NA NA NA 41
47 2-Heptanone 110-43-0 900.1747 971.3 888 NA 882 1160 889 NA NA NA NA 51
889
48 Non-trans-2-en-4-one 32 064-72-5 1115.155 1156.7 NA NA NA NA NA NA NA NA NA 51
49 Non-1-en-4-one 61 168-10-3 1084.331 1154.4 NA NA NA NA NA NA NA NA NA 51
50 α-Ethyl hexanoate 123-66-0 1021.078 1118 996 1001 997 1224 NA NA NA NA NA 6
997 1229
998 1244
1001 1270
51 1-Octen-3-ol 3391-86-4 990.474 1013.3 942 975 977 980 NA NA 1423 NA NA 41
978 991 1438
980 1465
52 2,4-Decadienoic acid 42 997-42-2 1235.616 1736.5 NA NA NA NA NA NA NA NA NA 14
Piperidide NA NA NA NA NA NA NA NA NA
53 Pellitorin 18 836-52-7 1519.16 1624.7 NA NA NA NA NA NA NA NA NA 14
54 Deca-trans,cis-2,4-dienal 25 152-83-4 1189.996 1212.5 1291 NA NA 1758 NA NA NA NA NA 51
1297
Deca-trans,trans-2,4-dienal 2363-88-4 ─ ─ NA NA NA NA NA NA NA NA NA 51
Deca-2,4-dienal 25 152-84-5 ─ ─ 1311 NA NA 1820 1832 NA NA NA NA NA 51
1314
1319
55 (E)-2-Octenal 2363-89-5 1010.999 1023.6 NA 1060 NA NA NA NA NA NA NA 41
56 N-Isobutyl-(2E,4E,12E)-octadecatrienamide 943 546-17-6 2222.115 2290 NA NA NA NA NA NA NA NA NA 14
57 N-Isobutyl-(2E,4E,14Z)-eicosatrienamide — 2397.239 2448.7 NA NA NA NA NA NA NA NA NA 14
58 Hexanal 66-25-1 836.3585 921.5 784 805 800 1067 NA NA 1075 NA NA 16 and 51
797 803 1093
799
800
819
59 2-Octanol 25 339-16-6 1019.923 981.9 NA NA NA NA NA NA NA NA NA 41
60 Nonane 111-84-2 964.4392 965.9 899 900 NA NA NA NA 900 NA NA 41
61 (E)-2-Tridecenal 7774-82-5 1448.809 1429.9 NA NA NA NA NA NA NA NA NA 43
62 Tetradecane 629-59-4 1402.249 1372.2 1116 NA NA 1399 1400 NA 1400 NA NA 14
1399
63 N-Isobutyl-(2E,4E)-octadecadienamide 54 794-70-6 2219.656 2266 NA NA NA NA NA NA NA NA NA 14
64 Pentadecanal 2765-11-9 1624.416 1660.3 1513 1711 NA NA NA NA NA NA NA 50
1687
1710
65 Hexadecane 544-76-3 1577.373 1531.4 1600 NA NA NA NA NA 1600 NA NA 14
66 Palmitic acid 57-10-3 1755.653 1811.2 1984 NA NA NA NA NA 2860 NA NA 14
Palmitic acid glyceride ─ ─ NA NA NA NA NA NA NA NA NA 6
67 Heptadecane 629-78-7 1664.935 1610.7 1700 NA NA NA NA NA 1700 NA NA 14
68 1-Octadecene 112-88-9 1759.766 1711.6 1793 NA NA NA 1774 NA NA NA NA 14
1794
69 Octadecane 593-45-3 1752.497 1689.9 1800 NA NA 1805 NA NA 1800 NA NA 14
70 Nonadecane 629-92-5 1840.059 1768.9 1900 NA NA NA NA NA 1900 NA NA 14
71 1-Eicosene 3452-07-1 1934.889 1869.5 1990 NA NA NA NA NA NA NA NA 14
1994
72 Eicosane 112-95-8 1927.621 1847.8 2000 NA NA NA NA NA 2000 NA NA 14
73 Heneicosane 629-94-7 2015.183 1926.7 2100 NA NA NA NA NA 2100 NA NA 14
74 Docosane 629-97-0 2102.745 2005.4 2200 NA NA NA NA NA 2200 NA NA 14
75 Nonadecanol 1454-84-8 2015.34 1901.6 NA 2156 NA NA NA NA NA NA NA 50
76 Hexanol 111-27-3 877.0338 846.4 867 NA 865 1351 NA NA 1325 869 NA 41
884 1354
1360
1379
1392
77 Amyl alcohol 71-41-0 789.4719 751.3 766 NA 766 1244 NA NA NA NA NA 41
768
78 Benzenepropanoic acid, ethyl ester 2021-28-5 1339.896 1411.3 1390 NA NA 1897 NA NA NA NA NA 43
1905
79 Methyl salicylate 119-36-8 1160.501 1248.3 1190 1190 NA NA NA NA NA NA NA 51
1191
1206
80 Guaiacol 90-05-1 1001.29 1087.9 1086 NA NA 1872 NA NA NA NA NA 41
1091 1875
1883
81 2-Methoxy-3-isobutylpyrazine 24 683-00-9 1055.625 1291 1135 NA NA 1540 NA NA NA NA NA 51
1171
82 Thymol 89-83-8 1189.021 1203.6 1290 1290 1308 NA NA NA NA NA NA 41 and 43
83 2-Methylnaphthalene 91-57-6 1210.977 1379.3 1281 NA 1295 NA NA NA NA NA NA 51
84 1-Methylnaphthalene 90-12-0 1163.889 1355.6 1298 NA 1312 NA NA NA NA NA NA 51
85 Piperamide C 9:1 (8E) 62 510-52-5 2232.683 2552.6 NA NA NA NA NA NA NA NA NA 14
86 4,5-Dihydropiperettine 583-34-6 2105.33 2419.8 NA NA NA NA NA NA NA NA NA 14
87 Dehydropipernonaline 107 584-38-3 2279.967 2579.6 NA NA NA NA NA NA NA NA NA 14
88 Piperine 94-62-2 1928.943 2235.5 NA NA NA NA NA NA NA NA NA 14
89 Piperanine 23 512-46-1 1932.372 2211.5 NA NA NA NA NA NA NA NA NA 14
90 1-Cinnamoyl piperidine 5422-81-1 1597.08 1759.2 NA NA NA NA NA NA NA NA NA 14
91 Piperolein B 30 505-89-6 2301.005 2626.8 NA NA NA NA NA NA NA NA NA 14
92 Geranial 5392-40-5 1182.447 1151.7 1240 NA NA NA NA NA NA NA NA 41
Neral 106-26-3 ─ ─ 1235 NA NA 1630 NA NA 1658 NA NA 41
1240 1690
1294 1695
93 Citronella 106-23-0 1155.695 1216.9 1153 NA NA 1425 NA NA NA NA NA 41, 42 and 46–49
1159 1485
1161 1488
94 Phenylacetaldehyde 122-78-1 1046.275 1112.2 1043 NA NA 1609 NA NA 1615 NA NA 51
1049 1671
95 Furfural 98-01-1 753.1899 858.1 830 NA NA 1458 832 NA NA NA NA 51
1474
1485
96 Oxalic acid 144-62-7 740.7731 852.3 NA NA NA NA NA NA NA NA NA 6
97 α-Hydroxypropionic acid 50-21-5 699.8166 862.4 NA NA NA NA 1058 NA NA NA NA 6
98 Howeverenedioic acid 110-16-7 888.9371 943.8 NA NA NA NA NA NA NA NA NA 6
99 Dihydrolimonen-10-al 3269-90-7 1223.518 1236 NA NA NA NA NA NA NA NA NA 41
100 Gluconate anion 608-59-3 1350.775 1570.7 NA NA NA NA NA NA NA NA NA 6
101 Erythritol 149-32-6 943.4734 1041.8 NA NA NA NA NA NA NA NA NA 6
102 Glycerin 56-81-5 758.5946 864.6 NA NA NA NA NA NA NA NA NA 6
103 Myrtenol 515-00-4 1159.949 1118.5 1194 NA NA NA NA NA NA NA NA 42, 44 and 47–49
1196
1202
1214
104 cis-p-Menth-2-en-7-oI 1185.016 1202.4 NA NA NA NA NA NA NA NA NA 41
105 Glucopyranose 492-62-6 1317.003 1440.1 NA NA NA NA NA NA NA NA NA 6
106 Geraniol 106-24-1 1175.015 1171.8 1255 NA 1240 1788 NA NA 1814 NA NA 41
1276 1850
1862
Nerol 106-25-2 ─ ─ 1228 NA NA 1753 NA NA 1770 NA NA 41 and 50
107 (2E,6E)-Farnesol 106-28-5 1606.869 1597.8 1706 NA NA 2371 NA NA NA NA NA 43
1722
(E,E)-Farnesol ─ ─ NA NA NA NA NA NA NA NA NA 41
α-Farnesol ─ ─ NA NA NA NA NA NA NA NA NA 44
(Z,Z)-Farnesol 4602-84-0 ─ ─ 1689 1713 1713 1713 NA NA NA NA NA NA 41
1718
(2Z,6Z)-Farnesol ─ ─ NA NA NA NA NA NA NA NA NA 43
(2E,6Z)-Farnesol 3879-60-5 ─ ─ 1734 1742 NA NA NA NA NA NA NA 43
1742 1743
1748
(E,Z)-Farnesol ─ ─ NA NA NA NA NA NA NA NA NA 41
(Z,E)-Farnesol 3790-71-4 ─ ─ 1697 NA NA NA NA NA NA NA NA 41
108 Phytol 150-86-7 1941.848 1928.7 1949 NA NA NA NA NA 2571 NA NA 43
109 (E)-Cinnamyl alcohol 4407-36-7 1155.272 1238.7 1305 NA NA NA NA NA NA NA NA 41
110 2-Methyl cinnamyl alcohol 1504-55-8 1212.211 1285.1 NA NA NA NA NA NA NA NA NA 41
111 Isoamyl alcohol 123-51-3 764.7509 679.6 734 NA 737 1169 NA NA 1182 NA NA 41
735 1206
1230
112 Hex-cis-3-enol 928-96-1 880.2674 870.4 857 NA NA 1378 NA NA 1357 849 NA 51
1401
1407
3-Hexenol 544-12-7 ─ ─ NA NA NA NA NA NA NA NA NA 41
113 Cumin alcohol 536-60-7 1204.248 1262.4 1287 NA NA 2099 NA NA NA NA NA 41
114 Biphenyl 92-52-4 1283.923 1486.7 1381 NA 1385 NA NA NA NA NA NA 51
115 Naphthalene 91-20-3 1131.721 1316 1179 NA NA NA NA NA 1718 NA NA 51
Open in a new tab
a

Not available.

Fig. 3 shows a plot of the RI of the external set predicted by CORAL software versus the RI predicted by Rojas et al..32 There is good agreement between the external predictions by the two methods.

Fig. 3. Plot of the RI of external set predicted by CORAL software versus the RI predicted by Rojas et al.

Fig. 3

Open in a new tab

4. Conclusions

In the present study, 40 QSPR models for the prediction of RI of 273 VOCs were developed from 10 random splits. The balance of correlation algorithm was used to design QSRR models. Four target functions, i.e. TF0 (without IIC or CII), TF1 (with IIC alone), TF2 (with CII alone) and TF3 (with IIC and CII, simultaneously) were employed to verify the significance of the present statistical method of QSPR model generation. The simultaneous use of IIC and CII (TF3) improves the predictive potential of the QSPR model. All suggested models render satisfactory predictive QSPR models for the RI of the VOCs, but the best predictive potential was computed withTF3 for split 6; thus it is specified as the best model. To evaluate the reliability and prediction ability of all created models, various statistical parameters, such as R2, IIC, CII, CCC, Q2, QF12, QF22, QF32, s, MAE, F, RMSE, Inline graphic, Inline graphic, CR2p and Y-test were utilized. A comparison of some statistical parameters of the present study, as analyzed by the QSPR model developed by Rojas et al.32 reveals that the R2 value for the training set has shown an improvement, increasing from 0.879 to 0.900. Similarly, the R2 value for the test set has also demonstrated an enhancement, rising from 0.915 to 0.931. In addition, the RMSD has exhibited a reduction, decreasing from 72.1 to 62.7 for the training set and from 55.4 to 54.4 for the test set. The applicability domain (AD) was studied based on “statistical defect” d(A). The structural attributes based on graph invariants and SMILES notation were also extracted from the split 6 (best model) and employed to recognize the promoters of RI increase and decrease. Morgan extended connectivity of zero-order for hydrogen atom as 1 (ec0-h…1…), Morgan extended connectivity of first-order for hydrogen atom as 4 (ec1-h…4…), Morgan extended connectivity of first-order for carbon atom as 7 (ec1-c…7…), Morgan extended connectivity of zero-order for carbon atom as 3 (ec0-c…3…), Morgan extended connectivity of first-order for carbon atom as 4 (ec1-c…10…) etc were some significant promoters of endpoint increase. The nearest neighbours codes for carbon equal to 413 (nnc-c…413), the nearest neighbours codes for carbon equal to 440 (nnc-c…440), a combination of the carbon atom, oxygen and branching (c…o…(…), and 28 as a sum of vertex degrees which take place at a topological distance of 2 relatively to carbon vertex (vs. 2-c…28) etc are some significant promoters of endpoint decrease.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Conflicts of interest

There are no conflicts to declare.

Supplementary Material

RA-014-D3RA07960K-s001
RA-014-D3RA07960K-s002
†

Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ra07960k

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

RA-014-D3RA07960K-s001
RA-014-D3RA07960K-s001.xlsx (85.9KB, xlsx)
RA-014-D3RA07960K-s002
RA-014-D3RA07960K-s002.pdf (111.8KB, pdf)

Data Availability Statement

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Articles from RSC Advances are provided here courtesy of Royal Society of Chemistry

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