Journal:Identification of Cannabis sativa L. (hemp) retailers by means of multivariate analysis of cannabinoids

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Full article title Identification of Cannabis sativa L. (hemp) retailers by means of multivariate analysis of cannabinoids
Journal Molecules
Author(s) Palmieri, Sara; Mascini, Marcello; Ricci, Antonella; Fanti, Federico;
Ottaviani, Chiara; Sterzo, Claudo L.; Sergi, Manuel
Author affiliation(s) University of Teramo
Primary contact Email: msergi at unite dot it
Editors Nikas, Spyros P.
Year published 2019
Volume and issue 24(19)
Page(s) 3602
DOI 10.3390/molecules24193602
ISSN 1420-3049
Distribution license Creative Commons Attribution 4.0 International
Website https://www.mdpi.com/1420-3049/24/19/3602/htm
Download https://www.mdpi.com/1420-3049/24/19/3602/pdf (PDF)

Abstract

In this work, the concentration of nine cannabinoids—six neutral cannabinoids (THC, CBD, CBC, CBG, CBN, and CBDV) and three acidic cannabinoids (THCA, CBGA, and CBDA)—was used to identify the Italian retailers of Cannabis sativa L. (hemp), reinforcing the idea that the practice of categorizing hemp samples only using THC and CBD is inadequate. A high-performance liquid chromatographytandem mass spectrometry (HPLC-MS/MS) method was developed for screening and simultaneously analyzing the nine cannabinoids in 161 hemp samples sold by four retailers located in different Italian cities. The hemp samples dataset was analyzed by univariate and multivariate analysis, with the aim to identify the associated hemp retailers without using any other information on the hemp samples such as Cannabis strains, seeds, soil and cultivation characteristics, geographical origin, product storage, etc. The univariate analysis highlighted that the hemp samples could not be differentiated by using any of the nine cannabinoids analyzed. To evaluate the real efficiency of the discrimination among the four hemp retailers, a partial least squares discriminant analysis (PLS-DA) was applied. The PLS-DA results showed very good discrimination between the four hemp retailers, with an explained variance of 100% and few classification errors in both calibration (5%) and cross validation (6%). A total of 92% of the hemp samples were correctly classified by the cannabinoid variables in both fitting and cross validation. This work helps to show that an analytical method coupled with multivariate analysis can be used as a powerful tool for forensic purposes.

Keywords: Cannabis sativa L., HPLC-MS/MS analysis, cannabinoids, multivariate analysis, partial least squares discriminant analysis (PLS-DA)

Introduction

In recent years, Cannabis sativa L. has become one of the most studied plants around the world.[1] Cannabis sativa L is a chemically complex plant which contains several classes of natural compounds, e.g., flavonoids, mono- and sesquiterpenes, steroids, nitrogenous compounds, and cannabinoids, associated with the medicinal properties of the plant.[2][3]

The main cannabinoid constituents are Δ9-tetrahydrocannabinol (THC), which possesses significant psychotropic properties, and other compounds with less or no psychotropic activity. This includes neutral cannabinoids like cannabidiol (CBD), cannabigerol (CBG), cannabichromene (CBC), cannabinol (CBN), and cannabidivarin (CBDV), as well as acidic cannabinoids like tetrahydrocannabinolic acid (THCA), cannabidiolic acid (CBDA), and cannabigerolic acid (CBGA). The species sativa is recognized as a monotypic classification that can be divided into different chemotypes based on the specific cannabinoid profile.[4][5]

The interest in Cannabis sativa L. has increased in Italy mainly due to December 2016 legislation (Legge 2 Dicembre 2016, n. 242). The legislation uses the concentration of THC to classify two types of Cannabis sativa L.: a fiber-type plant (hemp) with low levels of THC (<0.2% w/w) and a prohibited drug-type plant where the level of THC is >0.6% w/w.[6] There are hundreds of hemp strains available in the marketplace based on aroma, plant size, different cultivation, characteristic of the soil, and overall yield.[4][7][8] Therefore, there is a request to develop cost effective and easy-to-use quantitative and qualitative methods for the identification and classification of hemp products.[6]

THC and CBD are the traditional reference cannabinoids to extrapolate the phytochemical composition of hemp, but different works have proved that strains with similar THC/CBD content have different effects on human physiology.[9][10][11]

The present work focused on examining the chemical content of cannabinoids as a convenient tool to identify retailers of hemp without knowing any other relevant information about the sample, including strain, seed, soil and cultivation characteristics, geographical origin, product storage, etc. Moreover, the results of this work support the theory that using only concentrations of THC and CBD is not enough to discriminate among samples of commercial hemp.[9] The identification and quantification of cannabinoids was carried out by means of high-performance liquid chromatographytandem mass spectrometry (HPLC-MS/MS), overcoming the issue with phytocannabinoid decomposition due to heating found in methods like gas chromatography (GC).[12][13]

A partial least squares discriminant analysis (PLS-DA) approach correctly identified the hemp retailer associated with a sample by examining nine specific cannabinoids of 161 hemp samples, showing that an analytical method coupled with multivariate analysis can lead to a powerful tool for forensic purposes. Additionally encouraging is that such chemometric models have already been used to understand phytochemical diversity, showing the advantages of multivariate analysis.[9][14]

A number of works in the literature have reported on methods for the determination of THC and CBD concentration in hemp samples[8][15]; however, to the best of our knowledge, there is a lack of information regarding the evaluation of the comprehensive cannabinoid profile of hemp products with HPLC-MS/MS.[7][16][17]

Results and discussion

The dataset used for both univariate and multivariate analysis (see Table S1 in the supplementary material) was composed of 161 hemp samples processed in 2018 from four Italian retailers. The concentration of the the six neutral cannabinoids (THC, CBD, CBC, CBG, CBN, and CBDV) and the three acidic cannabinoids (THCA, CBGA, and CBDA) was determined for all of the samples.

As reported in Table 1, the hemp samples were sold in four Italian cities from three Italian regions. The hemp samples were acquired without any strain, seed, soil and cultivation characteristics, geographical origin, product storage, etc. information reported with the acquisition.

Table 1. Summary of the dataset used in this work. The 161 hemp samples were classified as sold by the four Italian retailers. Region and city of retailers were also reported.
Retailer Number of samples Region City Label
A 63 Lombardy Milan A1–63
B 43 Lombardy Mantova B1–43
C 38 Lazio Pomezia C1–38
D 17 Abruzzo Tortoreto D1–17

Data vectors belonging to the same hemp retailer were firstly evaluated by the analysis of variance via the graphical representation of a box and whisker plot, and afterwards, by two multivariate techniques, the unsupervised principal component analysis (PCA) and supervised PLS-DA.

As shown in Figure 1, the use of the nine cannabinoid variables led to no statistical differences between the hemp samples grouped as sold by the hemp retailers. Except for the high average concentration of THCA and CBGA found in the samples of retailer D, the cannabinoid analytical profile was in all cases the same, with high average concentrations of CBD and CBDA and low average concentrations of the other seven cannabinoids. CBN average concentration was found particularly high in the samples of retailers A and B. Interestingly, CBN is an oxidation product of THCA, and the high content of this cannabinoid can also be a marker of inflorescence quality. The average concentration of THC was in all cases below 0.35% w/w.


Fig1 Palmieri Molecules2019 24-19.png

Fig. 1 Box and whisker plot of the relative concentrations of the six neutral (THC, CBD, CBC, CBG, CBN and CBDV) and the three acidic cannabinoids (THCA CBGA and CBDA) in the 161 hemp samples. The hemp samples were grouped as sold by the four Italian hemp retailers. Concentration of cannabinoids was reported as % w/w. Y axis title = Concentration (% w/w). X axis Title = Hemp retailers. Median and average were depicted with a flat black line and a red cross, respectively.

The results of a Tukey HSD multiple comparison test (see Table S2 in the supplementary material) showed that the acidic cannabinoids had a lower capacity of discrimination than their neutral forms. In fact, the neutral cannabinoids showed a partial discrimination between the four hemp retailers, apart from CBDV.

The univariate data analysis highlighted that the hemp samples sold by the four retailers could not be differentiated only using the analysis of variance because of the overlap in cannabinoid composition of the hemp retailers.

The correlation among the nine cannabinoids analyzed in the hemp samples was analyzed by computing Pearson coefficients (Table 2). The data showed a partial positive correlation between neutral cannabinoids, especially between THC, CBD, and CBC. The only neutral cannabinoid without any correlation was CBDV, which belongs to a class of cannabinoids synthesized from a different precursor and is structurally different from the classical cannabinoids. No correlations were observed between the six neutral and two acidic cannabinoids THCA and CBGA or within the acidic forms. Only a weak correlation between CBG and CBGA could be remarked, as reported also by other work, due to the decarboxylation of CBGA that produces not only CBG but also the other cannabinoids.[18] The acidic cannabinoid CBDA slightly correlated with all six neutral cannabinoids.

Table 2. Correlation matrix (Pearson coefficients) between the nine cannabinoid variables (THC, CBD, CBC, CBG, CBN, CBDV, THCA CBGA and CBDA). The correlation coefficients were calculated using the relative concentrations of cannabinoids in the 161 hemp samples sold by the four Italian retailers.
Cannabinoid THC CBD CBC CBG CBN CBDV THCA CBGA CBDA
THC 1.00 0.80 0.81 0.61 0.50 0.19 0.34 -0.16 0.46
CBD 0.80 1.00 0.91 0.68 0.64 0.20 -0.17 -0.17 0.21
CBC 0.81 0.91 1.00 0.65 0.60 0.19 -0.19 -0.23 0.35
CBG 0.61 0.68 0.65 1.00 0.31 0.12 -0.17 0.44 0.19
CBN 0.50 0.64 0.60 0.31 1.00 -0.03 -0.03 -0.25 0.11
CBDV 0.19 0.20 0.19 0.12 -0.03 1.00 -0.01 -0.04 0.19
THCA 0.34 -0.17 -0.19 -0.17 -0.03 -0.01 1.00 0.01 0.18
CBGA -0.16 -0.17 -0.23 0.44 -0.25 -0.04 0.01 1.00 -0.04
CBDA 0.46 0.21 0.35 0.19 0.11 0.19 0.18 -0.04 1.00

These results agree with data reported by other works and can be explained by the biosynthesis of cannabinoids.[19][20][21]

This partial correlation between variables provided suitable contributions when treated with multivariate statistical procedures.

All data obtained with HPLC-MS/MS analysis were processed by PCA to find every possible cluster within the hemp samples dataset in an unsupervised way. Before applying the PCA algorithm, data were linearly normalized and auto-scaled (zero mean and unitary variance) in order to remove differences in concentration range. PCA was applied to inspect the multivariate data structure by decomposing the data matrix of the 161 hemp samples (in the matrix rows) and the nine cannabinoids analyzed (the matrix columns).

Figure 2 depicts the scores and loading plots of the first three principal components. The first component represents 42.7% of the variance, the second 15.8%, and the third 14.9%, accounting for 74.4% of the total variance for the first three principal components.


Fig2 Palmieri Molecules2019 24-19.png

Fig. 2 Scores plot (A) and loadings plot (B) obtained from the PCA on the matrix data of the 161 hemp samples (in the matrix rows) and the nine cannabinoids analyzed (the matrix columns). Plots of the first three components (explained variance: PC1 = 42.7%; PC2 = 15.8%; PC3 = 14.9%; total = 73.4%). Data have been auto-scaled (zero mean and unitary variance) before PCA. The four hemp retailers are marked with different colors: Green = A; Red = B; Yellow = C; Blue = D.

The score points (Figure 2A), representing the new coordinates of the hemp samples, were interpreted assuming that close distance in plot plane is a measure of the similitude between samples. PC1 separated well both hemp samples sold by retailers B and D, but in the Cartesian graph origin the hemp samples sold by retailers A and C clustered. PC2 did not influence the hemp samples from retailers B and D, but it contributed to the dispersion within the hemp samples sold by retailers A and C, highlighting a similar variance behavior of those two retailers that started to be separated only along the PC3 axis, which spread both samples sold by retailers B and D.

The loadings (Figure 2B), representing the contribution of each cannabinoid to the principal components, contributed mostly to the hemp sample separation on PC1 and PC3. The PC1 axis highlighted the differences among neutral and acidic cannabinoids. Neutral cannabinoids contributed significantly to the separation of the hemp samples sold by retailer B. On the other hand, the acid cannabinoid CBGA played an important role in separation of the hemp samples sold by retailer D. CBN, CBD, and CBC had very similar pattern recognition performance, contributing only in separating hemp samples on PC1. The hemp samples sold by retailers A and C were influenced by THCA, CBDA, and CBDV, contributing to the dispersion on PC2 and to the separation on PC3.

As such, the unsupervised PCA algorithm could partially discriminate hemp samples sold by the four Italian retailers. However, to evaluate the real efficiency of the discrimination among the four retailers, a supervised multivariate discriminant analysis was applied.

The dataset of 161 hemp samples and nine cannabinoid concentrations was used for this approach (see Table S1 of the supplementary material). As in any supervised classification techniques, the classes must be chosen a priori. The choice for the hemp samples in this case was to choose the hemp retailers as classes. With this classification scheme, a PLS-DA model was built. PLS-DA is an extension of PLS, by projecting intercorrelated X-variables from high dimensional space into low-dimensional space according to a Y-vector that encodes the class membership in a set of categorized variables (1 and 0 values, respectively).[22][23] A numerical evaluation of the classification properties was obtained by considering the cross validation of the PLS-DA method according to the "venetian blinds" technique.

The model was evaluated using the following parameters: component in model, explained variance in percentage, error rate in calibration, and error rate in cross-validation. Moreover, specificity sensitivity and precision of the four classes, corresponding to the four Italian hemp retailers, were computed in fitting and cross-validation.

The statistical summary results of the PLS-DA algorithm are shown in Table 3. The results show a very good discrimination between the four classes, with an explained variance of 100% and low classification errors in both calibration (5%) and cross validation (6%) by using eight model components previously optimized by the algorithm.

Table 3. PLS-DA classification results in fitting and cross-validation. A cross-validation "venetian blinds" technique was used, with the number of cv groups equal to three. The optimal components for the model was previously calculated using the MatLab toolbox from Milano Chemometrics and Quantitative Structure Activity Relationship (QSAR) Research Group.
PLS-DA results
Samples: 161
Variables: 9
Classes: 4
Component in model: 8
Explained variance (%): 100%
Calibration error rate: 0.05
Cross-validation error rate: 0.06
Retailer Specificity Sensitivity Precision
Fitting
A 1.00 0.86 1.00
B 1.00 0.88 1.00
C 0.88 1.00 0.72
D 1.00 0.94 1.00
Cross-validation
A 1.00 0.86 1.00
B 0.98 0.88 0.95
C 0.89 0.95 0.72
D 1.00 1.00 1.00

Retailers C and D had the highest sensitivity respectively for fitting and cross-validation, contributing to low classification errors. A very good sensitivity and precision in both calibration and cross-validation were found for retailers A, B, and D.

Real-predicted samples are shown in Table 4 using a confusion matrix format. A total of 92% of the samples have been correctly classified by cannabinoid variables in fitting and cross validation.

Table 4. Confusion matrix of the PLS-DA classification model (fitting and validation results are both reported). A cross validation "venetian blinds" technique was used, with the number of cv groups equal to three. True classes are read along the columns and estimated classes along the rows. The total accuracy was also reported.
Real/Predicted A B C D Accuracy
Fitting
A 54 0 9 0 86%
B 0 38 5 0 88%
C 0 0 38 0 100%
D 0 0 1 16 94%
Total 92%
Cross-validation
A 54 0 9 0 86%
B 0 38 5 0 88%
C 0 2 36 0 95%
D 0 0 0 17 100%
Total 92%

In fitting, retailers C and D showed 100% and 94% of correspondences between real and predicted samples. In cross-validation, this percentage decreased to 95% for retailer C and increased to 100% for retailer D. The retailers A and B had the highest percentage of misclassified samples, with all misclassified samples assigned to retailer C. Those results underlined a close analytical cannabinoids profile between the retailers A, B, and C, also highlighted by the PCA model. The class assigned to each of the 161 hemp samples by the PLS-DA model in fitting and cross validation was reported in Table S3 of the supplementary material.

Materials and methods

Sample collection

A total of 161 samples of cannabis were purchased from four Italian retailers and labeled A, B, C, and D. The samples were bought as whole flowers in 5, 10 or 32-g packages and stored at room temperature until use. All samples were in small zip-lock bags, as typically provided by shops.

Solvents and chemicals

Methanol, acetonitrile, and water were HPLC grade and were obtained from VWR (Milan, Italy). Formic acid (98%) of LC-MS grade and cannabinoid standards of the six neutral cannabinoids (THC, CBD, CBC, CBG, CBN and CBDV), the three acidic cannabinoids (THCA CBGA and CBDA), and internal standard (IS) tetrahydrocannabinol deuterated (Δ9-THC-D3) were purchased from Sigma-Aldrich (Steinheim, Germany). All standards were provided as 1.0 mg/mL solutions in methanol. Ethanol absolute anhydrous (>99%) was obtained from CARLO ERBA (Milan, Italy).

Sample preparation

The extracts were prepared using the procedure of Wang et al.[13], with slight changes. Briefly, before the extraction, every sample was homogenized. Dried sample was triturated three times, each for 10 seconds with a chopper (Kenwood Quad Blade CH580 Chopper), then crushed with a mortar, and finally sifted with a 1 mm sieve. Fine powder of plant material (10 mg) was accurately weighed into a 1.5 mL Eppendorf vial and extracted with 1 mL of ethanol in an ultrasonic water bath for 30 minutes, followed by centrifugation at room temperature at 10,000 rpm for 15 minutes. Prior to HPLC analysis, the supernatant was passed through a 0.2 µm PTFE filter, diluted 2000 times, and collected in an HPLC vial.

HPLC-MS/MS analysis

All analyses were performed on a Nexera LC20AD XR system, with a Prominence 20AD autosampler. The system was equipped with a vacuum degasser and column oven coupled with a 4500 Qtrap from Sciex (Concord, ON, Canada) equipped with a Turbo V electrospray ionization (ESI) source. For analysis of the nine cannabinoids of this work, we used a Kinetex C18-XB column (100 × 2.1 mm ID) from Phenomenex (Torrance, CA, USA) packed with core-shell particles of 2.6 μm held at a temperature of 35 °C. The mobile phase consisted of water containing 5 mM formic acid (phase A) and acetonitrile with 5 mM formic acid (phase B). Analysis was performed using the following gradient elution at a flow rate of 0.3 mL/min: from 0 to 1.1 minute gradient was held at 70% of phase B; from 1.1 to 2 minute phase B was increased from 70% to 90%; at 3 minutes, concentration of phase B was 99% and was held for 2 minutes. Gradient returned to initial condition in 0.2 minutes, followed by a 2.8 minute equilibration, in a total run time of 8 minutes. The injection volume was 3 μL and all samples were injected in triplicate. The analytes were detected in positive ionization (PI) with a capillary voltage of 5500 V, using air ion source gas at 60 psi and nitrogen ion source gas at 40 psi at a temperature of 500 °C. Two multi-reaction monitoring (MRM) transitions were chosen for each analyte. All source and instrument parameters for the monitored analytes were tuned by injecting each single standard solution at a concentration of 10 ng/μL at 7 μL/minute by a syringe pump. The ion currents were acquired in MRM mode, and quantitation was performed by the IS method by means of Multiquant Software from Sciex (Concord, ON, Canada) using THC-D3. All samples were analyzed in triplicate. The selected MRM transitions and HPLC–MS/MS parameters are reported in Table S4 of the supplementary material.

Analytical procedure validation

Limit of quantification (LOQ), limit of detection (LOD), linearity, precision, and accuracy were evaluated in the analytical procedure validation. For each analyte a calibration curve was built with 11 points, repeated in triplicate (0.1–250.0 ng mL−1) of standard solutions. For each concentration level, injections were performed in triplicate and the average value was used for the external standard calibration curves. Because of the absence of “blank” matrices, the LOD and LOQ were obtained at the signal-to-noise ratios of 3:1 and 10:1, respectively, by analyzing different diluted standard samples. For intraday relative standard deviation (RSD), one-day measures of six sample replicates (intraday precision or repeatability) were considered, whereas for interday RSD, samples were analyzed for three consecutive days and twice each day (interday precision or with reproducibility) at three different standard concentrations. The results of the validation experiments are shown in Tables S5–S7 of the supplementary material.

Statistical analysis

Univariate analysis was performed using XLSTAT software (Addinsoft, Long Island City, NY, USA). Experimental results were expressed as means ± standard deviations. Statistical significance was assessed using analysis of variance (ANOVA) with the Tukey HSD (honestly significant difference) multiple comparison analysis. The criterion for statistical significance of differences was P < 0.05 for all comparisons.

Multivariate statistical analysis was performed using two different approaches: PCA and PLS-DA by means of MatLab R2011b (Mathworks, Natick, MA, USA) integrated with two toolboxes for MatLab obtained from Milano Chemometrics and QSAR Research Group.[24][25] The data set consisted of 161 × 9, in which rows represented the samples (161 hemp samples), and columns the nine cannabinoid variables. Data have been auto-scaled (zero mean and unitary variance). Data vectors belonging to the same retailer were firstly analyzed by unsupervised PCA. This technique gives the possibility to project data from a higher to a lower dimensional space having a data overview without any preliminary assumptions.[26] Then, the supervised technique PLS-DA was applied to the auto-scaled data matrix of the nine cannabinoid profiles in order to improve the separation between hemp retailers. PLS-DA was used as a supervised deterministic classification technique capable of discriminating the observations on the basis of a class membership categorical matrix.[27][28] PLS-DA was performed on the dataset using also a cross-validation of the model by using a "venetian blinds" technique, with number of cv groups equal to three. Using confusion matrices, the reliability of the classification models achieved was studied in terms of recognition ability (percentage of the members of the training set correctly classified) and prediction ability (percentage of the members of the test set correctly classified using the rules developed in the training step).

Conclusions

The analysis of nine cannabinoids by means of HPLC-MS/MS was used to evaluate the feasibility of identifying samples from hemp retailers located in Italy without having any other information on the sold samples, including cannabis strain, soil and cultivation characteristics, geographical origin, product storage, etc.

The cannabinoid analytical profile was in all cases the same, with high concentrations of CBD and CBDA and low concentrations of the other seven cannabinoids. The univariate evaluation of the cannabinoids showed no statistical differences between the hemp samples, demonstrating that analyzing each cannabinoid individually was not enough to identify the hemp retailers.

On the other hand, the synergic contribution of the nine cannabinoid concentrations could identify the hemp retailers as demonstrated by PLS-DA algorithm. A total of 92% of the hemp samples were correctly classified by the cannabinoid variables in both fitting and cross-validation.

In conclusion, the present study contributes to the characterization of hemp samples sold by retailers without any other information, proving that a simple chemical analysis coupled with a robust chemometric method could be a powerful tool for forensic purposes.

Supplementary material

The following are available online:

  • Table S1: Relative concentrations of the nine cannabinoids in the 161 hemp samples grouped as sold by the four Italian hemp retailers. Region and city origin of the retailers were also reported. In bold the descriptive statistics of each retailer group. CV = coefficient of variation; SD = standard deviation. Concentration of cannabinoids was reported as % w/w.
  • Table S2: Analysis of variance (ANOVA) using the Tukey HSD (honestly significant difference) multiple comparison test. The criterion for statistical significance of differences was P < 0.05 for all comparisons.
  • Table S3: Comparison between retailer assigned classes (A) and classes calculated by the PLS-DA algorithm using fitting (F) and cross validation (V). The PLS-DA model calculated the classes using the relative concentrations of the nine cannabinoids in the 161 hemp samples and, as classes, the four hemp retailers.
  • Table S4: MS/MS parameters. Multi-reaction monitoring (MRM) transitions: Q1 MASS = precursor ion mass (amu); Q3 MASS = product ion mass (amu). TIME = dwell time. DP (V) = de-clustering potential (amu). EP (V) = entrance potential. CE (V) = collision energy. CXP (V) = cell exit potential.
  • Table S5: Limit of quantification (LOQ), limit of detection (LOD), calibration curve equation and correlation coefficient obtained in analytical procedure validation
  • Table S6: The accuracy results, reported in percentage (%), obtained in analytical procedure validation
  • Table S7: The intraday interday precision results, reported in percentage (%), obtained in analytical procedure validation

Acknowledgements

Author contributions

Conceptualization, M.M. and M.S.; Data curation, S.P., M.M., A.R. and F.F.; Formal analysis, S.P., F.F. and C.O.; Funding acquisition, A.R., C.L.S., M.M. and M.S.; Investigation, S.P., F.F. and C.O.; Methodology, S.P., M.M., A.R., F.F., C.L.S. and M.S.; Supervision, M.M., A.R., C.L.S. and M.S.

Funding

This research received no external funding.

Conflict of interest

The authors declare no conflict of interest.

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Notes

This presentation is faithful to the original, with only a few minor changes to presentation. Some grammar and punctuation was cleaned up to improve readability. In some cases important information was missing from the references, and that information was added. The original article states the supplementary material is available online, but it doesn't state where; a comment was added to the original article asking from where the material can be retrieved.