Received: 18 October 2017
Revised: 18 April 2018
Accepted: 7 May 2018
DOI: 10.1002/cem.3050
RESEARCH ARTICLE
Towards polypotent natural products: The Derringer desirability approach and nonparametric ranking for multicriteria evaluation of essential oils Filip Lj. Andrić University of Belgrade ‐ Faculty of Chemistry, Studentski trg 12‐16, 11000 Belgrade, Serbia Correspondence Dr Filip Lj. Andrić, assistant professor, Department of Analytical Chemistry, Faculty of Chemistry, University of Belgrade, Studentski trg 12‐16, 11000 Belgrade, Serbia. Email:
[email protected] Funding information Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant/Award Number: 172017
Abstract Chemical complexity of natural products often results in their pharmacological polypotency. However, selecting a natural product with desirable activity profile is not a straightforward task, especially if optimization of one feature results in deterioration of other facets. Recently, in the field of multiobjective optimization, the sum of ranking differences (SRD) has emerged as a simple and statistically sound method for fusion of multiple criteria. However, the data pretreatment seems to strongly influence the ranking outcome, which may lead to ambiguous or even false interpretations. Therefore, in the present study, the data of 55 essential oils originated from different plant species and tested on multiple bacterial and fungal strains as well as 4 antioxidative assays were studied. Essential oils were ranked using the classical Deringer desirability approach, and results were compared with the SRD analysis of primary activity data as well as the previously row‐wise standardized data, normalized data, and the data scaled to fit the preferences. Ultimately, the most promising candidate (polypotent) essential oils, as well as the most resilient and most sensitive bacterial and fungal strains, and antioxidative assays were identified. Data transformation based on the Deringer desirability approach, compared with the data that have not been previously transformed or those that transformed using a row‐wise standardization or normalization to the unit length vector, seemed to be the crucial step providing the sound and meaningful SRD ranking. KEYWORDS essential oils, multiobjective optimization, natural products, polypotency, sum of ranking differences
1 | INTRODUCTION The quest for the polypotent natural products, especially herbal remedies, dates back to ancient times and reflects the efforts of mankind for discovering the universal medicine (panacea). It closely relates to the culture of mixing, ethnic and cultural diversity, as well as to the modern notions of polypharmacology, network pharmacology, and drug synergism. An extensive overview of the topics is given by Gertsch.1 Here only a few points will be emphasized. First of all, even a single plant extract is a mixture of many compounds, mostly secondary metabolites with potential pharmacological profiles.2 Such chemical complexity is a consequence of evolutionary designed responses of plants to external Journal of Chemometrics. 2018;e3050. https://doi.org/10.1002/cem.3050
wileyonlinelibrary.com/journal/cem
Copyright © 2018 John Wiley & Sons, Ltd.
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stimuli, such as microbial or predator attacks, which lead to an increase in biosynthesis of several different classes of molecules rather than a single one.3,4 Second, some compounds may target several receptors simultaneously,5 through the so‐called substance‐ligand promiscuity, and modulate several metabolic routes. Third, some of the compounds may exert a synergistic effect, either by targeting different receptors of the same metabolic/signaling pathway5,6 or by changing pharmacokinetic, pharmacodynamic, or physicochemical properties of the mixture constituents, eg, by altering their solubility or bioavailability.7 By working in networks, phytochemicals may reach a therapeutic effect in significantly smaller doses, practically at the levels of low bioavailability, which are far away from the adverse effect concentrations. Therefore, natural remedies are still very effective therapeutics and usually have a low incidence of adverse effects. Rich chemical profiles of natural products such as essential oils (EOs) make them exerting multiple activity facets addressing various antibacterial, antifungal, and antioxidative properties.8 However, selecting a natural product with desired activity profile is not a straightforward task, especially if optimization of one property leads to complete deterioration of other aspects. Although application of experimental design for finding optimal mixtures of EOs has been reported,9 basically all statistical solutions dealing with multiple objectives and trade‐offs between conflicting criteria are perfectly suitable. Desirability‐based methods and Pareto‐based approaches, usually coupled with evolutionary algorithms, have been frequently applied in drug design and drug discovery, aiming to find viable candidates with optimal ratios between activity, toxicity, pharmacokinetics, and pharmacodynamics.10-12 However, recently, the sum of ranking differences (SRD) has emerged in the field of multiobjective optimization (MOO) as a statistically sound and simple method for ranking of alternative solutions based on multiple criteria. So far, the method has been applied for fusion of several outlier measures in order to enhance the selection of spectral outliers,13 merging agrochemical parameters for selection of multiperspective crops and products,14-16 fusion of multiple lipophilicity measures for ranking thiepine derivatives,17 and combining multiple model performance parameters for selection of the optimal models.18,19 Although Rácz et al19 have reported good agreement of the SRD and Derringer desirability approach,20 Csambalik et al14 have pointed out that initial data pretreatment, especially criteria scaling, may strongly influence the outcomes of the SRD analysis. However, despite its increasing use, there is still no comprehensive evaluation of the SRD applications in MOO and multicriteria decision making (MCDM) and no consensus or guidance on how to properly perform the SRD analysis in this context. Therefore, the aims of the present study are: (a) to pinpoint crucial advantages and disadvantages of the SRD in MCDM, (b) to investigate various data pretreatment methods prior the SRD analysis, and (c) to compare the outcomes of the SRD ranking with the classical Deringer desirability approach for selection of the multipotent natural products, here demonstrated on 2 case studies of EOs with various antimicrobial and antioxidative activities. We hope that the results of this study will facilitate the use of the SRD in the field of MCDM and MOO, especially in the chemistry of natural products, which exhibit multiple biological and pharmacological activities.
2 | MATERIAL A ND METHODS 2.1 | Data collection For the first case study, the data have been compiled from several works of Božin et al.21-24 The authors systematically examined 10 EOs all belonging to the family Lamiaceae. They comprehensively studied chemical composition and antioxidative and antimicrobial activities. Antioxidative activity was assessed by 4 assays measuring radical scavenging capacity and lipid peroxidation (LP) inhibition. Radical scavenging activity was evaluated using 2,2‐diphenyl‐1‐ picrylhydrazyl (DPPH) and OH radical scavenging assays. The latter was determined by measuring degradation of 2‐ deoxyribose by OH radicals formed in the Fenton reaction. Lipid peroxidation was measured by formation of malondialdehyde during liposome degradation, induced by 2 systems of peroxidation: Fe2+/ascorbic acid (LP1) and Fe2+/H2O2 (LP2). Six fungal strains and 13 bacteria (including highly antibiotic‐resistant forms) were used for assessment of antimicrobial activity. The authors maintained a high level of consistency in all published works. Djaković‐ Sekulić et al25 have recently summarized one portion of the data for multivariate data analysis. However, because of the missing half maximal inhibitory concentration values for DPPH and OH radical scavenging activities of 3 Mentha EOs, only 7 of 10 EOs have been included in this study. The data are summarized in Table 1. The data for the second case study are taken from the well‐known work of Hammer et al.26 The authors studied antimicrobial activity of 52 EOs from various plants, against 10 bacterial strains and 1 fungus (Candida albicans). Owing to missing data, 48 EOs of 52 have been included in the present study (Table 2).
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Antioxidative, antifungal, and antibacterial activities of essential oils: case study 1a
TABLE 1
Essential Oils Salvia nemorosa
Property/Activity
Rosmarinus officinalis
Salvia officinalis
Ocimum basilicum
Origanum vulgare
Thymus vulgaris
Melissa officinalis
Antioxidative Activity 2+
LP1 (Fe /ascorbic acid) 2+
LP2 (Fe /H2O2)
b
b
56.27
65.31
49.13
74.02
80.30
47.54
34.34
90.14
45.14
37.78
47.06
60.92
56.66
34.34
DPPHc
0.98
3.82
1.78
0.39
0.17
0.19
7.60
c
0.11
2.03
5.80
2.24
0.96
22.01
0.80
OH
Antifungal Activity d
Trichophyton mentagrophytes
100.3
15.3
60.0
8.3
1.0
2.2
15.0
Trichophyton rubrumd
100.0
15.0
60.0
8.3
1.2
2.0
15.0
100.0
15.2
60.0
8.0
1.0
2.2
15.0
200.0
30.2
100.2
15.2
2.0
2.2
30.0
Epidermophyton floccosum
200.0
30.0
100.0
15.0
2.0
4.0
30.0
Candida albicansd
200.2
30.2
200.0
30.0
2.0
4.0
30.0
e
250.7
30.0
100.0
15.0
1.0
4.0
30.0
200.2
30.2
100.3
15.2
2.2
4.2
30.0
T tonsurans
200.0
30.0
100.3
15.0
2.0
4.0
15.0
M canise
200.2
30.2
200.2
30.2
2.2
4.0
30.0
250.2
30.0
200.2
30.0
2.3
4.2
60.0
400.2
60.2
250.0
30.0
4.0
4.0
60.0
d
Trichophyton tonsurans d
Microsporum canis
d
T mentagrophytes e
T rubrum
e
e
E floccosum C albicans
e
f
Antibacterial Activity Pseudomonas aeruginosa (ATCC27853)
0.0
0.0
0.0
0.0
19.4
12.2
14.8
P aeruginosa (IPH‐MR)
0.0
0.0
0.0
0.0
20.0
0.0
0.0
Escherichia coli (ATCC35218)
0.0
23.0
20.4
19.4
42.6
25.2
17.2
E coli (ATCC25922)
0.0
25.0
24.6
18.2
50.2
25.2
39.8
E coli (IPH‐MR)
0.0
18.2
14.2
17.8
28.0
29.4
18.6
Salmonella enteritidis (IPH‐MR)
0.0
29.0
10.0
16.6
40.2
29.8
16.2
19.8
16.2
50.0
28.0
40.2
25.4
24.4
Salmonella typhi (IPH‐MR) Shigella sonnei (IPH‐MR)
17.6
19.6
13.2
23.6
44.6
30.6
38.4
Sarcina lutea (ATCC9341)
19.0
43.2
21.2
19.4
45.4
32.4
24.6
Micrococcus flavus (ATCC10240)
20.0
23.6
60.6
50.0
60.0
50.0
30.0
Staphylococcus aureus (ATCC6538)
19.6
29.0
20.0
28.0
40.2
39.8
19.4
Staphylococcus epidermidis (ATCC12228)
18.2
20.2
49.2
22.0
50.2
40.6
26.6
Bacillus subtilis (ATCC10707)
23.2
21.4
0.0
59.0
57.4
48.8
28.2
Abbreviations: DPPH, 2,2‐diphenyl‐1‐picrylhydrazyl; LP, lipid peroxidation; IPH, isolated from patient; MR, multiple resistant form. a
Data have been collected from previous studies.21-25
b
Given as the arithmetic mean of prooxidative activity inhibition (%) measured at 3 concentration levels of essential oils.
c
Given as half maximal inhibitory concentration (μL/mL).
d
Provided as the minimal inhibitory concentration (μL/mL).
e
Measured as the minimal fungicidal concentration (μL/mL).
f
Measured as the surface area of inhibition zone (mm) for 20% v/v solution of essential oil in hexane.
EO
Cedrus atlantica
Citrus aurantifolia
Citrus aurantium EO
Cedarwood
Lime
Orange
EO
Citrus reticulata var. madurensis
Commiphora myrrha
Coriandrum sativum
Cucurbita pepo
Cupressus sempervirens
Cymbopogon citratus
Cymbopogon martinii
Daucus carota
Eucalyptus polybractea
Mandarin
Myrrh
Coriander
Pumpkin
Cypress
Lemongrass
Palmarosa
Carrot seed
Eucalyptus
EO
EO
EO
EO
EO
FO
EO
EO
Citrus × paradisi EO
Grapefruit
EO
Citrus limon
Lemon
C aurantium var. EO bergamia
Bergamot
EO
C aurantium
Petitgrain
1.0
2.0
0.12
0.03
2.0
2.0
0.25
2.0
2.0
2.0
2.0
2.0
0.5
2.0
1.0
2.0
1.0
Cananga odorata EO
Ylang‐ylang
EO
1.0
Frankincense Boswellia carterii EO
0.12 2.0
Apium graveolens
Celery seed
EO
EO
Aniba rosaeodora
Rosewood
0.5
2.0
0.12
0.12
2.0
2.0
0.25
2.0
2.0
1.0
1.0
2.0
0.5
1.0
1.0
2.0
0.5
1.0
1.0
0.12
Aeromonas sobria
Acinetobacter baumannii
Extract Type
Common Name
Plant Source
Microbial Strains
1.0
2.0
0.06
0.06
2.0
2.0
0.25
2.0
2.0
1.0
2.0
1.0
0.25
1.0
2.0
2.0
1.0
1.0
1.0
0.25
Candida albicans
2.0
2.0
0.25
0.12
1.0
2.0
1.0
0.25
2.0
2.0
2.0
2.0
2.0
2.0
2.0
0.5
2.0
2.0
2.0
0.5
Enterococcus faecalis
1.0
2.0
0.06
0.06
2.0
2.0
0.25
2.0
2.0
2.0
2.0
1.0
0.25
2.0
1.0
2.0
2.0
1.0
2.0
0.12
Escherichia coli
2.0
2.0
0.25
0.25
2.0
2.0
0.5
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
0.5
2.0
2.0
2.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Klebsiella Pseudomonas pneumoniae aeruginosa
Antimicrobial activity of a series of 48 essential oils against 11 microorganisms (10 bacteria and 1 fungus)a
Essential Oils
TABLE 2
2.0
2.0
0.5
0.25
2.0
2.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
0.25
1.0
2.0
0.25
0.25
2.0
2.0
0.5
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
0.5
2.0
1.0
0.12
0.06
2.0
2.0
0.25
0.5
2.0
2.0
2.0
2.0
0.5
2.0
2.0
2.0
1.0
1.0
1.0
0.25
(Continues)
Salmonella Serratia Staphylococcus typhimurium marcescens aureus
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Gaultheria procumbens
Juniperus communis
Lavandula angustifolia
Macadamia integrifolia
Melaleuca alternifolia
Melaleuca cajuputi
Melaleuca quinquenervia
Mentha spicata
Ocimum basilicum
Oenothera biennis
Origanum majorana
Origanum vulgare
Pelargonium graveolens
Pimpinella anisum
Pimenta racemosa
Wintergreen
Juniper
Tasmanian lavender
Macadamia
Tea tree
Cajuput
Niaouli
Spearmint
Basil
Evening primrose
Marjoram
Oregano
Geranium
Aniseed
Bay
EO
EO
EO
EO
EO
FO
EO
EO
EO
EO
EO
FO
EO
EO
EO
EO
0.12
0.5
0.25
0.12
0.25
2.0
0.5
0.25
0.25
1.0
0.25
2.0
0.5
2.0
0.25
1.0
0.12
0.25
0.25
0.12
0.25
2.0
0.5
0.25
0.25
1.0
0.5
2.0
0.5
1.0
0.25
0.5
0.12
0.5
0.12
0.12
0.25
2.0
0.5
0.12
0.25
1.0
0.5
2.0
0.25
2.0
0.25
0.5
Candida albicans
0.5
2.0
0.5
0.25
2.0
2.0
2.0
2.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Enterococcus faecalis
0.12
0.5
0.25
0.12
0.25
2.0
0.5
0.25
0.25
1.0
0.25
2.0
0.25
2.0
0.5
0.5
Escherichia coli
0.25
2.0
2.0
0.12
0.5
2.0
2.0
0.5
0.5
2.0
0.5
2.0
2.0
2.0
1.0
2.0
1.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Klebsiella Pseudomonas pneumoniae aeruginosa
Data have been taken from the work of Hammer et al.26 Antimicrobial values have been given as minimal inhibitory concentrations (v/v %).
a
Abbreviation: EO, essential oil; FO, fixed oil.
Foeniculum vulgare
Fennel
Aeromonas sobria
Acinetobacter baumannii
Extract Type
Common Name
Plant Source
Microbial Strains
(Continued)
Essential Oils
TABLE 2
0.25
2.0
2.0
0.12
0.5
2.0
2.0
0.5
0.5
2.0
0.5
2.0
2.0
2.0
0.5
1.0
0.25
1.0
2.0
0.25
0.5
2.0
2.0
0.25
0.5
2.0
0.5
2.0
2.0
2.0
0.5
2.0
0.25
0.25
0.25
0.12
0.5
2.0
2.0
0.25
0.5
1.0
0.5
2.0
1.0
2.0
2.0
0.25
Salmonella Serratia Staphylococcus typhimurium marcescens aureus
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2.2 | Multiobjective optimization 2.2.1 | Scaling data to fit preferences In order to rank EOs according to increased polypotency, criteria to be fused should be expressed in the same scale, securing in that way the fair trade‐off between each of them. Considering the aim of MOO, it would be useful if scaling of original values could also reflect preference ordering; ie, the smaller the scaled value, the lower the preference should be and vice versa. The desirability approach proposed by Harrington27 and later modified by Derringer and Suich20 is particularly suitable because of its simplicity. The method defines the partial desirability transformation function dij for any criterion Cj and any value xij in the following manner. If the criteria are to be maximized, ie, the preference order should follow a natural order of original values, then 9 8 x ij −L1j r > > > > > > < L2j −L1j L1j > > > > ; : 1 x ij ≥L2j
(1)
If the criteria are to be minimized, ie, the preference order should follow reverse order of original values, then 9 8 L2j −Lij r > > > > > > < L −L L1j > > > > ; : 1 x ij ≥L2j
(2)
where L1j and L2j are lower and upper desirability limits, respectively. In this way, any value xij is scored between 0 and 1, depending on whether it falls between predefined desirability range, exceeds the upper limit (in which case it is scored as 1, complete desirability), or falls below the lower limit (in which case it is scored as 0, undesirable performance). Parameter r defines the shape of the partial transformation function. For the sake of simplicity, the linear dependence (r = 1) was presumed. For the first case study, the criteria are grouped in 5 blocks. Lipid peroxidation assays, LP1 and LP2, are considered as a part of the same block because they have been measured in the same fashion and expressed in the same units. The lower and upper desirability limits are defined as 0% and 100% of prooxidant activity inhibition, respectively. Similarly, DPPH and OH antioxidative activities are placed in another block. Antifungal activity expressed in minimal inhibitory concentrations was in the third block, while the same activity expressed differently (in minimal fungicidal concentrations) was placed in the fourth block. Antibacterial activities are put together in the last block, the fifth. The criteria belonging to the same or similar blocks may be considered to supplement each other, ie, being able to address, at least partially, different aspects of the same property/information. The lower and upper desirability limits are then defined for each block, on the basis of the global minima and maxima (Table 3). In this particular case, all criteria have been a priori considered as equally important.
2.2.2 | The overall Derringer desirability After scaling the data between 0 and 1, the overall desirability score Dj is assigned to each alternative Aj. In his work, the Deringer proposes the geometric mean of partial desirability scores as a fusion method (Equation 3). However, this is rather a rigorous condition. If only one score is zero, the overall desirability is zero as well. Instead of it, we have decided to use the arithmetic mean (Equation 4). sffiffiffiffiffiffiffiffiffiffiffi Dj ¼
n
n
∏ dij i¼1
(3)
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TABLE 3 Lower and upper limits (L1 and L2, respectively) of Derringer partial optimization function defined for the first and second case studies parameters Criteria
L1
L2
First case study Antioxidative activity (LP1 and LP2)
0
100 a
Antioxidative activity (DPPH and OH)
0.099
24.21b
Antifungal activity (MIC)
0.900a
220.22b
Antifungal activity (MFC)
0.900a
440.22b
Antibacterial activity
0.000
66.67b
0.0027a
2.20b
Second case study Antimicrobial activity (MIC, v/v %)
Abbreviations: DPPH, 2,2‐diphenyl‐1‐picrylhydrazyl; LP, lipid peroxidation; MFC, minimal fungicidal concentration; MIC, minimal inhibitory concentration. a
Value corresponds to the 10% below the global minimum.
b
Value corresponds to the 10% above the global maximum.
Dj ¼
1 n ∑ dij n i¼1
(4)
In the case of unequal importance of criteria, the simplest weighting scheme can be easily implemented by transforming the overall desirability score function as n
Dj ¼ ∑ wi dij
(5)
i¼1
where wi is a weight of a criteria i and the total sum of weights is unit n
∑ wi ¼ 1
(6)
i¼1
2.2.3 | Sum of ranking differences Sum of ranking differences is a simple, robust, nonparametric method for comparison and ranking of methods, models, solutions, alternatives, etc.28,29 In order to perform the SRD, the data are arranged in a matrix of alternatives placed in columns, while criteria to be fused are arranged in rows (Figure 1). Then, a reference column is added (step 2, Figure 1). In the first case study, the reference was carefully selected in order to maximize the values of LP1 and LP2 assays and antibacterial activity, while minimizing the values of antifungal activity, and DPPH and OH antioxidative assays. However, if the SRD is performed on the data already scaled to fit the preferences, then the reference is simply a row‐wise maxima or minima vector, depending on whether alternatives should be ranked according to the preference or against of it. For the antimicrobial activity data in the second case study, the reference was a row‐wise minima vector. After matrix arrangement, values are ranked in ascending order, taking average ranks for ties (step 3, Figure 1). Then, for each alternative, the ranks are subtracted from the reference ranking, and the absolute rank differences are summed up into a single SRD value (steps 4 and 5, Figure 1) (Equation 7). The lower the SRD value, the closer is that alternative to the reference (trade‐off optimum). In order to compare results of different SRD calculations, the SRD values are usually scaled between 0 and 100 (Equation 8): n SRDj ¼ ∑ r ij −r iref i¼1
(7)
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FIGURE 1 Crucial steps in a fusion of multiple criteria by the SRD ranking of alternatives: (1) data rescaling, (2) adding a reference, (3) ranking, (4) rank subtraction, (5) summation of ranks to the SRD scores, and (6) arranging of alternatives. SRD, sum of ranking differences
SRDnorm ¼ 100×
SRD SRD max
(8)
The ranking is validated in two ways. One is a comparison with random numbers. It is basically a randomization test that uses random ranks and yields the random distribution of SRD values. If an alternative falls under the bell‐shaped random distribution curve, it can be considered as statistically insignificant (cf the Gaussian‐shaped curve in Figures 3–7). The other way is a cross‐validation (CV) procedure, here performed by omitting one‐seventh of criteria for 7 times. Although the splitting ratio may be slightly altered, depending on the number of criteria/objects, significantly lower or higher ratios may underestimate or overestimate variability of the SRD scores. In the case of high number of criteria/objects (n > 14), 7‐fold splitting may be optimal. In the case of lower number of criteria (n < 10), the leave‐one‐out CV is more appropriate. Medians of the SRD values calculated from CV experiments are then used to test statistically significant differences, by the sign test or the Wilcoxon matched pairs test. The results are depicted as a box and whisker plot (cf Figures 4B and 5B). The SRD algorithm that takes into account tied values was used as a Microsoft Excel visual basic macro freely available at http://aki.ttk.mta.hu/srd/. Since results of the SRD analysis may depend on the number of digits of input data, the algorithm was set up to 3 digits.
3 | R E S U L T S AN D D I S C U S S I O N 3.1 | Selection of polypotent essential oils by Deringer desirability approach For the first case study, in order to reveal intrinsic relationships in trade‐offs between different activity aspects of EOs, the overall desirability scores have been calculated from partial desirability values belonging to (1) antioxidative activity data (LP1, LP2, DPPH, and OH), (2) antifungal activity, expressed in both minimal inhibitory concentrations and minimal fungicidal concentrations, and (3) antibacterial activity. For the second case study, the entire dataset was treated as a single block. For significance testing of desirability scores, the 95% confidence intervals have been estimated by CV. Considering small number of criteria in the case of the antioxidant activity data, as well as in the case of the second case study, the leave‐one‐out CV was used. However, the 7‐fold CV was used in the case of the antibacterial and antifungal activities from the first case study. Usually, confidence intervals of desirability scores are estimated by propagation of uncertainties of original variables. Since those uncertainties were unknown, the CV was used.
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FIGURE 2
Derringer desirability scores of essential oils form (A) the first case study and (B) the second case study. Vertical bars denote 95% confidence intervals estimated by the 7‐fold or leave‐ one‐out cross‐validation. Nonmonotonous, conflicting profiles of desirability scores in A, point out to the presence of significant trade‐offs among biological activities of essential oils
The overall desirability scores decrease monotonically from the highest value obtained for Origanum vulgare EO to the lowest value obtained for Salvia nemorosa EO (Figure 2A). Despite the monotonic decrease in the overall scores, partial desirability functions for antioxidative, antibacterial, and antifungal activities fluctuate, often in mutually conflicting trends, which demonstrate many trade‐offs between criteria. For example, EO of S nemorosa has the lowest overall antifungal activity while exhibiting the highest antioxidative properties. Similarly, Melissa officinalis EO has the lowest antioxidative power, while the antifungal activity scores very high. In the same way, the antibacterial activity of Thymus vulgaris EO is significantly higher than Ocimum basilicum or Rosmarinus officinalis EOs. However, antioxidative properties of O basilicum and R officinalis EOs are significantly higher than those of T vulgaris EO. This clearly demonstrates that selection of the polypotent EO is a delicate task. Also, individual contributions of antifungal, antioxidative, and antibacterial activities to the overall desirability profile are different. Clearly, the antifungal activities have the highest impact compared with the lowest influence of antibacterial properties. The overall desirability scores are monotonically decreasing from O vulgare to S nemorosa EOs separating them statistically significantly from the EOs positioned in between. Therefore, those 2 can be identified as the most and least polypotent products (Figure 2A, cf CV confidence intervals). In the second case study, the overall desirability scores are monotonically decreasing from the lemongrass, bay, oregano, palmarosa, and rosewood EOs (values > 0.9) to the least potent ones such as pumpkin, macadamia, pine, and ginger oils with score values < 0.1 (Figure 2B).
3.2 | Fusing multiple criteria by the sum of ranking differences There are several issues related to fusion of multiple criteria by the SRD. Some of them such as selection of relevant criteria and weighting criteria of higher or lower importance are of general significance and may be related to other MOO and MCDM methods as well. Rácz et al19 have tackled some of these problems while discussing advantages of
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FIGURE 3 SRD comparison of essential oils for the first case study: (A) untreated activity data, (B) row‐wise standardized data, and (C) row‐wise normalized data to the unit vector length result in different ranking patterns. Explanation of the position of essential oils under the random distribution curve or on the right side of the plot is rather intricate. CRRN, comparison with random numbers; SRD, sum of ranking differences
FIGURE 4 Sum of ranking differences (SRD) comparison of essential oils from the first case study based on the scaled data to fit the preferences: (A) comparison with random numbers (CRRN) and (B) the 7‐fold cross‐validation ranking. Dashed lines separate essential oils in 4 sections on the basis of the Wilcoxon matched pairs test and the sign test (P = .05). O vulgare essential oil was identified as the most polypotent one, while S nemorosa and S officinalis have the lowest potency
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FIGURE 5
Sum of ranking differences (SRD) comparison of 48 essential oils from the second case study, based on the data scaled to fit the preferences: (A) comparison with random numbers (CRRN) and (B) the 7‐fold cross‐validation ranking. Dashed lines divide oils into 6 major sections on the basis of the Wilcoxon matched pairs test and the sign test (P = .05). The lemongrass oil was identified as the most polypotent one
the SRD, which, according to them, may be considered as more “objective” approach since it does not assume any weighting scheme. Still, there are 2 major issues related to the SRD, which are not properly addressed in the present MOO and MCDM practices. The first one is that criteria are often expressed in different scales. Such differences may range from one to several orders of magnitude. The greater the differences are, and the smaller the number of criteria is, the more affected the results of the SRD analysis are. The second problem is that no cutoff values are usually defined for each criterion. In that way, irrelevant information is frequently included in the SRD analysis (eg, insignificant F ratios, huge model errors, and unacceptably low R values). The cause of the first problem lies in the rank transformation of original data, which is an inevitable part of the SRD itself. Rank transformation diminishes scale differences to various extent depending on the data structure, which consequently may produce artifacts and misleading results. To illustrate this, let us consider 2 alternatives A1 and A2, which should be compared with the reference R, all given as vectors of 3 criteria C1, C2, and C3 expressed in different scales: C1 = {10‐500}, C2 = {2‐30}, and C3 = {0.15‐2}; A1 = [10, 2, 0.15], A2 = [250, 15, 1.5]; and R = [500, 30, 2]. It is clear that alternative A2 is much closer to R than alternative A1 (compared by a simple vector dot product, Euclidian or Manhattan distance). However, after rank transformation, it becomes A1 = A2 = R = [1, 2, 3]. Moreover, what if any C1 < 20 and C3 < 1 are statistically insignificant or irrelevant values? After being replaced by zeros in A1 and following rank transformation, it becomes A1 = [1.5, 3, 1.5] and A2 = R = [1, 2, 3]. Therefore, the adequate data transformation prior the SRD is necessary in all cases involving criteria expressed in different scales or ranges (step 1, Figure 1). However, the choice of transformation method is not straightforward. The data can be interval scaled, standardized, normalized, etc. Furthermore, transformation can be performed column‐wise or row‐wise. Row‐wise transformation is essential in MCDM, simply because it covers one or multiple criteria across the population of alternatives. On the contrary, column‐wise transformation deals with each alternative separately and produces significant artifacts. In this work, the SRD of EOs has been performed on (1) primary data (without any transformation), (2) row‐wise
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FIGURE 6 SRD analysis of (A) antibacterial, (B) antioxidative, and (C) antifungal activity data from the second case study. DPPH, 2,2‐ diphenyl‐1‐picrylhydrazyl; LP, lipid peroxidation; SRD, sum of ranking differences
FIGURE 7 SRD ranking of antimicrobial activities of essential oils from the second case study. C albicans, S aureus, and E coli were identified as the most susceptible organisms to majority of essential oil, while P aeruginosa demonstrated high resistance. CRRN, comparison with random numbers; SRD, sum of ranking differences
standardized data, (3) row‐wise normalized data (to the unit vector length), and (4) the data transformed using the Deringer desirability approach as described in Section 2.2.1. The SRD analysis of primary and row‐wise standardized activity data provides almost the same ranking (Figure 3A and 3B). In both cases, EOs of O vulgare and T vulgaris were identified as the most potent ones, while both Salvia spp ranked the last. However, the row‐wise normalization places the M officinalis and O basilicum oils among the worst ones together with Salvia spp (Figure 3C). Meanwhile, two important features make the interpretation of the SRD results complicated. The first one is the presence of EOs on the right side of the plot, positioned out of the random distribution curve, such as Salvia spp, and the majority of oils in the case of normalized data. The second one is EOs positioned under the random distribution curve, such as R officinalis and/or M officinalis. In the first case, SRD values associated with such EOs can be explained by the reverse ranking of criteria (statistically opposite or negative relation to the reference). In the second case, the position of EOs can be explained by their inability to rank criteria in any systematic fashion, except a random one.
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However, the SRD analysis performed on the Derringer partial desirability scores results in a similar order of EOs as the previous methods (Figure 4A) and the same order as the Deringer multicriteria ranking (cf Section 3.1 and Figure 2 A) with one significant difference—all EOs are located on the left side of the plot, in the range between 10 and 30 SRD normalized units, far from the random distribution curve, being all statistically significantly close to the reference. Therefore, interpretation of the SRD is much easier. This is a significant improvement because, in addition to scaling criteria to the same range (between 0 and 1), only relevant information, selected by desirability limits, was included in the SRD analysis. However, a precaution should be taken when defining the desirability ranges. If the ranges are set in a way that in every criterion at least one zero and one unit occur, then the reference vector will result in series of units (row‐wise maximum) or zeros (row‐wise minimum). This will ultimately lead to skewed SRD results. In order to avoid such problem, a block‐wise (global) minima or maxima should be used instead of local ones, or a value that is a bit lower, or a bit higher (for approximately 10%) of the global minimum or maximum (see Table 3). Grouping of EOs in sections was performed on the basis of the 7‐fold SRD CV. The SRD values are arranged in ascending order of medians, and the statistically significantly different sections are indicated by dashed lines in the box and whisker plot (Figure 4B). The results of significance testing by the sign test and the Wilcoxon matched pairs test are given as the matrices of z scores (Tables S1a and S1B). Again, the most polypotent oil comes from O vulgare, denoted as I, which is closely followed by O basilicum and M officinalis. The last 2 are differentiated by the Wilcoxon matched pairs test but not by the sign test. Nevertheless, they are placed in group II. The oils made from R officinalis and T vulgaris cannot be distinguished from each other (group III). The least potent ones are Salvia officinalis and S nemorosa EOs (belonging to group IV). Inside the z score matrices, the most polypotent EOs can be found in the upper left corner (O vulgare), while the least polypotent ones are positioned in the lower right corner (S officinalis and S nemorosa). Black squares and shaded areas along matrix diagonal annotate statistically indistinguishable groups of EOs (Tables S1a and S1B). Although the SRD ranking of EOs from the second case study was performed on partial desirability scores, results are not significantly different from the ones obtained from untreated data (results not presented). This can be explained by the fact that the same method for testing antimicrobial activity of oils was applied to all microbial organisms. Significance testing separates all EOs in 6 groups. Both the sign test and the Wilcoxon matched pairs test give highly similar results (Tables S2A and S2B). The lemongrass EO was identified as the most polypotent one and statistically significantly different from the rest of EOs (Figure 5). The coriander, frankincense, and cajuput oils follow it as part of group II. The EOs belonging to the third group exhibit pseudo‐continuous ranking. Therefore, this group can be further divided into 4 subgroups (III‐A to III‐D). The term pseudo‐continuous means that distinction between the subgroups is not clear. This is demonstrated by overlapping between squares in the z score matrices (Tables S2A and S2B). In a similar fashion, the fourth group can be divided into 2 (IV‐A and IV‐B). The least potent EOs are obtained from lemon, juniper, cypress, cedarwood, and black pepper (group VI). These findings are in accordance with the claims of the original work of Hammer et al.26
3.3 | Assessment of criteria by the SRD: selection of the most sensitive antioxidative assays and microbial strains In order to identify the most susceptible and most resilient bacterial and fungal strains as well as the most prominent antioxidative assays, the SRD analysis was performed on the transposed matrices of partial desirability scores. In that way, EOs are placed in rows and used as multiple criteria. The row‐wise maximum was used as a reference. The procedure was the same for both case studies. However, in the first study, the blocks of antioxidative, antibacterial, and antifungal activities were analyzed separately. In the second case study, not all 48 EOs are used, but rather only the relevant ones, which differ statistically significantly from the random distribution in the previous SRD run. These are the first 23 EOs (Figure 5A), all belonging to groups I to III (Figure 5B). The rest of the EOs are discarded owing to irrelevance (low potent ones). Interpretation of the SRD results is straightforward. The lower the SRD is, the more sensitive/susceptible the test assay/microorganism is and vice versa. Micrococcus flavus and Salmonella typhi were identified as the most sensitive bacteria, with the lowest SRD scores, while the most resilient one is Pseudomonas aeruginosa (Figure 6A). The most sensitive antioxidative assay for measuring radical scavenging by EOs is the LP2 (Fe2+/H2O2 used as induction system), while the least sensitive is the LP1 (Fe2+/ascorbic acid used for induction) (Figure 6B). Trichophyton rubrum and Epidermophyton floccosum were identified as the most susceptible fungi to EOs from the first case study, while the most resilient fungus is C albicans. Trichophyton tonsurans, Trichophyton mentagrophytes, and Mycobacterium canis are in the middle (Figure 6C).
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Among the 10 microbial strains tested in the second case study, the SRD has identified C albicans and Staphylococcus aureus as the most sensitive microorganisms towards majority of EOs, while P aeruginosa is the most resilient one (Figure 7). All microbial strains are statistically significantly ranked, far from the random distribution.
4 | CONCLUSION Selection of the polypotent natural products, in this particular case the EOs, exhibiting multiple antibacterial, antifungal, and antioxidative properties, was successfully performed with the aid of the SRD and Derringer desirability approach as a part of MOO methods. The SRD has been strongly affected by the data pretreatment method. Row‐wise standardization and untreated activity data resulted in a similar ranking of EOs. However, row‐wise normalization to the unit length vector gave different results. In all, nevertheless, interpretation of the SRD analysis was not straightforward. Meanwhile, the SRD applied on the data scaled to fit the preferences provided coherent and easily interpretable results, which have been in accordance with the Derringer desirability ranking. Obviously, scaling to fit the preferences proved to be a crucial step in securing fair trade‐off between criteria and allowing only relevant information (between desirability limits) to be filtered into the SRD analysis. Such approach should be preferred whenever the SRD is used as MOO tool. Finally, the SRD combined with CV provided sensitive, straightforward, and statistically sound way of ranking and grouping EOs according to their potency. In the first case study, O vulgare was selected as the most polypotent EO by both the SRD and the Derringer approach, while the oils from S nemorosa and S officinalis ranked the worst. In the second case study, lemongrass, coriander, frankincense, and cajuput were selected as the most polypotent oils, tested against 11 microorganisms. The most resilient microorganism confirmed by both case studies was P aeruginosa. A C K N O WL E D G E M E N T This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, grant no 172017. ORCID Filip Lj. Andrić
http://orcid.org/0000-0001-7932-833X
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S UP PO RT ING I NF O RMA TI ON Additional supporting information may be found online in the Supporting Information section at the end of the article.
How to cite this article: Andrić FL. Towards polypotent natural products: The Derringer desirability approach and nonparametric ranking for multicriteria evaluation of essential oils. Journal of Chemometrics. 2018;e3050. https://doi.org/10.1002/cem.3050
