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Article Multivariate Chemometrics as a Strategy to Predict the Allergenic Nature of Food Proteins

Miroslava Nedyalkova 1 and Vasil Simeonov 2,*

1 Department of Inorganic Chemistry, Faculty of Chemistry and Pharmacy, University of Sofia, 1 James Bourchier Blvd., 1164 Sofia, Bulgaria; [email protected]fia.bg 2 Department of Analytical Chemistry, Faculty of Chemistry and Pharmacy, University of Sofia, 1 James Bourchier Blvd., 1164 Sofia, Bulgaria * Correspondence: [email protected]fia.bg



Received: 3 September 2020; Accepted: 21 September 2020; Published: 29 September 2020


Abstract: The purpose of the present study is to develop a simple method for the classification of food proteins with respect to their allerginicity. The methods applied to solve the problem are well-known multivariate statistical approaches (hierarchical and non-hierarchical cluster analysis, two-way clustering, principal components and factor analysis) being a substantial part of modern exploratory data analysis (chemometrics). The methods were applied to a data set consisting of 18 food proteins (allergenic and non-allergenic). The results obtained convincingly showed that a successful separation of the two types of food proteins could be easily achieved with the selection of simple and accessible physicochemical and structural descriptors. The results from the present study could be of significant importance for distinguishing allergenic from non-allergenic food proteins without engaging complicated software methods and resources. The present study corresponds entirely to the concept of the journal and of the Special issue for searching of advanced chemometric strategies in solving structural problems of biomolecules.

Keywords: food proteins; allergenicity; multivariate statistics; structural and physicochemical descriptors; classification

1. Introduction Food allergy is an atypical immunological reaction to food proteins, which causes an adverse clinical reaction. According to the data, approximately 5% of adults and 8% of children have a food allergy [1–3]. Allergy to cow’s milk, eggs, wheat, soy, peanut, tree nuts, fish and shellfish comprises the majority of food allergy reactions. A study from 2001 indicated that peanut allergies are a mainstream cause for anaphylaxis, and fatal outcomes due to food allergies are 63%–67% of the deaths toll [4]. It has been proposed recently that the thermal treatment (boiled or in fried form) of peanuts leads to fewer allergenic products than roasting. In the work of Maleki et al., the digestibility of the major allergens in peanut during boiling, frying or roasting and in refined form was considered [5,6]. Despite the social importance of this issue, there is still no valuable methodology for prediction of allergenic structure or a proper methodology for the treatment of food allergies. The structural features of proteins could possibly contribute towards their allergenicity prediction. Developing such an in silico classification model may validate an appropriate approach for assisting in the allergenic potential of novel proteins. The exploratory methods based on a three-dimensional structure of allergens is of significance importance to make prediction models for allergenicity, which would allow the interpretation of the possible reasons for allergenicity of the proteins by combination of experimental and theoretical approaches

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Why do proteins become allergens? This is a question that has triggered scientists to investigate what unique molecular features and properties make proteins become allergens. Information that the scientific community requires for allergy assessment should be developed by multiscale approaches and strategies with implications for different methods. Only strategies based on multilayer approaches can boost early potential allergenicity detection. In the study of Naneva et. al., where an effort for prediction of allergic properties of a large number of proteins (over 700) is done by the use of linear sequence or surface spacial distribution of amino acids is made. The partial least square-based discriminant analysis (PLS-DA) classification model based on allergenic transformed protein data were constructed. A cluster analysis (hierarchical) was tried as a classification method for the separation of allergic from non-allergic proteins based on protein sequences to meet the needs of biologists in terms of phylogenetic analysis and prediction of biological functions like allergenicity [7–11]. A new type of molecular descriptor based on surface properties has been used. This approach for generating a database of is based on introduction of new types of descriptors able to reach classification of the proteins using only protein amino acids surface properties. To define the amino acids like polar, non-polar or charged, a set of hydrophobic scales were applied to explore these properties [11]. In the study of Guarino and Sciarrillo [12], deals with the proteome variation to different red strawberry species in order to clarify changes in allergen content and proteome variation for the different plant species. The detected allergens of strawberry were mapped on a 2-DE plot, and they were matched with spots recognized by a series of patients with different allergic patterns. By this approach, the authors identified the allergen proteins in Fragaria ananassa Duch, a variety of strawberry, by application of proteomic strategy compared to traditional approaches including protein isolation processes for discovering the binding between a patient’s IgE (immunoglobulin E) and separated plant allergenic protein on a membrane. The obtained results revealed that the application of proteomics analyses enhanced identification of multiple allergens in plants in contrast to the well-known techniques. Therefore, besides for the conventional methods for noticing allergens, the use of the proteomic method has wide advantage and practical value in allergens studies concerning their detection and characterization. It is expected that a combination of proteomics and biological assays could substantially contribute to better understanding of the function the IgE-binding proteins. The cheminformatics methods have been widely established as a proper approach for drug discovery applications [8,9]. The principles used in drug development can also be useful in food chemistry as well [10]. The application of chemoinformatics for studies focused on food proteins reveals the broad spectrum of application of chemical information to elucidate structure–property relationships towards an object from food science in combination with data mining. This study reveals a workflow based on chemometric methods for prediction of the allergenicity nature of the most important food allergens causing IgE-mediated food allergy that is believed to be responsible for most immediate-type, food-induced hypersensitive reactions. Analysis and classification of the allergenic molecules by the proper choice of descriptors in the chemical space provide an overall model for prediction of the pattern for recognition of allergenic and non-allergenic proteins based on their properties. The aim of this study is to demonstrate the ability of different chemometric methods, using mainly easily assessable structural descriptors for protein molecules, to separate allergic from non-allergic proteins.

2. Materials and Methods In this stage of the work an attempt was made to separate (classify) allergenic from non-allergenic proteins using a set of descriptors of a molecular structural nature (totally 27) based on chemometric algorithms described in detail in [11–18]. The number of proteins involved in the separation procedure was 19–13 allergenic and 6 non allergenic proteins (from data sets with proven quality and correct qualification). Thus, the data set treated had dimensions 18 x 27. Symmetry 2020, 12, 1616 3 of 19

The following multivariate statistical methods for data mining were used: hierarchical cluster analysisSymmetry (HCA) 2020, 12 using, x FOR standardizedPEER REVIEW input data, Ward’s method of linkage, squared Euclidean3 of 20 distances as similarity measures and Sneath’s test for cluster significance. The following multivariate statistical methods for data mining were used: hierarchical cluster analysisNonhierarchical (HCA) using (K-means) standardized clustering input data, was Ward’s applied method as a supervised of linkage, patternsquared recognitionEuclidean method useddistances as confirmation as similarity of measures the results and from Sneath’s hierarchical test for cluster clustering. significance. Two-wayNonhierarchical joining (clustering)(K‐means) clustering was included was applied for as finding a supervised correspondence pattern recognition between method the objects and variablesused as of confirmation interest represented of the results on from a single hierarchical plot. clustering. Two‐way joining (clustering) was included for finding correspondence between the objects and Principal component analysis and factor analysis were used for studying the data set structure, variables of interest represented on a single plot. for reducingPrincipal the component number of analysis the initial and factor variables analysis and were for projectionused for studying of the the data data on set bivariate structure, plots. forThe reducing key goal the ofnumber the data of the mining initial variables was to revealand for patternsprojection of of similaritythe data on betweenbivariate plots. the objects of study (allergenicThe and key non-allergenic goal of the data mining proteins) was and to reveal reach patterns reliable of separation similarity between between the both objects classes, of study to determine of the(allergenic descriptors and responsiblenon‐allergenic for proteins) the formation and reach of both reliable classes separation and establish between similarity both classes, patterns to between the descriptorsdetermine of usedthe descriptors for possible responsible further for selection the formation of reduced of both number classes and of descriptorsestablish similarity for classification patterns between the descriptors used for possible further selection of reduced number of and to explain the significance of the descriptors for the classification procedure. descriptors for classification and to explain the significance of the descriptors for the classification procedure.All chemometric calculations were performed by the software package STATISTICA 8.0. All chemometric calculations were performed by the software package STATISTICA 8.0. 2.1. Data Preparation 2.1. Data Preparation The set of plant proteins included in the present study is shown in Figure1. Those proteins were classifiedThe as set allergens of plant by proteins the Protein included Data in the Bank present (PDB) study (https: is shown//www.rcsb.org in Figure 1./) Those or/and proteins by the Structural Databasewere classified of Allergenic as allergens Proteins by the (SDAP) Protein ( http:Data //Bankfermi.utmb.edu (PDB) (https://www.rcsb.org/)/). Each protein or/and was described by the by a set Structural Database of Allergenic Proteins (SDAP) (http://fermi.utmb.edu/). Each protein was of descriptors.described by The a set following of descriptors. types The of following descriptors types were of descriptors computed were (using computed MOE (using and MOE Alvadesc and software ) andAlvadesc are presented software in ) Tableand are1. presented in Table 1.

Allergenic group:

Figure 1. Cont.

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Non‐Allergenic group:

FigureFigure 1. Allergenic 1. Allergenic and and non-allergenic non‐allergenic protein protein structures. structures. Table 1. Molecular descriptors used and their explanation. Table 1. Molecular descriptors used and their explanation.

CODECODE DESCRIPTION DESCRIPTION

pro_asa_hphpro_asa_hph Water accessible Water accessible surface area surface of all area hydrophobic of all hydrophobic (|qi| < 0.2) (|qi| atoms. < 0.2) atoms. pro_asa_hydpro_asa_hyd Water accessible Water accessible surface area surface of all area hydrophilic of all hydrophilic (|qi| < 0.2) (|qi| atoms. < 0.2) atoms. pro_vdwpro_vdw Van der Waals Van der surface Waals surfacearea area pro_dipole_momentDipole Dipole moment moment calculated calculated from from the the partial partial charges charges of of the the molecule. pro_dipole_moment Mass density: molecular weight divided by van der Waals volume dens molecule. as calculated in the vol descriptor. Mass density: molecular weight divided by van der Waals volume pro_mobilitydens mobility pro_charge Totalas calculated charge of in the the molecule vol descriptor. (sum of formal charges). pro_mobilitypro_r_gyr mobility Radius of gyration. pro_r_solvpro_charge Total charge of the molecule Radius (sum of cross-section of formal charges). van der Waals volume calculated using a grid approximation pro_volumepro_r_gyr Radius of gyration. pro_r_solv Radius of cross(spacing‐section 0.75 A). a_acc Hydrogen bond acceptor atoms (number) van der Waals volume calculated using a grid approximation pro_volumea_acid Number of acidic atoms. a_aro(spacing Number 0.75 of A). aromatic atoms. a_basea_acc Hydrogen bond acceptor Number atoms of basic (number) atoms. a_acid Number of hydrogenNumber of bond acidic donor atoms. atoms (not counting basic atoms a_dona_aro but countingNumber atoms of aromatic that are both atoms. hydrogen bond donors and a_base Number acceptorsof basic atoms. such as -OH). b_1rotRNumber Fraction of hydrogen of rotatable bond singledonor bonds: atoms b_1rotN(not counting divided basic by b_heavy. KierFlex Kier molecular flexibility index: (KierA1) (KierA2) / n a_don atoms but counting atoms that are both hydrogen bond donors rings The number of rings. Log of theand octanol acceptors/water such partition as ‐OH). coeffi cient (including implicit SlogP b_1rotR Fraction of rotatable single bonds: hydrogens).b_1rotN divided by b_heavy. KierFlex Kier Polarmolecular surface flexibility area (Å2) index: calculated (KierA1) using (KierA2) group contributions / n to TPSA approximate the polar surface area from connection table (topological polar surfacerings area based on fragments) The number of rings. Log of the octanol/water partitioninformation coefficient only. (including implicit WeightSlogP Molecular weight (including implicit hydrogens) hydrogens). weinerPath Wiener path number weinerPolTPSA Polar surface area (Å2) calculated Wiener using polarity group number contributions to (topologicalZagreb polar index surface area approximate Zagreb the polar index: surface the sum area of from di2 over connection all heavy table atoms i. based on fragments) information only.

2.2. Cluster Analysis for Protein Separation Cluster analysis (CA) is a method to find optimal groupings of observations or their descriptive variables in such a way that the members of a cluster are similar to each other and the clusters formed are different from each other. Hierarchical clustering is a type of unsupervised machine learning algorithm. In unsupervised learning mode, the learner algorithm can be used to group the data, Symmetry 2020, 12, 1616 5 of 19 since the non-hierarchical clustering as a supervised pattern recognition method requires a priori determination of the number of groups for data interpretation. In order to interpret the data structure, a similarity measure should be introduced, such as Euclidean distance. Unwanted data rotations in the data structure are avoided by different data transformations, the most applied one being auto scaling or z-transformation. The graphical output of the analysis is known as a dendrogram plot. The next important step after auto scaling and distance determination is the linkage algorithm. There are many options, but hierarchical clustering relies often on Ward’s method of linkage and non-hierarchical on K-means mode. It must be mentioned that in non-hierarchical clustering, all a priori required clusters are simultaneously obtained, and this grouping does not possess hierarchy.

2.3. Principal Component Analysis for Protein Separation Principal component analysis (PCA) is a powerful mathematical technique used to reduce the dimensionality of the parameter space [19]. PCA was first carried out with the aim of reducing the input variables. Varimax rotation mode was used. Three latent factors explaining over 80% of the total variance were selected for estimation of the variable relationships by factor loadings. Only statistically significant loadings (higher than 0.7) were considered for interpretation purposes.

3. Results and Discussion

3.1. Cluster Analysis for Protein Classification Based on 2D and 3D Molecular Descriptors The essential findings presented in this study could be defined as a pattern recognition classifying an unknown pattern into one of two predefined categories (allergenic and non-allergenic groups). Cluster analysis can be considered an important strategy in pattern recognition aiming putting a set of patterns into classes (categories). The cluster analysis approach is a highly applicable sampling method. Sampling by clusters happens over multiple stages, and the resulting process is a defined by similarity path in data and pattern space. The clustering was performed using the linkage option of the method of Ward, which was found to be most suitable as it creates a small number of clusters. In order to check the option for separation of proteins into allergenic and non-allergenic classes using structural descriptors of the proteins, a data set of 18 food proteins was prepared (12 allergenic and 6 non-allergenic). All descriptors were z-score normalized prior to the analysis so that they were on the same dimensionless scale. The results and the comments of the data interpretation can be summarized as follows. In Figure2 the hierarchical dendrogram for linkage of 27 descriptors is presented. Two very well expressed clusters were formed. One of them mainly included descriptors for surface area, volume and shape descriptors. These descriptors depend on the structure connectivity and conformation (dimensions are measured in Å). The second group of descriptors was based on physical properties. The resulting physical properties could be calculated from the connection table (with no dependence on conformation states of the molecules) of a molecule and the Kier molecular flexibility index descriptor was also defined in this cluster. Next, Figure3 represents the linkage between 18 proteins, and the distinctive separation of the proteins in “allergenic” and “non allergenic” classes was obvious. The upper cluster consisted entirely of allergenic proteins, and the lower one of non-allergenic ones. In order to confirm the clustering found by HCA, nonhierarchical K-means clustering was also performed. The stated hypothesis was that both descriptors and protein should be separated into two predetermined clusters. Symmetry 2020, 12, 1616 6 of 19

Symmetry 2020, 12, x FOR PEER REVIEW 6 of 20

pro_asa_hph pro_asa_hyd pro_asa_vdw pro_dipole_moment pro_r_solv pro_mass pro_mobility pro_net_charge pro_r_gyr b_1rotR KierFlex SlogP TPSA Weight weinerPath pro_volume a_acc a_don a_acid b_1rotN weinerPol zagreb a_base a_aro b_ar rings a_number_S 0 20406080100120 (Dlink/Dmax)*100

Symmetry 2020, 12, x FOR PEERFigure REVIEW 2. Hierarchical dendrogram for linkage of 27 descriptors. 7 of 20 Figure 2. Hierarchical dendrogram for linkage of 27 descriptors.

Two very well expressed clusters were formed. One of them mainly included descriptors for surface area, volume and shape descriptors. These descriptors depend on the structure connectivity and conformation (dimensions are measured in Å). The second group of descriptors was based on physical properties. The resulting physical properties could be calculated from the connection table (with no dependence on conformation states of the molecules) of a molecule and the Kier molecular flexibility index descriptor was also defined in this cluster. Next, Figure 3 represents the linkage between 18 proteins, and the distinctive separation of the proteins in “allergenic” and “non allergenic” classes was obvious.

Figure 3. Hierarchical dendrogram for clustering of the 18 proteins.

InThe Table upper2, the cluster members consisted of both entirely clusters of for allergenic 27 descriptors proteins, are presented, and the lower and in one Table of2 non, the‐ membersallergenic ofones. two clusters are presented for 18 proteins. In order to confirm the clustering found by HCA, nonhierarchical K‐means clustering was also performed. The stated hypothesis was that both descriptors and protein should be separated into two predetermined clusters. In Table 2, the members of both clusters for 27 descriptors are presented, and in Table 2, the members of two clusters are presented for 18 proteins.

Table 2. Members of cluster 1 and cluster 2 for 27 descriptors.

Members of Cluster Number 1 and Distances from Respective Cluster Center Cluster Contains 15 Variabl ariable (2D Descriptors) Distance pro_asa_hph 0.149240 pro_asahyd 0.149240 pro_asa_vdw 0.149240 pro_dipole_moment 0.149240 pro_mass 0.149240 pro_mobility 0.149240 pro_net_charge 0.149240 pro_r_gyr 0.149240 pro_r_solv 0.149240 B_1rotR 0.243133 KierFlex 0.243133 SlogP 0.243133 TPSA 0.243133 Members of Cluster Number 2 and Distances from Respective Cluster Center Cluster Contains 12 Variabl ariable (2D Descriptors) Distance pro_volume 0.649643 a_acc 0.413425 a_acid 0.382602 a_aro 0,230073

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Table 2. Members of cluster 1 and cluster 2 for 27 descriptors.

Members of Cluster Number 1 and Distances from Respective Cluster Center Cluster Contains 15 Variables Variable (2D Descriptors) Distance pro_asa_hph 0.149240 pro_asahyd 0.149240 pro_asa_vdw 0.149240 pro_dipole_moment 0.149240 pro_mass 0.149240 pro_mobility 0.149240 pro_net_charge 0.149240 pro_r_gyr 0.149240 pro_r_solv 0.149240 B_1rotR 0.243133 KierFlex 0.243133 SlogP 0.243133 TPSA 0.243133 Members of Cluster Number 2 and Distances from Respective Cluster Center Cluster Contains 12 Variables Variable (2D Descriptors) Distance pro_volume 0.649643 a_acc 0.413425 a_acid 0.382602 a_aro 0,230073 a_base 0.469422 a_don 0.418075 a_number_S 1.026357 b_1rotN 0.322417 b_ar 0.231530 rings 0.236831 weinerPol 0.180442 zagreb 0.178149 Symmetry 2020, 12, 1616 8 of 19

As could be seen, the separation between the descriptors (variables) followed entirely that reached by HCA. The obtained results for the distribution profiles for each class of proteins based on a descriptor set were classified as allergenic and non-allergenic. Clearly, this particular selection of descriptors provided a pure dissimilarity in the profiles of allergenic and non-allergenic compounds. Tables3 and4 indicate the clustering of the proteins into two classes. Again, the similarity with HCA was almost perfect, as the only exception was protein barley defined as non-allergenic protein (PDB ID: 3wlj.pdb) belonging in K-means classification to the cluster of non-allergenic proteins rather than to the cluster of allergenic as expected.

Table 3. Members of cluster 1 for 18 proteins.

Members of Cluster Number 1 and Distances from Respective Cluster Center Cluster Proteins Contains 6 Cases Distance 3wlj 0.624337 3ur8 0.919784 3gdn 0.250043 2v3f 0.266641 3piu 0.357769 4j2f 0.929623

Table 4. Members of cluster 2 for 18 proteins.

Members of Cluster Number 2 and Distances from Respective Cluster Center Cluster Proteins Contains 12 Cases Distance 3smh 0.745996 3c3v 0.895197 2c3b 0.491340 1w2q 0.492303 2wql 0.569632 3vor 0.343808 5amw 0.490781 3fz3 0.660688 3zs3 0.633154 2ahn 0.616859 5mmu 0.672782 4cpv 0.928246

An important step in the chemometric analysis was to try to determine the role of the separate descriptors in the separation procedure. From the plot of means (Figure4) for the mean value of each descriptor for each of the identified clusters of proteins, it is readily seen that each protein cluster is described by different values of the descriptors. It was readily seen that almost all descriptors were very well separated from each other for each identified cluster of proteins. Except for the descriptor weinerPa, all descriptors for non-allergic proteins had higher average (standardized) values as compared to those for allergic proteins (cluster 2). In Figure5, the plot of means for each protein (object) for each identified cluster of descriptors is presented. Symmetry 2020, 12, 1616 9 of 19

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Plot of Means for Each Cluster 2,0

1,5

1,0

0,5

0,0

-0,5

-1,0

-1,5 pro_asa_vdw pro_r_solv a_don rings zagreb pro_mobility a_acid b_1rotR Weight Cluster 1 Variables Cluster 2

Symmetry 2020, 12Figure, x FOR 4. PEERPlot REVIEW of means for each descriptor for each identified cluster of proteins. 10 of 20 Figure 4. Plot of means for each descriptor for each identified cluster of proteins.

It was readily seen that almost all descriptors were very well separated from each other for each identified cluster of proteins. Except for the descriptor weinerPa, all descriptors for non‐allergic proteins had higher average (standardized) values as compared to those for allergic proteins (cluster 2). In Figure 5, the plot of means for each protein (object) for each identified cluster of descriptors is presented.

Figure 5.5.Plot Plot of of means means (standardized (standardized values) values) of each of protein each forprotein each identifiedfor each clusteridentified of descriptors. cluster of descriptors. These results implied that cluster dendrograms obtained by HCA can be reliably used to identify and gainThese deeper results insights implied in that the presentedcluster dendrograms results from obtained K-means by clustering. HCA can The be obtained reliably linearityused to identify and gain deeper insights in the presented results from K‐means clustering. The obtained linearity profile, related to the descriptors of proteins obtained as well as with HCA, since a second cluster with HCA shows a non‐linearly trend in each descriptor space. (to be deleted) The results in Figure 5 indicate that the clusters of descriptors identified by K‐means clustering separate very well allergenic from non‐allergenic proteins. It should be noted that protein 3wlj marked in advance as non‐allergenic is correctly classified by K‐means clustering since in hierarchical clustering its position is doubtful.

Two‐way clustering In the next step of the data mining two‐way clustering approach was applied. In Figure 6 the correspondence between the groups of objects and groups of descriptors is presented.

Symmetry 2020, 12, 1616 10 of 19

profile, related to the descriptors of proteins obtained as well as with HCA, since a second cluster with HCA shows a non-linearly trend in each descriptor space. (to be deleted) The results in Figure5 indicate that the clusters of descriptors identified by K-means clustering separate very well allergenic from non-allergenic proteins. It should be noted that protein 3wlj marked in advance as non-allergenic is correctly classified by K-means clustering since in hierarchical clustering its position is doubtful.

3.1.1. Two-Way Clustering In the next step of the data mining two-way clustering approach was applied. In Figure6 the correspondence between the groups of objects and groups of descriptors is presented. Symmetry 2020, 12, x FOR PEER REVIEW 11 of 20

Figure 6. TwoTwo-way‐way clustering of proteins and descriptors.

The output of thethe K-meansK‐means clusteringclustering waswas confirmed:confirmed: for non-allergicnon‐allergic proteins, the descriptordescriptor values were higherhigher thanthan thosethose forfor allergenicallergenic proteins.proteins.

3.1.2.Principal Principal components Components and factor and Factoranalysis Analysis Principal components components analysis analysis of of the the data data to tocorrect correct the the heavy heavy skewness skewness in some in some variables variables was wasperformed. performed. In Table 5 5,, thethe factorfactor loadings for for two two latent latent factors factors explaining explaining over over 85% 85% of ofthe the total total variance variance are arepresented. presented. Two latent factors explain over 85% of the total variance of the system. The first latent factor includes high factor loadings for the groupsTable of 5. descriptors Factor Loadings for physical properties and surface area, volumeFactor and Loadings shape and (Varimax the second Normalized) one includes Extraction: high factor Principal loadings Components from the descriptors (Marked connectedLoadings are >0.700000) Variable to groups atom counts andFactor bond 1 counts, Kier Hall connectivity and Kappa ShapeFactor Indices 2 in general, pro_mass it confirms the results from0.96464 cluster analysis. 0.236248 pro_mobility From this table is possible0.96464 to select a reduced number of variables (descriptors)0.236248 to try even better pro_net_chargeseparation of the proteins into0.96464 two classes. 0.236248 pro_r_gyr 0.96464 0.236248 pro_r_solv 0.96464 0.236248 pro_volume 0.17264 0.728891 a_acc 0.18398 0.890058 a_acid 0.31796 0.867425 a_aro 0.38478 0.907553 a_base 0.17497 0.864993 a_don 0.18896 0.886082 a_number_S 0.04313 0.346071 b_1rotN 0.35525 0.884013 b_1rotR 0.94226 0.244491 b_ar 0.38999 0.905283 KierFlex 0.94226 0.244491 rings 0.31002 0.924282

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Table 5. Factor Loadings.

Factor Loadings (Varimax Normalized) Extraction: Principal Variable Components (Marked Loadings are >0.700000) Factor 1 Factor 2 pro_mass 0.96464 0.236248 pro_mobility 0.96464 0.236248 pro_net_charge 0.96464 0.236248 pro_r_gyr 0.96464 0.236248 pro_r_solv 0.96464 0.236248 pro_volume 0.17264 0.728891 Symmetry 2020, a_acc12, x FOR PEER REVIEW 0.18398 0.890058 12 of 20 a_acid 0.31796 0.867425 SlogP a_aro0.94226 0.38478 0.907553 0.244491 TPSA a_base0.94226 0.17497 0.864993 0.244491 a_don 0.18896 0.886082 Weight 0.94226 0.244491 a_number_S 0.04313 0.346071 weinerPath −b_1rotN0.00924 − 0.35525 0.884013 0.568203 weinerPol b_1rotR0.27742 0.94226 0.244491 0.948778 zagreb b_ar0.27791 0.38999 0.905283 0.949411 Expl. Var % KierFlex50.83 0.94226 0.244491 36.79 rings 0.31002 0.924282 SlogP 0.94226 0.244491 Two latentTPSA factors explain over 85% 0.94226 of the total variance of the system. 0.244491 The first latent factor includes highWeight factor loadings for the groups 0.94226 of descriptors for physical properties 0.244491 and surface area, volume andweinerPath shape and the second one includes0.00924 high factor loadings from0.568203 the descriptors connected − − to groups atomweinerPol counts and bond counts, 0.27742 Kier Hall connectivity and Kappa 0.948778 Shape Indices in general, zagreb 0.27791 0.949411 it confirms the results from cluster analysis. Expl. Var % 50.83 36.79 From this table is possible to select a reduced number of variables (descriptors) to try even better separation of the proteins into two classes. Graphically, the the separation separation of of the the descriptor descriptor into into two two major major groups groups and and the the special special position position of the of descriptorthe descriptor Weiner Weiner Pa is Pa well is well illustrated illustrated on Figure on Figure7. 7.

Figure 7. Biplot PC1 vs. PC 2 for grouping of descriptors.

In Figure8 8,, the the same same distribution distribution is is shown. shown.

Symmetry 2020, 12, 1616 12 of 19 Symmetry 2020, 12, x FOR PEER REVIEW 13 of 20 Symmetry 2020, 12, x FOR PEER REVIEW 13 of 20

Figure 8. Projection of descriptors on the plane of the first two latent factors. Figure 8.8. Projection of descriptors on the plane of thethe firstfirst twotwo latentlatent factors.factors. The separation of the objects (proteins) is illustrated additionally in Figure 9. TheThe separationseparation ofof thethe objectsobjects (proteins)(proteins) isis illustratedillustrated additionallyadditionally in in Figure Figure9 .9.

.

Figure 9. Projection of objects (proteins) on the plane of the first two latent factors. Figure 9.9. Projection of objects (proteins) on the planeplane ofof thethe firstfirst twotwo latentlatent factors.factors. There was a clear separation between allergenic and non‐allergenic in each descriptor space and ThereThere waswas aa clearclear separation betweenbetween allergenicallergenic andand non-allergenicnon‐allergenic inin eacheach descriptordescriptor spacespace andand also showed a particularly good separation between two protein groups. alsoalso showedshowed aa particularlyparticularly goodgood separationseparation betweenbetween twotwo proteinprotein groups. groups. It was convincingly shown that the objects (proteins) were well separated into two classes: left It was convincingly shown that the objects (proteins) were well separated into two classes: left side—non‐allergic proteins, and right side—allergic proteins. Again, an exception was found side—non‐allergic proteins, and right side—allergic proteins. Again, an exception was found concerning the classification of the expectedly allergic protein 3wlj.pdb as non‐allergic. concerning the classification of the expectedly allergic protein 3wlj.pdb as non‐allergic.

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It was convincingly shown that the objects (proteins) were well separated into two classes: left side—non-allergic proteins, and right side—allergic proteins. Again, an exception was found concerning the classification of the expectedly allergic protein 3wlj.pdb as non-allergic.

3.1.3. Data Mining with Reduced Number of Descriptors The data mining procedure was carried out once more with significantly reduced number of descriptors. The selection of descriptors was done on the basis of the factor loadings table, and out of several descriptors with high loadings (strong correlation), only single representatives were used: pro_asa; a_acid; b_1rotN, b_1rotR, Kier Flex, rings, TPSA, Zagreb InSymmetry general, 2020 the, 12, resultsx FOR PEER of REVIEW all multivariate statistical analyses applied (as in previous14 of case) 20 were the same: Data mining with reduced number of descriptors Two clustersThe data weremining formed, procedure representative was carried out once of the more larger with significantly groups conditionally reduced number marked of as a_descriptorsdescriptors. and The pro_descriptors selection of descriptors (Figure was 10). done on the basis of the factor loadings table, and out of Twoseveral clusters descriptors were formed, with high namely loadings the (strong upper correlation), part—allergenic—and only single representatives the lower part—non were used: allergenic. This waypro_asa; of feature a_acid; reduction b_1rotN, b_1rotR, improved Kier the Flex, allocation rings, TPSA, of Zagreb protein 3wlj in the cluster of non-allergenic (Figure 11).In general, the results of all multivariate statistical analyses applied (as in previous case) were the same:

Tree Diagram for 8 Variables Ward`s method Squared Euclidean distances

pro_asa_hph

b_1rotR

KierFlex

TPSA

a_acc

b_1rotN

zagreb

rings

0 20406080100120 (Dlink/Dmax)*100

Figure 10. Hierarchical dendrogram for the clustering of 8 descriptors. Figure 10. Hierarchical dendrogram for the clustering of 8 descriptors.

Two clusters were formed, representative of the larger groups conditionally marked as a_descriptors and pro_descriptors (Figure 10). Two clusters were formed, namely the upper part—allergenic—and the lower part—non allergenic. This way of feature reduction improved the allocation of protein 3wlj in the cluster of non‐allergenic (Figure 11). The same separation of the descriptors into two clusters depicted in Figure 12 was observed with the reduced number of descriptors.

Symmetry 2020, 12, 1616 14 of 19 Symmetry 2020, 12, x FOR PEER REVIEW 15 of 20

Symmetry 2020, 12, x FOR PEER REVIEW 15 of 20

Figure 11. Hierarchical dendrogram for the clustering of 18 proteins.

The same separation of the descriptorsPlot of Means into two for clustersEach Cluster depicted in Figure 12 was observed with the2,0 reduced number of descriptors. Figure 11. Hierarchical dendrogram for the clustering of 18 proteins.

Plot of Means for Each Cluster 1,5 2,0

1,5 1,0

1,0 0,5

0,5

0,0 0,0

-0,5 -0,5

-1,0 -1,0

-1,5 pro_asa_hph b_1rotN KierFlex TPSA -1,5 a_acid b_1rotR rings zagreb Cluster 1 pro_asa_hph b_1rotN KierFlex TPSA Variables Cluster 2 a_acid b_1rotR rings zagreb Cluster 1

Figure 12. Plot of means (standardized)Variables for each descriptor for each identified cluster of proteins. Cluster 2 Figure 12. Plot of means (standardized) for each descriptor for each identified cluster of proteins.

Figure 12. Plot of means (standardized) for each descriptor for each identified cluster of proteins.

Symmetry 2020,, 12,, 1616x FOR PEER REVIEW 1516 of 1920

TheSymmetry separation 2020, 12, xof FOR the PEER descriptors REVIEW in this case was even better compared to the plot16 of 20of all 27 The separation of the descriptors in this case was even better compared to the plot of all descriptors. We did not present here the members of the two clusters of descriptors, but it resembled 27 descriptors.The We separation did not of present the descriptors here the in members this case ofwas the even two better clusters compared of descriptors, to the plot but of all it resembled 27 the outputs for 27 descriptors. More interestingly, the plot of means depicted in Figure 13 for each the outputsdescriptors. for 27 We descriptors. did not present More here interestingly, the members of the the plottwo clusters of means of descriptors, depicted but in Figureit resembled 13 for each protein for each identified cluster of descriptors had the same output as the case with all descriptors. proteinthe for outputs each identified for 27 descriptors. cluster ofMore descriptors interestingly, had the the plot same of means output depicted as the in case Figure with 13 allfor descriptors.each protein for each identified cluster of descriptors had the same output as the case with all descriptors.

Figure 13.FigurePlot 13. of Plot means of means (standardized) (standardized) for for each each descriptor for for each each identified identified cluster cluster of proteins. of proteins.

It proves that the reduction of the number of descriptors does not change the existing tendency It proves that the reduction of the number of descriptors does not change the existing tendency. Figure 13. Plot of means (standardized) for each descriptor for each identified cluster of proteins. Similar tendency without observed biases were reported for the results of the two-way clustering presentedIt proves in Figure that the 14 .reduction The same of trend the number was observed of descriptors for all descriptors. does not change the existing tendency

Figure 14. Two‐way clustering of proteins and descriptors.

Figure 14. TwoTwo-way‐way clustering of proteins and descriptors.

Symmetry 2020, 12, x FOR PEER REVIEW 17 of 20

Similar tendency without observed biases were reported for the results of the two‐way clustering presented in Figure 14. The same trend was observed for all descriptors.

Table 6. Factor loadings.

Factor Loadings (Varimax Normalized) Extraction: Principal Components (Marked Loadings are >0.700000) Variable Factor 1 Factor 2 pro_asa_hph 0.920048 0.292616 a_acid 0.272915 0.923270 b_1rotN 0.282057 0.936526 b_1rotR 0.959852 0.268366 KierFlex 0.959852 0.268366 TPSA 0.959852 0.268366 rings 0.294110 0.903245 zagreb Symmetry 2020, 12, 1616 0.232500 0.968740 16 of 19 Expl. Var % 48.81 47.32

This is also confirmedconfirmed on the biplot presented in Figure 15 above and on the projection plot for descriptors below as indicated in Figure 1616 andand TableTable6 6 for for the the factor factor loadings. loadings.

Symmetry 2020Figure, 12, x 15. FOR Projection PEER REVIEW of objects (2D descriptors) on the plane of the firstfirst two latent factors. 18 of 20

This is also confirmed on the biplot presented in Figure 15 and on the projection plot for descriptors, as indicated in Figure 16.

Figure 16. Projection plot of the variables.

ThisThe projection is also confirmed plot for on the the objects biplot (proteins) presented inproves Figure the 15 separation and on the into projection two classes plot for as descriptors, in the case aswith indicated all descriptors in Figure as 16 seen. in Figure 17. The projection plot for the objects (proteins) proves the separation into two classes as in the case with all descriptors as seen in Figure 17.

Figure 17. Projection of the cases on the factors.

This study relies on the hypothesis that if we could describe in a simple way the proteins with a proper set of 2D molecular descriptors defined as numerical properties that can be calculated from the connection table representation of a molecule (e.g., elements, formal charges and bonds, but not atomic coordinates) it would be beneficial for differentiating and finding a pattern for prediction of allergenic proteins based on 2D.

Symmetry 2020, 12, x FOR PEER REVIEW 18 of 20

Figure 16. Projection plot of the variables.

SymmetryThe2020 projection, 12, 1616 plot for the objects (proteins) proves the separation into two classes as in the17 case of 19 with all descriptors as seen in Figure 17.

Figure 17. Projection of the cases on the factors.

This study relies on the hypothesis that if we could describe in a simple way the proteins with a Table 6. Factor loadings. proper set of 2D molecular descriptors defined as numerical properties that can be calculated from the connection table representationFactor Loadings of a (Varimaxmolecule Normalized) (e.g., elements, Extraction: formal Principal charges Componentsand bonds, but not atomic coordinates)Variable it would be beneficial for(Marked differentiating Loadings are and> 0.700000)finding a pattern for prediction of allergenic proteins based on 2D. Factor 1 Factor 2 pro_asa_hph 0.920048 0.292616 a_acid 0.272915 0.923270 b_1rotN 0.282057 0.936526 b_1rotR 0.959852 0.268366 KierFlex 0.959852 0.268366 TPSA 0.959852 0.268366 rings 0.294110 0.903245 zagreb 0.232500 0.968740 Expl. Var % 48.81 47.32

This study relies on the hypothesis that if we could describe in a simple way the proteins with a proper set of 2D molecular descriptors defined as numerical properties that can be calculated from the connection table representation of a molecule (e.g., elements, formal charges and bonds, but not atomic coordinates) it would be beneficial for differentiating and finding a pattern for prediction of allergenic proteins based on 2D. Our ultimate goal is the development of highly accurate models for the prediction of the allergenicity toward plant proteins. In this context, analyzing the ability and proper choice of each molecular descriptor set to distinguish both forms is crucial. The results suggest that each descriptor set contains exceptional and complementary information to describe the final classification model. Obviously, variable selection methods based on PCA reduction are needed to identify the best descriptors from each descriptor set. These observations support the perspective that the combination of many different classes of chemical descriptors based on physical properties, subdivided surface areas, atom count and bond count descriptors, which are functions of the counts of atoms and bonds that are based on an approximate accessible van der Waals surface or pharmacophore feature descriptors, Symmetry 2020, 12, 1616 18 of 19 should be considered when constructing a classification model for the case of chosen proteins of families of these proteins. Using only descriptors from one type may result in a large loss of information and lack of a pattern. These results demonstrate how chemometric tools can provide us with an added layer of key information on such a complicated task, such as allergenicity prediction of food proteins. More effort is needed to validate and test for comprehension of this result; we will go further with a larger data set. In particular, the PCA-based approach has revealed a clear segregation between the groups as well as the obtained similarity pattern obtained by the HCA. In this paper, we propose a new mapping method for classification of allergenic plant proteins that incorporates a simple scheme based on molecular descriptors. Therefore, the proposed simple model is based on the protein structure.

4. Conclusions This study demonstrates the potential of exploiting chemometrics methods for separation and prediction between allergenic and non-allergenic food proteins. The complexity of the problem with a food allergy and especially the peanut allergies causing the majority of the annual emergency room admissions due to food allergies and approximately 63%–67% of deaths due to anaphylaxis with allergenicity nowadays is well documented. Our case study on the stated problem shows that generated descriptors could help in discriminating the groups in proteins and within the descriptors as well. Therefore, the workflow for the characterization of molecules could boost the prediction performances of models developed by PCA and HCA by a combination of different descriptors. This study paves the way to predictive abilities of the PCA and HCA models involving classical 2D molecular descriptors without a need for conducting more complicated model studies.

Author Contributions: Conceptualization, M.N.; methodology, M.N.; software, M.N.; validation, M.N. and V.S. formal analysis, M.N. and V.S.; investigation, M.N.; resources, M.N.; data curation, M.N.; writing—original draft preparation, M.N. and V.S.; writing—review and editing, M.N. and V.S.; visualization, M.N. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by “Information and Communication Technologies for a Single Digital Market in Science, Education and Security” of the Scientific Research Center, grant number NIS-3317 and National roadmaps for research infrastructures (RIs) grant number NIS-3318. Acknowledgments: The author M.N. is grateful for the additional support by the project “Information and Communication Technologies for a Single Digital Market in Science, Education and Security” of the Scientific Research Center, NIS-3317 and National roadmaps for research infrastructures (RIs) grant number NIS-3318. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Conflicts of Interest: The authors declare no conflict of interest.

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