ARTICLE IN PRESS

Journal of Theoretical Biology 254 (2008) 476– 482

Contents lists available at ScienceDirect

Journal of Theoretical Biology

0022-51

doi:10.1

� Corr

E-m

humber

journal homepage: www.elsevier.com/locate/yjtbi

Enzymes/non-enzymes classification model complexity based oncomposition, sequence, 3D and topological indices

Cristian Robert Munteanu a, Humberto Gonzalez-Dıaz b,�, Alexandre L. Magalhaes a

a REQUIMTE/Faculty of Science, Chemistry Department, University of Porto, Porto 4169-007, Portugalb Department of Microbiology and Parasitology, Faculty of Pharmacy, University of Santiago de Compostela, Santiago de Compostela 15782, Spain

a r t i c l e i n f o

Article history:

Received 15 March 2008

Received in revised form

15 May 2008

Accepted 6 June 2008Available online 14 June 2008

Keywords:

Protein models

Protein secondary structures

Star Graph

Python application

93/$ - see front matter & 2008 Elsevier Ltd. A

016/j.jtbi.2008.06.003

esponding author. Tel.: +34 981563100; fax:

ail addresses: muntisa@gmail.com (C.R. Munt

togd@gmail.com (H. Gonzalez-Dıaz), almagal

a b s t r a c t

The huge amount of new proteins that need a fast enzymatic activity characterization creates demands

of protein QSAR theoretical models. The protein parameters that can be used for an enzyme/

non-enzyme classification includes the simpler indices such as composition, sequence and connectivity,

also called topological indices (TIs) and the computationally expensive 3D descriptors. A comparison of

the 3D versus lower dimension indices has not been reported with respect to the power of

discrimination of proteins according to enzyme action. A set of 966 proteins (enzymes and non-

enzymes) whose structural characteristics are provided by PDB/DSSP files was analyzed with Python/

Biopython scripts, STATISTICA and Weka. The list of indices includes, but it is not restricted to pure

composition indices (residue fractions), DSSP secondary structure protein composition and 3D indices

(surface and access). We also used mixed indices such as composition-sequence indices (Chou’s pseudo-

amino acid compositions or coupling numbers), 3D-composition (surface fractions) and DSSP secondary

structure amino acid composition/propensities (obtained with our Prot-2S Web tool). In addition, we

extend and test for the first time several classic TIs for the Randic’s protein sequence Star graphs using

our Sequence to Star Graph (S2SG) Python application. All the indices were processed with general

discriminant analysis models (GDA), neural networks (NN) and machine learning (ML) methods and the

results are presented versus complexity, average of Shannon’s information entropy (Sh) and data/

method type. This study compares for the first time all these classes of indices to assess the ratios

between model accuracy and indices/model complexity in enzyme/non-enzyme discrimination. The use

of different methods and complexity of data shows that one cannot establish a direct relation between

the complexity and the accuracy of the model.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The fast growing amount of molecular biology data availablecreates necessity of fast computational chemistry methods topredict accurately protein properties. One of the most widelyused methods is the quantitative structure activity relationship(QSAR) that already has more than 1600 molecular descriptors(Devillers and Balaban, 1999; Karelson, 2000), most of all usedfor small molecules. At the same time, the number of DNAand protein QSAR studies is increasing (Agrawal et al., 2005;Arteca and Tapia, 1999; Hua and Sun, 2001; Randic and Balaban,2003) by the creation of new macromolecular descriptorsnamed topological indices (TIs) using graph theory. Thebranch of mathematical chemistry dedicated to encode the

ll rights reserved.

+34 981594912.

eanu),

h@fc.up.pt (A.L. Magalhaes).

DNA/protein information in graph representations by the use ofTIs has become an intense research area with interestingworks of Liao (Liao and Ding, 2005; Liao and Wang, 2004a, b;Liao et al., 2006), Randic, Nandy, Balaban, Basak and Vracko(Randic and Balaban, 2003; Randic, 2000; Randic and Basak,2001; Randic et al., 2000) or our group (Aguero-Chapin et al.,2006). In addition, the computational approaches and theoreticalanalyses, such as structural bioinformatics (Chou, 2004a, b),network approach (Chou et al., 2006a, b; Chou and Cai, 2006;Gonzalez-Dıaz et al., 2008), molecular docking (Chou et al., 2003;Gao et al., 2007; Li et al., 2007; Zhang et al., 2006; Wang et al.,2008; Zheng et al., 2007), pharmacophore modeling (Chou et al.,2006a, b; Sirois et al., 2004), protein cleavage site prediction(Chou, 1993, 1996; Du et al., 2005a, b), QSAR (Du et al., 2005a, b,2008; Gonzalez-Diaz et al., 2006a, b, c) and graphical operations(Althaus et al., 1993a, b; Andraos, 2008; Chou, 1989, 1990; Chouet al., 1994; Gonzalez-Dıaz et al., 2008), are providing very usefulinformation and insights for drug design during the course of drugdevelopment.

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Several papers are proposing methods to identify the proteinsas enzymes or non-enzymes, as well as the enzyme family class(Bate and Warwicker, 2004; Cai and Chou, 2005a, b; Cai et al.,2005; Chou, 2005; Chou and Elrod, 2003; Chou and Cai, 2004a, b;Dobson and Doig, 2003, 2005; Shen and Chou, 2008). Shen andChou (2007) presented the web-server called ‘‘EzyPred’’. This toolis a three-layer predictor where the first layer is identifying aprotein as enzyme or non-enzyme, the second layer evaluates themain functional class and the third layer is predicting the subfunctional class.

In the present work, we used protein structural parametersincluding composition, sequence, connectivity and 3D descriptorsin order to study the complexity of the enzyme/non-enzymeclassification model. Composition, sequence and connectivityparameters (Star Graph’s Tis, Randic et al., 2007) are simpler than3D parameters but they are less computationally expensive.However, TIs ignore important aspects of protein spatial structureand hence are expected to be inaccurate. In any case, a comparisonof 3D versus lower dimension indices has not been reported withrespect to the power of discrimination of proteins according toenzyme action. One of the most frequently used TIs are theWiener’s, Balaban’s, Connectivity, and others indices (Todeschiniand Consonni, 2000). In this study, we combine both 3DIs andStar Graph’s TIs in order to build models to assess the ratiosbetween model accuracy and indices/model complexity inenzyme/non-enzyme discrimination.

Table 1

2. Materials and methods

2.1. Protein set

This work is based on a sample of 996 proteins used in aprevious study by Dobson and Doig (2005), from which 498 areenzymes and 498 are non-enzymes. Dobson and Doig constructedthe dataset using function definitions obtained from DBGet(Fujibuchi et al., 1997) PDB Enzyme (Bairoch, 2000) cross-linksand structural relations from the Astral SCOP 1.63 superfamilylevel dataset (Brenner et al., 2000; Chandonia et al., 2002). Theyhave been estimated that 5–10% of proteins are orphans (nohomologues), 10% have only one homolog, and 30% belong tofamilies with less than 10 members (see details in Dobson andDoig, 2005).

The PDB files are downloaded with Python scripts from thePDB data bank (Berman et al., 2000). The DSSP files were obtainedfrom the PDB files using the DSSP application (Kabsch and Sander,1983). The length of the sequences is up to 1014, with an averageof 217 amino acids (AA), and the species origin is not specified.

Composition attributes

Attribute No. of attributes

Total residues number 1

Total surface 1

2S count 8+3 (2S grouped) ¼ 24

2S concentration 8+3 (2S grouped) ¼ 24

2S fractions 4

AA surface 21

AA concentration 21

AA propensity in 2S 21 (AA)�8 (2S) ¼ 168

21 (AA)�3 (2S grouped) ¼ 63

AA polarity concentration 5

AA polarity propensity in 2S 5 (polarities)�8 (2S) ¼ 40

HSE 21

CNb 21

Pseudo-composition 420

Total attributes 834

2.2. Composition and access attributes

This group includes 11 types of attributes: nine obtained withour Python code/Prot-2S Web Tool (http://www.requimte.pt:8080/Prot-2S/), one with Biopython and one with the pseudo-composition web interface (Shen and Chou, 2008). The concept ofpseudo AA composition was used for the first time to predict theprotein cellular attributes by Chou (Chou, 2001).

In the first step, the PDB files are transformed in DSSP filesfrom which specialized functions extract basic data such as AAsequences, secondary structure sequences and AA accessibilitysurfaces. In the second step, other Python functions extract ninetypes of attributes such as protein residue number, total and AAsurfaces, secondary structure (2S) count/concentration, AA con-centration/propensities in 2S motifs and AA polarity concentra-tion/propensities in 2S motifs. The AA set includes the 20 classical

ones plus X, which often appears in PDB files and means a non-defined residue in the sequence. The polarity code is the standardone: hydrophobic/non-polar residues (H) ¼ A, C, F, I, L, M, P, V;negative (N) ¼ D, E; positive (P) ¼ H, K, R; uncharged/polarresidues/hydrophilic (U) ¼ G, N, Q, S, T, W, Y; not known (*) ¼ X.

The eight 2S motifs are classified according to the DSSPnotation (Kabsch and Sander, 1983): H for a-helices, G for 3–10helices, I for p-helices, T for turns, E for b-sheets, B for isolatedb-sheets, S for bend (curved coils) and C for random coils.

These classes can be used as they are defined or can be groupedin helices (HGI), sheets (EB) and coils (SC), as fractions (helices/coils, sheets/helices, sheets/coils), and as a new fraction betweenthe 2S motifs that contain hydrogen bonds and the rest withoutthese interactions. The attributes are presented as countingnumbers, percents and fractions.

Biopython function used the PDB files in order to calculate thehalf sphere exposure (HSE) and beta coordination numbers (CNb).The pseudo-composition input was prepared with couple ofPython routines that download all the FASTA files in one singlefile. The calculations are made with the Liu’s web interface (Shenand Chou, 2008), using the ‘‘dipeptide-composition’’ option andthe chain results are averaged. A detailed list of the attributes canbe found in Table 1.

2.3. Topological indices

In addition, we used connectivity indexes that are extensivelyused in QSAR (Abou-Shaaban et al., 1996; Luco and Ferretti, 1997;Gramatica et al., 2001; Ren, 2002; Bruno-Blanch et al., 2003;Gonzalez et al., 2005a, b). The protein chain sequences aretransformed in Star Graph representations (Randic et al., 2007)and several TIs are calculated. All these operations are done withour own Python application called Sequence to Star Graph (S2SG)Python application (Numeric as matrix support). There areversions for Windows/Linux operating systems and for single/batch calculations. This is an interactive tool where the user canchoose the level of calculations such as embedded graph,additional weights for each AA, Markov normalization, power ofthe matrix connectivity, the input files (files with sequences,groups and weights), the output files and the level of details(files for summary and detailed results). The input sequence filecontains PDB name, chain letter and the chain sequence. Thegroup file has one line for each group of AA; for instance, in theexample presented here one group for each AA type. The weightscan be read from a file with two columns: one with the AA nameand the other with the values of the weights. These values can be

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any AA property and in our calculations, we used the 2S AApropensities values resulted from our set of proteins. The fieldseparator is the TAB character in all the files. The summary filecontains the following TIs:

�

The trace of the n connectivity matrices (Trn):

Trn ¼X

i

ðMnÞii, (1)

where n ¼ 0, y, power, M is the connectivity matrix (i� i

dimension); ii is the ith diagonal element;

� Harary number (H):

H ¼1

2�X

ij

mij

dij

� ��wnw

j , (2)

where dij are the elements of the distance matrix, mij are theelements of the M connectivity matrix, wj are the weightelements, nw can be Eq. (1) for selection or (0) for no selectionof weights calculations;

� Wiener index (W):

W ¼1

2�X

ij

dij �wnwj , (3)

�

Gutman topological index (S6):

S6 ¼X

ij

degi � degj �wnw

j

dij, (4)

where degi are the elements of the degree matrix;

� Schultz topological index (non-trivial part) (S):

S ¼1

2�X

ij

ðdegi þ degjÞ � dij �wnwj , (5)

�

Moreau–Broto, autocorrelation of topological structure (ATSn ,n ¼ 1, y, power); only with weights included:

ATSn ¼X

ij

dpnij �wi �wj, (6)

where dpnij are the elements of the pair distance matrix when

the distance is n ;

� A modified Balaban distance connectivity index (Jmodif):

Jmodif ¼ ðnodesþ 1Þ �X

ij

mij

Xk

dik �X

k

dkj �wnwj , (7)

where nodes+1 ¼ AA numbers/node number in the StarGraph+origin, Skdik ¼ node distance degree;

Table 2

�

Data scale complexity

Data SC

Kier–Hall connectivity index (0X):

0X ¼X

i

wnwiffiffiffiffiffiffiffiffiffi

degi

p , (8)

Composition 0.0

� Composition and weight 0.2

Sequence, no weight 0.4

Sequence and weight 0.6

2S without X-ray info 0.8

Sequence and 2S weight 1.0

3D info 1.2

Table 3Data scale complexity

Method MC

GDA 1

NN 2

ML 3

Randic connectivity index (1X):

1X ¼X

ij

mij �wnw

jffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidegi � degj

q . (9)

In addition, the detailed output file contains the groupslist (g), matrix connectivity (M) that is modified if the graph isembedded, matrix weights (Mw) where the values are only indiagonal, list of matrices to n power (Mn), list of normalized Mn

(MpN), distance matrix (d), degree matrix (deg), pair distancesmatrix (dp). The matrix connectivity contains the embeddedinformation too.

An Excel database is then constructed using results from theS2SG summary files, Python/Biopython scripts for composition/access and pseudo-potentials Web server. During the next step,we use several methods in order to test different models forenzyme/non-enzyme property of the present protein set.

2.4. Statistical analysis

We tested the main actual QSAR methods used for classifica-tion problems such as statistical General Discriminant Analysis(GDA; Kowalski and Wold, 1982; Van Waterbeemd, 1995.),neural networks (NN; Diederich, 1990) and machine learning(ML). The first two methods were carried out with the packageSTATISTICA 6.0 (StatSoft.Inc., 2002) and the last with Weka 3.4(Frank, 2005). In order to decide if a protein is classified asenzyme or non-enzyme, we added an extra dummy variable(EnzOrNot; 1 for enzymes and 0 for non-enzymes) and a cross-validation variable (CV). In statistical prediction, the followingthree cross-validation methods are often used to examinea predictor for its effectiveness in practical application: indepen-dent dataset test, subsampling test, and jackknife test (Chouand Zhang, 1995). However, as demonstrated in (Chou andShen, 2007) through a crystal clear analysis, only the jackknifetest has the least arbitrariness. A brief yet convincing eluci-dation in this regard was also given in (Chou and Shen, 2008).Therefore, the jackknife test has been increasingly used byinvestigators to examine the accuracy of various predictors(see Chou and Shen, 2008 and the references cited therein). Inthe actual work, the independent data test is used by splitting thedata at random in a training series (train) used for modelconstruction, a prediction one (val) for model validationand a model selection group (sel; only for Machine Learning).The CV column is filled by repeating three train, 1 val and 1 selvalues. All independent variables are standardized prior to modelconstruction. The quality of the analysis was determined byexamining the training, cross-validation and selection-fittingdecisions. In addition, we calculated other variables such are thefollowings combined complexity (CC) and average of Shannon’sentropy (Sh).

The CC is defined by the next formula:

CC ¼ logðVarsÞ � eSC � ½logðMCÞ þ 1�, (10)

where Var is the number of variables, SC is scale data complexityand MC is the method complexity. Data-scale complexity wasfixed by us in Table 2 and method complexity in Table 3.

The average of Shannon’s entropy for model fitting decisions isdescribed by the formula:

avgðShÞ ¼ �X

pðxiÞ � logðpðxiÞÞ, (11)

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Fig. 1. Detailed model accuracy for data type:method.

Fig. 2. Model accuracy versus empirical combined complexity.

C.R. Munteanu et al. / Journal of Theoretical Biology 254 (2008) 476–482 479

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where

pðxiÞ ¼zðxiÞP

xj, (12)

zðxiÞ ¼xik þ avgðxiÞ

sdðxiÞ

� �þminðxiÞ þ 1, (13)

p(xi) is the probability for a given fitting decision, z(xi) is thestandardization score for variable and sd(xi) is the standarddeviation of xi.

Xi is the SC-scale data complexity; Var is the variables; Coef isthe final equation coefficients; Tree the tree dimension; Leaves isthe number of leaves and Rules is the number of rules.

The following notation was used in the results presentedin the graphics: SG ¼ Star Graph; 2S ¼ secondary structure;SG-noW ¼ SG without 2S weight; SG-W ¼ SG with 2S weight;SG-ALL ¼ SG-noW+SG-W; Comp ¼ composition; Pse ¼ pseudo-amino acid composition; Access ¼ accessibility (ACC, HSE);NoSG ¼ Comp+Pse+2S+Access; ALL ¼ SG-ALL+NoSG.

The following classifiers were tested:

�

GDA: forward, backward and best subset; � NN: linear, multi-layer perception (MLP), probabilistic neural

network (PNN), generalized regression neural network(GRNN), radial basis functions (RBF);

�

Fig. 3. Behavior of model accuracy versus average. Shannon’s entropy of model

fitting complexity: (a) ideal behavior and (b) real behavior.

ML: rules.ConjunctiveRule, rules.DecisionTable, rules.JRip, ru-les.NNg, rules.OneR, rules.PART, rules.Ridor, trees.ADTree,trees.J48, trees.LMT, trees.RandomForest, trees.RandomTree,trees.REPTree, meta.AttributeSelectedClassifier, meta.Bagging,meta.ClassificationViaRegression, meta.Decorate, meta.Filter-edClassifier, lazy.IBk, functions.SimpleLogistic, functions.SMO,functions.VotedPerceptron and bayes.BayesNet.

3. Results

A number of 868 models were constructed using differentseparated/pure or combined 3D, composition, sequences and TIs.The statistical confidence of the fitting is limited by the ratiobetween the number of cases/proteins and the number ofadjustable parameters. For instance, in the case of GDA, thenumber of adjustable parameters is equal to ng� (nv+1), where ng

is the number of groups (enzyme and non-enzymes make twogroups) and nv is the number of variables in the model.For the reason, the results for all possible variables, NoSG&P-se&Comp or Pse&Comp&Access can be over fitted. In addition,Chou and Shen (2008) pointed out that, generally speaking, themore stringent in allowing homologous sequences in the bench-mark dataset, or the larger the number of the classes to beidentified, the harder for a predictor to yield a high overallsuccess rate.

Detailed results for the general classes of indices (SG with andwithout 2S propensities weights, composition, pseudo-composi-tion, 2S, access and all non-SG) and methods are presented inFig. 1 using the total values of accuracy evaluation. noSG:ML-bayes result is one example showing that TIs are not improvingthe quality of the prediction in the case of the enzyme–non-enzyme classification.

This plot shows that, in the case of our set of proteins, theevaluation of the enzymatic activity is not significantly improvedby adding more complicated data. In the cases where the fitting isvery accurate, the cross-validation test is below 70%. The SG datahave the lowest complexity, only the amino-acids sequence beingneeded. The access data are calculated using the Cartesiancoordinates from the PDB files having a higher complexity butgiving similar results with the SG ones.

The dependence of model accuracy on the CC for all methods ispresented in Fig. 2.

All the methods lie in the areas above 70% of accuracy in thecase of the average between the total values of the efficientclassified proteins and the non-classified ones. This is a generalview of the results but can hide a very good fitting of the modelwith a bad test of cross-validation. The same explanation can befound for the very low averaged accuracy of the model in thecase of the neural networks. Dobson and Doig created an enzyme/non-enzyme classification using a similar set of proteins, thesupport vector machine method and 52 protein’s attributes.

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They obtained a classification of 76.17% using 20% leave out(Dobson and Doig, 2003).

The real and ideal behaviors of the model accuracy for theaverage Shannon’s entropy are compared in Fig. 3.

The ideal behavior (Fig. 3a) draws a spiral that starts from theless complex models and increase directly with the increasing ofthe complexity. In contrast, the real results (Fig. 3b) show that theideal pattern is far from the reality for our enzyme/non-enzymemodels and our particular sample used in the increasing of thepower of the method did not increase automatically the accuracyof the model.

4. Discussion

This study compares for the first time all these classes ofindices to assess the ratios between model accuracy and indices/model complexity in enzyme/non-enzyme discrimination.

The use of several statistic/ML methods and different complex-ity of data shows that one cannot establish a direct relationbetween the complexity and the accuracy of the model.

The calculation of these 3DIs presumes the knowledge of 3Dstructure and may become a time-consuming calculation task forlarge protein databases (Estrada et al., 2004; Estrada, 2003). As aconsequence, we investigated the ability of composition, se-quences and TIs to evaluate the enzymatic propriety of the newproteins. The simplest family of descriptors, the TIs, shows thatone can encode in some way the protein 3D structure relatedinformation and this can be a fast alternative to the not significantmore accurate, but more complex and higher time-consuming 3Dmodel. It is a fact that almost all TIs can be derived by similarvector–matrix–vector multiplication of different matrices andcontain essentially connectivity information (Estrada, 2001;Gonzalez-Diaz et al., 2005c).

In conclusion, the actual work shows that increasing thecomplexity of the data or method does not always imply a signi-ficant improvement in the accuracy of the enzyme/non-enzymesmodel. These results suggest the use of simplest data and the GDAfastest methods for modeling.

Acknowledgments

Cristian R. Munteanu thanks the FCT (Portugal) for supportfrom grant SFRH/BPD/24997/2005. Gonzalez-Dıaz Humbertoacknowledges an Isidro Parga Pondal research contract supportedby Xunta de Galicia, University of Santiago de Compostela (Spain)and FSE (Fondo Social Europeo).

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