Research Article Linear and Nonlinear QSAR Study of N2 and...

Hindawi Publishing CorporationISRN Analytical ChemistryVolume 2013 Article ID 151464 8 pageshttpdxdoiorg1011552013151464

Research ArticleLinear and Nonlinear QSAR Study of N2 and O6 SubstitutedGuanine Derivatives as Cyclin-Dependent Kinase 2 Inhibitors

Nasser Goudarzi M Arab Chamjangali and Payam Kalhor

Faculty of Chemistry Shahrood University of Technology PO Box 316 Shahrood 3619995161 Iran

Correspondence should be addressed to Nasser Goudarzi goudarzishahroodutacir

Received 11 April 2013 Accepted 23 May 2013

Academic Editors J N Latosinska and C Y Panicker

Copyright copy 2013 Nasser Goudarzi et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The inhibitory activities (pIC50) of N2 andO6 substituted guanine derivatives as cyclin-dependent kinase 2 (CDK2) inhibitors have

been successfully modeled using calculated molecular descriptors Two linear (MLR) and nonlinear (ANN) methods were utilizedfor construction ofmodels to predict the pIC

50activities of those compoundsTheQSARmodels were validated by cross-validation

(leave-one-out) as well as application of the models for prediction of pIC50

of external set compounds Also the models werevalidated by calculation of statistical parameters and Y-randomization test Two methods provided accurate predictions althoughmore accurate results were obtained by ANNmodelThemean-squared errors (MSEs) for validation and test sets ofMLR are 00650069 and of ANN are 0017 and 0063 respectively

1 Introduction

The cyclin-dependent kinases (CDKs) are a class of enzymeswhich play a fundamental role in cell cycle regulation [1 2]Particularly as their name suggests CDKs activation partiallydepends on the binding of another class of proteins namedcyclins for example cyclins of the D family complex withCDK4 and CDK6 during G1 phase cyclin E with CDK2 inlate G1 cyclin A with CDK2 in S phase and cyclin B withCDK1 (also known as cdc2) in late G2M Then aberrantCDK control and consequent loss of cell cycle check pointfunction have been directly linked to themolecular pathologyof cancer [3] It is well known that phosphorylation in aconserved threonine residue of the CDK subunit is requiredfor its complete activation This task is performed by theCDK activating kinase These proteins properly regulate thecell cycle progress and DNA synthesis only as an activecomplex (T160pCDKcyclin) [4] Overall the activity of theCDKcyclin complex can be depleted by at least two differentmechanisms that contain the phosphorylation of the CDKsubunit at the inhibitory sites or the binding of the specializednatural inhibitors known as CDK inhibitors In the firstmechanism the amino acid residue Y15 and to a lesser extend

T14 (in CDK2) are phosphorylated by human Wee 1 Hu [5]This inhibitory phosphorylation is independent of previouscyclin binding [6] The second mechanism involves thebinding of natural CDK inhibitors Four major mammalianCDK inhibitors have been discovered P21 (CIP1WAF190)and P27 (KIP1) inactive CDK2 and CDK4 cyclin complexesby binding to themThe two other inhibitors are P16INK4 andP15INK4B that are specific for CDK4 and CDK6 They inhibitthe formation of the active cyclin complexes by bindingto the inactive CDK and they can also bind to the activecomplex [2 7] However it has been shown that natural CDKinhibitors are subexpressed in some carcinogenic cells andmedicinal chemists have put some of their effort in the searchfor new synthetic inhibitors to replace them [8ndash12] Someof them have entered in clinical field for instance flavopiri-dol induces cell cycle arrest and tumor growth inhibition[13]

The search for more potent and selective CDK inhibitorsis a daunting challenge due to the similarity of the ATPbinding site along the different CDK subtypes [14] Accord-ing to this the development and use of new strategies toovercome this problem are urgently needed Nowadays newand exciting strategies have emerged and become available to

2 ISRN Analytical Chemistry

find more potent and selective inhibitors and they normallyuse quantitative structure-activity relationships (QSARs)derived from different computational calculation approaches[15ndash19]

Quantitative structure-activityproperty relationship(QSARQSPR) was used for correlation of different activitiesand properties to characteristics of molecular structuresIn recent years several QSAR and QSPR models based onboth linear and nonlinear methods that aimed to predictdifferent activities and properties were used [20ndash30] Thereliable prediction of inhibition of CDK2 has an importantrole in medicinal researches The ultimate role of thedifferent formulations of the QSAR theory is to suggestmathematical models for estimating relevant endpoints ofinterest especially when these cannot be experimentallydetermined for some reason These studies simply rely onthe assumption that the structure of a compound determinesthe related activity The molecular structure is thereforetranslated into the so-called molecular descriptors throughmathematical formulae obtained from several theories suchas chemical graph theory information theory and quantummechanics [31 32] In this work we carried out a QSARstudy by predicting the inhibitory activity of a set of N2and O6 substituted guanine derivatives by using multiplelinear regression (MLR) and artificial neural network (ANN)dealing with linearity and nonlinearity respectively

2 Basic Theory

21 Multiple Linear Regression (MLR) The general goal ofmultiple linear regression (MLR) is to model the relationshipbetween some independent variables and a dependent vari-able by fitting a linear equation to observed data Generallythe multiple linear regression model is as the followingequation

119910 = 11988711199091+ 11988721199092+ 11988731199093sdot sdot sdot 119887119898119909119898+ 120576 (1)

where 119899 is the number of independent variables 1198871 119887

119899are

the regression coefficients and 119910 is the dependent variable[33]

22 Artificial Neural Network (ANN) ANNs have largenumbers of computational units connected in a vast parallelconstruction Neural networks do not need an obviousformulation of the handled problem They act as a meansto introduce scaled data to the network The data from theinput layer (input neurons) propagate through the networkvia interconnections Scalar weights are specialized to eachconnection A remarkable aspect of the neural networks istheir learning step In this step the value of weights and biaseswould be optimized based on a set of measured numericalvalues (training set) More details about neural networks aregiven in [34 35]

3 Materials and Methods

31 Data The experimental data used in the present study tomodel IC

50were taken from [36]Thewhole data set included

56 compounds whose biological activities (pIC50

values)were determined for inhibition of CDK2 It is worthy to saythat pIC

50values span a broad range from 411 to 722M In

this work the structure-activity model is generated by ANNandMLRThenames of these compounds their experimentaland calculated pIC

50values by ANN and MLR methods and

also their values using leave-one-out are shown in Table 1 Ascan be seen this set contains 56 inhibitory activity (pIC

50)

data of CDK2sThe data set was split into training validationand test sets to increase the networkrsquos generalization Thetraining set of 34 compounds with pIC

50values ranging from

411 to 722 was used to construct the model The validationset of 11 compounds with pIC

50values ranging from 419

to 662 was used to prevent overtrainingover fitting of theANNmodel The test set of 11 compounds with pIC

50values

ranging from 419 to 696 was used as an external set toevaluate the predictive ability of the model

32 Descriptor Generation and Screening The inhibitoryactivation of compounds is related to some of their structuralelectronic and geometric properties The value of theseproperties can be encoded quantitatively by numerical valuesnamed molecular descriptors These molecular parametersare to be used to search for the best QSAR model of theinhibitory activationThe 2D structures of themoleculesweredrawn usingHyperchem8 software [37]Themolecular struc-tures were optimized using the Polak-Ribiere algorithm untilthe root-mean-square gradient was 0001 kcalmolminus1 Theresulting geometry was transferred into the Dragon programpackage and 1481 descriptorswere produced [38]Then thesedescriptors were given to SPSS 17 for statistical work [39] It isworth mentioning that in the first preselected analysis somedescriptors were removed because many of them includedzero or other constantnear-constant values and did nothave enough information of structure On the other handto decrease the redundancy existing in the descriptor datamatrix the correlation coefficient 119877 of the descriptors witheach other (Pearsonrsquos correlation) was examined and thecollinear descriptors (with 119877 gt 09) were removed Bydoing so 238 descriptors were remained Then by using thestepwise mode for regression 14 models were given Withconsidering some parameters such as 119865 119905 119877 and standarderror (SE) model number 14 containing 10 descriptors wasused as MLR model to predict of pIC

50 These descrip-

tors are 3D-MoRSE-signal 20unweighted (Mor20u) Gearyautocorrelation-lag 2weighted by atomic Sanderson elec-tronegativities (GATS2e)119877 autocorrelation of lag 5weightedby atomic polarizabilities (R5p) Moran autocorrelation-lag 2weighted by atomic Sanderson electronegativities(MATS2e) mean topological charge index of order 6 (JGI6)mean topological charge index of order 6 (JGI4) 119877 autocor-relation of lag 5weighted by atomic masses (R1m) leverage-weighted autocorrelation of lag 0weighted by atomic masses(HATS0m) 3D-MoRSE-signal 20weighted by atomic vander Waals volumes (Mor06v) 1st component accessibilitydirectional WHIM indexweighted by atomic electrotopo-logical states (E1s) The name class and meaning of thesedescriptors are shown in Table 2

ISRN Analytical Chemistry 3

Table 1 The names of compounds their experimental and calculated pIC50 values by ANN and MLR methods and also their values werecalculated using leave-one-out

No Name pIC50 ANN MLR ANN(LOO)

MLR(LOO)

1 6-Propoxy-9H-purin-2-amine 417 422 40983 42054 442442 6-Butoxy-9H-purin-2-amine 432 426 43 43073 439913 6-Pentyloxy-9H-purin-2-amine 431 431 427 44568 432894 6-Isopropoxy-9H-purin-2-amine 412 425 45953 43075 407675 6-Sec-butoxy-9H-purin-2-amine 46 438 431 44773 440616 6-Isobutoxy-9H-purin-2-amine 438 454 41 46696 466647 6-(2-Methylbutoxy)-9H-purin-2-amin 482 469 493 47491 472958 6-(Isopenthyloxy)-9H-purin-2-amin 459 449 4505 45325 448899 6-(Hex-5-enyloxy)-9H-purin-2-amine 433 428 44022 4964 4424110 6-((E)-Hex-3-enyloxy)-9H-purin-2-amin 416 409 44578 40104 4049111 6-(Allyloxy)-9H-purin-2-amine 411 422 41781 43261 3761712 6-(2-Methylallyloxy)-9H-purin-2-amin 446 443 433 44437 4478613 6-(2-Methylenebutoxy)-9H-purin-2-amin 468 456 35157 4842 4897314 6-(3-Methyl-2-ethylenebutoxy)-9H-purin-amin 48 486 467 50957 4830515 6-(Cyclopentyl methoxy)-9H-purin-2-amin 468 469 50611 49247 4772816 6-(Cyclopentenyl methoxy)-9H-purin-2-amin 451 465 442 47164 4673317 6-(Cyclohexelymethoxy)-9H-purin-2-amin 466 449 46965 44498 4422218 6-((Cyclohex-3-enyl)methoxy)-9H-purin-2-amin 48 471 50266 4773 4867819 6-(2-Cyclohexylethoxy)-9H-purin-2-amin 436 455 448 44313 448220 6-(Benzyloxy)-9H-purin-2-amine 446 45 45365 4512 4484321 6-(Phenethyloxy)-9H-purin-2-amine 419 413 428 42465 4198722 6-(22-Diethoxypropoxy)-9H-purin-2-amin 47 464 41429 50631 4700423 6-((2-Isopropyl-13-dioxolan-2-yl)methoxy)-9H-purin-2-amine 419 426 404 45904 425924 6-(Cyclohexylmethoxy)9H-purin-2-amin 477 492 47561 44964 4503525 6-(Cyclohexylmethoxy)-N-phenyl-9H- purin-2-amin 601 619 5826 60775 5988626 6-(Cyclohexylmethoxy)-N- methyl-9H-purin-2-amin 53 518 492 52791 5274127 6-(Cyclohexylmethoxy)-N-ethyl-9H-purin-2-amin 555 578 56238 52692 52628 N-(3-Chlorophenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 564 541 576 54811 5707729 N-(3-Bromophenyl)-6-(cyclohexylmethoxy)9H-purin-2-amine 517 534 4947 54014 5389630 (3-(6-(Cyclomethylmethoxy)9H-purin-2-ylamino)phenyl)methanol 64 648 64982 62763 631731 6-(Cyclohexylmethoxy)-N-(3-methoxyphenyl)-9H-purin-2-amine 574 629 608 60901 6051532 6-(Cyclohexylmethoxy)-N-(3-(methylthio)phenyl)-9H-purin-2-amine 577 596 59264 59645 5931233 6-(Cyclohexylmethoxy)-N-(4-methoxyphenyl)-9H-purin-2-amine 619 637 599 57645 5958934 6-(Cyclomethylmethoxy)N-(4-(methylsulfonyl)phenyl)-NN-dimethyl-9H-purin-2-amine 619 637 599 57645 5958935 6-(Cyclomethylmethoxy)-N-(4-(methylsulfonyl)phenyl)-9H-purin-2-amine 722 724 67582 6773 6916836 6-(Cyclohexylmethoxy)-N-(4-(methylsulfonyl)phenyl)-9H-purin-2-amine 700 707 68456 65432 6668337 6-(Cyclohexylmethoxy)-N-(4-(ethyl sulfonyl)phenyl)-9H-purin-2-amine 668 682 667 64289 691238 4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)benzamide 619 64 674 63105 6536739 4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)-N-methylbenzamide 67 691 67797 64012 6583740 4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)-NN-dimethylbenzamide 67 65 64905 65163 6634941 6-(Cyclohexylmethoxy)-N-(4-(prop-1-en-2-yl)phenyl)-9H-purin-2-amine 652 644 70214 6416 6552742 1-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)phenyl)ethanol 61 65 668 64374 6476943 2-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)phenyl)acetonitril 652 636 63441 65529 6453

44 N-(4-(2-(4-Methylpiperazin-1-yl)ethylsulfonyl)pheyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 692 705 68082 69098 68732

45 N-(4-(2-(Piperidin-1-yl)ethylsulfonyl)phenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 647 661 666 66328 665246 N-(4-(2-Thiomorpholinoethylsulfonyl)phenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 627 641 7347 5983 6124947 N-(4-(2-(Diethylamino)ethylsulfonyl)phenyl)-6-(cylohexylmethoxy)-9H-purin-2-amine 635 638 63132 67114 6613


Table 1 Continued


MLR(LOO)

48 N-(4-(2-(4-Isopropylpiperazin-1-yl)ethylsulfonyl)phenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 647 64 68005 68036 66025

49 2-(4-(2-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)phenylsulfonyl)ethyl)piperazin-1-yl)ethanol 659 663 659 67072 68705

50 2-(1-(2-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)phenylsulfonyl)ethyl)piperidin-4-yl)ethanol 662 653 636 66902 66265

51 2-(2-(4-(2-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-ylamino)phenylsulfonyl)ethyl)piperazin-1-yl)ethoxy)ethanol 651 644 65378 64673 6636

52 N-(4-(2-(4-(Ethylpiperazin-1-yl)ethylsulfonyl)phenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 659 672 66713 67344 64404

53 1-(4-(2-(4-(6-(Cyclohexylmethoxy)-9H-purin-2-yl amino)phenylsulfonyl)ethyl)piperazin-1-yl)ethanone 664 667 62815 66566 66462

54 N-(4-(2-(4-(2-(Methoxyethyl)piperazin-1-yl)ethylsulfonyl)phenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 654 647 68 60738 66812

55 N-(4-(2-(Pyrrolidin-1-1yl)ethylsulfonyl)phhenyl)-6-(cyclohexylmethoxy)-9H-purin-2-amine 674 689 68736 65724 6637556 6-(Cyclohexylethoxy)-9H-purin 696 656 696 68179 65037

Table 2 Descriptors were selected for construction of model

No Symbol Class Meaning1 Mor20u 3D-MoRSE 3D-MoRSE-signal 20unweighted2 GATS2e 2D autocorrelation Geary autocorrelation-lag 2weighted by atomic Sanderson electronegativities3 R5p GETAWAY 119877 autocorrelation of lag 5weighted by atomic polarizabilities4 MATS2e 2D autocorrelation Moran autocorrelation-lag 2weighted by atomic Sanderson electronegativities5 JGI6 Galvez topol Charge Mean topological charge index of order 66 JGI4 Galvez topol Charge Mean topological charge index of order 47 R1m GETAWAY 119877 autocorrelation of lag 5weighted by atomic masses8 HATS0m GETAWAY Leverage-weighted autocorrelation of lag 0weighted by atomic masses9 Mor06v 3D-MoRSE 3D-MoRSE-signal 20weighted by atomic van der Waals volumes10 E1s WHIM 1st component accessibility directional WHIM indexweighted by atomic electrotopological states

Table 3 Correlation matrix for the selected descriptors

Mor20u GATS2e R5p MATS2e JGI6 JGI4 R1m HATS0m Mor06v E1sMor20u 1GATS2e 012 1R5p 0121 0163 1MATS2e minus058 minus0599 0088 1JGI6 0614 0117 minus022 minus0528 1JGI4 minus0459 0304 0106 0199 minus0102 1R1m 0226 minus0225 0238 0097 0248 minus0043 1HATS0m minus0452 minus0079 0157 0333 0126 0148 0419 1Mor06v 0601 minus0045 minus0141 minus0512 0558 minus0462 0332 minus0138 1

E1s 0354 minus0195 minus0017 minus024 0352 minus0205 0373 minus0112 0431 1

The correlation matrix for the selected 10 descriptorspresented in the model is shown in Table 3 These resultsshow there is not any correlation between the selecteddescriptors

4 Results and Discussion

The prediction ability of QSARQSPR models is affected bytwo factors one is the descriptors which should carry enough


Table 4 The training settings for the ANN model

No of descriptors Training fcn Transfer fcn No of nodes in hidden layers No of epochs MSE10 Levenberg- Log sigmoid 4 5 0017110 Bayesian Log sigmoid 6 5 001866 Levenberg- Tan sigmoid 7 3 0028510 Bayesian Tan sigmoid 3 4 00218

Table 5 Comparison of the statistical parameters obtained from ANN and MLR models

Parameter Test set (119873 = 11) Validation set (119873 = 11)MLR ANN MLR ANN

MAE () 1343 1329 1382 10405MSE 0069 0063 0065 00171PRESS 01394 01333 01349 00693SEP 0964 0956 0936 09821198772 08122 07422 05518 04181

RMAE 3607 3433 368 2221

information of molecular structure for the interpretationof the activityproperty The other is the modeling methodemployed [20] The number of descriptors available forQSARQSPR studies is often so large that it is difficult toobtain a model including all of them Therefore identifyingimportant descriptors certainly plays an important role inQSARQSPR

Descriptors should represent the maximum informationin activity variations and collinearity among them mustbe kept to a minimum As can be seen from the corre-lation matrix (Table 3) there is no significant correlationbetween the selected descriptors In the present work thesedescriptors were used for construction of both linear andnonlinear models The following linear model was obtainedby the training set compounds and 10 selected moleculardescriptors

pIC50= 11746 + 0684 Mor20u minus 2228 GATS2e minus 18175

R5p minus 5114 MATS2e + 6507 JGI6 minus 40405 JGI4 + 2155 R1mminus 4434 HATS om minus 0149 Mor06v minus 0715 E1s

This model was then used to predict the validation andtest sets of data Then artificial neural network (ANN)was used to make a nonlinear model to calculate theinhibitory activities (pIC

50) of the compounds To do so a

3-layer feedforward network with backpropagation patternwas used in which mean squared error (MSE) was appliedas the performance function The MLR selected descriptorswere used as the input layer of the network To have astrong network 5 parameters were optimizedThe optimizedparameters are (1) the number of descriptors (between 2 and10) (2) the number of nodes in the hidden layer (3) thetransfer function (including log sigmoid and tan sigmoid) (4)training function (includingBayesian regulation (trainbr) andLevenberg-Marquardt (trainlm)) and finally (5) number ofepochs Table 4 shows the training settings of the optimizednetwork It should be noted that the training of the networkfor the prediction of pIC

50was interrupted when the MSE of

the validation set started to increase to avoid overfittingAccording to Table 4 a network with a Levenberg-

Marquardt training function and log-sigmoid transfer func-tion with 10 descriptors (the same MLR descriptors) has the

least MSE value (00171) In order to evaluate the predictiveability of the linear and nonlinear models and to comparethem we employed the percentage of mean absolute error(MAE) mean squared error (MSE) predictive residual sumof squares (PRESSs) standard error of prediction (SEP)determination coefficient (1198772) percentage of relative errorprediction (REP ()) and relative mean absolute error(RMAE) These statistical parameters for MLR and ANN arelisted in Table 5

As can be seen from Table 5 all the error parametersrsquovalues of ANN for both test and validation sets are smallerthan those ofMLRThis is believed to be due to the nonlinearcapabilities of the ANNmodel

The used statistical parameters are defined as

1198772= 1 minus

sum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs minus 119910meas)

2

RMSEP = radicsum119899

119894=1(119910pred minus 119910obs)

2

119899

RSEP () = 100 times radicsum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs)

2

MAE () = 100119899times radic

119899

sum

119894=1

10038161003816100381610038161003816(119910pred minus 119910obs)

10038161003816100381610038161003816

MSE =sum (119910obs minus 119910pred)

119899

RMSE = radic(119910obs minus 119910pred)

2

119899

119865 =

sum((119910pred minus 119910)2

119901)


119899 minus 119901 minus 1)

(2)


Table 6 1198772 values of the test set after several Y-randomization tests

Iteration 1198772 test set

1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966

Figure 1 Plot of the predicted values versus the experimental onesfor the validation set

where 119910119894is the experimental value 119910

119894is the predicted value

119910 is the mean value and 119899 is the number of compoundsTo avoid chance correlation and to guarantee the net-

workrsquos predictability power Y-randomization test was carriedout The results of several repetition of this test are shown inTable 6 The low values of 1198772 show that there is no chancecorrelation in the developed model

Figures 1 and 2 show plots of the predicted values versusexperimental ones of ANN and MLR models for validationand test sets The obtained results show the superiorityof ANN model than MLR to predict of pIC

50of these

compounds The ANN and MLR residuals of leave-one-out are plotted against the experimental values in Figure 3The symmetric distribution of residuals at both sides of thezero line indicates that no systematic error exists in thedevelopment of the MLR and ANNmodels

5 Conclusion

From the analysis of the obtained results we can concludethat (1) the proposed models can sufficiently representstructure-activity relationship of the compounds (2) By com-parison of results from the MLR and ANN the performanceof the ANN model is clearly better than that of MLR whichindicates that nonlinear model can simulate the relationshipbetween the structures of the compounds and their activities

335

445

555

665

775

8

4 45 5 55 6 65 7Experimental

Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test

Figure 2 Plot of the predicted values versus the experimental onesfor the test set

002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)

Figure 3 Plot of the ANN and MLR residuals of leave-one-outversus experimental values

more accurately (3) The calculated statistical parameters ofthesemodels reveal the superiority ofANNoverMLRmodel

References

[1] C Norbury and P Nurse ldquoAnimal cell cycles and their controlrdquoAnnual Review of Biochemistry vol 61 pp 441ndash470 1992

[2] D O Morgan ldquoPrinciples of CDK regulationrdquo Nature vol 374no 6518 pp 131ndash134 1995

[3] M Hall and G Peters ldquoGenetic alterations of cyclins cyclin-dependent kinases and Cdk inhibitors in human cancerrdquoAdvances in Cancer Research vol 68 pp 67ndash108 1996

[4] T M Sielecki J F Boylan P A Benfield and G L TrainorldquoCyclin-dependent kinase inhibitors useful targets in cell cycle


regulationrdquo Journal of Medicinal Chemistry vol 43 no 1 pp1ndash18 2000

[5] N Watanabe M Broome and T Hunter ldquoRegulation of thehumanWEE1Hu CDK tyrosine 15-kinase during the cell cyclerdquoEMBO Journal vol 14 no 9 pp 1878ndash1891 1995

[6] K Coulonval L Bockstaele S Paternot and P P Roger ldquoPhos-phorylations of cyclin-dependent kinase 2 revisited using two-dimensional gel electrophoresisrdquo Journal of Biological Chem-istry vol 278 no 52 pp 52052ndash52060 2003

[7] N P Pavletich ldquoMechanisms of cyclin-dependent kinase regu-lation structures of Cdks their cyclin activators and Cip andINK4 inhibitorsrdquo Journal of Molecular Biology vol 287 pp 821ndash828 1999

[8] M D Losiewicz B A Carlson G Kaur E A Sausville andP J Worland ldquoPotent inhibition of Cdc2 kinase activity bythe flavonoid L86-8275rdquo Biochemical and Biophysical ResearchCommunications vol 201 no 2 pp 589ndash595 1994

[9] A M Senderowicz and E A Sausville ldquoPreclinical and clinicaldevelopment of cyclin-dependent kinase modulatorsrdquo Journalof the National Cancer Institute vol 92 no 5 pp 376ndash387 2000

[10] I R Hardcastle B T Golding and R J Griffin ldquoDesigninginhibitors of cyclin-dependent kinasesrdquo Annual Review ofPharmacology and Toxicology vol 42 pp 325ndash348 2002

[11] M Knockaert P Greengard and L Meijer ldquoPharmacologicalinhibitors of cyclin-dependent kinasesrdquoTrends in Pharmacolog-ical Sciences vol 23 no 9 pp 417ndash425 2002

[12] P L Toogood ldquoProgress toward the development of agents tomodulate the cell cyclerdquo Current Opinion in Chemical Biologyvol 6 pp 472ndash478 2002

[13] G I Shapiro ldquoPreclinical and clinical development of thecyclin-dependent kinase inhibitor flavopiridolrdquo Clinical CancerResearch vol 10 no 12 pp 4270sndash4275s 2004

[14] M Vieth R E Higgs D H Robertson M Shapiro E AGragg and H Hemmerle ldquoKinomicsmdashstructural biology andchemogenomics of kinase inhibitors and targetsrdquo Biochimica etBiophysica Acta vol 1697 no 1-2 pp 243ndash257 2004

[15] M Fernandez A Tundidor-Camba and J Caballero ldquoModel-ing of cyclin-dependent kinase inhibition by 1H-pyrazolo[34-d]pyrimidine derivatives using artificial neural network ensem-blesrdquo Journal of Chemical Information andModeling vol 45 no6 pp 1884ndash1895 2005

[16] M P Gonzalez J Caballero A M Helguera M Garriga GGonzalez and M Fernandez ldquo2D autocorrelation modellingof the inhibitory activity of cytokinin-derived cyclin-dependentkinase inhibitorsrdquo Bulletin of Mathematical Biology vol 68 no4 pp 735ndash751 2006

[17] H Dureja and A K Madan ldquoTopochemical models for predic-tion of cyclin-dependent kinase 2 inhibitory activity of indole-2-onesrdquo Journal ofMolecularModeling vol 11 no 6 pp 525ndash5312005

[18] J Z Li H X Liu X J Yao M C Liu Z D Hu and B TFan ldquoStructure-activity relationship study of oxindole-basedinhibitors of cyclin-dependent kinases based on least-squaressupport vector machinesrdquo Analytica Chimica Acta vol 581 pp333ndash342 2007

[19] S Samanta B Debnath A Basu S Gayen K Srikanth andT Jha ldquoExploring QSAR on 3-aminopyrazoles as antitumoragents for their inhibitory activity of CDK2cyclin Ardquo EuropeanJournal of Medicinal Chemistry vol 41 no 10 pp 1190ndash11952006

[20] M Goodarzi and M P Freitas ldquoPredicting boiling points ofaliphatic alcohols through multivariate image analysis appliedto quantitative structure-property relationshipsrdquo Journal ofPhysical Chemistry A vol 112 no 44 pp 11263ndash11265 2008

[21] M Goodarzi and M P Freitas ldquoAugmented three-mode MIA-QSAR modeling for a series of anti-HIV-1 compoundsrdquo QSARand Combinatorial Science vol 27 no 9 pp 1092ndash1097 2008

[22] M Goodarzi T Goodarzi andN Ghasemi ldquoSpectrophotomet-ric simultaneous determination of manganese(ii) and iron(ii)in pharmaceutical by orthogonal signal correction-partial leastsquaresrdquo Annali di Chimica vol 97 no 5-6 pp 303ndash312 2007

[23] N Goudarzi M H Fatemi and A Samadi-Maybodi ldquoQuanti-tative structure-properties relationship study of the 29Si-NMRchemical shifts of some silicate speciesrdquo Spectroscopy Lettersvol 42 no 4 pp 186ndash193 2009

[24] N Goudarzi and M Goodarzi ldquoPrediction of the logarithmicof partition coefficients (log 119875) of some organic compoundsbyleast square-support vector machine (LS-SVM)rdquo MolecularPhysics vol 106 pp 2525ndash2535 2008

[25] N Goudarzi and M Goodarzi ldquoPrediction of the acidic disso-ciation constant (pKa) of some organic compounds using linearand nonlinear QSPR methodsrdquo Molecular Physics vol 107 no14 pp 1495ndash1503 2009

[26] NGoudarzi andMGoodarzi ldquoPrediction of the vapor pressureof some halogenatedmethyl-phenyl ether (anisole) compoundsusing linear and nonlinear QSPR methodsrdquo Molecular Physicsvol 107 no 15 pp 1615ndash1620 2009

[27] N Goudarzi and M Goodarzi ldquoQSPR models for predictionof half wave potentials of some chlorinated organic compoundsusing SR-PLS andGA-PLSmethodsrdquoMolecular Physics vol 107pp 1739ndash1744 2009

[28] Z Elmi K Faez M Goodarzi and N Goudarzi ldquoFeatureselection method based on fuzzy entropy for regression inQSAR studiesrdquoMolecular Physics vol 107 no 17 pp 1787ndash17982009

[29] N Goudarzi M Goodarzi M C U Araujo and R K HGalvao ldquoQSPR modeling of soil sorption coefficients (KOC) ofpesticides usingSPA-ANN and SPA-MLRrdquo Journal of Agricul-tural and Food Chemistry vol 57 pp 7153ndash7158 2009

[30] N Goudarzi M Goodarzi and M Arab Chamjangali ldquoPredic-tion of inhibition effect of some aliphatic and aromatic organiccompounds using QSAR methodrdquo Journal of EnvironmentalChemistry and Ecotoxicology vol 2 pp 47ndash50 2010

[31] N Trinajstic Chemical Graph Theory CRC Press Boca RatonFla USA 1992

[32] A R Katritzky V S Lobanov and M Karelson ldquoQSPR thecorrelation and quantitative prediction of chemical and physicalproperties from structurerdquo Chemical Society Reviews vol 24no 4 pp 279ndash287 1995

[33] N R Draper and H Smith Applied Regression Analysis WileySeries in Probability and Statistics New York NY USA 1998

[34] J Zupan and J Gasteiger Neural Networks in Chemistry andDrug Design Wiley-VCH Weinheim Germany 1999

[35] N K Bose and P Liang Neural Networks FundamentalsMcGraw-Hill New York NY USA 1996

[36] J H Alzate-Morales J Caballero A Vergara Jague and FD Gonzalez ldquoInsights into the structural basis of N2 andO6 substituted guanine derivatives as cyclin-dependent kinase2 (CDK2) inhibitors prediction of the binding modes andpotency of the inhibitors by docking andONIOM calculationsrdquoJournal of Chemical Information andModeling vol 49 no 4 pp886ndash899 2009


[37] HyperChem Release 7 HyperCube Inc httpwwwhypercom

[38] R Todeschini Milano Chemometrics and QSPR Group httpmichemdisatunimibitchmstaffstaffhtm

[39] SPSS for windows Statistical package for IBM PC SPSS Inchttpwwwspsscom

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

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Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


find more potent and selective inhibitors and they normallyuse quantitative structure-activity relationships (QSARs)derived from different computational calculation approaches[15ndash19]

Quantitative structure-activityproperty relationship(QSARQSPR) was used for correlation of different activitiesand properties to characteristics of molecular structuresIn recent years several QSAR and QSPR models based onboth linear and nonlinear methods that aimed to predictdifferent activities and properties were used [20ndash30] Thereliable prediction of inhibition of CDK2 has an importantrole in medicinal researches The ultimate role of thedifferent formulations of the QSAR theory is to suggestmathematical models for estimating relevant endpoints ofinterest especially when these cannot be experimentallydetermined for some reason These studies simply rely onthe assumption that the structure of a compound determinesthe related activity The molecular structure is thereforetranslated into the so-called molecular descriptors throughmathematical formulae obtained from several theories suchas chemical graph theory information theory and quantummechanics [31 32] In this work we carried out a QSARstudy by predicting the inhibitory activity of a set of N2and O6 substituted guanine derivatives by using multiplelinear regression (MLR) and artificial neural network (ANN)dealing with linearity and nonlinearity respectively

2 Basic Theory

21 Multiple Linear Regression (MLR) The general goal ofmultiple linear regression (MLR) is to model the relationshipbetween some independent variables and a dependent vari-able by fitting a linear equation to observed data Generallythe multiple linear regression model is as the followingequation

119910 = 11988711199091+ 11988721199092+ 11988731199093sdot sdot sdot 119887119898119909119898+ 120576 (1)

where 119899 is the number of independent variables 1198871 119887

119899are

the regression coefficients and 119910 is the dependent variable[33]

22 Artificial Neural Network (ANN) ANNs have largenumbers of computational units connected in a vast parallelconstruction Neural networks do not need an obviousformulation of the handled problem They act as a meansto introduce scaled data to the network The data from theinput layer (input neurons) propagate through the networkvia interconnections Scalar weights are specialized to eachconnection A remarkable aspect of the neural networks istheir learning step In this step the value of weights and biaseswould be optimized based on a set of measured numericalvalues (training set) More details about neural networks aregiven in [34 35]

3 Materials and Methods

31 Data The experimental data used in the present study tomodel IC

50were taken from [36]Thewhole data set included

56 compounds whose biological activities (pIC50

values)were determined for inhibition of CDK2 It is worthy to saythat pIC

50values span a broad range from 411 to 722M In

this work the structure-activity model is generated by ANNandMLRThenames of these compounds their experimentaland calculated pIC

50values by ANN and MLR methods and

also their values using leave-one-out are shown in Table 1 Ascan be seen this set contains 56 inhibitory activity (pIC

50)

data of CDK2sThe data set was split into training validationand test sets to increase the networkrsquos generalization Thetraining set of 34 compounds with pIC

50values ranging from

411 to 722 was used to construct the model The validationset of 11 compounds with pIC

50values ranging from 419

to 662 was used to prevent overtrainingover fitting of theANNmodel The test set of 11 compounds with pIC

50values

ranging from 419 to 696 was used as an external set toevaluate the predictive ability of the model

32 Descriptor Generation and Screening The inhibitoryactivation of compounds is related to some of their structuralelectronic and geometric properties The value of theseproperties can be encoded quantitatively by numerical valuesnamed molecular descriptors These molecular parametersare to be used to search for the best QSAR model of theinhibitory activationThe 2D structures of themoleculesweredrawn usingHyperchem8 software [37]Themolecular struc-tures were optimized using the Polak-Ribiere algorithm untilthe root-mean-square gradient was 0001 kcalmolminus1 Theresulting geometry was transferred into the Dragon programpackage and 1481 descriptorswere produced [38]Then thesedescriptors were given to SPSS 17 for statistical work [39] It isworth mentioning that in the first preselected analysis somedescriptors were removed because many of them includedzero or other constantnear-constant values and did nothave enough information of structure On the other handto decrease the redundancy existing in the descriptor datamatrix the correlation coefficient 119877 of the descriptors witheach other (Pearsonrsquos correlation) was examined and thecollinear descriptors (with 119877 gt 09) were removed Bydoing so 238 descriptors were remained Then by using thestepwise mode for regression 14 models were given Withconsidering some parameters such as 119865 119905 119877 and standarderror (SE) model number 14 containing 10 descriptors wasused as MLR model to predict of pIC

50 These descrip-

tors are 3D-MoRSE-signal 20unweighted (Mor20u) Gearyautocorrelation-lag 2weighted by atomic Sanderson elec-tronegativities (GATS2e)119877 autocorrelation of lag 5weightedby atomic polarizabilities (R5p) Moran autocorrelation-lag 2weighted by atomic Sanderson electronegativities(MATS2e) mean topological charge index of order 6 (JGI6)mean topological charge index of order 6 (JGI4) 119877 autocor-relation of lag 5weighted by atomic masses (R1m) leverage-weighted autocorrelation of lag 0weighted by atomic masses(HATS0m) 3D-MoRSE-signal 20weighted by atomic vander Waals volumes (Mor06v) 1st component accessibilitydirectional WHIM indexweighted by atomic electrotopo-logical states (E1s) The name class and meaning of thesedescriptors are shown in Table 2




MLR(LOO)





Table 1 Continued


MLR(LOO)






















MAE () 1343 1329 1382 10405MSE 0069 0063 0065 00171PRESS 01394 01333 01349 00693SEP 0964 0956 0936 09821198772 08122 07422 05518 04181

RMAE 3607 3433 368 2221














1198772= 1 minus

sum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs minus 119910meas)

2


119894=1(119910pred minus 119910obs)

2

119899


119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs)

2


119899

sum

119894=1

10038161003816100381610038161003816(119910pred minus 119910obs)

10038161003816100381610038161003816


119899


2

119899

119865 =


119901)


119899 minus 119901 minus 1)

(2)




1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966







50of these


5 Conclusion


335

445

555

665

775

8


Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test


002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)



References




















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




MLR(LOO)





Table 1 Continued


MLR(LOO)






















MAE () 1343 1329 1382 10405MSE 0069 0063 0065 00171PRESS 01394 01333 01349 00693SEP 0964 0956 0936 09821198772 08122 07422 05518 04181

RMAE 3607 3433 368 2221














1198772= 1 minus

sum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs minus 119910meas)

2


119894=1(119910pred minus 119910obs)

2

119899


119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs)

2


119899

sum

119894=1

10038161003816100381610038161003816(119910pred minus 119910obs)

10038161003816100381610038161003816


119899


2

119899

119865 =


119901)


119899 minus 119901 minus 1)

(2)




1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966







50of these


5 Conclusion


335

445

555

665

775

8


Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test


002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)



References




















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Table 1 Continued


MLR(LOO)






















MAE () 1343 1329 1382 10405MSE 0069 0063 0065 00171PRESS 01394 01333 01349 00693SEP 0964 0956 0936 09821198772 08122 07422 05518 04181

RMAE 3607 3433 368 2221














1198772= 1 minus

sum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs minus 119910meas)

2


119894=1(119910pred minus 119910obs)

2

119899


119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs)

2


119899

sum

119894=1

10038161003816100381610038161003816(119910pred minus 119910obs)

10038161003816100381610038161003816


119899


2

119899

119865 =


119901)


119899 minus 119901 minus 1)

(2)




1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966







50of these


5 Conclusion


335

445

555

665

775

8


Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test


002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)



References




















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






MAE () 1343 1329 1382 10405MSE 0069 0063 0065 00171PRESS 01394 01333 01349 00693SEP 0964 0956 0936 09821198772 08122 07422 05518 04181

RMAE 3607 3433 368 2221














1198772= 1 minus

sum119899

119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs minus 119910meas)

2


119894=1(119910pred minus 119910obs)

2

119899


119894=1(119910pred minus 119910obs)

2

sum119899

119894=1(119910obs)

2


119899

sum

119894=1

10038161003816100381610038161003816(119910pred minus 119910obs)

10038161003816100381610038161003816


119899


2

119899

119865 =


119901)


119899 minus 119901 minus 1)

(2)




1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966







50of these


5 Conclusion


335

445

555

665

775

8


Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test


002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)



References




















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




1 0292 0023 0004 0095 0006 0007 0468 0019 01310 001

335

445

555

665

775

3 35 4 45 5 55 6 65 7

Pred

icte

d

Experimental

Validation

ANN R2 = 0972

MLR R2 = 0966







50of these


5 Conclusion


335

445

555

665

775

8


Pred

icte

d

ANN R2 = 09446

MLR R2 = 09431

Test


002040608

3 35 4 45 5 55 6 65 7 75 8

Resid

ual

ANN

Experimental

minus02

minus04

minus06

minus08

minus1

(a)

00102030405

3 4 5 6 7 8

MLR

minus01

minus02

minus03

minus04

minus05

minus06

Resid

ual

Experimental

(b)



References




















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of
















































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Research Article Linear and Nonlinear QSAR Study of N2 and...

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Transcript of Research Article Linear and Nonlinear QSAR Study of N2 and...