the principal aim of this laboratory is the synthesis of conjugated unsaturated ketones as candidate antineoplastic agents .
these compounds interact with thiols but in general , they have little or no affinity for amino and hydroxyl groups which are found in nucleic acids ( 1 - 3 ) .
hence thiol alkylators may not have the genotoxic properties associated with a number of contemporary anticancer drugs ( 4 ) .  
however after an initial chemical insult , certain neoplasms are more vulnerable to a subsequent cytotoxic effect than various non - malignant cells ( 5 , 6 ) .
hence by mounting the 1,5-diaryl-3-oxo-1,4-pentadienyl pharmacophore [ ar - c = c - c(o)-c = c - ar ] on heterocyclic and cycloaliphatic scaffolds , two sequential interactions with cellular thiols can take place which may be more detrimental to tumours than normal tissues .
such considerations led to the development of 3,5-bis(benzylidene)-4-piperidones 1a - d which demonstrated potent cytotoxic properties with the ic50 values in the low micromolar range against human molt 4/c8 and cem t - lymphocytes as well as murine l1210 lymphocytic leukemia cells ( 7 , 8) .
the hypothesis of sequential cytotoxicity was advanced that the 1,5-diaryl-3-oxo-1,4-pentadienyl group interacts at a primary binding site and a side chain on the piperidine nitrogen may align at an auxiliary binding site which could enhance cytotoxic potencies . in order to evaluate this hypothesis , a novel series of n - aroyl-3,5-bis(benzylidene)-4-piperidone derivatives 2 - 7 were synthesized ( 8) . in these compounds , the side chain contains atoms and groups capable of forming hydrogen and van der waals bonds and also an ionic bond in series 3 - 6 which could bind at an auxiliary binding site . when the potencies of the compounds in series 3 - 6 were compared with that of the analogs 1a - d which have the same aryl substituent , the ic50 values of the amides 3 - 6 were lower in 48% of the comparisons made while equipotency was noted in 35% of the cases ( 8) .
the proposed primary and auxiliary binding sites of cytotoxic n - aroyl-3,5-bis(benzylidene)-4-piperidone analogs   the objectives of the present investigation are two folds .
first , to gain some insight into the physicochemical properties of the 3,5-bis(benzylidene)-4-piperidone derivatives 1 - 7 that influence cytotoxic potencies , and second , to derive predictive 2d - qsar models that will be helpful to design new analogs with improved bioactivity .
the in - vitro cytotoxic data used in this study were taken from the literature ( 8) . the reported ic50 values were converted into logarithmic scale ( pic50 ) and then were used for qsar analysis as dependent variables .
the data set ( n = 25 ) was divided randomly into two groups : calibration set ( n = 19 ) and prediction set ( n = 6 ) .
( table 1 ) ( asterisk sign in the table demonstrate the prediction set ) .  

descriptor generation 
  the chemical structure of molecules was constructed using a hyperchem package ( version 7 ; hypercube inc . ,
gainesville , fl , usa ) and primarily were energetically minimized ( 100 steepest descent steps using mm force field with a gradient convergence value of 0.1 kcal / mol ) using hyperchem software .
the z - matrices of the structures were provided by the software and were then transferred to the gaussian 98 program .
gaussian 98 was used for semi - empirical molecular orbital calculations ( am1 ) of the structures .
a large number of molecular descriptors were calculated using hyperchem , gaussian 98 and dragon packages ( 10 ) .
different functional descriptors such as topological , geometrical , and constitutional descriptors were calculated using dragon software . moreover ,
some chemical parameters including molecular volume ( mv ) , molecular surface area ( sa ) , hydrophobicity ( logp ) , heat of formation and hydration energy ( he ) were calculated using hyperchem software . 
 data processing and modeling 
  the calculated descriptors were collected in a data matrix and generated descriptors were scaled using auto scaling procedure .
firstly , the descriptors were checked for constant or near - constant values and those detected were removed from the original data matrix .
then the correlation of descriptors with each other s and with the potency data was determined . among the detected collinear descriptors ( r > 0.8 ) ,
one of them demonstrating the highest correlation with potency was retained , and the rest were omitted . in the model development step ,
leave - one - out cross - validation was used to optimize the models ( e.g. , selection of variables or no . of principal components ) .
the final models were validated using a set of 6 molecules in the test set , which did not contribute to the model development .  
two different methods were used for the development of qsar equations ( i ) stepwise multiple linear regression ( mlr ) , ( iii ) genetic algorithm  partial least squares ( ga - pls ) .
these methods are well documented in the literature ( 11 ) . in stepwise regression ,
the basic procedures involve ( i ) identifying an initial model , ( ii ) iteratively ' stepping ' , that is , repeatedly altering the model at the previous step by adding or removing a predictor variable in accordance with the ' stepping criteria ' ( in our case , probability of f = 0.05 for inclusion ; probability of f = 0.1 for exclusion for the forward selection method ) , and ( iii ) terminating the search when stepping is no longer possible given the stepping criteria , or when a specified maximum number of steps have been reached .
specifically , at each step , all variables are reviewed and evaluated to determine which one will contribute most to the equation .
this variable will then be included in the model , and the process starts again .
a limitation of the stepwise regression search approach is that it presumes there is a single ' best ' subset of x variables and seeks to identify it .
there is often no unique ' best ' subset , and all possible regression models with a similar number of x variables as in the stepwise regression solution should be fitted subsequently to study whether some other subsets of x variables might be better . in the present study , mlr with stepwise selection and elimination of variables
the resultant models were validated by a leave - one - out cross - validation procedure ( using matlab software ) to check their predictive power and robustness .
a genetic algorithm uses genetic rules such as reproduction , cross - over , and mutation to build pseudo organisms that are then selected , on the basis of a fitness criterion to survive and pass information on to the next generation .
to select the most relevant set of descriptors , the evolution of population was simulated ( 12 - 15 ) .
pls is a generalization of regression , which can handle data with strongly correlated and  or numerous x variables ( 15 ) .
the linear pls model finds ' new variables ' ( latent variables or x scores ) that are a linear combination of the original variables . to avoid over fitting ,
a strict test for the significance of each consecutive pls component is necessary and then stopping when the components are non - significant .
cross - validation is a practical and reliable method of testing this significance ( 14 ) .
application of pls thus allows the construction of larger qsar equations while avoiding over fitting and eliminating most variables .
pls is normally used in combination with cross - validation to obtain the optimum number of components ( 15)19 ] . in the ga - pls procedure
, for each subset of descriptors ( i.e. , for each chromosome of the ga ) , a pls model was developed separately and consequently the number of latent variables was optimized .
the pls regression method used was the nipals - based algorithm found in the chemometrics toolbox of matlab software ( version 6.5 ; math work inc . ,
based on the haaland and thomas f - ratio criterion we performed the leave - one - out cross - validation procedure as it was applied in our previous article ( 16 ) .
the matlab pls toolbox developed by eigenvector company was used for pls and ga modeling.the predicted power of obtained equations was validated using cross - validated squared correlation coefficient ( q2 ) . in order to calculate q following equation was used . 

q 
  = 1  (ypred  yact)2/  ( yact  ymean ) where ypred , yact , and ymean are predicted , actual , and mean values of the pic50 , respectively .
(ypred - yact ) is the predictive residual error sum of squares ( press ) ( 17 ) .
moreover , the predictive squared correlation coefficients  rpred  was used for further evaluation of the predictive potential of obtained equations . to calculate
ytest)/(ytest  ytraining ) where ypred(test ) and ytest are predicted and observed activity values , respectively , of test set compounds , and ytraining is the mean activity value of training set ( 17 ) . 
 variable importance in the projection 
  in order to evaluate the relative importance of the variable appeared in the final ga - pls , variable importance in projection ( vip ) was employed ( 18 ) .
vip is the sum over all model dimensions of the contributions variable influence ( vin ) . for a given pls dimension , a ( vin)ak is equal to the squared pls weight ( wak)2 of that term , multiplied by the explained ss of that pls dimension ( 19 ) .  

y - randomization test 
  y - randomization test is the technique ensures the robustness of a qsar model . in this procedure , for each created models , the dependent variable vector pic50 is randomly shuffled , and a new qsar model is developed using the original independent variable matrix . for acceptable specific qsar model , the new obtained qsar equation ( after several repetitions ) is expected to have low r and q values ( 16 ) .
the structural features and the experimental cytotoxic potencies ( represented as pic50 ) of the 3,5-bis(benzylidene)-4-piperidone derivatives 1 - 7 used in this study are shown in table 1 ( 8) .
a sar study of these compounds demonstrated that the attachment of the n - aroyl group to the 3,5-bis(arylidene)-4-piperidones resulted in enhanced cytotoxic potencies toward murine l1210 lymphocyte leukemia cells and two human t - lymphocytes molt4/c8 and cem .
it was suggested that in the case of various members of series 2 - 7 , alignment of the n - aroyl groups with auxiliary binding sites takes place reinforcing the interaction of the 1,5-diaryl-3-oxo-1,4-pentadienyl pharmacophore with a primary binding site .  
chemical structures of the n - aroyl-3,5-bis(arylidene)-4-piperidones 1 - 7 used in this study and their experimental and cross - validated predicted cytotoxic potencies ( by ga - pls ) toward murine l1210 cells and human molt 4/c8 and cem t - lymphocytes   reprelative error of prediction .    the compounds are included in the prediction set in order to find important structural features of the n - aroyl-3,5-bis(benzylidene)-4-piperidones which contribute to the cytotoxic potencies
, a qsar study was performed using different molecular descriptors and chemometrics tools . in this study ,
the chemometrics methods such as stepwise multi - linear regression ( mlr ) and genetic algorithm - partial least squares ( ga - pls ) were used for modeling the relationship between the biological activity and molecular descriptors and the results were compared to find the best predictive cytotoxicity models .  
separate stepwise selection - based mlr analyses were performed using different types of descriptors , and then a mlr equation was obtained using the pool of all calculated descriptors . as there are 19 molecules in the training set and according to the rule of thumb ( the ratio of 5:1 for molecule  variable ; toplis ratio ) ( 16 ) , mlr models with a maximum number of 3 or 4 variables were selected .
a small difference between the conventional and cross - validated correlation coefficients of the different mlr equations ( table 2 ) reveals that none of the models are over fitted , which can be partially attributed to the absence of collinearity between the variables in one hand and using no extra variables on the other hand .
the correlation coefficient ( r ) matrix for the descriptors used in different mlr equations shows that no significant correlation exists between pairs of descriptors ( table 3 ) .
the results of multiple linear regression ( mlr ) analysis for the compound in series 1 - 7 with different type of descriptors   squared correlation coefficient ;    standard error of regression ;    root mean square of cross validation ;    leave - one - out cross - validation correlation coefficient ( rcv ) ;    f-statistics.squared correlation coefficient ( r ) was calculated using following equation : 1-( ( y experimental 
experimental ) ) ) equation for calculation of standard error of regression : [ se=  ( ( y experimental  y calculated)/n - p ' ) ( n= number of samples , p'= number of model parameters ) ] correlation coefficient ( r ) matrix for descriptors used in multiple linear regression equations 1 - 3 . 

l1210 cell line 
 . stepwise selection and elimination of variables produced a three - parametric qsar equation 1 , having moderate statistical quality ( r = 0.70 , se = 0.38 , q = 0.50 , rmscv = 0.45 and rpred = 0.69 ) ( table 2 and 4 ) .
the selected variables demonstrate that chemical ( heat of formation ) , topological and spatial parameters ( molecular density and narumi harmonic topological index ( hnar ) mainly affect the cytotoxic potential of the 3,5-bis(arylidene)-4-piperidone derivatives against the l1210 cell line .   
the mlr equation 2 obtained from the pool of the calculated descriptors for the cem cell line possesses good statistical quality ( r = 0.85 , se = 0.25 , q = 0.77 , rmscv = 0.29 and rpred = 0.81 ) ( table 2 and 4 ) and demonstrates that the anticancer property of the compounds is mainly dependent on chemical ( heat of formation ) , topological and spatial ( molecular density and average connectivity index chi-4:x4a ) properties of the molecule .
these results show that the parameters that influence anticancer properties of the compounds against the cem line are similar to those obtained for the l1210 cell line .   
the three - parametric qsar equation 3 ( table 2 ) demonstrates the quantitative effects of the structural parameters on the cytotoxic potential of 3,5-bis(arylidene)-4-piperidone derivatives on the molt / c8 cell line .
this model demonstrated high statistical quality ( r = 0.81 , se = 0.31 , q = 0.72 , rmscv = 0.34 , and rpred = 0.64 ) ( table 2 and 4 ) which reveals the significant effects of quantum ( homo , dipole moment x ( dmx ) ) and spatial parameter ( molecular density ) on the cytotoxic activity of the compounds .
it is revealed that the molecular density plays a determinant effect on the cytotoxic potential of the compounds on this cell line .
therefore , the molecular density and topological parameter are important descriptors that should be taken into consideration in the designing of potent cytotoxic 3,5-bis ( arylidene)-4-piperidones analogs . the results of qsar analysis by mlra and ga - plsb methods for the compounds in series 1 - 7   multiple linear regressions ,    genetic algorithm - partial least square ,    correlation coefficient of regression ,    leave - one - out cross - validation correlation coefficient ( rcv ) ,    standard error of prediction regression ,    correlation coefficient of prediction regression   in pls analyses , the descriptors data matrix is decomposed into orthogonal matrices , the scores of which are constrained to have inner relationships with the dependent variables .
therefore the multi - collinearity problem in the descriptors is omitted by pls analysis . to find a more convenient set of descriptors in pls modeling ,
, many different ga - pls runs were conducted using different initial sets of populations .
given 19 calibration samples , the leave - one - out cross - validation procedure was used to find the optimum number of latent variables for each pls model .
for the l1210 cell line , the ga - pls model that resulted in the best fit contained 7 indices ( two of these indices such as molecular density and heat of formation were also obtained by mlr in this cell line ) .
moreover , similar to the results of mlr analysis , ga - pls analysis also showed that topological parameters affect the cytotoxic potencies of the compounds in the l1210 cell line .
as per ga - pls modeling , a combination of chemical ( heat of formation , melting point ) , quantum chemical ( dipole moment x ) , conformational ( torsion energy ) and spatial ( molecular density ) descriptors account for the cytotoxic potential of the compounds toward l1210 cells .
the resulted ga - pls model possess very good statistical quality ( i.e. , r= 0.86 , q= 0.66 ) .
the predictive ability of the model was measured by application to 6 external test set molecules ( rpred = 0.81 and sepred = 0.37 ) .
the calculated values of pic50 obtained by the pls model in the l1210 assay ( refined from cross - validation of external prediction set ) are shown in table 1 . to measure the significance of the 7 selected pls descriptors , the variable importance in projection ( vip ) was calculated for each descriptor . according to the method described by eriksson et al .
( 20 ) , x - variable ( predictor variable ) could be classified according to their relevance in explaining y - variable ( predicted variable ) i.e. vip > 1.0 ( highly influential ) , vip < 0.8 ( less influential ) , and 0.8 < vip < 1.0 ( moderately influential ) . the vip analysis of the descriptors of the input variables used in the pls equation ( figure 2a ) shows that the parameters such as topological index ( chi3 ) , molecular density and heat of formation are the most important indices in the qsar equation derived by pls analysis for l1210 cell line .
the regression coefficients of the selected variables obtained by ga - pls model of qsar analysis for three different cell lines are illustrated in figure 3 .
variable importance for projection ( vip ) of the selected variables obtained by ga - pls model for the qsar analysis of three different cell lines : ( a ) l1210 , ( b ) cem , and ( c ) molt / c8 regression coefficients of the selected variables derived by the ga - pls model for qsar analysis of three different cell lines : ( a ) l1210 , ( b ) cem , and ( c ) molt / c8   the best ga - pls model to predict cytotoxic activities of the compounds in series 1 - 7 toward the cem cell line includes 10 indices ( three of the indices are similar to that obtained by the mlr analysis ) . a combination of topological ( x1a ) , chi-1(average connectivity index ) , pw3 ( randic shape index ) , x3av ( average valance connectivity ) , sic2 ( structural information content : symmetry 2-order ) ) , geometrical ( sph ( spherocity of molecule ) ) , chemical ( logp ) , spatial ( molecular density ) , electrotopological state ( sum of the e - state value for the ch group in the aromatic ring ( s_aach ) and sum of the e - state value for the methyl group ( s_sch3 ) ) indices account for the cytotoxic properties of the 3,5-bis(arylidene)-4-piperidones toward the cem cell line .
the resulted ga - pls model showed high statistical quality ( i.e. , r = 0.87 and q = 0.71 ) .
the predictive ability of the model was measured by application to 6 external test set molecules ( rpred = 0.83 and sepred = 0.35 ) .  
the pic50 values used in the pls model ( refined from cross - validation of external prediction set ) are shown in table 1 .
the vip analysis of pls equation presented in figure 2b suggests that among the selected descriptors , topological and electrotopological parameters such as x1a , pw3 , x3av and estate keys ( s_sch3 and s_aach ) are important influential descriptors .
similar to the l1210 cell line , the molecular density of the compounds is also a determinant parameter that influence cytotoxicity of 3,5-bis(arylidene)-4-piperidones against the cem cell line .  

molt 4/c8 cell line 
  a combination of 8 selected variables such as chemical ( hydration energy ) , topological ( x2a ) , geometrical ( pw3 , j3d ( 3d - balaban index ) , sph ) , spatial ( molecular density ) and electrotopological state indices ( sum of the e - state value for the ch group in the aromatic ring ( saach ) and sum of the e - state value for the methyl group ( s_sch3 ) ) influence cytotoxic potencies of the compounds in series 1 - 7 against the molt 4/c8 cell line as indicated by the best ga - pls model .
most of these variables contribute significantly to the ga - pls model as discussed previously for the cem cell line .
the resultant ga - pls model demonstrated very high statistical quality [ r = 0.91 and q = 0.77 ] [ figure 3c ] .
the predictive ability of the model was measured by applying to 6 external test set molecules and the squared correlation coefficient for prediction ( rpred ) was found to 0.82 .
the vip analysis of the ga - pls model presented in figure 2c showed that the molecular density , topological ( x2a ) , geometrical ( sph , j3d ) and electrotopological state indices influence the cytotoxicity of the compounds in series 1 - 7 .
the plots of the predicted pic50 values ( cross - validated ) against the experimental values for the l1210 , cem and molt4/c8 cell lines by ga - pls analysis showed r values 0.86 , 0.87 and 0.91 , respectively ( figure 4 ) which indicates that the qsar models are reliable to predict cytotoxicity of the 3,5-bis(benzylidene)-4-piperidones 1 - 7 .  
plots of the cross - validated predicted cytotoxic potency values of activity by ga - pls against the experimental values for three different cell lines : ( a ) l1210 , ( b ) cem , and ( c ) molt / c8 cell line all of the generated ga - pls models were further validated by applying the y - randomization test .
several random shuffles of the y vector were performed and the results are shown in table 5 .
the low r and q values indicate that the good results in our original model are not because of a chance correlation or structural dependency of the training set .
r and q values of ga - pls models after several y - randomization tests the statistical parameters of qsar analysis by mlr and ga - pls are demonstrated in table 4 .
the results indicate that ga - pls analysis is more accurate for predicting the cytotoxic potential of 3,5-bis(arylidene)-4-piperidones in all three cell lines .
the cross - validation statistics reported in table 4 suggest the higher prediction ability of the ga - pls model .
this can be a result of the more number of descriptors used by ga - pls with respect to mlr analysis .
as far as the less parametric model is obtained by mlr analysis , the results of mlr analysis are more descriptive for interpretation of the structure - cytotoxic relationship .
however for the prediction of the cytotoxic potential of novel compounds of these series , the ga - pls model is more useful .
it is clearly understood that some of the spatial , ( electro ) topological and chemical descriptors are important structural parameters that mainly affects the cytotoxic potencies of these compounds in all three cell lines .
the  molecular density  of compounds is one of the most important spatial descriptors that should be considered in the design of novel compounds of these series .
as the results of the sar study of various members of these series suggest , alignment of the n - aroyl groups with auxiliary binding sites takes place reinforcing the interaction of the 1,5-diaryl-3-oxo-1,4-pentadienyl pharmacophore with a primary binding site ( 8) . this result can be interpreted by the important structural descriptor  molecular density  .
it is obvious that the orientation of n - aroyl group for better interaction with a corresponding binding site is affected by molecular density .
other topological descriptors also affect this desirable orientation of the ligand and therefore play a determinant role in the binding of the ligands with its target receptors .  
the other important electro - topological parameter that should be considered is the electro - topological state indices which encode the electronic state of each atom type in the molecule :  atom - type e - state indices  .
the results demonstrate that the sum of the electro - topological state of  aromatic ch 
( s_aach ) and the sum of the electro - topological state indices of methyl groups ( e - state keys : s_sch3 ) are among the important influential descriptors in the cytotoxic potential of 3,5-bis(arylidene)-4-piperidones especially toward cem and molt / c8 cell lines .
the sum of the electro - topological state indices of the aromatic ch and methyl groups especially should be considered in the employment of different n - acyl substituents .  
the results demonstrate that similar structural descriptors affect the cytotoxic potential of n - aroyl-3,5-bis(arylidene)-4-piperidones in three different cell lines .
this result indicates that similar molecular mechanisms are involved in the cytotoxic activity of the compounds in these cell lines .
in addition , the previous quantitative - cytotoxic activity study of asymmetrical 2,6-bis(benzylidene)cyclohexanones against mcf-7 , sk - n - mc and mda - mb-231 cell lines ( 20 ) , reported the spatial and topological parameters as determinant structural descriptors in cytotoxic potential of these compounds against the cell lines .
this finding also confirms that the same molecular mechanisms are involved in the cytotoxic activity of different analogues of this scaffold .
 1-[4-(2-alkylaminoethoxy ) phenylcarbonyl]-3,5-bis(arylidene)-4-piperidones are a novel class of potent cytotoxic agents . 
 these compounds demonstrate low micromolar to submicromolar ic50 values against human molt 4/c8 and cem t - lymphocytes and murine leukemia l1210 cells . in this study , 
 a comparative qsar investigation was performed on a series of 3,5-bis ( arylidene)-4-piperidones using different chemometric tools to develop the best predictive models for further development of analogs with improved cytotoxicity . 
 all the qsar models were validated by internal validation tests . 
 the qsar models obtained by ga - pls method were considered the best as compared to mlr method . the best qsar model obtained by ga - pls analysis on l1210 , cem and molt4/c8 demonstrated good predictively with r2pred values ranging from 0.94 - 0.80 . molecular density , 
 topological ( x2a ) and geometrical indices of the molecules were found to be the most important factors for determining cytotoxic properties . 