malamas et al . reported seven series of compounds based on benzofuran / benzothiophene biphenyl moiety . we had performed the qsar analysis of all these series having 138 compounds , out of which only 106 compounds could be subjected to 2-d qsar analysis , because of the non - availability of physicochemical substituent values and exact ic50 values for some substituted compounds . the 2d qsar study was carried out in the following steps : the values for the physicochemical constants for various substituents were determined from the literature . the determined parameters for a series included , the hansch constant (  ) , molar refractivity (  ) , sigma / hammet constant (  ) , field effect ( f ) , and the indicator value ( i ) . to get the generated model we had clubbed all the series together for the sake of simplicity . we had designated different rings and positions as shown in the chemical structures , as ( u , v , w , x ) and ( a , b , c , d , e , f ) , respectively . to simplify and make all the series collinear to each other the use of the indicator variable had been included . thus , the compounds of the seven series were designated as follows : series i : as to x of v ring [ figure 2 ] , we had assigned this position as [ a ] , which was either oxygen or sulfur , so we had considered o=1 and s=0 as the indicator variable , vai . structure of benzofuran and benzothiophene biphenyls r substitution was assigned as [ b ] , so different physicochemical parameters were designated on the basis of ring and position , as vb , vb , and vb . r substitution position was [ c ] , so the presence of an aceto moiety had been considered as an indicator variable with value 1 and the others as 0 , and hence this position was considered as xci ( where x - ring , c - position , i- indicator ) . the parameters for the substituents on this aceto moiety had been designated as xci , xci , xci , fxci . due to the substitution on the aceto moiety , there occurred the presence of a chiral center , due to which most of the compounds were enantiomers . therefore , an indicator variable xcei , ( r=1 , s=1 , dl=0 ) was included , where the x - ring , c - position , e - enantiomer , i - indicator variable , and the value of xcei= 1 , -1 , 0 depended on the optical rotation . series ii : similar to the first series , vai was considered as an indicator variable [ figure 3 ] . structure of 2-benzyl benzofuran and benzothiophene biphenyls r position of the second series was considered as [ d ] , so different parameters for the r position had been designated as xd , xd , xd , fxd . r position was [ e ] , so parameters of r position were xe , xe , xe , fxe . r position was designated as x ci , xcei , xci , xci , xci , fxci . series iii : benzofuran attached to biphenyl through the x linkage [ figure 4 ] , which was designated as [ f ] , so the corresponding parameters were f , f , f , ff . structure of 2-butyl benzofuran biphenyls similarly the r position was [ d ] and the parameters were xd , xd , xd , fxd position [ e ] was xe , xe , xe , fxe position [ c ] was xci . series iv : r position [ figure 5 ] was [ c ] , so the earlier assigned r position was an indicator variable , as xci , , and its substitutions were as xci , xci , xci , fxci structure of substituted oxazole biphenyls r and r position parameters were xd , xd , xd , fxd and xe , xe , xe , fxerespectively . as the isoxazole ring attached to either at third or fourth position , the indicator variable position was assigned as vwpi ( position of attachment of v and w rings as indicator parameters at the fourth position as 1 , and at the third position as 0 ) . series v : r position [ figure 6 ] was earlier designated as xci , xci , xci , xci , fxci structure of 2-butyl benzofuran naphthalenes r position was [ e ] here and thus parameter r position was termed as xe , xe , xe , fxe the x group linkage between benzofuran and the naphthalene ring position was designated as [ f ] , so the parameter of the x group became f , f , f , ff . series vi : as r , on the phenyl sulfono ring [ figure 7 ] was attached to position [ c ] of ring x , the r position was assigned to xc3r ( x - ring , c - position , 3-third position of the phenyl ring , and r as the indicator ) . structure of 2-benzyl benzofuran / benzothiophne sulfono biphenyls wherever r was -oh , xc3r = 1 , for -cooh , xc3r = 0 wherever r was cooh , there xc4r = 1 , wherever r was oh , there xc4r = 0 r was [ d ] position and thus the parameter of r position was designated as xd , xd , xd , fxd r was [ e ] position and thus the parameters were xe , xe , xe , fxe . as x was in a v ring , which was assigned position [ a ] , the indicator variable vai series vii : similar to the sixth series except that r was taken as vai [ figure 8 ] wherever the benzofuran ring comes structure of sulfono biphenyls vai = 1 , when r was benzofuran vai = 0 , when r was either benzothiophene or other . however , when it was considered to club all 26 variables of the series , in the fifth series the biphenyl ring was replaced by a naphthalene ring , and the presence of the biphenyl ring was considered as variable iwx iwx = 1 , where the w , x rings are present as biphenyl = 0 , where the w , x rings are present as naphthalene thus for all 106 compounds , the value of the substituent constant for all 27 variables was obtained from literature . the correlation matrix for all the 27 variables along with the biological activity was determined using the program the most significant parameters of the ptpase inhibiting activity were chosen on the basis of their correlation ship and interco relationship . systat for the ptpase inhibiting activity , that is , -logic50 was considered as a dependent variable and all the 27 physicochemical parameters were considered as independent variables . malamas et al . reported seven series of compounds based on benzofuran / benzothiophene biphenyl moiety . we had performed the qsar analysis of all these series having 138 compounds , out of which only 106 compounds could be subjected to 2-d qsar analysis , because of the non - availability of physicochemical substituent values and exact ic50 values for some substituted compounds . the 2d qsar study was carried out in the following steps : the values for the physicochemical constants for various substituents were determined from the literature . the determined parameters for a series included , the hansch constant (  ) , molar refractivity (  ) , sigma / hammet constant (  ) , field effect ( f ) , and the indicator value ( i ) . to get the generated model we had clubbed all the series together for the sake of simplicity . we had designated different rings and positions as shown in the chemical structures , as ( u , v , w , x ) and ( a , b , c , d , e , f ) , respectively . to simplify and make all the series collinear to each other the use of the indicator variable had been included . thus , the compounds of the seven series were designated as follows : series i : as to x of v ring [ figure 2 ] , we had assigned this position as [ a ] , which was either oxygen or sulfur , so we had considered o=1 and s=0 as the indicator variable , vai . structure of benzofuran and benzothiophene biphenyls r substitution was assigned as [ b ] , so different physicochemical parameters were designated on the basis of ring and position , as vb , vb , and vb . r substitution position was [ c ] , so the presence of an aceto moiety had been considered as an indicator variable with value 1 and the others as 0 , and hence this position was considered as xci ( where x - ring , c - position , i- indicator ) . the parameters for the substituents on this aceto moiety had been designated as xci , xci , xci , fxci . due to the substitution on the aceto moiety , there occurred the presence of a chiral center , due to which most of the compounds were enantiomers . therefore , an indicator variable xcei , ( r=1 , s=1 , dl=0 ) was included , where the x - ring , c - position , e - enantiomer , i - indicator variable , and the value of xcei= 1 , -1 , 0 depended on the optical rotation . series ii : similar to the first series , vai was considered as an indicator variable [ figure 3 ] . structure of 2-benzyl benzofuran and benzothiophene biphenyls r position of the second series was considered as [ d ] , so different parameters for the r position had been designated as xd , xd , xd , fxd . r position was [ e ] , so parameters of r position were xe , xe , xe , fxe . r position was designated as x ci , xcei , xci , xci , xci , fxci . series iii : benzofuran attached to biphenyl through the x linkage [ figure 4 ] , which was designated as [ f ] , so the corresponding parameters were f , f , f , ff . structure of 2-butyl benzofuran biphenyls similarly the r position was [ d ] and the parameters were xd , xd , xd , fxd position [ e ] was xe , xe , xe , fxe position [ c ] was xci . series iv : r position [ figure 5 ] was [ c ] , so the earlier assigned r position was an indicator variable , as xci , , and its substitutions were as xci , xci , xci , fxci structure of substituted oxazole biphenyls r and r position parameters were xd , xd , xd , fxd and xe , xe , xe , fxerespectively . as the isoxazole ring attached to either at third or fourth position , the indicator variable position was assigned as vwpi ( position of attachment of v and w rings as indicator parameters at the fourth position as 1 , and at the third position as 0 ) . series v : r position [ figure 6 ] was earlier designated as xci , xci , xci , xci , fxci structure of 2-butyl benzofuran naphthalenes r position was [ e ] here and thus parameter r position was termed as xe , xe , xe , fxe the x group linkage between benzofuran and the naphthalene ring position was designated as [ f ] , so the parameter of the x group became f , f , f , ff . series vi : as r , on the phenyl sulfono ring [ figure 7 ] was attached to position [ c ] of ring x , the r position was assigned to xc3r ( x - ring , c - position , 3-third position of the phenyl ring , and r as the indicator ) . structure of 2-benzyl benzofuran / benzothiophne sulfono biphenyls wherever r was -oh , xc3r = 1 , for -cooh , xc3r = 0 wherever r was cooh , there xc4r = 1 , wherever r was oh , there xc4r = 0 r was [ d ] position and thus the parameter of r position was designated as xd , xd , xd , fxd r was [ e ] position and thus the parameters were xe , xe , xe , fxe . as x was in a v ring , which was assigned position [ a ] , the indicator variable vai series vii : similar to the sixth series except that r was taken as vai [ figure 8 ] wherever the benzofuran ring comes structure of sulfono biphenyls vai = 1 , when r was benzofuran vai = 0 , when r was either benzothiophene or other . however , when it was considered to club all 26 variables of the series , in the fifth series the biphenyl ring was replaced by a naphthalene ring , and the presence of the biphenyl ring was considered as variable iwx iwx = 1 , where the w , x rings are present as biphenyl = 0 , where the w , x rings are present as naphthalene thus for all 106 compounds , the value of the substituent constant for all 27 variables was obtained from literature . the correlation matrix for all the 27 variables along with the biological activity was determined using the program the most significant parameters of the ptpase inhibiting activity were chosen on the basis of their correlation ship and interco relationship . systat for the ptpase inhibiting activity , that is , -logic50 was considered as a dependent variable and all the 27 physicochemical parameters were considered as independent variables . the determined parameters for a series included , the hansch constant (  ) , molar refractivity (  ) , sigma / hammet constant (  ) , field effect ( f ) , and the indicator value ( i ) . to get the generated model we had clubbed all the series together for the sake of simplicity . we had designated different rings and positions as shown in the chemical structures , as ( u , v , w , x ) and ( a , b , c , d , e , f ) , respectively . to simplify and make all the series collinear to each other the use of the indicator variable had been included . thus , the compounds of the seven series were designated as follows : series i : as to x of v ring [ figure 2 ] , we had assigned this position as [ a ] , which was either oxygen or sulfur , so we had considered o=1 and s=0 as the indicator variable , vai . structure of benzofuran and benzothiophene biphenyls r substitution was assigned as [ b ] , so different physicochemical parameters were designated on the basis of ring and position , as vb , vb , and vb . r substitution position was [ c ] , so the presence of an aceto moiety had been considered as an indicator variable with value 1 and the others as 0 , and hence this position was considered as xci ( where x - ring , c - position , i- indicator ) . the parameters for the substituents on this aceto moiety had been designated as xci , xci , xci , fxci . due to the substitution on the aceto moiety , there occurred the presence of a chiral center , due to which most of the compounds were enantiomers . therefore , an indicator variable xcei , ( r=1 , s=1 , dl=0 ) was included , where the x - ring , c - position , e - enantiomer , i - indicator variable , and the value of xcei= 1 , -1 , 0 depended on the optical rotation . series ii : similar to the first series , vai was considered as an indicator variable [ figure 3 ] . structure of 2-benzyl benzofuran and benzothiophene biphenyls r position of the second series was considered as [ d ] , so different parameters for the r position had been designated as xd , xd , xd , fxd . r position was [ e ] , so parameters of r position were xe , xe , xe , fxe . r position was designated as x ci , xcei , xci , xci , xci , fxci . series iii : benzofuran attached to biphenyl through the x linkage [ figure 4 ] , which was designated as [ f ] , so the corresponding parameters were f , f , f , ff . structure of 2-butyl benzofuran biphenyls similarly the r position was [ d ] and the parameters were xd , xd , xd , fxd position [ e ] was xe , xe , xe , fxe position [ c ] was xci . series iv : r position [ figure 5 ] was [ c ] , so the earlier assigned r position was an indicator variable , as xci , , and its substitutions were as xci , xci , xci , fxci structure of substituted oxazole biphenyls r and r position parameters were xd , xd , xd , fxd and xe , xe , xe , fxerespectively . as the isoxazole ring attached to either at third or fourth position , the indicator variable position was assigned as vwpi ( position of attachment of v and w rings as indicator parameters at the fourth position as 1 , and at the third position as 0 ) . series v : r position [ figure 6 ] was earlier designated as xci , xci , xci , xci , fxci structure of 2-butyl benzofuran naphthalenes r position was [ e ] here and thus parameter r position was termed as xe , xe , xe , fxe the x group linkage between benzofuran and the naphthalene ring position was designated as [ f ] , so the parameter of the x group became f , f , f , ff . series vi : as r , on the phenyl sulfono ring [ figure 7 ] was attached to position [ c ] of ring x , the r position was assigned to xc3r ( x - ring , c - position , 3-third position of the phenyl ring , and r as the indicator ) . structure of 2-benzyl benzofuran / benzothiophne sulfono biphenyls wherever r was -oh , xc3r = 1 , for -cooh , xc3r = 0 wherever r was cooh , there xc4r = 1 , wherever r was oh , there xc4r = 0 r was [ d ] position and thus the parameter of r position was designated as xd , xd , xd , fxd r was [ e ] position and thus the parameters were xe , xe , xe , fxe . as x was in a v ring , which was assigned position [ a ] , the indicator variable vai series vii : similar to the sixth series except that r was taken as vai [ figure 8 ] wherever the benzofuran ring comes structure of sulfono biphenyls vai = 1 , when r was benzofuran vai = 0 , when r was either benzothiophene or other . however , when it was considered to club all 26 variables of the series , in the fifth series the biphenyl ring was replaced by a naphthalene ring , and the presence of the biphenyl ring was considered as variable iwx iwx = 1 , where the w , x rings are present as biphenyl = 0 , where the w , x rings are present as naphthalene thus for all 106 compounds , the value of the substituent constant for all 27 variables was obtained from literature . the correlation matrix for all the 27 variables along with the biological activity was determined using the program the most significant parameters of the ptpase inhibiting activity were chosen on the basis of their correlation ship and interco relationship . systat for the ptpase inhibiting activity , that is , -logic50 was considered as a dependent variable and all the 27 physicochemical parameters were considered as independent variables . the correlation matrix [ table 1 ] reveals the dependency of various parameters on the biological activity and among themselves . those which have a high value of correlation ship for biological activity and the least inter - corelationship between themselves are considered for multiple regression analysis . the multiple regression analysis is generated following the qsar model : correlation matrix between physicochemical parameter and biological activity -logic50 = 0.020( 0.004 ) vb + 0.297 (  0.041 ) xd - 0.057( 0.18 ) f + 0.546( 0.113 ) xc3r + 0.069( 0.105 ) n=101 , r=0.86 , s=0.234 , f=42.697 the derived qsar equation showed a very good r ( correlation coefficient ) value of 0.86 with 76.93% of the variation in biological activity being explained by the equation . this was associated with a low value of standard error of estimate , s , of 0.23 . the equation was found to be highly statistically significant , with an f - test value of 42.697 and the critical f - test value at 99.95% confidence limit being 4.82 . perusal of the above - mentioned equation indicated that molar refractivity at the vbposition and the hydrophobic substituent at the xd position contributed positively to the biological activity , while any substitution between biphenyl and benzofuran / benzothiophene , that is , at the f position had a detrimental effect on the biological activity of the compounds . the model also suggested that substitution on the aceto moiety also had a positive contribution for biological activity , as suggested by the qsar model . these findings were in agreement with the pharmacophore model , as reported earlier , which suggested that the benzofuran / benzothiophene ring should be attached directly to biphenyl , which should have some phenyl moiety attached to it . a different set of descriptors may give a different correlation with activity and this must be considered while interpreting the equation . the qsar equation generated presently for benzofuran biphenyl is in agreement with the literature reports for ligand requirements based on the structure - activity relationships ( sar ) . thus from the qsar model , appropriate variations of the substituent at various positions can be effected to obtain an effective molecule , which may be remarkable to experimentally confirm the predictive power of the qsar model by actual synthesis and its biological evaluation of the most potent theoretical compound . the regression model shows that the molar refractivity and hydrophobic substituent at the vb and xd positions , respectively , are the significant descriptors responsible for describing the downregulation of ptpase 1b . besides this , any substitution between biphenyl and benzofuran / benzothiophene has a detrimental effect on the biological activity , which is also an important parameter to be taken into consideration while designing new inhibitors belonging to the above said class of compounds . the qsar model is statistically and chemically sound and explains more than 95% variance in experimental activity . finally , it can be concluded that the study presented here will play an important role in understanding the relationship of the physicochemical parameters with the structure and biological activity of the ptpase 1b inhibitor and will help in choosing a suitable substituent for obtaining the active compound with maximum potency .
objectives : insulin resistance is associated with a defect in protein tyrosine phosphorylation in the insulin signal transduction cascade . 
 the ptpase enzyme dephosphorylates the active form of the insulin receptor and thus attenuates its tyrosine kinase activity , therefore , the need for a potent ptpase inhibitor exists , with the intention of which the qsar was performed.materials and methods : quantitative structure - activity relationship ( qsar ) has been established on a series of 106 compounds considering 27 variables , for novel biphenyl analogs , using the systat ( version 7.0 ) software , for their protein tyrosine phosphatase ( ptpase-1b ) inhibitor activity , in order to understand the essential structural requirement for binding with the receptor.results:among several regression models , one per series was selected on the basis of a high correlation coefficient ( r , 0.86 ) , least standard deviation ( s , 0.234 ) , and a high value of significance for the maximum number of subjects ( n , 101).conclusions : the influence of the different physicochemical parameters of the substituents in various positions has been discussed by generating the best qsar model using multiple regression analysis , and the information thus obtained from the present study can be used to design and predict more potent molecules as ptpase-1b inhibitors , prior to their synthesis .