Indian Journal o f Chemi stry Vol. 40B. August 2001 , pp. 688-697

QSAR of matrix metalloproteinase inhibitor (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino )butyric acids using principal component factor analysis

KUllal Royt Di vision of Pharmaceutical Chemi stry. Seemanta Institute of Pharmaceutical Sciences. Jharpokharia, Mayurbhanj 757 086.

Orissa, India

Received 20 Jlllle 2000; accepted (revised) 22 Jalluary 2001

Quantitative structure-acti vity relationship studies of matrix metalloproteinase inhibitor (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric ac ids have been performed to explore the contribution pattern of phenyl ring substituents on the activities. Principal component factor analysis was used as the preprocessing step to identify the important molecular parameters (physicochemical and structural variables) describing the activities against different metalloproteinases (pC " pC2, pC .. , pC?, pC9 and pC 13) and to remove collinearities from the equations. The study reveals that volume of 4' substituents on the biphenyl moiety has positive contribution to the activities like pC2, pC9 and pC 13. This suggests possibility o f di spe rsion interactions with the receptor in these cases. High electronic influence (e itper withdrawl or donation) of 4'-substituents on the phenyl ring has negative impact on pC" pC2, pC9 and pC 13• For pC I and pC9, the presence of 4'-methoxy or 4'-methyl group is fa voured. For pC3 and pC?, a 4' substituent, except amino, contributes to the activity. Further. vo lume of meta (3') substituent on the phenyl ring or mere presence of meta substituent has negative impact on all the acti vities except pC9. Quantitati ve activity-acti vity relations among the activities have also been explored.

Matrix metalloproteinases (MMPs)) , a family of zinc dependent endopeptidases, are capable of efficient degradation of different components of extracellular matrix (e.g., fibrillar and nonfibrillar collagens, basement membrane collagens, fibronectin, elastin, gelatins, proteoglycans, amelogenin etc.) at physiological pH2. These enzymes play significant physiological role in tissue remodeling in normal growth and development3. Upregulation of MMPs has been implicated in the pathogenesis of several disease states like destruction of cartilage and bone in rheumatoid arthritis, tumor growth and metastatis in cancer, degeneration of aortic wall in abdominal aortic aneurysms and cardiac dilation in patients with congestive heart failure3. Besides these, involvement of MMPs in periodontal disease, skin ulceration, corneal ulceration, gastric ulcer, liver fibrosis etc. has also been reported2• This has created recent interest in the design and development of MMP inhibitors as possible anticancer, antiarthritis, antiintlammatory or other pharmacotherapeutic agents to stop imbalance of MMP regulation in these pathological states) -3 .

Recently, O'Brien et al.3 have reported a series of biphenylsulfonamide MMP inhibitors . The present communication has been attempted to explore QSAR

t Address for correspondence: C/o Dr. A. G. Saha. Flat No. 2E. 8. Dr. Ashutosh Sastry Road, Calcutta 700 DI D (Indi a) e-mail : kunalroy_in @yahoo.com

4'

Figure 1-General structure of matrix metalloproteinase i nhi bitor (S)-3-methy 1-2 -( 4' -substituted bi pheny 1-4- su I fony lamino)-butyric acids

of the compounds and also quantitative actlvlty-activity relationships (QAAR) among the activities against different MMPs. Though the original authors attempted structural variations at different regions of the molecules, due to insufficient data points covering some structural features, some compounds have not been considered in the present study. A series of fourteen (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric acids were subjected to QSAR analysis with different physicochemical and structural parameters using principal component fac tor analysis as the preprocessing step.

Factor analysis4.5 The principal objectives o f factor analysis are to

display multidimensional data in a space of lower dimensionality with mini mal loss of information and to extract bas ic features behind the data with ultimate

ROY: QSAR OF MATRIX METALLOPROTEINASE INHIBITOR BUTYRIC ACIDS 689

Table I -Strctural variations and in vitro MMP inhibitory activities of (S)-3-methyl-2-(substituted biphenyl -4-sulfonylamino)butyric acids

SI R MMPI MMP2 MMP3 MMP7 MMP9 MMPI3 No. ICso* pC 1# ICso* pC2#

H 5.4 2.268 0.040 4.398 2 4-F 4.2 2.377 0.039 4.409 3 3-F 8.6 2.066 0.049 4.310 4 4-Br 6 2.222 0.004 5.398 5 3-Br 100 1.000 0.535 3.272 6 4-CI 6.5 2.187 0.011 4.959 7 2-F,4-Br 3.6 2.444 0.005 5.301 8 4-CH3 2.2 2.658 0.002 5.699 9 4-0CH) 1.5 2.824 0.003 5.523 10 4-NH2 26 1.585 0.036 4.444 II 4-CF3 4.2 2.377 0.013 4.886 12 4-CN 18 1.745 0.033 4.482 13 4-CHO 3.2 2.495 0.012 4.921 14 4-N02 12 1.921 0.061 4.215

*ICso va lues against different MMPs (MMPj ) are in 11M scale #pCj = - log [lCso (mM)]j

ICso*

0.038 0.010 0.0 17 0.007 0.290 0.009 0.016 0.003 0.008 0.036 0.009 0.006 0.008 0.015

goal of interpretation and/or prediction. Factor analysis can be performed as the data preprocessing step for regression analysis to eliminate collinearities and to reduce the number of equations to be calculated by judicious selection of the variables

connected with biological potency . If a factor analysis is performed on a data set containing biological activity (log lie) and all descriptor variables which are to be considered, the extracted factors are first rotated, preferably by V ARIMAX rotation, to obtain Thurston's simple structure and then the following conclusions could be drawn from the resuting factor pattern :

(i) Only variables with non-zero loadings in such

factors where biological potency also has non-zero loading are important in explaining variance of the acti vi ty.

(ii) Only variables with non-zero loadings in different factors may be combined in regression equations.

~ i i i) The factor pattern indicates whether in the parameter space the biological potency can be explained in a satisfactory manner. If not, a different set of variables are to be chosen .

QSAR using factor analysis

The present QSAR analysis was attempted using lydrophobicity (n) , steric (MR) and electronic (0") Jarameters as the descriptor variables and when these Nere found insufficient to satisfactorily describe ' ariance of the response variable (log I/C) , some

pC/ ICso* pC/ ICso* pC/ ICso* pC 1/

4.420 71 1.149 26 1.585 0.062 4.208 5.000 4.8 2.319 64 1.194 0.043 4.367 4.770 22 1.658 65 1.187 0.150 3.824 5.155 7.2 2.143 7.9 2.102 0.008 5.097 3.538 100 1.000 100 1.000 0.710 3.149 5.046 7.5 2.125 16 1.796 0.048 4.3 19 4.796 2.1 2.678 4.9 2.310 0.007 5.155 5.523 4.5 2.347 3.9 2.409 0.011 4.959 5.097 7.2 2.143 2.2 2.658 0.006 5.222 4.444 31 1.509 20 1.699 0. 105 3.979 5.046 7.9 2.102 20 1.699 0.023 4.638 5.222 7.0 2.155 59 1.229 0.037 4.432 5.097 4.5 2.347 17 1.770 0.016 4.796 4.824 5.6 2.252 38 1.420 0.102 3.991

indicator variables (structural descriptors) were tried. The factors were extracted by principal component method and then rotated by V ARIMAX rotation to obtain Thurston's simple structure. Only factors describing ~ 5% of the total variance were considered.

Although different combinations of predictor variables were required to be used for factor analysis to extract the factors that are highly loaded in different molecular parameters describing the activity , only the final combinations are reported here for brevity .

The structural variations (Figure 1) and activity of

the compounds against different MMPs as reported by O'Brien et al. 3 are presented in Table I. It is observed that out of total fourteen compounds, only three

possess meta or or/IIO substituents. At first, these (compounds 3, 5 and 7) were excluded and QSAR analysis of rest (n = 11) of the compounds was performed to explore the contribution pattern of 4'-substituents. Factor analysis of the activity matrix (pex) was performed to explore interrelation among the activities as long as contribution of 4' -substituents is concerned. In next step, data matrix of inter-related response variables along with physicochemical parameters and/or structural descriptors was subjected to factor analysis to select the important predictor variables which satisfactorily describe the response variable(s) and are least autocorrelated. Next, regression analysis was performed and quality of the equations was judged by the statistical parameLers6

690 INDIAN J. CHEM., SEC S, AUGUST 2001

like explained variance (EY%), coefficient of variation (CY%), cOITelation coefficient (r or R), standard error of estimate (SEE), variance ratio (F) at specified degree of freedom (df) and average of absolute values of residuals (AYRES)7. The

significance of the regression constants was checked by 't' test. ]n case wherein intercept of an equation was statistically insignificant and omission of the same did not affect the quality of the equation,

exclusion of the intercept gave statistically more acceptable equation. The stability of the best equations of each activity series was checked from "PRESS" statistics 7.8. A compound was considered as

an outlier when the residual value exceeded twice the SEE of the equation. For equations having outlier(s), an attempt was made to improve quality of the equations on exclusion of the outlier(s).

Though the number of data points for ortho and meta substituents are insufficient to explore contribution pattern of meta (3') and ortho (2') substituents, a preliminary attempt was made to include compounds 3, 5 and 7 in the QSAR analysis. For this, indicator variable (1m : representing presence or absence of 3'-substituent) and steric parameters

(MR3' and MR2+ 3' : considering involvement of steric bulk of aromatic ortho and meta substituents during various ligand receptor interactions, e.g., steric hindrance due to ortho substituents9, influence of size of meta substituents on the proper orientation of ligand molecule lo etc.) were included in the data matrix containing specific activity with important variables for 4'-substituents (obtained from previous analysis) for subsequent factor and regression analyses. Finally, quantitative actlVlty-actlVlty relationships were also explored. The data matrix containing all activity values and important descriptor variables emerged from previous study was subjected to factor analysis to select important variables for QAAR equations.

The factor analysis was performed by statistical software MIN]T AB version 13". The regression analyses and calculation of PRESS statistics were performed by the GW-BASIC programs RRR98, KRPRESI and KRPRES2 developed by the author l2. The physicochemical parameter values (Table II) were taken from the Ii terature I ).

Table II - Physicochemical par~eters of the aromatic substituents"

Substituent 1[ MRb (J (para)

F 0. 14 0.092 0.06 Br 0.86 0.888 0.23 CI 0.71 0.603 0.23 CH3 0.56 0.565 -0.17 OCH3 -0.02 0.787 -0.27 NH2 -1.23 0.542 -0.66 CF3 0.88 0.502 0.54 CN -0.57 0.633 0.66 CHO -0.65 0.688 0.42 N02 -0.28 0.736 0.78 H 0.00 0. 103 0.00

"Taken from reference 13. bScaled by a factor of 0.1 as usual.

Results and Discussion

QSAR of (S)-3-methyl-2-(4'-substituted biphenyl-4 sulfonylamino)butyric acids (n = 11)

The results of principal component factor analyi and regression analysis of the compounds (excludin; those with meta or ortho substitution) are shown il Tables III and IV. The stability of the best equation as revealed from PRESS statistics is presented il Table V.

Factor analysis of the activity data (Table lila revealed that the activities could be divided into thre groups: (i) pC I (highly loaded with factor 3), (ii) pC: pC9 and pCI3 (highly loaded with factor 1) and (iii pC) and pC7 (highly loaded with factor 2). These thre> factors explain 95.3% of the total variance.

Factor analysis of the data matrix containing pC with physicochemical parameters could not reveal th paramter(s) satisfactorily describing the activit) When two dummy parameters lOCH) (denotin. presence or absence of 4'-OCH3 or 4'-CH) group) ani IN (denoting presence or absence of groups like NO; NH 2/CN) were included, the activity was found to b loaded highly with factor I and moderately wit factor 3 (Table IlIb). Again, factor 1 is highly loadel in IN and 0'/ and factor 3 in lOCH). Accordingl) regression analysis involving pC I was performed. Th equations Al and A2 (Table IV) explaining 87.79 and 62.4% respectively of the total variance of pC

involve the parameters IOCH3' IN and 0'/' The positiv coefficients of lOCH) in the equ ations suggest the presence of a 4'-methoxy or 4'-methyl group i conducive to the activity (pC I ). Again, negativ coefficient of 0'/ in Eq. A2 suggests that the L,

ROY: QSAR OF MATRIX METALLOPROTEINASE INHIBITOR BUTYRIC ACIDS 691

Table III -Factor loadings of the variables (after varimax rota~ion) for QSAR of (S)-3-methyl-2-(4'-substituted biphenyl-4-sulfonylamino)butyric acids (n = 11)

(a) Data matrix : pCI> pC2. pC). pC7• pC9• pCI)

Variable Factor 1 Factor 2 Factor 3 Communality

pC I 0.440 -0.2 15 -0.868 0.993 pC2 0.897 -0.332 -0.263 0.984 pC) 0.381 -0.886 -0.145 0.952 pC7 0.036 -0.958 -0.157 0.943 pC9 0.937 -0.009 -0.261 0.947 pC I) 0.744 -0.405 -0.423 0.897

% Variance 0.430 0.337 0.186 0.953

(b) Data matrix: pCI> 7t4·. 7t/. M~· . M~.2 , cr4'. cr/, lOCH), IN

Variable Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Communality

pC I -0.747 0.083 -0.461 0.347 -0.163 0.924

7t4' -0.497 0.060 -0.018 0.076 -0.850 0.979 , 0.237 0.159 0.180 -0.918 0.000 0.957 7t4'-

M~· 0. 152 0.976 -0.094 -0.075 -0.059 0.994 M~.2 0.027 0.987 -0.045 -0.006 -0.015 0.977

cr4' 0.264 0.237 0.557 0.626 -0.375 0.968 , 0.927 0.214 0.177 0.008 0.085 0.944 cr4'-

IOCH3 -0.216 0.180 -0.948 0.117 -0.037 0.992

IN 0.940 0.079 0.083 -0.082 0.275 0.979

% variance 0.305 0.234 0.167 0. 154 0.109 0.968

(c) Data matrix : pC2• pC9, pC I), 7t4'. 7t/. M~·, M~.2. cr4', cr/

Variable Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Communality pC2 0.471 -0.668 0.395 -0.371 0.00 1 0.963 pC9 0.514 -0.454 0.666 -0.241 0.075 0.977 pC I ) 0.459 -0.827 0.125 -0.192 0.129 0.964

7t4' 0.015 -0.324 -0.093 -0.934 0.084 0.998 , 0. 130 0.141 0.153 0.075 -0.965 0.998 7t4'-

M~· 0.983 -0.052 -0.029 -0.005 -0. 137 0.988 MR/ 0.957 -0.138 -0.048 -0.008 -0.043 0.939

cr4' 0.224 0.187 -0.887 -0.192 0.262 0.978

cr/ 0.361 0.749 -0.293 0.341 -0.182 0.926

% variance 0.309 0.231 0.169 0.140 0.120 0.970

(d) Data matrix : pC9, MR4" cr4', cr/, IOCH3' In

Variable Factor I Factor 2 Factor 3 Factor 4 Communality pC9 -0.379 -0.650 0.549 -0.336 0.981 M~· 0.200 -0. 163 0.952 0.136 0.991

cr4' 0.113 0.250 0.092 0.956 0.998 , 0.923 0. 162 0.158 0.234 0.958 cr4'-

locm -0. 158 -0.954 0.135 -0.207 0.996 IN 0.976 0.152 0.023 -0.015 0.977

% variance 0.338 0.245 0.210 0.191 0.983

(e) Data matrix : pC), pC7, 7t4', 7t/, M~· , M~.2, cr4', cr/, Ind

Variable Factor I Factor 2 Factor 3 Factor 4 Factor 5 Communality pC) 0.892 0.210 0.265 -0.035 0.080 0.917 pC7 0.943 0.204 0.016 0.166 0.084 0.965 7t~ . 0.255 0.013 0.946 0. 101 0.Q38 0.971

(COl/ld)

692 INDIAN J. CHEM., SEC B, AUGUST 2001

Table III -Factor loadings of the variables (after varimax rotation) for QSAR of (S)-3-methyl-2-(4'-substituted biphenyl-4-su lfonylamino)butyrlc acids (n = II )-Col1ld

1 -0. 184 0.152 -0.105 -0.121 -0.950 0.986 1I4'-

M~· 0.282 0.931 -0.067 0.101 -0.174 0.991

MR/ 0.274 0.968 0.009 0.066 -0.031 0.991

04' 0.274 0.079 0.082 0.907 0.216 0.958 1 -0.082 0. 197 -0.650 0.611 -0.317 0.941 04'-

Ind -0.862 ·0.257 -0.220 -0.289 -0.192 0.978

% variance 0.304 0.225 0.162 0.150 0.126 0.966

Table IV - Relations of matrix metalloproteinase inhibition activities of (S)-3-methy l-2-(4'-substilUted biphenyl-4-sulfonylamino)butyric acids with physicochemical and structural parameters [n = II (if not stated otherwise)]

Eq. Equations@ Statistics No. EV O/O CY% FI7

(r or R) (SEE) (AYRES)

Al pC I = 0.420 (± 0.247) lOCH) -0.571 (± 0.214) IN 87.7 5.9 36.7

+ 2.321 (± 0.123) (0.950) (0.131 ) (0.098)

A2 pC I = 0.440 (± 0.439) lOCH) -0.957 (± 0.833) 0 / 62.4 10.2 9.3

+ 2.349 (± 0.259) (0.836) (0.229) (0.165)

A3 pC2 = 1.487 (± 0.796) MR4· -1.876 (± 0.949) 0 / 73 .5 5.4 14.9

+ 4.387 (± 0.460) (0.888) (0.262) (0. 181 ) A3A# pC2 = 1.409 (± 0.555) MR4· -1.615 (± 0.685) 0 / 84.3 3.7 25.1

+ 4.322 (± 0.322) (0.937) (0.177) (0.120)

A4 pC) = - 0.680 (± 0.316) Ind +5.112 (± 0.135) 69.4 3.6 23.7

(0.851 ) (0.179) (0. 105) A4A# pC) = - 0.629 (± 0.202) Ind + 5.061 (± 0.090) 84.9 2.2 51.7

(0.931 ) (0.111 ) (0.068) A4Bs pC) = - 0.663 (± 0.132) Ind + 5.094 (± 0.062) 94.6 1.4 141.4

(0.976) (0.070) (0.045)

A5 pC7 = - 0.886 (± 0.226) Ind +2.2 15 (± 0.096) 88.6 6.2 78.9

(0.947) (0. 128) (0.128)

A6 pC9 = 1.339 (± 0.789) MR4· -0.458 (± 0.476)* 0 4' 70.0 14.2 8.6

-1.087 (± 0.997) 0 / + 1.320 (± 0.510) (0.887) (0.253) (0. 192)

A7 pC9 = 0.769 (± 0.603) MR4· + 0.691 (± 0.387) locm 82.6 10.7 16.9

- 0.363 (± 0.333) IN (0.937) (0. 191 ) (0. 11 9)

+ 1.322 (± 0.386) A8 pC u = 1.184 (± 0.768) MR4• - 1.528 (± 0.9(6) 0 / 65.2 5.6 10.4

+ 4. 185 (± 0.444) (0.849) (0.253) (0. 177)

#Excluding compound 8 (n = (0); $ Excluding compounds 8 and 14 (n = 9) @95% confidence intervals of regression constan ts are shown within parentheses; 't' values of the regression constants are significant at 95% level unless superscripted with * (Sign ificant at 90% level) Idf= n-np-I: n = no. of data points; np = no. of predictor variables]

I7 F values are significant at 99% level; df= (np, n-np-I ).

substitution should not be highly electron donating or electron withdrawing due to resonance effect. This is corroborated by the negat ive coefficient of IN in Eq. A 1 :cyano (J p = 0.66) and nitro (ap = 0.78) are strong electron withdrawing groups while am ino (ap = -0.66) is a strong e lectron releasing group through resonance

effect. The PRESS statistics (Table V) of Eq. A I suggests robustness of the equation.

The data matrix containing pC2, pCq and pC I3 and physicochemical parameters could be described by 5 factors (Table I1Ie). The steric (MR4-) and electronic (a/; additionally, a4' for pC9) parameters showed

ROY: QSAR OF MATRJX METALLOPROTEINASE INHIBITOR BUTYRIC ACroS 693

Table V -Summary of PRESS statistics

Model equation pCj = I~iXi + a, n = II

Reference Average* regression constants (standard deviation) PRESS statistics

Eq. pCj ~, ~2 ~) (sd) (sd) (sd)

Al pC, 0.420 lOCH, -0.571 IN

(0. 150) (0.362)

A3 pC2 1.483 M~· -1.8760/

(0.398) (0.884)

A4 pC) -6801nd

(0.403)

A5 pC4 -886 Ind

(0.486)

A7 pC5 0.765 MR4, + 0.692 lOCH) -0.362 IN

(0.235) (0.209) (0.238)

A8 pC6 1 . 184M~, -1.5190/

(0.329) (0.719)

* Average of II PRESS equations

importance in describing the activities. The important regression equations for pC2• pC9 and pC'3 (Eqs. A3, A3A, A6, A8) are shown in Table IV. The positive coefficients of MR4• in all the cases indicate positive contribution of steric bulk of 4' -substituents suggesting possible dispersion interaction with the active site. The negative coefficients of 0'/ indicate that the electronic influence (donation and withdrawl) of the 4'-substituents (due to resonance) on the phenyl ring should be minimum. The optimum value of 0'4' for pC9 was calculated to be -0.21 (moderately electron releasing) from Eq. A6. The PRESS statistics of Eqs. A3 and A8 are shown in Table V. However, crossvalidation of Eq. A6 shows high dependence of the equation on compound 10. Hence factor analysis of the data matrix of pC9• M~·. 0'4. 0'/ alongwith locH3 and IN (Table IIId) was performed and this

showed importance of loc"'3 and IN alongwith MR4,. The cOlTesponding regression equation A 7 is of high statistical quality (Table IV) and robustness (Table V). The equation suggests that apart from positive contribution of steric bulk of 4'-substituents, the presence of 4'-methoxy or 4'-methyl groups and the absence of groups like N02/NH 2/CN are conducive for the activity (pCg).

For pC3 and pC7, no physicochemical parameters were found to be important contributor. However, when an indicator variable Ind (denoting presence or

a EVO/O SEE AVRES

(sd)

+2.321 80.1 0.895 0.167 0.139

(0.599)

+4.391 65.1 0.807 0.301 0.246

( 1.086)

+5.112 65.1 0.807 0.191 0.119

( 1.278)

+2.215 74.J 0.864 0.190 0.148

(0.572)

+ 1.323 66.6 0.836 0.265 0. 193

(0.355)

+4,185 55.9 0.747 0.285 0.236

( 1.037)

absence of 4'-NH2/4'-H group) was included in the data matrix for factor analysis (Table IIIe), the activities were found be highly loaded with the variable Ind. The corresponding regression equations (A4 and AS) and their PRESS statistics are given Tables IV and V respectively. The negative coefficient of Ind indicates that a 4' -substituent, excluding amino, favours the activities.

QSAR of (S)-3-methyl-2-( substituted biphenyl-4-sulfonylamino)butyric acids (n = 14)

The QSAR analysis of all 14 compounds are given Tables VI and VII. The factor analysis of the data matrix involving the activities showed that the factor pattern of the activities as found in case of data set of 4'-substituted compounds (n = 11) was almost retained except that the interrelation between pC, and pC) increased.

The factor analysis of the data matrix involving pC, (Table VIa) showed the importance of MR), and

MR2+ 3' apart from IOCH3 and IN. The equations involving MR3, and MR2+ 3' were statistically equivalent though the later was slightly better and shown in Table VII. The negative contributions of MR), and MR2+ 3' suggest that bulk of orlho and meta substituents is negative contributor to the activity.

The factor analysis of the data matrix involving pC2• pCg and pC'3 (Table VIb) showed that MR)' and

694 INDIAN J. CHEM .• SEC B. AUGUST 2001

Table VI - Factor loadings of the variables (after varimax rotation) for QSAR of (S)-3-methyl-2-(substituted biphenyl-4-

sulfonylamino)butyric acids (n = 14)

(a) Data matrix: pC" locH). IN. 1m. MR3". MR2+ 3"

Variable Factor I Factor 2 Factor 3 Factor 4 Communality

pC I 0.660 0.523 -0.414 0.318 0.98 1 IOCHJ 0.059 0.120 -0.988 0.065 0.998 I N 0.074 -0.983 0.104 0.107 0.994 1m -0.445 0. 100 0.094 -0.884 0.999 MRy -0.962 0.052 0.043 -0.260 0.998 MR2+ 3· -0.962 0.050 0.041 -0.262 0.998

% variance 0.416 0.2 12 0. 195 0.172 0.995

(b) Data matrix: pC2• pC9• pC13, MR4·• 0 4', 0 /, 1m. MR3·• MR2+ 3'

Variable Factor I Factor 2 Factor 3 Factor 4 Factor 5 Communality

pC2 -0.842 -0.455 -0.187 -0.059 -0.148 0.975 pC9 -0.913 -0. 173 -0. 110 -0.263 -0. 144 0.966 pC IJ -0.825 -0.407 -0.189 0.104 -0.265 0.963 MR4· -0.854 -0. 106 0.422 0.207 -0.079 0.968

04' 0.030 -0.054 0. 189 0.976 -0.044 0.993

0 / 0.092 -0. 132 0.952 0.198 -0. 11 2 0.983

1m 0.427 0.432 -0.23 1 -0.077 0.754 0.997 MRJ· 0.264 0.944 -0. 105 -0.040 0. 159 0.999 MR2+)" 0.269 0.943 -0.103 -0.041 0. 158 0.998

% variance 0.365 0.267 0.142 0.125 0.084 0.983

(c) Data matrix: pC3• pC7• 1nd, 1m, MR)". MR2+ 3'

Variable Factor 1 Factor 2 Factor 3 Communality

pC3 0.743 0.495 -0.342 0.914 pC7 0.456 0.714 -0.474 0.942 1nd 0.085 -0.981 -0.1 3 1 0.987 1m -0.419 0.022 0.903 0.992 MRy -0.950 -0.005 0.301 0.994 MR2+ )" -0.949 -0.008 0.303 0.993

% variance 0.458 0.286 0.226 0.970

Table VII - Relations of matrix metalloproteinase inhibition activities of (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric acids with physicochemical and structural parameters [n = 14 (if not stated otherwise)]

Eq. Equations@ Stati stics No. EV% CV% FI7

(r or R) (SEE) (AYRES)

B I pC I = 0.44 J (± 0.26 1) locm- 0.549 (± 0.223) IN 90.2 6.9 40.8

- 1.653 (± 0.444) MR2+ 3+2.640 (± 0.164) (0.961) (0.148) (0.104)

B2 pC I = 0.468 (± 0.404) ' ocm- 0.87 J (± 0.740) 0/ 76.7 10.6 15.2 - 1.675 (± 0.697) MRz+ 3+ 2.662 (± 0.268) (0.906) (0.228) (0. 157)

B3 pC2 = 1.456 (± 0.6 J 7) M~·- J. 708 (± 0.853) 0 4.2 83.8 5.5 23.5 - 1.539 (± 0.832) MR3+ 4.490 (± 0.405) (0.936) (0.259) (0. 164)

B3A # pC2 = 1.396 (± 0.419) M~·- 1.493 (± 0.592) 0/ 91.8 3.7 46.0 - 1.461 (± 0.565) MR3· + 4.427 (± 0.280) (0.969) (0.172) (0. 103)

B4 pC3 = - 0.6 18 (± 0.353) Ind- 1.92 J (± 0.610) MR3" 8 1.1 4.3 28.9

+ 5.248 (± 0.167) (0.9 J 7) (0.208) (0. J 22) (COIlId)

ROY : QSAR OF MATRIX METALLOPROTEINASE INHIBITOR BUTYRIC ACIDS 695

Table VII- Relations of matrix metalloproteinase inhibition activities of (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric acids with physicochemical and structural parameters [n = 14 (if not stated otherwise)]-Collld

B4A# pC) = -0.571 (± 0.263) Ind- 1.862 (± 0.453) MR)· 88.9 3.2 49.0 +5 .195 (± 0.129) (0.953) (0.152) (0. 101 )

85 pC7 = -0.932 (± 0.383) Ind- 0.932 (± 0.383) 1m 78.4 IJ.3 24.6 + 2.26 1 (± 0. 156) (0.904) (0.225) (0. 165)

86 pCg = 1.568 (± 0.558) M~·- 0.472 (± 0.437) 04' 75.8 14.4 14.6 - 0.974 (± 0.861) 0/ + 1.132 (± 0.349) (0.902) (0.247) (0. 183)

87 pC9 = 1.1 14 (± 0.460) M~+0.645 (± 0.375) l OCH) 83.2 12.0 22.4 - 0.396 (± 0.3 I 9) IN + 1.1 36 (± 0.285) (0.933) (0.206) (0. 126)

88 pC n = 1.399 (± 0.625) M~·- 1.450 (± 0.865) 0/ 80.2 5.9 18.6 - 1.28 1 (± 0.843) MR3" +4.147(± 0.410) (0.921) (0.262) (0.1 80)

#Excluding compound 8 (n = 13); @95% confi dence intervals of regression constants are shown within parentheses; 't' values of the regression constants are

significant at 95% level [df = n-np- I ; n = no. of data points; np = no. of predictor variables) vF values are significant at 99% level; df = (np. n-np-1 ). Table VIII -Calculated MMP inhibitory activities of (S)-3- methy l-2-(substituted biphenyl-4-sulfonylamino) butyric ac ids

SI. pC I pC2 pC) pC7 pC9 pC 13 No. Cal. Res. Cal. Res. Cal. Res. Cal. Res. Cal. Res. Cal. Res.

I 2.300 -0.032 4.482 -0.084 4.432 -0.0 12 1.329 -0.180 1.250 0.335 4.159 0.048 2 2.300 0.077 4.460 -0.05 1 5.050 -0.050 2.261 0.058 1.238 -0.044 4.138 0.228 3 2.3 18 -0.252 4.499 -0.189 5.071 -0.30 1 1.329 0.329 1.250 -0.063 4.173 -0.349 4 2.300 -0.077 5.535 -0.137 5.050 0.105 2.26 1 -0. 11 8 2. 125 -0.022 5.181 -0.840 5 1.002 -0.002 3.274 -0.003 3.542 -0.004 1.329 -0.329 1.250 -0.250 3. 154 -0.005 6 2.300 -0. 11 2 5.120 -0. 161 5.050 -0.004 2.26 1 -0.136 1.807 -0.0 11 4.782 -0.463 7 2.3 18 0.126 5.535 -0.234 5.050 -0.254 2.26 1 0.417 2. 125 0.185 5.181 -0.260 8 2.74 1 -0.083 5. 106 0.593 5.050 0.473 2.261 0.086 2.410 -0.001 4.764 0. 195 9 2.74 1 0.083 5.354 0.169 5.050 0.047 2.26 1 -0. 11 8 2.657 0.001 5.0 11 0.211 10 1.750 -0.1 65 4.377 0.066 4.432 0.012 1.329 0.180 1.344 0.355 4.142 -0. 163 11 2.300 0.077 4.565 0.32 1 5.050 -0.004 2.261 -0.159 1.695 0.004 4.295 0.344 12 1.750 -0.005 4.510 -0.029 5.050 0.172 2.261 -0.106 1.445 -0.2 16 4.269 0.162 13 2.300 0.195 5.033 -0. 11 2 5.050 0.047 2.261 0.086 1.902 -0. 132 4.722 0.074 14 1.750 0.171 4.365 -0. 150 5.050 -0.226 2.26 1 -0.009 1.560 -0. 140 4.163 -0. 172

Cal. = Calculated val ues Res. = Observed-Calculated values Values calculated accord ing to (i) Eq. B 1 for pC I> (ii ) Eq. 8 3 for pC2• (i ii ) Eq. 84 for pC}. (iv) Eq. B5 for pC7• (v) Eq. 87 for pCg and (vi) Eq. 88 for pCn .

MR2+ 3' were important only for pC2 and pC 13. The quality of the equations in volving MR3' was slightly better than that with MR2+ 3' and the former types are reported in Table VII . The equations reveal negati ve

impact of meta (and poss ibly ortho) substituents on pC2 and pC I3 due to steric bulk. However. pC9 was not fo und to be significantly contributed by non-para substituents.

The factor analysis of the data set involving pC3 and pC7 (Table VIc) showed that the former is dependent on MRy and MR2+ y while the later on fill' The colTesponding regress io n equations are shown in Table VII. For pC3, steric bulk of meta (and ortho)

substituents is negative contributor. while for pC7•

mere presence of meta substituents is detrimental to the activity.

Though preliminary attempt was made to explore contribution pattern of 3' and 2'-substituents, more compounds having such groups are required to reach any conclusion. The calculated activity values of the compounds according to the best equations of the individual series along with corresponding res iduals are shown in Table VIII.

Through molecular modeling study, O'Brien et al. 3 suggested that during interaction with the receptor site, the biphenyl moiety of the compounds remains within PI' subsite where it may be involved in

696 INDIAN 1. CHEM .• SEC B. AUGUST 2001

Table IX - Factor loadings of the variables (after varimax rotation) for QAAR equations

Data matrix : pCI> pC2• pC). pC7• pC9.pCn . MR4·• 0 /. IOCfl). IN. Ind. 1m. MR)·

Variable Factor I Factor 2 Factor 3 Factor 4 Factor 5 Communality

pC, 0.774 -0.297 0.389 -0. 100 0.307 0.943

pC2 0.622 -0.616 0.227 -0.114 0.367 0.966 pC, 0.842 -0.220 -0.065 -0.356 0.243 0.947 pC7 0.624 -0.442 -0.074 -0.586 -0.001 0.934 pC9 0.319 -0.759 0.232 0.049 0.499 0.983

pC n 0.624 -0.667 0.219 -0. 159 0.220 0.956

M~· 0.227 -0.868 -0.303 -0.265 0.066 0.970

0 / 0.075 -0.079 -0.957 -0.005 -0. 128 0.944

loc,-,] 0.142 -0. 192 0.132 -0.072 0.954 0.990

IN -0.025 0.038 -0.973 0.134 -0.066 0.971 Ind -0.006 0.064 -0. 141 0.981 -0.065 0.990

1m -0.665 0.540 0.250 -0.192 0.022 0.833 MR)· -0.939 0.149 0.149 -0.102 0.004 0.937

% variance 0.306 0.219 0.184 0.125 0.117 0.951

Table X - QAAR equations among matrix metalloprotei nase inhibition activities of (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric acids [n = 14]

Eq. Equations@ Statistics No. Ev% Cv% F'"

(r or R) (SEE) (A YRES)

C I pC2 = 0.939 (± 0.350) pC,+ 0.925 (± 0.558) M~· 84.5 5.3 36.5

+ 2.230 (± 0.720) (0.932) (0.253) (0.163) C2 pC, =0.782 (± 0.356) pC}- 0.853 (± 0.844) 0 / 65.4 12.9 13.3

- 1.509 (± 1.727)* (0.84 1 ) (0.278) (0.2 14)

C3 pC, = 0.626 (± 0.397) PCr 0.497 (± 0.451) IN 55.7 14.6 9.2

+ 1.012 (± 0.822) (0.791 ) (0.315) (0. 198)

C4 pC, =0.692 (± 0.428) PCr 0.914 (± 1.023) 0/ 49.7 15 .6 7.4

+ 0.919 (± 0.868) (0.758) (0.335) (0.227)

C5 pC7 = 0.569 (± 0.418) pC,- 0.625 (± 0.544) Ind 57.1 15.9 9.6

+ 0.859 (± 0.938)* (0.798) (0.317) (0.233)

C6 pC9 = 0.595 (± 0. 160) pC,+ 0.842 (± 0.596) MR4· 70.5 15.9 293.5

(0.853) (0.273) (0.224) C7 pC, ] =0.85 1 (± 0.281) pC,+0.910 (± 0.449) MR4· 88.1 4.6 49.2

+ 2. 133 (± 0.579) (0.948) (0.203) (0. 136)

C8 pC2 = 0.903 (± 0.065) pC]+ 1.060 (± 0.568) MR4· 86.3 5.0 1866.5

-1.323 (± 0.772) 0 / (0.940) (0.238) (0. 186)

C9 pC2 = 0.789 (± 0.518) pC7+ 0.798 (± 0.690) locfl ) 61.2 8.5 11.3

+ 3.042 (± 1.044) (0.820) (Q.40 1) (0.276)

C IO pC2 = 1.156 (± 0.345) pC9+ 2.744 (± 0.617) 80.0 6.1 53.2

(0.903) (0.287) (0.235)

C II pC2 = 1.065 (± 0.028) pC,} 88.7 4.6 6792.2

(0.942) (0.2 16) (0.172)

C I2 pC] = 0.793 (± 0.374) pC7+ 3.273 (± 0.766) 61.0 6.2 21.3

(0.800) (0.299) (0.220)

C I3 pC7 = 0.332 (± 0.077) pC)+ 0.758 (± 0.638) M~· 64.4 14.5 346.5

(0.8 19) (0.288) (0.203)

C I4 pC, ] =0.841 (± 0.071)pC)+1.01O(± 0.628)MR4· 80. 1 5.9 1343.2

- 1.1 03 (± 0.853) 0 / (0.912) (0.263) (0. 196) (COl/u(

ROY: QSAR OF MATRIX METALLOPROTEINASE INHIBITOR BUTYRIC ACIDS 697

Table X-QAAR equations among matrix metalloprotei nase inhibition acti vi ties of (S)-3-methyl-2-(substituted biphenyl-4-sulfonylamino)butyric acids [n = 14]- Contd

Eq. No.

Equations@ EY%

(r or R)

Stati stics CY% F'" (SEE) (AY RES)

C I5 pC7 = 0.441 (± 0.429) pC9- 0.738 (± 0.594) Ind + 1.343 (± 0.776)

46.8

(0.741 )

17.7 6.7+

(0.353) (0.244) CI6 pC, ) = 0.527 (± 0.563) pC7+ 1.110 (± 0.976) MR4·

- 1.179 (± 1.066) cr/ + 3.000 (± 1.232)

70.5

(0.879)

7.2 11.3

(0.321 ) (0.220) C I7 pC9 = 0.717 (± 0.290) pC, ) - 1.464 (± 1.296) 68.4 16.5 29.1

(0.84 1) (0.283) (0.2 15)

@95% confidence intervals of regression constants are shown within parentheses; 't' values of the regression constants are significant at 95% level unless superscripted with * (Significant at 90% level ) [df= n-np-i; n = no. of data points; np = no. of predictor vari ables; i = 1 if intercept is present, i = 0 otherwi se]

"'F values are significant at 99% level except + (significant at 95% level); df= (np, n-np-i) .

hydrophobic interaction and 7t-7t stacking with aromatic amino acid residues. The present analysis has shown that steric bulk of the 4'-substituents has positive impact on pC2• pC9 and pC I3 suggesting possibility of dispersion interaction . Again, high electron withdrawing or electron donating 4'-substituents have detrimental effect on pCI> pC2• pC9 and pCI) and this suggests that optimum electronic distribution of phenyl ring is required for 7t-7t stacking. Again , except for pC9, sterk bulk of meta (and possily ortho also) substituent or mere its presence decreases the activities and this is indicative of the presence of narrow channel in the active site which is in good agreement with the results of X-ray study on the enzymes3.

Exploring QAAR For deriving QAAR equations, factor analysis of

the data matrix consisting of all activity values and important predictor variables was made (Table IX) and from the pattern of factor loadings, the QAAR equations (Table X) were constructed. The equations may be helpful in determining selectivity of the compounds for specific activity and determining one activity when the other is known .

Acknowledgement The author thanks Prof. (Mrs.) C Sengupta, Prof. A

U De and Sri Dipak Kumar Pal of Department of Pharmaceutical Technology of Jadavpur University, Calcutta (India) for inspiration.

References and Notes 1 Whittaker M, Floyd C D, Brown P & Gearing A J H, Chelll

Rev,99, 1999,2735. 2 Scozzafava A & Supuran C T, J Med Chem, 43,2000, 1858. 3 O'Brien P M, Ortwine D F, Pavlovsky A G, Picard J A,

Sli skovic D R, Roth B D, Dyer R D, Johnson L L, Man C F & Hallak H, J Med Chem, 43, 2000, 156.

4 Franke R & Gruska A in Chemometric Methods in Molecular Design, edited by H van de Waterbeemd (YCH, Wei nheim) 1995, pp 113-157.

5 Franke R, Theoretical Drug Design Methods, (Elsevier, Amsterdam) 1984, pp 184-193.

6 Snedecor G W & Cochran W G, Statistical Methods, (Oxford & IBH Publishing Co Pvt Ltd, New Delhi ) 1967, pp 38 1- 41 8.

7 Kier L B & Hall L H in Advances in Drug Design, Yol. 22, (Academic Press, New York) 1992, pp 1-38.

8 Wold S & Eriksson L, in Chemometric Methods ill Molecular Design, edited by H van de Waterbeemd (YCH, Weinheim) 1995,3 12.

9 Franke R, Theoretical Drug Desigll Methods, (Elsevier, Amsterdam) 1984, 41 .

10 For example: Roy K, Pal D K. De A U & Sengupta C, Illdial! J Chem, 38B, 1999, 1194.

II MINIT AB is a statistcal package of Minitab Inc. (New York). 12 The GW-BASIC programs RRR98, KRPRESI and KRPRES2

were developed by Kunal Roy ( 1998) and standardized on known datasets.

13 Kubinyi H, in Burger's Medicillal Chemistry and Drug Discovery, edited by M E Wolff, 5th edition, Yol. 1, (John Wiley & Sons, New York) 1995, pp 507-509.