Development of QSAR Model of Substituted Benzene Sulphonamide using Multiple Regression Analysis

In continuation of our earlier work in this paper we studied 50 substituted Benzenesulphonamide using substituent nanofluorobutyl sulphonyl chloride (C4F9SO2Cl) and pentafluoro benzene sulphonyl chloride (C6F5SO2Cl) Accordingly we have development QSAR model of studied compounds. These models were derived using the parameters Balaban Index, Balaban-type index,(Jhetz, Jhetm, Jhetv, Jhete, Jhetp) Balaban related index (F,G.) and Randic connectivity index (χ1). The best suitable model is predicted on the basis of Maximum-R2 (R-squared).

physiologically highly relevant isoform.It is highly efficient catalyst for the reversible hydration of carbon dioxide: At physiological pH, aromatic and heterocyclic unsubstituted sulphonamides (R-SO 2 NH 2 ),which are known to inhibit CA-II have an ionisable sulphonamide group (pK a -6-10).Upon binding the sulphonamide group displaces the water molecule/hydroxide substantially decreases the activity due to steric hindrance 3,4 .The aromatic side chains of sulphonamide interacts with hydrophobic amino acid residues in the binding site e.g.Phe 131, Leu 141, Val 143, Ala 145 and stabilize the reaction.Unsubstituted amides such i.e.R-CO 2 NH 2 such as urethane, phenyl carbamate are a second albeit much less potent, class of known CA-II inhibitor.
In contrast to sulphonamides the compounds are basic and much weaker.CA-II inhibitor amidst such as SCN -, ClO 4 -, I-are also weak inhibitor with K ( binding constant) values of 8-13/um(5)

Methodology
A QSAR , model is developed on the basis of topological indices.The values of topological indices were calculated by applying Graph Theory to the chemical structure.A graph G) G(V,E) is an ordered pair consisting of two sets V) V(G) and E) E(G).Elements of the Set V(G) are called vertices and elements of the set E(G) , involving the binary relation between the vertices, are called edges.By removing all hydrogen atoms from the chemical formula of a chemical compound containing covalent bonds, one obtains the hydrogen-depleted ( or hydrogensuppressed) molecular graph of that compound.In (B) Pentafluoro benzene sulphonyl chloride ( C 6 F 5 SO 2 Cl).
Graph theory, the atoms are considered as vertices and the bonds as "edges" Vertices are represented by " and edges by "-".In this study, the expressions "molecular graph" and "." "molecule", "vertex" and "atom", "edge" and "bond" are used interchangeably.This can be well explained by following example: The methodology used in present investigation is to model the CA-II inhibitory activities of CA-II inhibitors collected from the literature (6-8) .The topological indices are calculated using softwares : Dragon (9) and ACD Labs(10) used for structure optimization The molecular descriptors evaluated in present work are: Balabanindex (J) (11) , Balaban-type index : "Z" weighted (Jhetz), mass-weighted (Jhetm), vanderWalls weighted (Jhetv), electronegativityweighted (Jhete) and polarisability-weighted(Jhetp) Balaban related index (F&G) (12) and the Firstorder connectivity index or Randic connectivity index(X1) 13 .

Balaban index
Balaban Index J (average distance-sumconnectivity index) is defined by 12 Where M is the number of edges in a graph G,µ is the cyclomatic number of G. di's (i=1,2,3,4.. is the number of vertices in G) are the distance sums of atoms in G.
Balaban index is extended for the calculation of atom and bond parameters for heteroatomcontaining molecules used in computing graph theoretic invariants.This generates a series of Balaban-type index.The different parameters are "Z" weighted (Jhetz), mass-weighted (Jhete), van der Waals weighted (Jhetm), electronegativity-weighted (Jhete) and polarisability-weighted Balaban index.In this approach, the atom and bond weights are computed on the basis of relative atom and bond parameters, using carbon as standard.The new definition of the atom and bond parameters leads to a periodic variation versus the atomic number (Z), with a more natural variation when compared with the parameters defined only by Z.This approach is used to define and compute topological indices based on graph distance.The most used molecular graph descriptors in establishing quantitative structure-property relationships (QSPRS) and quantitative structure-activity relationships (QSAR's) are topological indices [14][15][16][17][18][19] .

Balaban related index
For those properties where not only the "shape" but also the size of the graph influence the property/activity, two indices related to "J" have been developed.The first of these index is F, defined as: This index is able to separate graph size, cyclicity and branching 20 .
The other J-related index "G" is more convenient for correlations.It is defined as 20 : First -order connectivity index (χ1) : the connectivity-index graph (χ1) of a graph G is defined by Randic as under 21 .
Drug-designing will be performed using correlation analysis employing NCSS 22 software.
The methodology used being the method of maximum-R 2 employing multiple regression analysis 23 R 2 ( R-squared) is the correlation coefficient between experimental values and model prediction on the test set.Maximum R2 method is used to identify prediction of model.According to Tropsha's group [24][25][26] a QSAR model is considered predictive, if the following condition is satisfied : R 2 is the correlation coefficient between experimental values and model prediction on the test set.Mathematical definitions of R20 R2 and K1 are presented clearly in literature (26) and are not described here for brevity.

Table 2 (b):
Table-2(A), we conclude that model 2 to 9 gives R2>0.6 and in Table-2(B) model 4 to 9 shows significant R2.On comparing observations in Table-2(A) and (B), Model 9 in Table-2(A) shows maximum-R2 i.e.0.8647.This model should be considered as best suitable model for inhibition of Carbonic Anhydrase.The Model is as follows: t h e s e o b s e r va t i o n s i n d i c a t e s that substituent nanofluoro buty1 sulphony1 chloride(C 4 F 9 SO 2 Cl).