QSAR study for diarylguanidines, noncompetitive NMDA receptor antagonists. A new topological index A Ad derived from local invariants of the chemical graphs of diarylguanidines

The binding affinities for NMDA receptor ion channel and σ receptor sites of four classes of diarylguanidines have been correlated with values of molecular descriptors implemented in CODESSA and PRECLAV programs: twenty-one derivatives of N, N ′ - diphenylguanidines type ( 1 ), eight N, N ′ - dinaphthylguanidines type ( 2 ), eighteen N – naphthyl - N ′ - phenylguanidines type ( 3 ) and two miscellaneous guanidines ( 4) . A new topological index A Ad based on local invariants of the chemical graphs has been defined and used in QSAR studies generating an increasing of correlation coefficient value r


Results obtained with CODESSA program
][34] For [ 3 H]-5 (MK-801) the regression equation has the form: Values of coefficients obtained with the CODESSA program and definition of variables are given in Table 1.In Figure 3 the experimental versus estimated log A data correlation is presented.The statistical parameters of the fit are: N=49 r =0.880 s = 0.451 F = 13.05Q = 1.951R 2 = 0.774 cross validated R 2 = 0.672 where N is the number of data points, R and R 2 denote correlation coefficients, s is the standard deviation of the fit, F is the Fisher test and Q is the quality factor.

Results obtained with the PRECLAV program
The second set of QSAR correlations was obtained using the PRECLAV program developed by L. Tarko. 35,36sults with PRECLAV program for [ 3 2.In Figure 4 the experimental versus estimated log A data correlation is presented.The statistical parameters of the fit are: N=49 r =0.932 s = 0.308 F = 25.56Q = 3.026 R 2 = 0.868 cross validated R 2 = 0.802 where N is the number of data points, R and R 2 denote correlation coefficients, s is the standard deviation of the fit, F is the Fisher test and Q is the quality factor.
In Table 3 are listed the experimental and estimated biological activities of diarylguanidines obtained with CODESSA program (eq.2) and PRECLAV program (eq.3) for NMDA receptor ion channel.

Results with CODESSA program for [ 3 H]-6 (DTG)
For [ 3 H]-6 (DTG) the regression equation has the form: Values of coefficients obtained with the CODESSA program and definition of variables are given in Table 4.In Figure 5 the experimental versus estimated log A data correlation is presented.The statistical parameters of the fit are: N=49 r =0.914 s = 0.423 F = 19.32Q = 2.160 R 2 = 0.836 cross validated R 2 = 0.737 where N is the number of data points, R and R 2 denote correlation coefficients, s is the standard deviation of the fit, F is the Fisher test and Q is the quality factor.

Results with PRECLAV program for [ 3 H]-6 (DTG)
Values of coefficients obtained with the PRECLAV program and definition of variables are given in Table 5.In Figure 6 the experimental versus estimated log A data correlation is presented.The statistical parameters of the fit are: N=49 r =0.938 s = 0.319 F = 28.45Q = 2.940 R 2 = 0.880 cross validated R 2 = 0.814 where N is the number of data points, R and R 2 denote correlation coefficients, s is the standard deviation of the fit, F is the Fisher test and Q is the quality factor.
In Table 6 are listed the experimental and estimated biological activities of diarylguanidines obtained with CODESSA program (eq.4) and PRECLAV program (eq.5) for σ receptor.

New topological index A Ad derived from local invariants
; thus the elements of E are 2-element subsets of V.The elements V are the vertices and E are the edges of the graph G.When V represents the atoms of a molecule and elements of E symbolize covalent bonds between pairs of atoms, then G becomes a molecular graph . 37A graph invariant is a topological property that is conserved by molecular isomorphism.An inclusive graph invariant is one, which is the same for two or more graphs (i.0][41]43 ARKAT USA, Inc To obtain a local invariant set X one method is to solve a linear system of equations: where Q is a matrix derived from the adjacency matrix, R is a column vector and X is the column vector of local invariants x i . 42,43n the present QSAR study, we considered the distance matrix (D) obtained using MOPAC program as Q matrix, the diagonal terms being replaced with the value of the topological index J (Balaban) 39,40,[44][45][46][47] for the considered molecule.Column vector R was obtained multiplying the adjacency matrix (A) corresponding to the chemical graph with a column vector Z whose elements are the atomic numbers z i .The equations (eq.7) becomes: Using the local invariant set X we built a new topological index A Ad named Beteringhe-Filip-Tarko index, defined in equation 8, which has been included in the QSAR study of the interaction of diarylguanidines with the two types of receptors: 2 8 where q is the number of edges in the molecular graph, N is the number of vertices in the molecular graph and x i are the local vertex invariants.
A better correlation of binding affinity (logA) of diarylguanidines for σ receptor was observed including the new Beteringhe-Filip-Tarko topological index A Ad in the QSAR equation.

Results with CODESSA program for [ 3 H]-6 (DTG) including A Ad in the correlation
Values of coefficients and definition of variables are given in Table 7.In Table 8 are listed the experimental and estimated biological activities of diarylguanidines for σ receptor.In Figure 7 the experimental versus estimate log A data correlation is presented.The statistical parameters of the fit are: N=49 r =0.942 s = 0.412 F = 24.4Q = 2.286 R 2 = 0.887 cross validated R 2 = 0.795 where N is the number of data points, R and R 2 denote correlation coefficients, s is the standard deviation of the fit, F is the Fisher test and Q is the quality factor.

Discussion
In Tables 1-8 QSAR correlation equations are presented, either with experimental and calculated values for the binding affinity (log A) of forty-nine diarylguanidines for the NMDA receptor ion channel site and the σ receptor.The diagrams presented in Figures 3-7 show a linear dependence between experimental and calculated values of binding affinity (log A), the corresponding linear correlation equation is also presented.Comparing the values of correlation coefficient r obtained using the CODESSA and PRECLAV programs for the same number of descriptors, somewhat higher values were obtained when using PRECLAV program (r = 0.932 in case of NMDA receptor ion channel site and 0.938 in case of σ receptor) than when CODESSA program was used (r = 0.880 in case of NMDA receptor ion channel site and 0.914 in case of σ receptor).
In the study performed with CODESSA, quantum-chemical descriptors (NBOAvg -Average bond order of a N atom -being retained as specific descriptor in the models for both receptors) have the highest weight in QSAR models for both receptors while in the study performed with PRECLAV, grid-field descriptors have the highest weight.
Grid electrostatic descriptors are resultant forces (F), repulsive (R) and attractive (A), between net atomic charges of the studied molecules and probe atoms placed in the evenly distributed points of a virtual network.Forces F, R and A represent a measure of the interaction of the molecule with the active site of the receptor in a certain zone of space.
Grid geometric descriptors are the parallaxes of atom pairs meaning the angle under which can be seen that pair of atoms from a point of the virtual network ; for every network point the parallaxes are calculated for all atom pairs, then maximum parallaxes (P) and average parallaxes (M); the parallaxes are a measure of the section area of the molecule seen from a certain point of space.
The fact that in the final QSAR equations obtained with PRECLAV more grid descriptors are included than global descriptors, shows that electrostatic interactions and host-guest like interactions of the molecules with the active site are more important than other molecular characteristics (molecular mass, number of atoms of a certain type, type of chemical bonds).
When the new Beteringhe-Filip-Tarko topological index A Ad , derived from local invariants of the chemical graphs of the diarylguanidines, is used an increase of the correlation coefficient (r = 0.942) is observed in the QSAR model corresponding to the σ receptor done using CODESSA, leading to the idea that a better structural characterization of diarylguanidines is represented in this new index.This is accountable to the fact that the new Beteringhe-Filip-Tarko index A Ad was devised using the geometric characteristics of the molecule.

Conclusions
In this study the binding affinities for the NMDA receptor ion channel and σ receptor sites of four classes of diarylguanidines have been correlated with values of molecular descriptors implemented in CODESSA and PRECLAV programs: twenty-one derivatives of N, N′ -Diphenylguanidines type (1), eight N, N′ -Dinaphthylguanidines type (2), eighteen N -Naphthyl -N′ -phenylguanidines type (3) and two miscellaneous guanidines (4).
Correlation coefficient, r, has a higher value when the PRECLAV program is used for building the QSAR model for the NMDA receptor ion channel site and σ receptor, due to the use of grid/field descriptors which show that electrostatic/host-guest interactions of the molecules with a certain site are more important than other molecular specific features.
Introduction of the new Beteringhe-Filip-Tarko topological index A Ad in QSAR model for σ receptor increased the predictive value of the model.
obtained with the PRECLAV program and definition of variables are given in Table

Figure 3 .
Figure 3. Experimental vs. estimated biological activity of diarylguanidines for NMDA receptor ion channel site obtained with CODESSA.

Figure 4 .
Figure 4. Experimental vs. estimated biological activity of diarylguanidines for NMDA receptor ion channel site obtained with PRECLAV.

Figure 5 .
Figure 5. Experimental vs. estimated biological activity of diarylguanidines for σ receptor obtained with CODESSA.

Figure 6 .
Figure 6.Experimental vs. estimated biological activity of diarylguanidines for σ receptor obtained with PRECLAV.

Figure 7 .
Figure 7. Experimental vs. estimated biological activity of diarylguanidines for σ receptor when in the QSAR equation A Ad is used.

Table 1 .
Coefficients and variables in equation 2

Table 2 .
Coefficients and variables in equation 3

Table 3 .
Experimental vs. estimated biological activity of diarylguanidines for NMDA receptor ion channel site obtained with CODESSA program (eq.2) and PRECLAV program (eq.3)

Table 4 .
Coefficients and variables in equation 4

Table 5 .
Coefficients and variables in equation 5

Table 7 .
Coefficients and variables in equation 9

Table 8 .
Values of topological index A Ad and experimental vs. estimated biological activity of diarylguanidines for σ receptor