Theoretically Predicted Descriptors Based Quantitative Structure Activity Relationship Study of the Activity of Acridines Against B-16 Melanoma

Problem statement: The probability of success and reducing time and c oast in drug discovery process could be increased on the basis o f QSAR techniques. The study involves the QSAR investigation of 20 bioactive acridines that have a ctivity against Approach: Molecular descriptors, total energy, van der Waals volume, molecular volum e, HOMO energy, HOMO-LUMO energy gap, polarizability, refractivity, bond angle of C8-N9-C 2 and bond length of C14-N6 were calculated. Initial geometry optimizations were carried out wit h RM1 Hamiltonian. Lowest energy conformers were subjected to single point calculations by DFT method. Several models for the prediction of biological activity have been drawn up by using the multiple regression technique. Results: Four models with R2 ranges from 0.88-0.93 were predicted . A model with hepta-parametric equation with R2 0.93 was used to predict the biological activiti es, the agreement between the observed and the predicted values was up to 93%. Conclusion: The biological activity of the studied acridines c an be modeled with quantum chemical molecular descriptors .


INTRODUCTION
The physiological and biological properties of acridines are well discussed and large number of this kind of compounds have been prepared and evaluated for their biological activities (Su et al., 2006;Cheng et al., 2008). Many of acridine derivatives posses antimicrobial, antiviral and anticancer properties. They are known to be DNA-binding agents as well they interact withother biological targets such as I and II DNA topoisomerase, telomerase, polymerase and protein kinase (Goodell et al., 2009;Kukowska-Kaszuba et al., 2011).
Quantum chemical descriptors have been extensively used in Quantitave Structure-Activity Relationship studies in biochemistry. Numerous reviews have been published on the applications of quantum chemical descriptors (Parthasarthi et al., 2004). The use of quantum chemical descriptors in the development QSAR has received attention due to reliability and versatility of prediction by these descriptors. For the calculation of the quantum chemical molecular descriptor used in QSAR studies, semi empirical methods such as AM1 and PM3 mainly have been used (Saeed and Elias, 2010;Saeed et al., 2010a;2010b). However, DFT method has been used recently for the prediction of physiochemical and biological properties of organic molecules (Shaik et al., 2010;Siu and Che, 2006).

MATERIALS AND METHODS
The studied acridines have been taken with their reactivity from literature (Hansch et al., 2001). Chemical structures and experimental biological activities are gathered in Table 1.
The general formula of the chemical structures of the studied compounds is shown in Fig. 1. Biological activities are presented as log 1/C. All geometries of the acridines are minimized with the semi-empirical RM1 Hamiltonian. Single point calculations have been made at the B3LYP/6-31G level with the RM1 geometry.  Linear regression analyses are performed to find the best correlation between various biological activity indices and the biological activities of the studied acridines. The values of the descriptors used to develop the Eq. 5 and the predicted activities from this equation are listed in Table 2.
In Eq. 3 another geometrical parameter, C14-N6 bond length, is included. R2 value for this model is of comparable value of that in Eq. 2.
n = 20, R 2 = 0.88, s= 0.317, F= 19.0 outliers: 4-Cl; 4-Me; 4-CH 2 CH(NH 2 )COOH In this model the decrease in the bond angle of C8-N9-C2 and bond length of C14-N6 will increase the activity of the acridines. This is also the case with µ and Ref. In contrast an increase in vWV will increase the activity.
The best models concerning the present study the two hepta-parametric equations 4-5. For Eq. 4: n = 20, R 2 = 0.93, s = 0.290, F = 27.2 outliers: 4-Cl; 4-CH 2 CH(NH 2 )COOH According to this equation, ε HOMO is of major rule and the negative value suggests that biological activity of acridines increases with a decrease in ε HOMO . A comparable rule is also clear for ∆ε, while vWV acts in the opposite direction. The predicted activities of the studied acridines as calculated by Eq. 5 are gathered in Table 2, in addition a comparison between observed and predicted values of log 1/C for acridines used in the development of Eq. 5 is shown in Fig. 2.
The presence of the outliers could be accounted for as a result of the possibility that the molecules may act by different mechanisms or interact with the receptor in different binding modes and due to the intrinsic noise associated with both the original data and methodological aspects involved in the construction of a QSAR model (Hansch et al., 2001).
The values of R 2 for the QSAR models (Eq. 1-5) range from 0.83-0.93 which suggest that these models explain 83-93% of the variance in the data (Polanski et al., 2006). In addition the smaller the value of s and the larger the value of F, the better the QSAR model. The values of s in the Eq. 1-5 range from 0.284-0.355, while the values of F range from 19.0-27.2 which are statistically significant at the 99% level. The values of R 2 , s and F suggest that the QSAR models (Eq. 1-5) are predictive and validate.

CONCLUSION
The study indicated that QSAR of biological activity represented by log 1/C of acridines can be modeled with density functional theory based quantum mechanical molecular descriptors. The regression equations developed in this study can explain 88-93% of the variance in the data. In addition s and F values support the validity of the models.