Survey of literatures exposed that organoantimony compounds show diversity in their biological activity [ 1,2,3,4,5,6,7,8]. They show their antitumor, antimicrobial (viz., anti-fungal and anti-leishmanial) and insecticidal (viz., contact, stomach, anti-feedant and acaricidal) activities mostly in +III and +V oxidation states [ 1]. We know that experimental determination of various activity viz., pharmacological, toxicological, biochemical as well as human health end points of any compound are time and wealth-consuming. Hence, mathematical models were, are and will be of important use to predict these activities [ 9]. Gap between experimental and theoretical measurement is now bridged by computer simulation techniques [ 10]. In our previous work anti-fungal and insecticidal activities of perfluorophenyl antimony(III) and antimony(V) chlorides were rescaled by us using mathematical model after experimental work and the results were exciting [ 1]. This boost us to draw mathematical models for rescaling anti-leishmanial activities of carboxylates and their antimony(III) complexes. The quantum chemical parameters used in this study were well described in our previous publications [ 11,12,13].

Carboxylates and their antimony(III) complexes listed inTable 1 are the study materials for the present study [ 14]. The IC₅₀ of these compounds were taken from the literature against five leishmanial strains viz., L. major, L. major (Pak), L. tropica, L. mex mex, and L. donovani (Table 2,Table 3,Table 4,Table 5). For prediction of biological activity (IC₅₀) of these compounds, multiple linear regression analysis has been performed on Project Leader Program associated with CAChe [ 15,16,17]. The quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 2,Table 3,Table 4,Table 5,Table 6 as dependent variables. For this the molecular modeling and geometry optimization of the all the eight compounds have been performed on workspace program of CAChe Pro software of Fujitsu by opting B88-PW91GGA energy functional with DZVP basis set in DFT method [ 18].

Leishmania is a parasitic protozoan. There are more than twenty species of this. These different species are morphologically indistinguishable, but they can be differentiated by isoenzyme analysis, molecular methods, or monoclonal antibodies [ 19]. They are responsible for the disease leishmaniasis. Leishmaniasis is transmitted by the bite of infected female phlebotomine sand flies. Here anti-leishmanial activities are divided into five sets on the basis of their five different species.

For sake of simplicity, the anti-leishmanial activity of each leishmanial species has been studied separately as described below.

Leishmania major

Prediction of anti-leishmanial of compounds listed inTable 1 against this strain in terms of 50% inhibition was scanned by using following equation:

In this case quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 2 as dependent variables. Various mathematical models were developed in which above model was selected as reliable. In this model (Eq.1) molecular electronegativity is the first descriptor and global softness is the second descriptor. r² is the correlation coefficient (values higher than 0.5 have predictive power) and r²_CV is the cross-validated correlation coefficient (values higher than 0.25 have predictive power). MLA is widely used method for building QSAR model. The coefficients of model have negative sign with respect to both χ and S. Thus, χ and S show inverse relationship with activity. A close examination of theTable table shows that there is little difference between the values of experimental and theoretical inhibitory activities as evident by their residual values (Δ).

Leishmania major (Pak)

Prediction of anti-leishmanial of compounds against this strain in terms of 50% inhibition was scanned by using following equation:

In this case quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 3 as dependent variables. Various mathematical models were developed in which above model was selected as reliable. In this model (Eq.2) dipole moment is the first descriptor and total energy is the second descriptor. The coefficients of model have positive sign with respect to both μ and E_T. Thus, μ and E_T show direct relationship with activity.

Leishmania tropica

Prediction of anti-leishmanial of compounds against this strain in terms of 50% inhibition was scanned by using following equation:

In this case quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 4 as dependent variables. Various mathematical models were developed in which above model was selected as reliable. In this model (Eq.3) ionization potential is the first descriptor and electron affinity is the second descriptor. The coefficients of model have positive sign with respect to I.P. and have negative sign with respect to E.A. Thus, I.P. shows direct relationship with activity, while E.A. shows inverse relationship with activity.

Leishmania mex mex

Prediction of anti-leishmanial of compounds against this strain in terms of 50% inhibition was scanned by using following equation:

In this case quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 5 as dependent variables. Various mathematical models were developed in which above model was selected as reliable. In this model (Eq.4) absolute hardness is the first descriptor and total energy is the second descriptor. The coefficients of model have negative sign with respect to η and have positive sign with respect to E_T. Thus, η shows inverse relationship with activity, while E_T shows direct relationship with activity.

Leishmania donovani

Prediction of anti-leishmanial of compounds against this strain in terms of 50% inhibition was scanned by using following equation:

In this case quantum chemical properties listed inTable 1 were used as independent variables and the experimental IC₅₀ of the compounds listed inTable 6 as dependent variables. Various mathematical models were developed in which above model was selected as reliable. In this model (Eq.5) ionization potential is the first descriptor and global softness is the second descriptor. The coefficients of model have negative sign with respect to both I.P. and S. Thus, I.P. and S show inverse relationship with activity.

The reliability of correlation between experimental activities and predicted activities are r² = 0.826, r²_CV = 0.426 (L. major,Table 2); r² = 0.905, r²_CV = 0.507 (L. major (Pak),Table 3); r² = 0.980, r²_CV = 0.932 (L. tropica,Table 4); r² = 0.781, r²_CV = 0.580 (L. mex mex,Table 5) and r² = 0.634, r²_CV = 0.376 (L. donovani,Table 6), and a comparison of the experimental values and the values obtained by theoretical calculations has been presented pictorially (Figure 1,Figure 2,Figure 3,Figure 4,Figure 5) that shows close resemblance. The study reflected that descriptors derived from DFT methods have sufficient reliability to understand quantitative structure-activity relationship and also to predict the activity of new complex of this series from theoretically derived properties within limited time by QSAR models.

The authors are thankful to Dr. O.P. Mishra, Ex.Principal, M.L.K. (P.G.) College, Balrampur, for providing the laboratory facilities to conduct the calculation.