Application of graph theory: prediction of glycogen synthase kinase-3 β inhibitory activity of thiadiazolidinones as potential drugs for the treatment of Alzheimer's disease

The relationship of Wiener's index, a distance-based topological descriptor; Zagreb group parameter, M1, an adjacency-based topological descriptor and eccentric connectivity index,an adjacency-cum-distance based topological descriptor with the glycogen synthase kinase-3 β inhibitory activity of thiadiazolidinones has been investigated. A training set comprising 28 analogues of substituted thiadiazolidinones was selected for the present investigations. The values of the Wiener's index, Zagreb group parameter, and eccentric connectivity index for each of 28 analogues comprising the data set were computed. Resulting data was analyzed and suitable models developed after identification of active ranges. Subsequently, biological activity was predicted for each analogue involved in the data set using these models, which was then compared with the reported glycogen synthase kinase-3 β inhibitory activities. Accuracy of prediction was found to vary from a minimum of ∼83% for model based on Zagreb group parameter to a maximum of ∼87% for model based on Wiener's index.