## 3 Results and Discussion
### Fragment-Based Topological Design of Virtually Versatile Anti-Lung-Cancer Molecules  
As mentioned above, PTML-MLP models have also been applied to perform fragment-based topological design (FBTD) of new molecules virtually exhibiting desired activity, reduced toxicity, and/or adequate pharmacokinetic profiles [35; 39; 46; 63]. To do so, two aspects are required: (a) the physicochemical and structural interpretations of the \(D[GBI]ej\) descriptors, and (b) the design of new molecules based on the physicochemical and structural interpretations of the \(D[GBI]ej\) descriptors. To apply the first of the two aforementioned aspects, we rely on the analysis of the significance of each \(D[GBI]ej\) descriptor present in the PTML-MLP model. In this sense, we conducted a global sensitivity analysis (Figure 1). It is important to highlight that global sensitivity analysis enables the calculation of the sensitivity values (\(SVs\)). Notice that \(SVs\) rate the importance of the models' input variables [68]. When applied to our PTML-MLP model, the \(SVs\) are quantitative measures of the relative importance of the \(D[GBI]ej\) descriptors (inputs); the higher the \(SV\) for a \(D[GBI]ej\) descriptor, the greater its information content and discriminatory power. This means that the physicochemical properties and structural moieties characterized by the \(D[GBI]ej\) descriptors with the highest \(SVs\) are the ones with the greatest importance in the molecules present in the dataset used to build the PTML-MLP model. Consequently, such physiochemical properties and structural moieties should also be present in any designed molecule. When physicochemically and structurally interpreting the \(D[GBI]ej\) descriptors present in the PTML-MLP model, it is important to emphasize the following detail. If one observes Equations (1) and (2), it will be easy to deduce that \(D[GBI]ej\) descriptors conserve the same type of physicochemical and structural information as the \(GBI\) indices (\(TDs\) and \(NTDs\)) from which they originated. Consequently, by mathematical definition, those \(D[GBI]ej\) descriptors derived from the bond-based spectral moments (\(MGBI03\), \(MGBI04\), \(MGBI07\), \(MGBI08\), \(MGBI09\), \(MGBI14\), and \(MGBI15\)) can describe the presence of multiple \(SG\)/generic fragments and how the different physicochemical properties are concentrated in those \(SG\)/generic fragments [69; 70; 71]. They will also be able to contain information regarding important 3D aspects such as dihedral angles [72]. The \(D[GBI]ej\) descriptors derived from atom-(\(MGBI05\) and \(MGBI10\)) and bond-based (\(MGBI01\), \(MGBI02\), \(MGBI06\), \(MGBI11\), \(MGBI12\), and \(MGBI13\)) connectivity indices characterize the presence of specific \(SG\)/generic fragments [73; 74; 75]. However, the key difference is  
Figure 1: Relative importance of the \(D[GBI]ej\) descriptors estimated by their \(SVs\). The codes of the \(D[GBI]ej\) descriptors are the same as in Table 1.  
in terms of the 3D properties these descriptors characterize; while \(D[GBI]ej\) descriptors derived from the atom-based connectivity indices are measures of molecular accessibility (the ability of a molecule to interact with the surrounding medium) [76], the ones derived from the bond-based connectivity indices account for the molecular volume [77]. Altogether, the \(D[GBI]ej\) descriptors used to generate the PTML-MLP model characterize the presence and frequency of different \(SG/\)generic fragments, which characterize the presence of different functional groups and/or substructural features in the molecules (Figure 2). At the same time, Table 4 depicts different aspects of the present in the PTML-MLP model. One of these aspects is how the \(D[GBI]ej\) descriptors should vary their values to increase the anti-lung-cancer activity. Thus, for each \(D[GBI]ej\) descriptor, two means were calculated from the training set: one for molecules correctly classified as active and another determined for molecules correctly classified as inactive [35; 46; 63].