## 3 Data and Statistical Performance of PTML Models for Antibacterial Discovery
### PTML Models for Antibacterial Discovery of Small Organic Molecules
The PTML-LDA model achieved _Sens_ and _Spec_ values > 92% and enabled the estimation of the quantitative contributions of different molecular fragments (e.g., functional groups, rings, aliphatic chains, etc.) to all the biological endpoints under study. In  
Figure 2: Chemical structures of several wide-spectrum, FDA-approved, and investigational antibacterial drugs; the multi-strain antibacterial activities, toxic effects, and/or pharmacokinetic properties of these drugs were correctly predicted by some of the PTML models discussed in this work. a simulation experiment, the PTML-LDA model could correctly predict different multi-strain activity, toxicity, and pharmacokinetic profiles of the wide-spectrum (investigational) antibacterial drug JNJ-Q2 (Figure 2) at _in vitro_ and _in vivo_ levels. Several studies have also employed PTML models for multi-strain antibacterial discovery against Gram-negative pathogens [73; 74; 75]; these models were then employed to validate the potent multi-strain antibacterial activity, low toxicity, and suitable pharmacokinetics of FDA-approved drugs such as delafloxacin (Figure 2). However, here, we will focus on two works that offered specific insights regarding the physicochemical properties and structural features that may be required to enable the identification/design of novel molecules virtually displaying multi-target (multi-strain inhibitory) antibacterial activity against Gram-negative bacterial strains. The first of these works was devoted to the generation of a PTML-LDA model for the simultaneous prediction of multi-protein inhibitors against biomolecular targets present in Gram-negative bacteria [76]. In this investigation, 4286 cases were used where each molecule had been experimentally tested against at least 1 out of 123 proteins belonging to Gram-negative pathogens and by considering two different activity endpoints, namely inhibition constant (K\({}_{\text{i}}\)) and half-maximal inhibitory concentration (IC\({}_{50}\)). In this study, different labels of assay protocols were also considered. The PTML-LDA model, which was based on ten _MLDs_ derived from the probabilistic atom-based quadratic indices, exhibited _Sens_ and _Spec_ values above 98%. The rigorous interpretation of the _MLDs_ in the PTML-LDA model enabled the assessment of physicochemical properties and substructural moieties responsible for the multi-protein inhibitory profiles. The other work intended to create a PTML model to be employed as a tool for the _de novo_ design of new molecules virtually exhibiting multi-strain inhibitory activity against different Gram-negative bacteria, as well as reduced toxicity and suitable pharmacokinetics [77]. In this research, a dataset comprising 46,229 cases was used, and different biological (activity, toxicity, and pharmacokinetic) endpoints were measured against multiple targets (e.g., proteins, bacterial strains, cell lines, etc.) and across diverse assay protocols. The PTML model used six _MLDs_ (derived from probabilistic quadratic indices) as inputs, achieving _Acc_ > 97%. The FBTD approach was applied to the physicochemical and structural interpretation of the six _MLDs_ of the PTML model. This led to the retrieval and analysis of several molecular fragments, which were assembled (using the aforementioned interpretations as guidelines) to design new molecules (Figure 3). It should be highlighted that the designed molecules, which exhibited acceptable drug-likeness, were predicted by the PTML model to display potent multi-strain antibacterial activity, low toxic effects, and enhanced pharmacokinetic properties. Finally, we would like to conclude this subsection with recent research, which intended to advance the search for novel chemicals with multi-strain antibacterial activity against both Gram-positive and Gram-negative pathogens [78; 79].