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Review

Perturbation-Theory Machine Learning for Multi-Objective Antibacterial Discovery: Current Status and Future Perspectives

by
Valeria V. Kleandrova
,
M. Natália D. S. Cordeiro
and
Alejandro Speck-Planche
*
LAQV@REQUIMTE/Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(3), 1166; https://doi.org/10.3390/app15031166
Submission received: 15 November 2024 / Revised: 11 January 2025 / Accepted: 22 January 2025 / Published: 24 January 2025
(This article belongs to the Section Biomedical Engineering)
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Abstract

:
Antibacterial drugs (commonly known as antibiotics) are essential for eradicating bacterial infections. Nowadays, antibacterial discovery has become an imperative need due to the lack of efficacious antibiotics, the ever-increasing development of multi-drug resistance (MDR), and the withdrawal of many pharmaceutical industries from antibacterial discovery programs. Currently, drug discovery is widely recognized as a multi-objective optimization problem where computational approaches could play a pivotal role, enabling the identification of novel and versatile antibacterial agents. Yet, tackling complex phenomena such as the multi-genic nature of bacterial infections and MDR is a major disadvantage of most of the modern computational methods. To the best of our knowledge, perturbation-theory machine learning (PTML) appears to be the only computational approach capable of overcoming the aforementioned limitation. The present review discusses PTML modeling as the most suitable cutting-edge computational approach for multi-objective optimization in antibacterial discovery. In this sense, we focus our attention on the development and application of PTML models for the prediction and/or design of multi-target (multi-protein or multi-strain) antibacterial inhibitors in the context of small organic molecules, peptide design, and metal-containing nanoparticles. Additionally, we highlight future applications of PTML modeling in the context of novel drug-like chemotypes with multi-protein and/or multi-strain antibacterial activity.

1. Introduction

Bacterial infections have always been widely acknowledged as life-threatening medical conditions, being related to high morbidity and mortality, as well as ever-increasing economic costs in terms of medical treatment options. A 2022 epidemiological study reported the occurrence of 13.7 million infection-related deaths; more than half of these deaths involved 33 pathogenic bacteria [1].
Antibacterial agents have been essential for fighting and eradicating bacterial infections, but their discovery and development have been impeded mainly by two factors. On one side, current antibacterial agents/antibiotics exert their therapeutic activity by acting through single mechanisms of action. Therefore, they have become less effective due to the emergence and development of multi-drug resistance (MDR) [2]. It is important to highlight that MDR is a very complex biological phenomenon that has been increasing over time and has shown no signs of slowing down [3]. In this sense, MDR is now a very common phenomenon among both Gram-positive [4] and Gram-negative [5] bacteria, with the latter also exhibiting intrinsic MDR to current antibacterial agents/antibiotics [6]. On the other hand, it is now well known that antibacterial discovery has become a therapeutic area with a remarkably low lucrative value. As a result, many pharmaceutical companies are abandoning their antibacterial discovery projects, which seems to be associated with limited success and budget constraints [2,7]. This has led to the emergence of initiatives such as the Community for Open Antimicrobial Drug Discovery (CO-ADD) [8,9,10], whose purpose is to conduct a worldwide and free-of-charge high throughput screening of untested chemical libraries against a key panel of drug-resistant bacterial strains (E. coli, K. pneumoniae, Acinetobacter baumannii, P. aeruginosa, and methicillin-resistant S. aureus) [8,11]. In any case, searching for novel and versatile antibacterial agents capable of coping with the ever-increasing infections and development of MDR is an imperative need.
Computational approaches are widely recognized as pillars of the drug discovery process [12]. In the context of antibacterial discovery, pharmacophore modeling [13,14,15], molecular dynamic simulations [13,14,15,16,17,18], quantum mechanical methods [17,19,20], molecular docking [13,15,16,17,18,19,20,21,22], and in silico models based on machine learning techniques [18,22,23,24,25] continue to be at the forefront regarding the study and analysis of novel antibacterial agents. Yet, these computational approaches have one or more of the following major limitations. First, they usually focus on the modeling of very small datasets of chemically similar molecules with low structural variability, thus preventing a deeper and more insightful exploration of the chemical space to search for antibacterial agents. Second, physicochemical and structural interpretation is often insufficient, and therefore, it is not possible to establish adequate guidelines on the design of new chemotypes exhibiting antibacterial activity. Last and most important, it is well established that, as a process, drug discovery (and, in this context, the identification of novel and versatile antibacterial molecules) is a multi-objective optimization (MOOP) problem [26,27]. It is important to note that MOOP involves the identification of chemicals that simultaneously display potent activity (at both target-based and phenotypic levels), as well as reduced toxicity and adequate pharmacokinetic profiles [28]. All the computational approaches mentioned above have been almost uniquely applied to single-objective optimization, focusing solely on antibacterial activity against a single biological target (protein or bacterial strain); this is detrimental because it impedes the possibility of identifying versatile (multi-target and/or multi-strain) antibacterial agents capable of tackling MDR.
The perturbation-theory machine learning (PTML) approach has emerged to solve all the aforementioned limitations [29]. In this sense, PTML models can fuse chemical data with biological information at different levels of diversity and complexity; this characteristic confers PTML models the ability to apply MOOP in the sense of simultaneously predicting multiple biological profiles under dissimilar experimental conditions. Thus, PTML models have been applied to a plethora of different multidisciplinary fields such as antineoplastic agents [30,31,32,33,34,35], immunology research [36,37,38], toxicology [39,40,41], neurological disorders [42,43,44,45,46], molecular discovery against infectious diseases [47,48,49,50,51,52], and other relevant research areas [53,54]. This review discusses PTML modeling as a cutting-edge computational approach that can accelerate antibacterial discovery through the MOOP paradigm. In doing so, we focus our attention on highlighting the potentialities of the PTML models for the design and/or prediction of multi-protein or multi-strain inhibitors against pathogenic bacteria in the context of small organic molecules, bioactive peptides, and metal-containing nanoparticles (MCNPs). We also discuss the limitations of PTML models, provide recommendations to address these limitations, and envisage future applications of PTML modeling in the context of novel drug-like chemotypes with multi-protein and/or multi-strain antibacterial activity.

2. Main Aspects of PTML Models for MOOP

In general terms, PTML models can be viewed as multi-objective quantitative structure–activity relationship models, which means they predict molecular behavior based on chemical structure and can be optimized for multiple outcomes, such as potency and pharmacokinetic properties [29]. Following this, we summarize the main aspects that make PTML modeling a suitable approach for MOOP applied to drug discovery (Figure 1):
  • Within the MOOP paradigm, PTML models can be used to predict outcomes by simultaneously considering multiple objectives such as biological effects, targets, and assay protocols.
  • It is possible to physicochemically and structurally interpret PTML models.
  • The PTML modeling approach is highly adaptable, which enables its application to different chemistry realms, such as small organic molecules, peptides, and MCNPs.
We will now focus on giving more details on the three aspects mentioned above. We want to start by stating that the key element of PTML modeling is the application of the Box–Jenkins approach [29]. Let us consider any experimental condition as a combination of three aspects, namely measures of endpoints/biological effects, targets, and assay protocols. Each of these three aspects has multiple categories/labels. For instance, the aspects known as “targets” will contain multiple categories/labels corresponding to the names of different targets (microbial strains, cell lines, laboratory animals, etc.). The same line of thought can be applied to the other two aspects. The power of the Box–Jenkins approach relies on fusing the chemical information (characterized utilizing molecular descriptors) of the molecules with the biological information provided by the different aspects (and their multiple labels) of the experimental condition [29]. As a result, new numeric variables known as multi-label descriptors (MLDs) will be created, integrating both chemical data related to the structure of the molecules and biological information on various biological endpoints, targets, and assay protocols [29].
Depending on its purpose, a PTML model can be further subdivided into multi-target models for quantitative structure–activity relationships (mt-QSAR), multi-condition QSAR (mtc-QSAR), or multi-tasking quantitative structure–biological effect relationships (mtk-QSBER) [29]. In the case of mt-QSAR models, they can predict a single activity endpoint by simultaneously considering multiple targets. In the case of mtc-QSAR models, they can predict multiple activity endpoints against different activity-related targets. Notice that multi-target drug discovery can be considered as a special case of MOOP where one or more activity/potency endpoints can be predicted by a PTML (mt-QSAR or mtc-QSAR) model against different biomolecular targets (usually proteins). Finally, mtk-QSBER models represent the most advanced evolution of PTML modeling and can predict multiple in vitro and in vivo activity, toxicity, and pharmacokinetic endpoints by considering multiple targets and many assay protocols. For the case of simplicity, we will use the unified term PTML to refer to all models discussed in this review. When applied to antibacterial discovery, PTML models can be employed to simultaneously predict antibacterial activity endpoints (e.g., minimum inhibitory concentration, minimum bactericidal concentration, etc.) across different targets (bacterial proteins or strains) and many assay protocols (i.e., MTT, resazurin, and others). Additionally, PTML models can incorporate toxicity and pharmacokinetic data for molecules, even when these differ from those with reported antibacterial activity outcomes.
Currently, PTML models are interpretable. However, the interpretation of PTML models differs from other approaches, such as explainable artificial intelligence (XAI) [55,56,57,58]. Notice that XAI focuses on analyzing the contributions of each of the inputs (molecular descriptors) to the predictions performed by a model. In contrast, a PTML model will have a direct physicochemical and structural interpretation obtained by applying the fragment-based topological design (FBTD) approach [29,59]; this will lead to the design of novel molecules virtually exhibiting desirable biological profiles (potent activity, low toxicity, and/or adequate pharmacokinetic properties). We would also like to finish this subsection by saying that, in our experience, PTML models can, in principle, be applied to model biological profiles of a wide variety of chemical species. Although the main focus of PTML modeling has been on small organic molecules, in the upcoming subsections, we show that the bioactivity (in this context, antibacterial activity) of peptides and MCNPs can also assessed via PTML modeling.

3. Data and Statistical Performance of PTML Models for Antibacterial Discovery

This section aims to provide the necessary information in terms of chemical and biological data and statistical performance metrics associated with the PTML models in the context of antibacterial drug discovery. In this sense, chemistry-based and bioactivity data associated with small molecules (both natural products and those of synthetic origin) were retrieved from the online chemico-biological repository known as ChEMBL [60,61,62]. Furthermore, PTML models were also developed in the fields of antibacterial peptides and antibacterial nanoparticle discovery, for which chemical and biological data were extracted from DBAASP [63,64,65] and articles retrieved from the scientific literature, respectively. All the PTML models reported in the context of multi-target antibacterial discovery are classification models where linear discriminant analysis (LDA), artificial neural networks (ANN), Bayesian networks (BN), k-nearest neighbors (KNN), binary logistic regression (BLR), and random forests (RF) have been used as machine learning algorithms. Therefore, to unify the nomenclature when referring to the statistical quality and predictive power of the PTML models, we have used the symbology SI > vSI. Notice that SI refers to a statistical performance-based index such as sensitivity (Sens), specificity (Spec), or accuracy (Acc), while vSI is expressed in percentage. The symbology SI > vSI means that for a defined SI, its value was higher than vSI in both training and test series (comprising up to 80% and 20% of each dataset, respectively).

4. PTML Models: The Road to the Design and Prediction of Multi-Protein and/or Multi-Strain Antibacterial Inhibitors

4.1. PTML Models for Antibacterial Discovery of Small Organic Molecules

Small molecule drug discovery is the area with the largest number of reports on PTML modeling for discovering multi-protein/multi-strain inhibitors against pathogenic bacteria. Most of the PTML models have been created for one of two potential applications. One of them is the in silico prediction of antibacterial profiles, toxicity, and/or pharmacokinetics of investigational drugs or those approved by the Food and Drug Administration (FDA). The structures of these antibacterial drugs are shown in Figure 2.
The other application is the de novo design of new molecules virtually exhibiting potent multi-strain activities, low toxic effects, and adequate pharmacokinetic profiles. Following this, we will discuss the development of PTML models and their applications to the simultaneous predictions of multi-strain antibacterial activity, toxicity, and pharmacokinetics of wide-spectrum multi-strain investigational and FDA-approved drugs.
A series of three works reported the development of PTML models to speed up the discovery of multi-strain antimycobacterial agents. In the first of these investigations, the created PTML-LDA model was able to simultaneously predict phenotypic antituberculosis activity and in vivo toxicity against Mus musculus and Rattus norvegicus [66]. In this work, the dataset included 12,096 cases, with two of the four descriptors used as inputs in the PTML-LDA model being MLDs derived from the topological indices named bond-based spectral moments (SMs). The PTML-LDA model had Sens and Spec values above 91%. The second work, employing a dataset comprising 34,629 data points, applied PTML modeling to the simultaneous prediction of inhibitory multi-strain activity against different antimycobacterial strains, as well as in vivo toxicity effects and pharmacokinetic properties [67]. Here, the PTML model, which was built from six MLDs based on SMs, had Acc > 94%. This PTML model could calculate the quantitative contributions of different molecular fragments to the multi-strain antimycobacterial activity, toxicity, and pharmacokinetics. This model was also used to predict multiple (experimentally determined) activity, toxicity, and pharmacokinetic endpoints of bedaquiline, which was formerly known as TMC-207 (Figure 2). The PTML model could correctly predict all the aforementioned biological endpoints. The third work was applied to the early discovery of multi-strain inhibitors of M. tuberculosis under 24 experimental conditions (combinations of different biological endpoints, diverse M. tuberculosis strains, and many assay protocols containing multiple assay times) [68]. This PTML model, an ensemble of ANNs, was created using 1571 cases and twelve MLDs derived from atom-based local stochastic quadratic indices. This model had Acc > 85%. In a virtual screening scenario, the PTML model was applied to the prediction of the multi-strain antituberculosis activity of 8898 agency-regulated molecules (investigational and FDA-approved drugs, as well as chemicals with other uses); the PTML model could correctly identify several drugs with proven antituberculosis activity, including the multi-strain antituberculosis drug macozinone (Figure 2).
The discovery of multi-strain inhibitors against Gram-positive bacteria was also explored by several works that developed PTML models [69,70,71,72]. The most promising of these investigations intended to accelerate the search for multi-strain antibacterial inhibitors to prevent the emergence of both acquired and transferred resistance among Gram-positive cocci (Staphylococcus spp., Streptococcus spp., and Enterococcus spp.) [72]. Towards this end, a dataset comprising 48,874 cases was used to create and validate a PTML-LDA model containing seven MLDs derived from SMs. This model successfully predicted in vitro and in vivo endpoints associated with multi-strain anti-cocci activity, toxicity, and pharmacokinetics. 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 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 (Ki) and half-maximal inhibitory concentration (IC50). 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]. Here, the most promising study used 169,130 data points containing experimental outcomes from more than 300 antibacterial activity endpoints, >90 Gram-positive and Gram-negative pathogens, and more than 40 bacterial MRNs [79]. The PTML model obtained in this investigation used seven descriptors as inputs, with four of them being MLDs based on Shannon entropies; the PTML model achieved Sens > 88% and Spec > 90%. This PTML model was applied to the prediction of the multi-strain antibacterial activity of several experimentally tested terpenes, confirming the potential of these natural products to be used as starting point molecules for the future discovery of multi-strain antibacterial inhibitors against MDR bacteria.

4.2. PTML Modeling for Virtual Design of Versatile Antibacterial Peptides

There is a plethora of reports devoted to accelerating the search for antibacterial peptides [80,81,82,83,84,85,86,87]. However, most of these works are limited to relatively short peptides (usually ≤50 amino acids in the peptides’ sequences), and the antibacterial activity is remarkably dependent on the composition of the peptides, particularly the presence and amount of positively charged amino acids (e.g., lysine, arginine, etc.) [80,81,82,83,84,85,86,87]. Furthermore, antibacterial activity is often predicted generically without specifying the bacterial strains targeted by the peptides [80,84,85,86,87]. With such limitations, it is not possible to fully exploit the chemical diversity of peptides. In addition, although the presence and number of positively charged amino acids are beneficial to the increase of antibacterial activity, there is a detrimental effect in mammal cell lines (e.g., induction of hemolysis in erythrocytes) [88,89].
In this sense, there have been two investigations focused on the use of PTML modeling for the design and prediction of antibacterial peptides that overcome the aforementioned disadvantages (Figure 4).
The first of these studies developed a PTML model to identify bioactive peptides as multi-strain inhibitors of Gram-positive bacteria [90]. Before generating the PTML model, a dataset containing 2488 cases was considered. By using six MLDs based on Kier–Hall connectivity indices derived from the peptides’ amino acid sequences and LDA, the PTML achieved Sens > 92% and Spec > 94%. This work implemented for the first time two approaches that permitted the calculation of the quantitative contribution of an amino acid (in a defined position of the peptide’s amino acid sequence) to the antibacterial activity across multiple bacterial strains. This approach provided deeper theoretical insights into the structural modifications that could enhance a peptide’s multi-strain antibacterial activity.
The second work was based on the creation of a PTML-LDA model to design antibacterial peptides as multi-strain inhibitors [91]. The dataset used to develop the model included 3592 cases of peptides with assay information focused on activity against Gram-negative pathogens, cytotoxicity in diverse mammalian cell lines, and hemotoxicity in erythrocytes from various animal species. The four MLDs used as inputs for the PTML-LDA model were derived from the Broto–Moreau autocorrelations calculated from the peptides’ amino acid sequences. For this PTML-LDA model, Acc > 97% was obtained. A similar procedure to the one described in the first report mentioned above was implemented for the calculation of quantitative contributions of amino acids to the increase in the activity and the diminution of the cytotoxicity and hemotoxicity. The physicochemical and sequence-based interpretation of the PTML-LDA model enabled the design of ten new peptides; these were predicted by the PTML-LDA model to display high multi-strain activity, as well as reduced cytotoxicity and hemotoxicity.

4.3. Accelerating Multi-Strain Antibacterial Discovery of Metal-Containing Nanoparticles via PTML Modeling

The role of MCNPs in drug research has been discussed in a series of recent reports, with applications in drug delivery, direct therapeutic action, or diagnostic agents [92,93,94,95,96]. In the context of multi-target (multi-strain) antibacterial drug discovery, MCNPs have demonstrated great potential due to their unique mechanisms of action, which include (but are not limited to) the adherence to the surface of the bacterial membranes/cell walls, cell penetration and posterior interaction with cell organelles and biomolecules, and induction of oxidative stress and cytotoxicity-related processes [97]. In the discovery of MCNPs for multi-strain antibacterial solutions, PTML modeling has prioritized the search for seemingly potent and versatile antibacterial MCNPs by optimizing experimental aspects such as nanoparticle size and external morphology (shape), the presence and chemical structure of the coating agents and/or antibacterial molecules to synergistically enhance antibacterial activity, and the chemical composition of the metal-containing cores (Figure 5).
The first of these works on multi-strain antibacterial discovery reported a pair-based PTML model to predict the inhibitory activity of MCNPs against both Gram-positive and Gram-negative bacterial strains [98]. This work considered not only the experimental aspects mentioned but also other elements, such as the conditions employed to measure the nanoparticle size and the assay times under which the different bacterial strains were exposed to MCNPs. The dataset used here involved 69,231 cases (MCNPs–MCNPs pairs), and through the use of six MLDs (derived from physicochemical properties and topological indices), the pair-based PTML model achieved Sens > 98% and Spec > 97%. To demonstrate the usefulness in prioritizing the identification of MCNPs with multi-strain antibacterial profiles, the pair-based PTML model was employed to predict a previously tested copper–silver nanoalloy of different sizes and chemical compositions. The pair-based PTML model was applied to predict the multi-strain antibacterial activity of a previously tested copper–silver nanoalloy with varying sizes and chemical compositions.
Another work was developed to enable the identification of molecule–MCNP antibacterial combinations [99]. This study involved a very large dataset containing more than 165,000 and 300 assays performed on organic molecules and MCNPs, respectively. The antibacterial activity endpoints were determined for multiple pathogenic bacterial strains. The MLDs encompassed all the experimental aspects mentioned in the first work, plus additional elements associated with the chemical structures of the organic molecules present in the molecule–nanoparticle combinations. Different PTML models based on LDA, ANN, BN, and KNN were created; all the PTML models exhibited Sens > 73% and Spec > 88%. Due to its simplicity combined with good statistical performance, the PTML-LDA model was chosen to perform different simulations, including one with a prediction accuracy of 100% for 80 molecule–nanoparticle antibacterial combinations.
A third report was carried out to search for MCNPs with multi-strain antibacterial activity by building diverse PTML models [100]. The dataset used in this work was formed by 5327 cases containing assays of 300 experimentally tested MCNPs against at least 1 out of 34 bacterial strains. As in the other reports mentioned above, the present research also considered multiple experimental aspects (coatings, measures of activity endpoints, etc.). Using MLDs derived from Shannon entropy, the best linear PTML model, based on BLR, achieved Sens > 79% and Spec > 99%. Among non-linear models, the PTML-RF model outperformed others, achieving Sens and Spec values above 98%. A peculiarity of this investigation is that the information on the bacterial strains was numerically introduced in the PTML models in the form of bacterial metabolic reaction networks (MRNs). This factor enabled the prediction of the multi-strain antibacterial activity of MCNPs against new bacterial strains not present in the original dataset used to build the PTML models.
A fourth investigation combined data from the second and third reports mentioned above; the purpose was to optimize the search for molecule–MCNP antibacterial systems [101], where information on bacterial strains was also introduced as bacterial MRNs. Here, PTML-LDA and PTML-ANN models were generated from a dataset formed by more than 160,000 cases and MLDs based on Shannon entropies. The PTML-LDA model exhibited Sens > 79% and Spec > 89%, while for the PTML-ANN models, values higher than 94% were obtained for both Sens and Spec. The PTML-LDA model was selected to simulate more than 140,000 data points, which involved 102 experimentally determined molecule–MCNP antibacterial systems and many diverse bacterial MRNs of wild-type and putative MDR bacterial strains. These results suggest that PTML modeling is an effective computational approach for MDR surveillance.

5. Future Perspectives of PTML Modeling for Antibacterial Discovery

A recent review has been reported, containing detailed information on how some of the current antibacterial drugs act through different multi-target mechanisms of action [102]. However, the fact that none of the antibacterial agents mentioned in this report have been able to stop the rise of MDR indicates (a) their limited effectiveness against biomolecular bacterial targets (proteins) or biochemical pathways and (b) their chemical structures, which rely on limited chemotypes, enabling bacterial pathogens to adapt. All the sections discussed until now demonstrate the potentialities of PTML modeling in the context of MOOP for antibacterial discovery. Therefore, here we offer four elements that may improve the impact of PTML modeling toward the in silico prioritization/generation (and future experimental validation) of versatile antibacterial agents.
First, as discussed throughout the different subsections of the present review, PTML models have been applied to the simultaneous prediction of multi-target (multi-protein and/or multi-strain) antibacterial activity in the context of small organic molecules, bioactive peptides, and MCNPs. While these results open new horizons for multi-target antibacterial discovery, many chemistry domains remain unexplored and could constitute novel sources of multi-target antibacterial discovery. In this sense, PTML modeling could be applied to identify or design multi-target antibacterial agents from chemical classes such as micro-ribonucleic acids, aptamers, and dendrimers; these chemical families have emerged as novel sources of antibacterial agents [103,104,105,106]. Furthermore, it could facilitate the discovery of hybrid chemotypes containing one or more moieties from these different chemical families.
A second aspect is related to the potential of the PTML models to prioritize the search for multi-target/multi-strain antibacterial molecules. In the context of virtual screening, PTML models have the advantage of simultaneously predicting multiple multi-target antibacterial activity endpoints, as well as toxicity measures and pharmacokinetic profiles. However, as it occurs with any other computational approach or model, the predictions will be accurate to a certain extent because the chemical space contained in the datasets used to create the PTML models (although there can be tens or hundreds of thousands of data points/cases) will still be considerable smaller than the chemical space to be virtually screened. In this sense, in addition to the potential of performing virtual screening, we recommend the application of PTML models as tools for de novo design. This can be accomplished by applying the FBTD approach to the PTML models; FBTD enables the direct physicochemical and substructural interpretation of the MLDs (derived from topological indices) used as inputs in the PTML models [29,59]. Following these interpretations, it is possible to quantitatively analyze the contribution of many molecular fragments to multiple endpoints and subsequently connect/fuse the most suitable one to design new molecules with the desired biological profiles [29,59]. In the context of multi-target antibacterial discovery, the application of FBTD to PTML models would enable the rational design of molecules virtually exhibiting potent multi-target (multi-protein and multi-strain) inhibitory activity against different bacterial pathogens, as well as decreased toxicity and adequate pharmacokinetics. To the best of our knowledge, reference [77] is the first and only work reported in this area, which means that the potentialities of FBTD in MOOP for antibacterial discovery remain to be fully exploited.
Third, although PTML models have been able to integrate chemical and antibacterial data at different levels of diversity and complexity, the availability of clinical data is a limiting factor preventing PTML models from reaching their full applicability. If possible, we recommend researchers from academia and the industrial sector (since the latter may not want to invest further in antibacterial drug discovery) share their clinical data based on both efficacy and safety. Notice that we are not saying that clinical data are not being shared; however, more efforts should be made in this direction. In that way, it could significantly enhance the impact on antibacterial discovery, from in vitro assays to in vivo preclinical studies and clinical trials.
Fourth, the previous subsections have shed light on the potentialities of PTML models as tools to perform both virtual screening and de novo design of antibacterial chemicals under multiple experimental conditions. However, we recommend the use of more experimental data on antibacterial activity predicted by the PTML models. In addition to further validating PTML model predictions and confirming their utility as MOOP tools for antibacterial discovery, it will also accelerate the identification and design of novel, versatile molecular entities with multi-protein and multi-strain antibacterial activity.
Last, we would like to highlight that, given the advantages of PTML modeling over all the computational approaches mentioned in this work, there is a great need for computational tools capable of implementing PTML models for different purposes in antibacterial drug discovery and beyond. In this sense, at present, two software packages, QSARCo [107] and QSAR-Co-X [108], are available for the fully automated generation of PTML models. Both programs include modules for model development, statistical validation, and virtual screening of external datasets. Nevertheless, it is important to highlight that when it comes to developing PTML models, these tools incorporate only a limited portion of the mathematical framework associated with the Box–Jenkins approach (outlined in Section 2 as the foundation of PTML modeling). Therefore, as PTML modeling faces challenges such as handling larger datasets and predicting multiple endpoints simultaneously in antibacterial drug discovery and other fields, it becomes crucial to develop new software or update existing platforms. This will ensure the comprehensive automation of PTML model implementation while avoiding a significant increase in computational resource requirements.

6. Conclusions

Experimental and computational approaches should focus on identifying/designing new and biologically active chemotypes with the ability to overcome MDR. In this sense, computational approaches for MOOP in antibacterial discovery can accelerate the search for promising therapeutic solutions against infections caused by pathogenic bacteria while also diminishing the risk of the emergence of antibiotic resistance. Such a challenge of searching for effective antibacterial agents should be accomplished by PTML modeling, which seems to be particularly suited for both virtual screening and de novo molecule generation in MOOP scenarios associated with antibacterial discovery. Thus, PTML modeling could play an essential role in guiding the identification of multi-target/multi-strain inhibitors for antibacterial discovery through multiple stages.

Author Contributions

Conceptualization, A.S.-P.; methodology, A.S.-P.; software, A.S.-P. and V.V.K.; validation, A.S.-P.; formal analysis, A.S.-P.; investigation, A.S.-P., V.V.K. and M.N.D.S.C.; resources, A.S.-P., V.V.K. and M.N.D.S.C.; writing—original draft preparation, A.S.-P., V.V.K. and M.N.D.S.C.; writing—review and editing, A.S.-P.; visualization, A.S.-P. and V.V.K.; supervision, A.S.-P.; project administration, A.S.-P. and V.V.K.; funding acquisition, M.N.D.S.C. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the Foundation for Science and Technology/the Ministry of Science, Technology and Higher Education of the Government of Portugal through grant UIDB/50006/2020.

Conflicts of Interest

The authors confirm that there are no conflicts of interest.

Abbreviations

AccAccuracy
ANNArtificial neural networks
BLRBinary logistic regression
BNBayesian networks
ChEMBLChemogenomic database from the European Molecular Biology Laboratory
CO-ADDCommunity for Open Antimicrobial Drug Discovery
DBAASPDatabase of antimicrobial activity and structure of peptides
FBTDFragment-based topological design
FDAFood and Drug Administration
IC50Half-maximal inhibitory concentration
KiInhibition constant
KNNK-nearest neighbors
LDALinear discriminant analysis
MCNPsMetal-containing nanoparticles
MBCMinimum bactericidal concentration
MDRMulti-drug resistance or multi-drug resistant
MICMinimum inhibitory concentration
MLDsMulti-label descriptors
MOOPMulti-objective optimization
mt-QSARMulti-target quantitative structure–activity relationships
mtc-QSARMulti-condition quantitative structure–activity relationships
mtk-QSBERMulti-tasking model for quantitative structure–biological effect relationships
PTMLPerturbation-theory and machine learning
RFRandom forests
SensSensitivity
SIStatistical index
SMsBond-based spectral moments
SpecSpecificity
vSINumeric value for a particular statistical index
XAIExplainable artificial intelligence

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Figure 1. Main steps leading to the development and application of a PTML model for antibacterial discovery.
Figure 1. Main steps leading to the development and application of a PTML model for antibacterial discovery.
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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.
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.
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Figure 3. General structures of the molecules that were designed by applying the FBTD approach to the PTML model. The designed molecules were predicted to virtually exhibit potent multi-strain antibacterial activity, low toxicity, and suitable pharmacokinetic properties. Here, X1 = –OH, –CN, –NH2, or –OCH3; X2 = –OH, –CN, or –NH2; X3 = –OH or –NH2; Y1 = –COOH; Y2 = –OH; Z1 = –OH; Z2 = –NH2.
Figure 3. General structures of the molecules that were designed by applying the FBTD approach to the PTML model. The designed molecules were predicted to virtually exhibit potent multi-strain antibacterial activity, low toxicity, and suitable pharmacokinetic properties. Here, X1 = –OH, –CN, –NH2, or –OCH3; X2 = –OH, –CN, or –NH2; X3 = –OH or –NH2; Y1 = –COOH; Y2 = –OH; Z1 = –OH; Z2 = –NH2.
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Figure 4. Summarized workflow on PTML modeling for the discovery of multi-strain antibacterial peptides. For more information on details steps, please check Figure 1.
Figure 4. Summarized workflow on PTML modeling for the discovery of multi-strain antibacterial peptides. For more information on details steps, please check Figure 1.
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Figure 5. Identification of multi-target MCNPs via PTML modeling. The inhibitory activity at 50% (IC50), minimum inhibitory concentration (MIC), and minimum bactericidal concentration (MBC) are used as measures of antibacterial activity.
Figure 5. Identification of multi-target MCNPs via PTML modeling. The inhibitory activity at 50% (IC50), minimum inhibitory concentration (MIC), and minimum bactericidal concentration (MBC) are used as measures of antibacterial activity.
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Kleandrova, V.V.; Cordeiro, M.N.D.S.; Speck-Planche, A. Perturbation-Theory Machine Learning for Multi-Objective Antibacterial Discovery: Current Status and Future Perspectives. Appl. Sci. 2025, 15, 1166. https://doi.org/10.3390/app15031166

AMA Style

Kleandrova VV, Cordeiro MNDS, Speck-Planche A. Perturbation-Theory Machine Learning for Multi-Objective Antibacterial Discovery: Current Status and Future Perspectives. Applied Sciences. 2025; 15(3):1166. https://doi.org/10.3390/app15031166

Chicago/Turabian Style

Kleandrova, Valeria V., M. Natália D. S. Cordeiro, and Alejandro Speck-Planche. 2025. "Perturbation-Theory Machine Learning for Multi-Objective Antibacterial Discovery: Current Status and Future Perspectives" Applied Sciences 15, no. 3: 1166. https://doi.org/10.3390/app15031166

APA Style

Kleandrova, V. V., Cordeiro, M. N. D. S., & Speck-Planche, A. (2025). Perturbation-Theory Machine Learning for Multi-Objective Antibacterial Discovery: Current Status and Future Perspectives. Applied Sciences, 15(3), 1166. https://doi.org/10.3390/app15031166

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