Over time, there has been a significant shift in global dietary habits and lifestyle standards. Poor dietary choices, irregular eating patterns, extended working hours, and sedentary behaviors have contributed to a trend towards an unhealthy lifestyle . This shift has resulted in a rise in chronic degenerative diseases among the elderly population. These diseases encompass a diverse range of conditions characterized by the gradual deterioration of bodily structures and functions . Although the exact causes leading to these diseases remain unidentified, there is evidence that oxidative damage plays a crucial role in the progressive neuronal cell death, particularly through the generation of reactive oxygen and nitrogen species . In this regard, Alzheimer’s and Parkinson’s diseases are the most severe and untreatable conditions. Conventional drug treatment methods, such as acetylcholinesterase inhibitor drugs, often encounter obstacles due to their inadequate solubility, limited bioavailability, and inability to effectively penetrate the blood–brain barrier (BBB) . Therefore, there is an urgent need to focus on the advancement of novel neurodegenerative disease drugs (NDDs) . The major obstacle encountered by NDDs is the selectivity of the BBB, which limits the number of therapeutic substances able to reach the brain in order to induce a positive effect. Recently, many efforts have been made to develop systems that facilitate the passage of NDDs through the BBB.

Interestingly, nanoparticle (NP) systems are gaining increasing interest among the possible nanomedicine strategies for NDD transport to the central nervous system (CNS) . For simplicity, we are going to call them nanoparticle neuronal diseases drug delivery systems (N2D3Ss). N2D3Ss have the ability to protect NDDs from chemical and enzymatic degradation, direct the active compound towards the target site with a substantial reduction of toxicity for the adjacent tissues, and help the NDDs to pass physiological barriers, increasing bioavailability without resorting to high dosages . Therefore, researchers are studying and developing new treatment approaches that use N2D3Ss for diagnosis and treatment .

Also, over the last few years, artificial intelligence/machine learning (AI/ML) models have been applied successfully to solve problems in different disciplines, especially in the interface of chemistry and ND research . In this regard, we consider AI/ML to be helpful in the development of N2D3Ss to select the most efficient combination of NP and drug, taking into account properties regarding chemical absorption, distribution, metabolism, excretion, and toxicity (ADMET), and the biological activity regarding NDs . Nevertheless, there is relatively limited experimental data on NPs reported in the scientific literature in comparison to drugs, which increases the difficulty of designing systems based on AI/ML techniques.

An additional essential downside of developing N2D3Ss with AI/ML techniques is the great complexity of the data to be explored. As a result, N2D3S development by the additive approach requires an AI/ML technique to achieve multioutput and multilabel classification . In addition, the AI/ML technique includes a pre-processing step to perform information fusion (IF) of the preclinical NDD assay and NP cytotoxicity datasets. Nevertheless, most of the AI/ML methods reported to date only consider the structural/molecular descriptors of the NDDs or NPs as input. Therefore, these methods exclude completely non-structural parameters, specifically experimental conditions of the assays, in order to list NDD or NP labels. Consequently, the resulting model cannot predict multioutput properties and/or labels such as different organisms or cell lines . Sizochenko et al. reported a new methodology for NP safety estimation in different organisms . Predicting NP safety instead of biological activity has been the objective of other studies as well .

As a new strategy to tackle this problem, González-Díaz et al. have developed IFPTML, a multioutput, and input-coded multilabel ML method, which stands for information fusion (IF) + perturbation theory (PT) + machine learning (ML) algorithm . In recent investigations, the IFPTML model has shown to be a powerful tool in molecular sciences and NDD research for the analysis of big datasets that include both structural and non-structural parameters. Application examples are drug screening, protein targeting, the prediction of coated-NP drug release systems , multitarget networks of neuroprotective compounds for a theoretical study of new asymmetric 1,2-rasagiline carbamates , a TOPS-MODE model of multiplexing neuroprotective effects of drugs, an experimental/theoretical study of new 1,3-rasagiline derivatives potentially useful in neurodegenerative diseases , as well as QSAR and complex networks in pharmaceutical design, microbiology, parasitology, toxicology, cancer, and neurosciences . Furthermore, this new model also has been used for very similar systems to this research work such as NP systems, taking into account NP structure and coating agents, synthesis conditions of NPs and loaded drugs, cancer co-therapy drugs, or assay conditions . Here we developed IFPTML models for the proposal of N2D3Ss containing NDD and NP components.

Figure 1: Detailed information processing workflow of the IFPTML models. Steps 2.1 and 2.2: data collection (ChEMBL dataset of NDDs and NP cytotoxicity dataset); step 2.3: data pre-processing and information fusion (NP and NDD assays); step 2.4: definition of objective and reference functions; step 2.5: calculation of the perturbation theory operator (PTO).

Figure 2: Connection of the current IFPTML model to other PTML models developed by our research group.

In this study, we utilized the IFPTML model to investigate N2D3Ss, encompassing assays of ADs and preclinical assays for NPs. To achieve this, we conducted the IF of AD and NP databases, curated the data, combined the objective and reference functions, and calculated the PTO.

First, we described and acquired the objective value in order to design the IFPTML model for N2D3S. We defined the target function by applying the vectors of descriptors for all cases Dk to use as the input variable in the ML model. The target function is commonly achieved by a mathematical conversion of the original theoretical or observed feature of the scheme under analysis . In this IFPTML model, it includes two groups of observed values, specifically vij(cd0) and vnj(cn0). In addition, it contains two types of input vectors, Ddk and Dnk, for the preclinical NDD and NP assays, respectively. Moreover, in this dataset was a large number of different biological parameters cd0 and cn0. For example, there are properties such as half the maximum inhibitory concentration (IC50 (nM)), half the maximum effective concentration (EC50 (nM)), or the lethal concentration of a substance for an organism (LC50 (nM)). Another difficulty is that the majority of vij(cd0) and vnj(cn0) values collected are numbers with decimals. Furthermore, in order to acquire the optimum N2D3S, we prioritize some properties and deprioritize others. In this context, we introduced a “desirability” parameter to tackle this problem

The desirability value was established as d(cd0) = 1 or d(cn0) = 1 when the value of vij(cd0) or vnj(cn0) needs to be maximized, otherwise d(cd0) = −1 or d(cn0) = −1. The different NDD and NP properties/characteristics possess a large number of designations or labels cd0 and cn0, respectively, and increase the unreability of the data, making it more laborious to build a regression model. For example, in context of a specific case, biological activity parameters cd0 with d(cd0) = 1 are Bmax (fmol/mg), the total number of receptors expressed in the same units, activity (%), and Cp (nM). Whereas parameters with d(cd0) = −1 are, for example, EC50 (nM), IC50 (nM), and Imax (%). To address this problem, we used a cutoff value to divide AD and NP assays into favorable and non-favorable assays. It is worth mentioning that using a cutoff is a common practice in drug discovery processes. As a result, acquiring the final target function, the pre-processing of all observed vij(cd0) and vnj(cn0) values is crucial in order to remove or reduce imprecisions. Eventually, IF processing of the parameters vij(cd0) and vnj(cn0) enabled us to obtain a target function of the N2D3Ss.

We also used a cutoff to rescale the parameters of vij(cd0) and vnj(cn0) to obtain the Boolean (dummy) functions f(vij(cd0))obs and f(vnj(cn0))obs. These values were obtained as f(vij(cd0))obs = 1 if vij(cd0) > cutoff and d(cd0) = 1, or vij(cd0) < cutoff and desirability d(cd0) = −1; otherwise f(vij(cd0)) = 0. Similarly, f(vnj(cn0))obs = 1 if vnj(cn0) > cutoff and d(cn0) = 1, or vnj(cn0) < cutoff and d(cn0) = −1; else f(vij(cd0), vnj(cn0)) = 0. The values f(vij(cd0))obs = 1 and f(vnj(cn0))obs = 1 mean to have a positive desired effect of both NDDs and NPs. As a result, the target function was described as f(vij(cd0), vnj(cn0))obs = f(vij(cd0))obs·f(vnj(cn0))obs. Therefore, the outcome of the IF scaling f(vij(cd0), vnj(cn0))obs is determined by the i-th NDD compound and the n-th NP measurement conditions. The remaining cases, f(vij(cd0), vnj(cn0))obs = 0, indicate that at least one of the abovementioned conditions fail.

Figure 3: Reference function calculation workflow.

As we mentioned in the previous section, we acquired the results of many cytotoxicity preclinical assays of different NPs . Complementarily, we obtained the data of preclinical assays for NDDs from the ChEMBL database . It included the calculation of the vectors Dnk and Ddk of structural descriptors for all NPs and NDDs. In addition, we constructed the vectors cnj and cdj in order to list each label and assay condition for all preclinical assays of NPs and NDDs. Subsequently, we obtained the values ΔDdk(cdj) and ΔDnk(cnj) of the respective moving average deviation PTOs.

The NDD vector lists each element Ddk = [Dd1, Dd2]. Precisely, these elements are the NDD structural descriptors, which have enabled the development of various strategies to characterize and classify the structure of potential bioactive molecules . These structural descriptors are Dd1 = logarithm of the n-octanol/water partition coefficient (LOGPi) and Dd2 = topological polar surface area (PSAi). In contrast, the cytotoxicity NP vector lists the elements as Dnk = [Dn1, Dn2, Dn3, Dn4, Dn5, Dn6, Dn7, Dn8, Dn9, Dn10, Dn11, Dn12, Dn13, Dn14, Dn15, Dn16, Dn17, Dn18, Dn19, Dn20]. Specifically, they are Dn1 = NMUn (number of monomer units), Dn2 = Lnp (NP length), Dn3 = Vnu (NP volume), Dn4 = Enu (NP electronegativity), Dn5 = Pnu (NP polarizability), Dn6 = Uccoat (unsaturation count), Dn7 = Uicoat (unsaturation index), Dn8 = Hycoat (hydrophilic factor), Dn9 = AMR coat (Ghose–Crippen molar refractivity), Dn10 = TPSA(NO)coat (topological polar surface area using N,O polar contributions), Dn11 = TPSA(Tot)coat (topological polar surface area using N,O,S,P polar contributions), Dn12 = ALOGPcoat (Ghose–Crippen octanol/water partition coefficient), Dn13 = ALOGP2coat (squared Ghose–Crippen octanol/water partition coefficient (logP^2)), Dn14 = SAtotcoat (total surface area from P_VSA-like descriptors), Dn15 = SAacccoat (surface area of acceptor atoms from P_VSA-like descriptors), Dn16 = SAdoncoat (surface area of donor atoms from P_VSA-like descriptors), Dn17 = Vxcoat (McGowan volume), Dn18 = VvdwMGcoat (van der Waals volume from McGowan volume), Dn19 = VvdwZAZcoat (van der Waals volume from the Zhao–Abraham–Zissimos equation), and Dn20 = PDIcoat (packing density index).

To develop the ML models, each of the sample cases are assigned to either the training (subset t) or validation (subset v) series. The process of assignment ought to be random, illustrative, and stratified . Because of the nature of this combinatory system, our sampling also has to take into account the IF scaling procedure. Initially, we obtained the NDD activity dataset from the open database ChEMBL, which has been compiled from primary published literature. The preclinical NP cytotoxicity assays were acquired from journal articles. Afterwards, we prepared each case as the following labels cd0, cd1, cd2, cd3, cd4, cd5, cd6, cd7, cd8, cn0, cn1, cn2, cn3, and cn4. These cases were organized by ranking the labels alphabetically from A to Z (as we mentioned before, they are non-numeric variables in nature). The preference order of the labels on the procedure of ranking was cd0 → cn0 → cd1 → cn1 → cd2 → cn2→ cd3 → cn3. In other words, we organized the cases first by cd0, then by cn0, and so forth. This preference order considers the IF step by interchanging labels from AD and NP datasets. Afterwards, we assigned three quarters of the cases to subset t and the remaining quarter to subset v. This random assignment improves the likelihood that nearly all categories of individual labels are denoted by subsets t and v (stratified or proportional random sampling). In addition, this boosts the possibility that practically all cases for each label are in a distribution of 3/4 in subset t and 1/4 subset v, known as representative sampling. It is worth mentioning that the 75% and 25% proportion between training and validation is the most used one in big data analysis .

In many big data systems, the linear discriminant analysis (LDA) model is the most commonly used tool to seek the preliminary model because of the simplicity of this technique. In this regard, within this model we applied a forward stepwise (FSW) process that can select automatically the most essential input variables for N2D3Ss. We obtained all results by using the software STATISTICA 6.0 . Afterwards, we applied the expert-guided selection (EGS) heuristic in order to retrain the LDA method using the most crucial parameters selected by the FSW process along with other missing aspects. All IFPTML models were obtained by calculating different statistical parameters, specifically sensitivity (Sn), specificity (Sp), accuracy (Ac), chi-square (χ2), and the p-level .

Table 1: IFPTML-LDA N2D3S model results summary.