Advanced QSPR modeling of profens using machine learning and molecular descriptors for NSAID analysis

Aminoprofen is a nonsteroidal anti-inflammatory agent of the propionic acid class, which also includes other drugs, such as ibuprofen. Aminoprofen is chemically designed by substitution of an amine group with the basic structure of ibuprofen. Aminoprofen inhibits the enzyme cyclooxygenase, which is responsible for the biosynthesis of prostaglandins, chemicals in the body that mediate inflammation, pain, and fever^1,2. Aminoprofen works by inhibiting prostaglandin production to help mitigate pain, reduce inflammation, and lower fever. It is usually prescribed for arthritis, muscle ache, and other inflammatory diseases. Medication can be used for moderate-to-mild pain problems, such as headaches and dental pain^3,4. Similar to other NSAIDs, aminoprofen could have possible adverse effects, more so with longer use, related to gastrointestinal problems or even cardiovascular risks. Molecular structure of aminoprofen is shown in Fig. 1(a).

Fenoprofen is an NSAID that belongs to the class of propionic acid drugs, such as ibuprofen and naproxen. The phenoxy group attached to the backbone of propionic acid contributed to the pharmacological action of fenoprofen. Fenoprofen acts by inhibiting the enzyme cyclooxygenase, which is important in the synthesis of prostaglandins, which are mediators of pain, inflammation, and fever. By inhibiting prostaglandin synthesis, fenoprofen suppresses pain and inflammation in several disease states^5,6. Its indications include the treatment of rheumatoid arthritis, osteoarthritis, and mild-to-moderate pain, which may be caused by musculoskeletal injury or menstrual cramps. Similar to other NSAIDs, fenoprofen may produce a range of adverse effects, including gastrointestinal irritation, cardiovascular risks, and impairment of kidney function, particularly if the drug has been taken for a period of time or in conditions that predispose one to these problems^7,8. Molecular structure of fenoprofen is shown in Figure 1(b).

Flurbiprofen is a nonsteroidal anti-inflammatory drug composed of propionic acid derivatives, such as ibuprofen and fenoprofen. It has specific chemical properties; its activity and specificity are enhanced by the attachment of a fluorine atom to the propionic acid backbone^9,10. Flurbiprofen acts mainly by inhibiting COX enzymes, mainly COX-1 and COX-2, which are responsible for the production of prostaglandins, lipid compounds involved in processes such as inflammation, pain, and fever¹⁸. Flurbiprofen is used in the management of disorders such as rheumatoid arthritis and osteoarthritis, which it manages effectively; additionally, it may alleviate mild to moderate pain, including dental pain and post-operative discomfort. Topical ophthalmic preparations exist to prevent or decrease inflammation following eye operations and prevent miosis during the procedure^11,12. Common adverse effects of flurbiprofen include gastrointestinal irritation, dizziness, and headache see Fig. 1. Serious risks include cardiovascular events or renal impairment with prolonged use or in susceptible individuals. Molecular structure of flurbiprofen is shown in Figure 1(c).

Ibuprofen, a derivative of propionic acid, is one of the most widely used NSAIDs. It is chemically synthesized by modification of isobutylbenzene, where a carboxylic acid group is introduced into its structure, which is crucial for its anti-inflammatory activity. Ibuprofen works by inhibiting COX enzymes, specifically COX-1 and COX-2, which subsequently reduce the production of prostaglandins, which are chemical mediators of inflammation, pain, and fever^13,14. Ibuprofen is widely used for mild to moderate pain relief, reduction of inflammation, and fever. Ibuprofen is considered effective in treating headaches, menstrual cramps, toothache, muscle ache, arthritis, and other musculoskeletal disorders. It exists in the form of tablets, capsules, liquid suspensions, and topical gels. Generally well-tolerated, ibuprofen has possible side effects such as gastrointestinal irritation, nausea, or, rarely, kidney or cardiovascular problems associated with long-term or high-dose use^15,16. It is generally recommended to consume ibuprofen with food to avoid stomach upset. Molecular structure of ibuprofen is shown in Fig. 2(a).

Ketoprofen is an NSAID and is classified under the propionic acid derivatives, which also includes ibuprofen and naproxen. It is prepared by modifying the benzoyl group on the propionic acid backbone to enhance its anti-inflammatory and analgesic activities^17,18. It exerts its therapeutic effect by inhibiting COX-1 and COX-2, enzymes responsible for the production of prostaglandins, which are mediators of pain, inflammation, and fever. The most common indications for the use of ketoprofen are pain and inflammation in rheumatoid arthritis, osteoarthritis, ankylosing spondylitis, other bone and joint diseases, and other painful conditions, such as postoperative, dental, or dysmenorrhea. Dosage forms include tablets, capsules, topical gels, and injections^19,20. Although effective, it has possible side effects, such as gastrointestinal irritation, dizziness, and, rarely, some cardiovascular or kidney malfunctions see Fig. 2. It is usually prescribed to be consumed with food or according to the prescription of a medical professional to lessen possible adverse effects. Molecular structure of ketoprofen is shown in Fig. 2(b).

Loxoprofen is a propionic acid derivative, a class of nonsteroidal anti-inflammatory drugs, and one of the most popular drugs prescribed in East Asian nations, especially Japan^21,22. It is a prodrug. After administration, it undergoes metabolism in the liver to form an active compound called trans-OH-loxoprofen, which inhibits COX enzymes. This, in turn, reduces the synthesis of prostaglandins, mediators of pain, inflammation, and fever, via inhibition of both COX-1 and COX-2 by loxoprofen. Loxoprofen is used for the treatment of pain and inflammation caused by rheumatoid arthritis, osteoarthritis, and musculoskeletal injury. It is versatile in the treatment of mild or moderate pain, including headaches, dental pain, and dysmenorrhea. Loxoprofen is administered as an oral tablet, topical gel, and transdermal patch. Because it is a prodrug, it causes fewer gastrointestinal adverse events than other NSAIDs because it minimizes stomach irritation^23,24. However, similar to all NSAIDs, chronic administration can have some risks of kidney impairment or even cardiovascular events, although these may be uncommon. Molecular structure of loxoprofen is shown in Fig. 2(b).

Zaltoprofen is one of the most common NSAIDs and is structurally related to the propionic acid-derivative class. The naphthalene group attached to the propionic acid backbone contributes to the anti-inflammatory and analgesic properties^25,26. Specifically, the drug acts by inhibiting COX enzymes, specifically COX-1 and COX-2, which are responsible for the synthesis of prostaglandins. It is mainly used for various conditions, including rheumatoid arthritis, osteoarthritis, ankylosing spondylitis, gout, and tendinitis. Commonly, this agent is used in the treatment of mild to moderate pain, which includes headache, menstrual cramps, dental pain, and ache in the muscles. Among NSAIDs, naproxen has a relatively long half-life; hence, it can be taken twice daily in most patients^27,28. It is available in many preparations such as tablets, capsules, liquid suspensions, and extended-release formulations. Although naproxen is generally well tolerated, gastrointestinal irritation, nausea, or dizziness may occur. Long-term or high-dose therapy may increase the risk of adverse cardiovascular events, renal impairment, or gastrointestinal bleeding, especially in susceptible individuals see Fig. 3. Often, it is taken with food or according to instructions from a healthcare provider to minimize risks. Molecular structure of naproxen is shown in Fig. 3(a).

Pranoprofen is a nonsteroidal anti-inflammatory drug belonging to the class of propionic acid derivatives. The general structure of this molecule consists of a propionic acid backbone with an attached phenyl group, providing its characteristic anti-inflammatory, analgesic, and antipyretic properties²⁹. Pranoprofen suppresses the activity of COX enzymes, mainly COX-2, inhibiting prostaglandin synthesis, which is a key player in the process of pain, inflammation, and fever. Pranoprofen is widely used in ophthalmology as an eye drop to manage inflammation and pain associated with allergic conjunctivitis, postoperative inflammation, and other ocular inflammatory disorders. Topical applications minimize systemic absorption and reduce the risk of systemic side effects compared with oral NSAIDs³⁰. It is valued for its efficacy in reducing ocular discomfort and inflammation, while maintaining a favorable safety profile. Molecular structure of pranoprofen is shown in Fig. 3(b).

Suprofen is an NSAID that is also used frequently owing to its analgesic and anti-inflammatory properties. It functions by inhibiting COX enzymes, which diminishes the levels of prostaglandins responsible for pain and inflammation³¹. Although previously available in oral forms and utilized for arthritis treatment, as well as mild to moderate pain, its current major application is in the form of an ophthalmic solution. This form is indicated for the management of postoperative ocular inflammation or for preventing miosis during ocular surgery³². Suprofen is of particular value for providing local relief from inflammation with minimal systemic side effects. Molecular structure of suprofen is shown in Fig. 5(c).

Generally well tolerated, it can cause minor side effects, such as eye irritation, redness, or a burning sensation upon application. Pranoprofen is usually prescribed under the guidance of a medical professional, and it is recommended that the user be cautious with dosing to avoid complications. Non-steroidal anti-inflammatory drugs(NSAIDs) are a class of medicines widely used for relieving the symptoms of cold, flu, sprain, headache, strains, and painful periods by reducing inflammation and lowering temperature. The first NSAIDs to be developed were from salicylate based on 1829 when salicylate was successfully isolated from willow bark by a German scientist. Their annual sales can estimate the importance of NSAIDs, USA which are more than 30 billion prescriptions on the counter sale³³. Most prominent class of NSAIDs is Propionic acid derivatives include aminoprofen, fenoprofen, flurbiprofen, loxoprofen, ketoprofen, ibuprofen, naproxen, pranoprofen, and suprofen. Chemically, these compounds contain 2-arylpropionate as the central functional group, with a stereocenter at the alpha position of the propionate moiety. Primarily NSAIDs target \(COX-1\) and \(COX-2\) and act through their inhibition. COX is responsible for the production of prostaglandin, chemical substances responsible for inflammation, and their production is inhibited by the inhibition of COX.

Prostaglandins mediate inflammation that results in pain, edema, and vasodilation. Drugs exert an anti-inflammatory effect through the inhibition of these compounds and generate an analgesic effect³⁴. Inhibition of \(COX-1\) by NSAIDs results in reduced renal function and platelet aggregation, whereas inhibition of \(COX-2\) leads to bone formation and the healing process. NSAIDs are unique in terms of having a ceiling effect; therefore, they are not advised in cases of pain resulting from serious injuries owing to their ineffectiveness in such situations. These drugs do not have addictive potential, and are not responsible for sedation or respiratory stress. To obtain the desired results from NSAIDs, their dose is tuned; for analgesic purposes, a lower dose is administered, while for anti-inflammatory actions, a higher dose is required³⁵. In addition to analgesic and anti-inflammatory purposes, NSAIDs have been proposed for Alzheimer’s disease (AD), a dementia disease in elderly persons with symptoms of memory loss, with varying degrees of efficacy. AD results from the aggregation of \(\beta\) amyloid protein precursors into oligomers, sheets, and fibrils, and these conformations are highly toxic to neurons and limit their function. Some studies have also reported \(\alpha \beta\) oligomers^36,37 are the main neurotoxins resulting in AD in the elderly^38,39. In most cases, the treatment of AD focuses on the prevention of \(\alpha \beta\) fibril and oligomer formation, and this strategy is effective. Future drug development processes should focus on this strategy. NSAIDs act through a similar phenomenon, and exert anti-aggregation activity and prevent the formation of neurotoxic conformations of \(\alpha \beta\) peptides⁴⁰. Among propionic acid-derived NSAIDs, naproxen has the most anti-aggregation effect and prevents the formation of \(\alpha \beta\) sheets, while others include ketoprofen and ibuprofen^41,42.

In mathematics, a graph G is a collection of points, known as vertices V(G), and the lines, called edges E(G), connect them. Graphs have been used to model relationships and structures in several areas of study, including computer science, biology, and social network analysis. Degree \(d_{v}\) of a vertex in a graph is defined as the number of edges connected to it. For example, in an undirected graph with three edges at any vertex, the degree of the vertex is 3. In a directed graph, the degree splits into in-degree edges pointing toward the vertex and out-degree edges pointing away from it. The degree of vertices offers an important measure of the connectivity of a graph, and degree analysis can disclose hubs or critical nodes in networks. In a graph, the distance between two vertices is the length of the shortest path that connects them, which is counted by the number of edges traversed⁵¹. This measure is important to the concept of the graph’s eccentricity, where for a vertex, it is the largest distance from that vertex to any other vertex in the graph. Eccentricity provides an insight into how the central or peripheral vertex is within the graph. The vertex of the minimum eccentricity is called the center of the graph, because it is the most centrally located⁵². These concepts are very important in the analysis of graph structures, for example, in determining the shortest paths, bottlenecks, or network efficiency.

Gutman and Polansky introduced the first and second Zagreb indices⁴³ as

The forgotten index was introduced by Furtula and Gutman⁴⁴ as:

The hyper-Zagreb index was introduced by Rajasekharaiah et al.⁴⁵ as

The first, second, and third redefined indices were presented by Rajini⁴⁶ as follows:

Topological indices are numerical values associated with chemical structures that can be used to predict the various properties and activities of compounds. Recent studies have explored the application of these indices in quantitative structure-property relationship (QSPR) analysis for different drug classes. Shirakol et al.⁴⁷ investigated distance-based topological indices, whereas Gnanaraj et al.⁴⁸ focused on degree-based indices for nonsteroidal anti-inflammatory drugs. Mondal et al.⁴⁹ proposed novel neighborhood degree-based descriptors and developed an algorithm for their computation. Sardar and Hakami⁵⁰ applied topological indices to Alzheimer’s disease drugs using regression models to correlate structural features with physicochemical properties. Their study found that the Randic index, first Zagreb index, and atom-bond connectivity index were particularly useful for understanding structure-activity relationships⁵¹. These investigations demonstrate the potential of topological indices in drug discovery and design, offering insights into compound properties, while minimizing experimental costs.

Almohanna et al.⁵² demonstrated the correlation of topological descriptors with the Gibbs free energy of semiconducting allotropes of carbon with the help of sophisticated curve-fitting models. Almohanna et al. point to the predictive value of topological indices towards the modeling of the thermodynamic properties of nanomaterials. Huang et al.⁵³ applied machine learning algorithms, including multiple regression models and XGBoost, to perform QSPR modeling of glaucoma drugs. Their research proved that sophisticated algorithms are effective in forecasting drug pharmacological properties based on molecular descriptors. Tamilarasi and Balamurugan⁵⁴ carried out QSPR and QSTR modeling of antifungal drugs to analyze their toxicity and pharmacokinetic characteristics by employing topological descriptors. The work of Tamilarasi and Balamurugan testifies to the efficacy of graph-theoretical descriptors in drug efficacy and toxicity prediction. Qin et al.⁵⁵ carried out a QSPR study of pulmonary cancer drugs through Python-based topological modeling methodologies. The results reinforce the strength and potential of computer-based tools and topological descriptors in drug optimization and property prediction. Hakeem et al.⁵⁶ offered computational insights into flavonoid molecular architecture through the application of QSPR models based on degree-based molecular descriptors. The work reinforces the importance of descriptor-based methods in interpreting and anticipating the behavior of bioactive compounds. Qin et al.⁵⁷ created a Python-based QSPR model to predict physicochemical properties of anti-arrhythmia drugs based on topological descriptors. The work of Qin et al. supports the application of computational modeling to make drug profiling process more efficient. Arockiaraj et al.⁵⁸ carried out a QSPR study comparing degree, neighborhood, and reverse degree-based indices of drugs that are used to treat lung cancer. The work of Arockiaraj et al. provides evidence of the relative superiority of different topological descriptors in drug-related property modeling.